Post on 17-Feb-2019
Universita degli Studi di Ferrara
FACOLTA DI SCIENZE MATEMATICHE FISICHE E NATURALI
Dottorato di Ricerca in Fisica
Ciclo XX
Measurements of Partial Branching Fractions
for Charmless Semileptonic B Decays
with the BABAR Experiment
and Determination of |Vub|
Dottorando:
Dott. Antonio Petrella
Tutore:
Dott. Livio Piemontese
Correlatore:
Dott. Concezio Bozzi
Anni 2005-2007
Contents
Introduction v
1 CKM Matrix and Semileptonic B Decays 1
1.1 The Electroweak Sector of the Standard Model . . . . . . . . . . . . . . . . 1
1.2 Inclusive Semileptonic B Decays . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 |Vub| Extraction from Charmless Semileptonic B Decays . . . . . . . . . . . 12
1.3.1 Calculation of the Total Decay Rate . . . . . . . . . . . . . . . . . 13
1.3.2 Decay Rates in Restricted Phase Space Region . . . . . . . . . . . . 16
1.3.3 Experimental Approaches . . . . . . . . . . . . . . . . . . . . . . . 21
2 The BABAR Experiment 23
2.1 The PEP-II Asymmetric Collider . . . . . . . . . . . . . . . . . . . . . . . 25
2.1.1 PEP-II Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2 The BABAR Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.1 Silicon Vertex Tracker (SVT) . . . . . . . . . . . . . . . . . . . . . . 30
2.2.2 Drift Chamber (DCH) . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.3 Cerenkov Light Detector (DRC) . . . . . . . . . . . . . . . . . . . . 35
2.2.4 Electromagnetic Calorimeter (EMC) . . . . . . . . . . . . . . . . . . 37
2.2.5 Instrumented Flux Return (IFR) . . . . . . . . . . . . . . . . . . . . 41
2.2.6 Trigger System (TRG) and Data Acquisition (DAQ) . . . . . . . . . 49
3 Event Reconstruction 51
3.1 Charged Particle Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 52
3.2 Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
i
3.2.1 Electron Identification . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2.2 Muon Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2.3 Charged Kaon Identification . . . . . . . . . . . . . . . . . . . . . . 58
3.3 Neutral Particles Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4 Meson Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.4.1 π0 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.4.2 K0S Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.4.3 D Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.5 Semi-exclusive Reconstruction Method . . . . . . . . . . . . . . . . . . . . 66
3.5.1 Definition of ∆E and mES . . . . . . . . . . . . . . . . . . . . . . . 68
3.5.2 Study of the Y System . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.5.3 ∆E Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.5.4 Multiple Candidates and Definition of Purity . . . . . . . . . . . . . 72
4 Data and Monte Carlo Samples 75
4.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.2 Monte Carlo Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.2.1 Generic bb Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . 76
4.2.2 Resonant Models for B → Xu`ν . . . . . . . . . . . . . . . . . . . . 76
4.2.3 Non-Resonant Model for B → Xu`ν . . . . . . . . . . . . . . . . . . 77
4.2.4 BABAR Hybrid Model for B → Xu`ν . . . . . . . . . . . . . . . . . . 79
4.2.5 Reweighting Hybrid Model for B → Xu`ν . . . . . . . . . . . . . . 80
5 Event Selection 83
5.1 Reconstruction of the Recoil System . . . . . . . . . . . . . . . . . . . . . 84
5.2 Selection of Semileptonic Decays . . . . . . . . . . . . . . . . . . . . . . . . 86
5.2.1 Selection of Charmless Semileptonic Decays . . . . . . . . . . . . . 87
5.3 Fit to the mES Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3.1 Modeling of mES Distribution with 3 PDFs . . . . . . . . . . . . . 94
5.3.2 Modeling of mES Distribution with 2 PDF . . . . . . . . . . . . . . 99
ii
5.3.3 Study of Truth-Matching Criteria . . . . . . . . . . . . . . . . . . . 101
5.3.4 Strategy for mES Fits . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.3.5 Binned vs. Unbinned Fits . . . . . . . . . . . . . . . . . . . . . . . 104
5.4 Data/Monte Carlo Comparison . . . . . . . . . . . . . . . . . . . . . . . . 106
6 Partial Charmless Branching Fraction Measurements 115
6.1 Measurement Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.2 Monte Carlo Fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.3 One Dimensional MX Fit and Results . . . . . . . . . . . . . . . . . . . . . 120
6.4 One Dimensional P+ Fit and Results . . . . . . . . . . . . . . . . . . . . . 125
6.5 Two Dimensional (MX , q2) Fit and Results . . . . . . . . . . . . . . . . . . 130
7 Systematic Uncertainties 137
7.1 Detector-related Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.1.1 Charged Particle Tracking . . . . . . . . . . . . . . . . . . . . . . . 137
7.1.2 Neutral Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.1.3 KL Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.1.4 Lepton Identification . . . . . . . . . . . . . . . . . . . . . . . . . . 140
7.1.5 Charged Kaon Identification . . . . . . . . . . . . . . . . . . . . . . 140
7.2 Uncertainties Related to the mES Fits . . . . . . . . . . . . . . . . . . . . 140
7.3 Signal Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.4 Background Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
8 Measurement of |Vub| 147
8.1 Input Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
8.2 |Vub| Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
8.2.1 (MX , q2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
8.2.2 MX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
8.2.3 P+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
8.3 Compatibility of the |Vub| Determinations . . . . . . . . . . . . . . . . . . . 151
iii
8.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Bibliography 155
iv
Introduction
This thesis presents measurements of inclusive semileptonic decays of B mesons in charm-
less final states, by using a data sample collected by the BABAR detector at the PEP-II
Asymmetric B Factory, located at the Stanford Linear Accelerator Center.
Charmless semileptonic B meson decays give the cleanest determinations of the CKM
matrix element |Vub|. The study of inclusive decays, where no attempt is made to com-
pletely reconstruct the final state, are particularly interesting since the relevant contribu-
tions to the dominant theoretical uncertainty can be factorized and computed systemati-
cally to a high level of accuracy.
The experimental approach presented in this thesis uses Υ(4S) → BB transitions to
study charmless semileptonic decays of a B meson recoiling against a B meson which is
fully reconstructed in an hadronic final state. The dominant background due to semilep-
tonic decays with charm, about a factor 50 larger than charmless decays, is reduced by
kinematic requirements which allow to identify phase space regions with a manageable
signal over background ratio. In general, these requirements introduce sizeable theoretical
uncertainties when the extrapolation to the full phase space, needed in order to determine
|Vub|, is performed. The determination of |Vub| therefore depends on the interplay between
a careful optimization of signal over background ratio and the minimization of theoretical
uncertainties.
This thesis is organized as follows. The theory of inclusive charmless semileptonic
B decays is reviewed in Chapter 1, together with a brief reminder of the electroweak
sector of the standard model and the CKM mechanism. Chapter 2 shows an overview
of the BABAR detector. The experimental techniques used to reconstruct events, identify
particles and resonances, and fully reconstruct a B meson into hadronic final states, are
v
presented in Chapter 3. The event samples used in this thesis, consisting of both real and
simulated data, are detailed in Chapter 4. Chapter 5 shows the selection criteria applied
in order to select the signal sample. Measurements of partial branching fraction for
inclusive charmless decays in regions of restricted phase space are reported in Chapter 6,
the associated systematic uncertainties are discussed in Chapter 7. Determinations of the
CKM matrix element |Vub| and conclusions are presented in Chapter 8.
The results obtained in this thesis work represent the most precise and up-to-date
determinations of |Vub| with inclusive charmless semileptonic decays. They have been
submitted to and shown at the European Physical Society Conference on High Energy
Physics, held in Manchester in July 2007, and at the XXIII International Symposium on
Lepton and Photon Interactions at High Energy, held in Daegu, Korea, in August 2007.
They have been subsequently submitted for publication [1] on Physical Review Letters.
vi
Chapter 1
CKM Matrix and Semileptonic BDecays
1.1 The Electroweak Sector of the Standard Model
The electroweak sector of the SM is a gauge theory based on the local group SUL(2) ⊗UY (1), which describes the symmetries of the matter field. The Yang-Mills electroweak
Lagrangian is [2]
L = −1
4ΣAW
AµνW
Aµν − 1
4BµνB
µν + ΨLiγµDµΨL + ΨRiγ
µDµΨR (1.1)
where the spinors ΨL and ΨR represent the matter fields in their chiral components, and
the field strength tensors are given by:
Wµν = ∂µWν − ∂νWµ − gεABCWBµ W
Cν and Bµν = ∂µBν − ∂νBµ (1.2)
Here WA and B are the SU(2) and U(1) gauge fields, with the coupling constants g and g′
and εABC is the totally anti-symmetric Levi-Civita tensor. The corresponding covariant
derivative is:
DµΨL,R =
[∂µ + igΣtAL,RWAµ + ig′
1
2YL,RBµ
]ΨL,R, (1.3)
where tAL,R and 1/2YL,R are the SU(2) (weak isospin) and U(1) (hypercharge) generators.
The electric charge generator is related to the isospin and hypercharge by:
Q = t3L +1
2YL = t3L +
1
2YR. (1.4)
The left and the right fermion components have different properties under the gauge group.
The left component behave as doublets while the right as singlets. In the symmetric limit
1
the two chiral component cannot interact each other, and thus mass term for fermions
(of the form ΨLΨR) are forbidden. To give mass terms to fermions as well as to gauge
bosons without loosing the symmetry properties, the electroweak theory is realized with
a vacuum state invariant only under the UEM(1) electric charge gauge transformation.
This phenomenon is known as “spontaneous symmetry breaking”. The gauge theories
spontaneous broken allow to introduce mass terms for the gauge boson and the fermion
fields without loosing the gauge invariance, and the renormalizability of the theory. The
mechanism by which, starting from a degenerate vacuum state, mass terms are introduced
is known as Higgs mechanism [3]. The Higgs Lagrangian term is:
LHiggs = (Dµφ)†(Dµφ)− V (φ†φ)− ΨLΓΨRφ− ΨRΓ†ΨLφ†, (1.5)
where φ is the isospin doublet of the Higgs scalar fields and the quantities Γ (which include
all coupling constants) are matrices that make the Yukawa couplings invariant under the
Lorentz gauge groups. The general form of the Higgs potential is:
V (φ†φ) = µ2φ†φ+ λ(φ†φ)2, (1.6)
and it is not possible to include terms with higher dimension without breaking the renor-
malizability of the SM. To have a vacuum state (the minimum of the potential) degenerate,
the µ2 coefficient should be negative, while the coefficient λ should be positive to guarantee
the potential bound from below. Under these hypotheses the vacuum state of the Higgs
field satisfies |φ|2 = −µ2/2λ = v2. The field φ can be expanded around one of its ground
states; in choosing a particular ground state (φ0 =
(0ν
)), the SUL,R(2)⊗UY (1) symmetry
is spontaneously broken.
The mass terms for the gauge bosons are coming from the kinetic part of the Higgs
Lagrangian once it is expanded around the Higgs vacuum state. The correct quantum
numbers of the Higgs field are fixed by the requirement that the Lagrangian (1.5) is gauge
invariant.
Since the SUL(2) ⊗ UY (1) is spontaneously broken into UEM(1), only the linear com-
bination of gauge fields with the quantum numbers of the photon remains mass-less. A
general linear combination between the gauge bosons associated to the generator in Eq. 1.4
2
can be written: (Aµ
Zµ
)=
(− sin θW cos θW
cos θW sin θW
) (W 3
µ
Bµ
)(1.7)
where the angle θW is known as the Weak or Weinberg mixing angle. Once the symmetry
is spontaneously broken through the interaction with the Higgs field, Aµ remains mass-less
while Zµ, W+µ and W−
µ acquire a mass term. W+µ and W−
µ are defined as:
W±µ =
1√2(W 1
µ ± iW 2µ). (1.8)
The bi-linear terms in the fields Zµ and W±µ in Eq. 1.5 can be identified as the mass terms:
M2Z =
v2g2
2 cos2 θW
(1.9)
M2W = cos2 θWM
2Z (1.10)
which implies tan θW = g′/gYφ. In terms of these new fields the fermionic currents are:
J±µ = Σf Ψf (1− γ5)γµt
±Ψf (1.11)
J0µ = Σf Ψ
fγµ
[(1− γ5)t
3 − 2Q sin2 θW
]Ψf , (1.12)
Jemµ = Σf Ψ
fγµQΨf , (1.13)
where Ψf represents the isospin doublet for the fermion fields (see Tab. 1.1) with f acting
Family Quantum Numbers1 2 3 t t3 Y Q = Y/2 + t3
(νe
e
)
L
(νµ
µ
)
L
(ντ
τ
)
L
1/21/2
+1/2−1/2
−1−1
0−1
eR µR τR 0 0 −2 −1
(ud
)
L
(cs
)
L
(tb
)
L
1/21/2
+1/2−1/2
+1/3+1/3
+2/3−1/3
uR cR tR 0 0 4/3 +2/3dR sR bR 0 0 −2/3 −1/3
Table 1.1: Electroweak interaction multiplets. t indicates the isospin, t3 is the third isospin component,Y indicates the hyper-charge and Q indicates the electric charge.
as a family index, (1 − γ5) is the left-handed chiral projector, and t± are the isospin
3
generator associated to the fields W±. The first current describes interactions which
change the electric charge, while the other two, produce transitions charge-conserving.
The Lagrangian (1.1) could be rewritten in two terms: one including interactions between
the neutral current and the Aµ and Zµ bosons, and another describing the interactions of
the W±µ with the charged current:
LED = LCC + LNC, (1.14)
LCC =g2
2√
2(J+
µ W+µ + J−µ W
−µ ), (1.15)
LNC = −eJemµ Aµ +
g2
2 cos θW
J0µZ
µ, (1.16)
where e is defined as e = g2 sin θW .
Starting from the same doublet which gives masses to the gauge bosons it is possible
to introduce mass terms for the fermion fields. This imposes others restrictions on the
Higgs field. To obtain fermion mass terms like:
−ΨLΓΨRφ− ΨRΓΨLφ where φ = iσ2φ†, (1.17)
invariant under SUL,R(2) transformations, the Higgs field is required to have isospin equal
to 1/2. The Γ matrices contain the Yukawa constants, which determine the strength of
the fermion couplings to the Higgs fields.
The fermion mass matrix is obtained from the Yukawa couplings expanding φ around
the vacuum state:
M = ψL MψR + ψRM†ψL , (1.18)
with
M = Γ · v . (1.19)
It is important to observe that by a suitable change of basis we can always make
the matrix M Hermitian, γ5-free, and diagonal. In fact, we can make separate unitary
transformations on ψL and ψR according to
ψ′L = LψL, ψ′R = RψR, (1.20)
4
and consequently
M→M′ = L†MR . (1.21)
This transformation does not alter the general structure of the fermion couplings in L.
Weak charged currents are the only tree level interactions in the SM that may induce a
change of flavor. By emission of a W boson an up-type quark is turned into a down-type
quark, or a ν` neutrino is turned into a `− charged lepton. If we start from an up quark
that is a mass eigenstate, emission of a W turns it into a down-type quark state d′ (the
weak isospin partner of u) that in general is not a mass eigenstate. In general, the mass
eigenstates and the weak eigenstates do not in fact coincide and a unitary transformation
connects the two sets: d′
s′
b′
= V
dsb
, (1.22)
where V is the Cabibbo-Kobayashi-Maskawa matrix (CKM)[4]. Thus in terms of mass
eigenstates the charged weak current of quarks has the form:
J+µ ∝ uγµ(1− γ5)t
+V d, (1.23)
Since V is unitary (i.e. V V † = V †V = 1) and commutes with T 2, T3 and Q (because
all d-type quarks have the same isospin and charge) the neutral current couplings are
diagonal both in the primed and unprimed basis. If the Z down-type quark current is
abbreviated as d′Γd′ then, by changing basis we get dV †ΓV d and V and Γ commute; it
follows that d′Γd′ = dΓd. This is the Glashow - Iliopoulos - Maiani (GIM) mechanism [5]
that ensures natural flavor conservation of the neutral current couplings at the tree level.
With three fermion generations the matrix V could be expressed in terms of three
angles and one irremovable complex phase [6]. The CKM matrix is usually represented
as:
V =
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
. (1.24)
The irremovable phase in the CKM matrix allows possible CP violation.
5
The measurement of the elements of the CKM matrix is fundamental to test the validity
of the SM. Many of them (actually the first two rows of the matrix) are measured directly,
namely by tree-level processes. Using unitary relations one can put constraints on the top
mixing |Vti|. Moreover the B mixing measurements, that involve box diagrams, can give
information also about Vtd and Vtb.
The CKM-matrix can be expressed in terms of four Wolfenstein parameters (λ,A, ρ, η)
with λ = |Vus| = 0.22 playing the role of an expansion parameter and η representing the
CP -violating phase [7]:
V =
1− λ2
2λ Aλ3(ρ− iη)
λ 1− λ2
2Aλ2
Aλ3(1− ρ− iη) −Aλ2 1
+O(λ4). (1.25)
λ is small, and for each element in V , the expansion parameter is actually λ2.
The Wolfenstein parametrization offers a transparent geometrical representation of the
structure of the CKM matrix. The unitarity of the matrix implies various relations among
its elements. Three of them are very useful for understanding the SM predictions for CP
violation:
VudV∗us + VcdV
∗cs + VtdV
∗ts = 0, (1.26)
VusV∗ub + VcsV
∗cb + VtsV
∗tb = 0, (1.27)
VudV∗ub + VcdV
∗cb + VtdV
∗tb = 0. (1.28)
Each of these three relations requires the sum of three complex quantities to vanish and
so can be geometrically represented in the complex plane as a triangle. These are “the
Unitarity Triangles”. If the CP symmetry is violated the area of the triangles is not zero.
The B physics is related to the third triangle at least for what the B factory can access.
The study of the parameters of this triangle encompasses the physics of CP violation in
the SM. The openness of this triangle, due to the fact that all the three sides are of the
same order of magnitude, predicts large CP asymmetries.
It should be remarked that the Wolfenstein parametrization is an approximation and
neglecting O(λ4) terms could be wrong in particular processes. An improved approxi-
6
mated parametrization of the original Wolfenstein matrix is given in [8]. Defining
Vus = λ, Vcb = Aλ2, Vub = Aλ3(ρ− iη), (1.29)
one can then write
Vtd = Aλ3(1− ρ− iη), (1.30)
=(Vcd) = −A2λ5η, =(Vts) = −Aλ4η, (1.31)
where
ρ = ρ(1− λ2/2), η = η(1− λ2/2), (1.32)
turn out to be excellent approximations to the exact expressions. Depicting the rescaled
Unitarity Triangle in the (ρ, η) plane, the lengths of the two complex sides are
Rb ≡√ρ2 + η2 = 1− λ2/2
λ
∣∣∣∣Vub
Vcb
∣∣∣∣ , (1.33)
Rt ≡√
(1− ρ)2 + η2 =1
λ
∣∣∣∣Vtd
Vcb
∣∣∣∣ . (1.34)
The rescaled Unitarity Triangle (Fig. 1.1) is derived from Eq. 1.28 by choosing a phase
convention such that (VcdV∗cb) is real, dividing the lengths of all sides by |VcdV
∗cb|, aligns
one side of the triangle with the real axis and makes the length of this side equal to 1.
The form of the triangle is unchanged. Two vertexes of the rescaled Unitarity Triangle
are thus fixed at (0,0) and (1,0). The coordinates of the remaining vertex are denoted
by (ρ, η). Both angles and sides can be measured in a B factory and they can offer
two independent tests of the Standard Model. Inconsistencies between these two tests
would indicate the presence of New Physics. The constraints on the apex of the Unitarity
Triangle, obtained from different measurements, now overlap in one small area in the
first quadrant in the (ρ, η) plane [9, 10]. The constraints from the lengths of the sides
and independently those from CP violating processes indicate the consistent regions on
the (ρ, η) plane. The |Vub| /|Vcb| constraint shown in Fig. 1.2 can be directly derived
from Eq. 1.33. The CKM elements |Vub| and |Vcb| therefore provide a test of the SM by
7
Figure 1.1: The rescaled Unitarity Triangle, all sides divided by V ∗cbVcd.
8
ρ-1 -0.5 0 0.5 1
η
-1
-0.5
0
0.5
1γ
β
α
sm∆dm∆ dm∆
Kε
cbVubV
ρ-1 -0.5 0 0.5 1
η
-1
-0.5
0
0.5
1
Figure 1.2: Unitarity Triangle constrains from different measurements of the Standard Model parametersin the (ρ, η) plane, updated to the Summer 2006 results [9]. Allowed region for (ρ, η), using all availablemeasurements,is shown with closed contours at 68% and 95% probability. The full lines correspond to95% probability regions for the constraints, given by the measurements of |Vub| /|Vcb| , εK , ∆md/∆ms,α, β, γ, ∆Γd/Γd, ∆Γs/Γs, Ad
SL and the dimuon asymmetry from D0.
9
over-constraining the (ρ, η) plane vertex with other measurements. These elements can
be directly determined from b→ u`ν and b→ c`ν decays respectively.
While |Vcb| has been measured with a 2% uncertainty [11], |Vub| still remains one of
the least known elements of the CKM matrix and dominates the error on the length of
the side opposite to the angle β.
The Unitarity Triangle analysis shows the impressive success of the CKM picture in
describing CP violation in the SM, but, with the increasing precision of the experimental
results, a slight disagreement between sin 2β and |Vub| is appeared in the UT fit, as shown
in Fig. 1.2. This disagreement could be due to some problem with theoretical calculation
and/or with the estimate of the uncertainties on the |Vub| measurements. So an effort
must be done for a substantial improvement of the theoretical and experimental accuracy
for this quantity. In the future, if the |Vub| value will be confirmed by more precise data
and theory calculations, the disagreement in the UT fit might reveal a bound of New
Physics phase in Bd mixing [9].
1.2 Inclusive Semileptonic B Decays
Semileptonic B decays (Fig. 1.3 shows a Feynman diagram of a charmless semileptonic B
decay), due to their simplicity, provide an excellent laboratory in which to measure |Vcb|and |Vub|. These processes also allow us to study the effects of non-perturbative QCD
interactions on the weak-decay process. These goals may sound contradictory: “how can
be measured standard-model parameters if complicated hadronic effects are present?”
Figure 1.3: Feynman diagram for a charmless semileptonic decay B → Xu`ν.
First of all, it is notable that even if the effects of strong interactions on semileptonic
10
decays are difficult to calculate, they are isolated to the hadronic current. As a conse-
quence, these effects can be rigorously parametrized in terms of a small number of form
factors, which are functions of the Lorentz-invariant quantity q2, the square of the mass
of the virtual W.
Particular and specific care is needed in case it is intended to study |Vcb| or |Vub|.For b → c`ν decays, the large masses of both the b and c quarks provide the key to
reliable theoretical predictions based on the Heavy-Quark Effective Theory (HQET) for
exclusive decays and Heavy-Quark Expansions (HQE) for inclusive decays [12, 13, 14].
In the Heavy-Quark Symmetry limit (mb → ∞ and mc → ∞), the hadronic system is
undisturbed by replacing one heavy quark by the other one. Since the b and c quark masses
are not truly infinite, there are corrections to these predictions, but they are relatively
small. So the Heavy-Quark symmetry relates form factors to each other, reducing the
number of independent functions and gives the normalization at zero recoil configurations
(when the daughter charm hadron has zero momentum with respect to the parent b
hadron). Charmless b→ u`ν decays are more difficult because in this case the zero recoil
configuration does not provide a solid normalization point, due to the small value of the
u quark mass.
While the determination of |Vub| is improving, both experimentally and theoretically,
there are still large uncertainties. The problem with exclusive decays is that the strong
hadronic dynamics can not be calculated from first principles, and it has to resort to
models, light-cone sum rules, or lattice QCD calculations to obtain the form factor. So
inclusive decays should provide a straightforward means to measure |Vub|: one considers
the sum over all possible final-state hadrons, ignoring the detailed breakdown among the
individual decay modes that contribute to the semileptonic rate. Experimentally, it is
necessary to observe only the lepton, eliminating reconstruction difficulties that are often
complex decay sequences of the daughter hadrons. Theoretical calculations of inclusive
properties have certain advantages of simplicity as well, since calculations in which the
heavy quark is assumed to decay as a free particle (with the light quark acting merely as
a spectator) provide a good starting point for predictions.
11
1.3 |Vub| Extraction from Charmless Semileptonic B Decays
The theoretical tools that we have for calculating decay rates and spectra in heavy-quark
physics have as underlying theme the separation of short-distance from long-distance
physics, which is natural due to the presence of the large mass scale mQ À ΛQCD, which
is far above the scale of nonperturbative hadronic physics. Factorization theorems state
that short and long-distance contributions to a given observable can be separated into
Wilson coefficient functions Ci and nonperturbative matrix element Mi. Generically, one
has
Observable ∼∑
i
Ci(mQ, µ)Mi(µ) + . . . (1.35)
Such a factorization formula is useful, since by virtue of it the dependence on the high
scale mQ is calculable, and often the number of matrix elements Mi is smaller than the
number of observables that can be expressed in the form shown above. The factorization
scale µ serves as an auxiliary separator between the domains of short and long-distance
physics. Observables are formally independent of the choice of µ; however, they inherit
some residual dependence once the Wilson coefficient Ci are computed at finite order in
perturbation theory. The dependence gets weaker as higher orders in the perturbative
expansion are included.
Processes involving energetic light partons require a more sophisticated form of the
factorization theorem, which generally can be expressed as
Observable ∼∑
i
Hi(Q,µ)Ji(√QΛ, µ)⊗ Si(µ) + . . . (1.36)
Here QÀ ΛQCD is the hard scale of the process, e.g. a heavy-quark mass or the center-
of-mass energy. The hard function Hi capture virtual effects from quantum fluctuation
at the hard scale. The jet functions Ji describe the properties of the emitted collinear
particles, whose characteristic virtuality or invariant mass scales as an intermediate scale√QΛ between Q and QCD scale ΛQCD. For the inclusive processes the jet scale is in
the perturbative domain (√QΛ À ΛQCD). Finally, the soft functions Si describe the
(nonperturbative) physics associated with soft radiation in the process. The symbol ⊗implies a convolution, which arises since the jet and soft functions share some common
12
variables, such as some small momentum components of order ΛQCD.
The theoretical basis of the factorization theorem (Eq. 1.36) is a generalization of the
euclidean operator product expansion to the time-like domain derived in the soft-collinear
effective theory [15, 16, 17, 18].
1.3.1 Calculation of the Total Decay Rate
The total decay rate B → Xu`ν is directly proportional to |Vub|2, and can be calculated
reliably and with small uncertainties using the Operators Product Expansion (OPE), as
a double expansion in powers of ΛQCD/mb and αs(mb) [12], according to Equation 1.35.
The b-quark decay mediated by weak interactions takes place on a time scale that is
much shorter than the time it takes the quarks in the final state to form physical hadronic
states. Once the b-quark has decayed on a time scale t¿ Λ−1QCD, the probability that the
final states will hadronize somehow is unity, and it is needed not to know the probability
of hadronization into specific final states. Moreover, since the energy release in the decay
is much larger than the hadronic scale, the decays is largely insensitive to the details of
the initial state hadronic structure.
This intuitive picture is formalized by the OPE, presented in [19], which expresses the
inclusive rate as an expansion in inverse power of the heavy quark mass with the leading
term corresponding to the free quark decay. Let us consider, as an example, the inclusive
semileptonic b → c decay, mediated by the operator Osl = −4GF/√
2Vcb(Jbc)α(Jlν)α,
where Jαbc = (cγαPLb) and Jβ
lν = (lγβPLν). The decay rate is given by the square of the
matrix element, integrated over phase space (Φ) and summed over final states (Xc),
Γ(B → Xc`ν) ∼∑Xc
∫d[Φ]|〈Xclν|Osl|B〉|2 (1.37)
Since the leptons have no strong interactions, it is convenient to factorize the phase space
into B → XcW∗ and a perturbative calculable leptonic part, W ∗ → lν. The nontrivial
part is the hadronic tensor,
W αβ ∼∑Xc
δ4(pB − q − pXc)|〈B|Jα†bc |Xc〉〈Xc|Jβ
bc|B〉|2 (1.38)
∼ =∫dx e−iq·x〈B|TJα†
bc (x), Jβbc(0)|B〉, (1.39)
13
where the second line is obtained using the optical theorem, and T denotes the time
ordered product of the two operators. This is convenient because the time ordered product
can be expanded in local operators in the mb À ΛQCD limit. In this limit the time ordered
product is dominated by short distances, x ¿ Λ−1QCD, and one can express the nonlocal
hadronic tensor Wαβ as a sum of local operators.
Schematically,
b b
p =mv+k
q q
p =mv-q+kq
b
= �����b ��� � ����Rb����+
0
mb �����b ��� � ����Rb����+
1
m2b �����b ��� � ����Rb
����+ . . . .
(1.40)
At leading order the decay rate is determined by the b quark content of the initial state,
while subleading effects are parametrized by matrix element of operators with increasing
number of derivatives that are sensitive to the structure of the B meson.
There are no O(ΛQCD/mb) corrections, because the b meson matrix element of any
dimension-4 operator vanishes. As the coefficients in front of each operator are calculable
in perturbation theory, this leads to a simultaneous expansion in powers of the strong
coupling constant αS(mb) and inverse powers of the heavy b quark mass (more precisely,
of mb−mq). The leading order of this expansion is the parton model semileptonic width:
Γ0 =G2
F |Vcb| 2m5b
192π3(1− 8ρ+ 8ρ3 − ρ4 − 12ρ2 ln ρ), (1.41)
where ρ = m2q/m
2b . Non-perturbative corrections are suppressed by at least two powers
of mb. The resulting expression for the total rate of the semileptonic B → Xc`ν has the
form
Γb→c = Γ0
[1 + A
[αS
π
]+B
[(αS
π)2β0
]+ 0
[ΛQCD
mb
]+ C
[Λ2
QCD
m2b
]+O(α2
S,Λ3
QCD
m3b
,αS
m2b
)
]
(1.42)
where the coefficients A, B, C depend on the quark masses mc,b. The perturbative
corrections are known up to order α2Sβ0. Non-perturbative corrections are parametrized
by matrix elements of local operators. The O(Λ2QCD/m
2b) corrections are given in terms
14
of the two terms matrix elements
λ1 =1
2MB
〈B|hv(iD)2hv|B〉, λ2 =1
6MB
〈B|hvg
2σµνG
µνhv|B〉 (1.43)
The dependence on these matrix elements is contained in the coefficient C ≡ C(λ1, λ2).
Up to higher order corrections, the connection to an alternative notation is λ1 = −µ2π
and λ2 = µ2G/3. At order 1/m3
b there are two additional matrix elements. Thus, the total
decay rate depends on a set of non-perturbative parameters, including the quark masses
with the number of such parameters depending on the order in ΛQCD/mb one is working.
The same expansion can be written in case of b → u semileptonic transitions, with the
Equation 1.41 and 1.42 that have perturbative corrections, known through order α2S [20],
as follows:
Γb→usl =
G2Fm
5b
192π3|Vub| 2
[A0
(1− µ2
π − µ2G
2m2b
)− 2
µ2G
2m2b
+O( 1
m3b
)], (1.44)
with the leading order corrections given in terms of µ2π e µ2
G. The leading term includes
purely perturbative corrections (embedded in the coefficient A0).
These perturbative effects have been calculated, and no significant uncertainties are
expected from yet uncalculated higher order perturbative effects.
The corrections depend on αS and mb which are scale dependent. The largest term
is proportional to 1/m2b and thus is of order 5%, leading to a reduction in the decay
width by ≈ 4%. Similar results can be derived for differential distibutions, as long as
the distributions are sufficiently inclusive. To quantify this last statement, it is crucial
to remember that the OPE does not apply to fully differential distributions but requires
that such distributions be smeared over enough final state phase space. The size of the
smearing region ∆ introduces a new scale into the expressions for differential rates and
can lead to non-perturbative corrections being suppressed by powers of ΛnQCD/∆
n rather
than ΛnQCD/m
nb . Thus, a necessary requirement for the OPE to converge is ∆ À ΛQCD,
although a quantitative understanding of how experimental cuts affect the size of smearing
regions is difficult.
15
1.3.2 Decay Rates in Restricted Phase Space Region
The measurement of B → Xu`ν suffers from a large background from the decay B →Xc`ν. The reason for the large background is that |Vcb| À |Vub|, meaning that the b quarks
“likes” to decay to a c quark much more than to a u quark. In order to eliminate the
background we have to look at regions of phase space where particles containing charm
cannot be produced.
In order to analyze inclusive decays one can start answering to a simple question
“How many kinematical variables are needed to describe an inclusive event?”. We are
looking at a decay of a B meson into n particles, where n − 1 of them have known
mass. The “particle” X has unspecified invariant mass. In general for a decay into n
particles there are 3n− 4 kinematical variables, but not all of them are determined from
the dynamics. Since we do not have information about the spin of the hadronic state X
or the spin/polarization of the other decay products, the only four vectors we have at
our disposal are PB, the four momentum of the B meson, p1 ≡ PX the four momentum
of X and p2, . . . , pn. Lorentz invariance implies then that the possible variables are the
(n+1)(n+2)/2 scalar products of these n+1 vectors. Since the masses of all the particles
apart from p1 are known, we have n constraints of the form p2i = m2
i , (i = B, 2, . . . , n).
Conservation of momentum would allow us to eliminate all the pairs that contain PB
(since PB =∑n
i=1 pi), i.e. eliminating n + 1 variables. That leaves us with n(n − 1)/2
independent variables. The rest of the variables are undetermined from the dynamics and
can be integrated over. This arguments hols for n ≤ 3, since at 4 dimensions at most 4
vectors (corresponding to n = 3) can be linearly independent. For n > 3 the argument
needs to be modified. For B → Xu`ν we have n = 3 and three relevant variables (see
Table 1.2). There are various choices in the literature for these variables, and in order
to understand them we have to say a few words about the dynamic of the decay. First
we need to distinguish between the hadronic level, which looks at the decay as a decay
of hadrons, and the partonic level, which looks at the decay as a decay of quarks. At
the hadronic level we have a B meson carrying momentum PB ≡ MBv decaying into a
leptonic pair (the lepton and anti-neutrino) carrying momentom total q, and a hadronic
16
Scalar Products Constraints
¡¡P 2B »»»PBPX »»»PBP` »»»PBPν PB = PX + P` + Pν
P 2X PXP` PXPν
¡¡P2l »»»PlPν (PX + P` + Pν)2 = M2
B , P 2` = 0
¡¡P2ν P 2
ν = 0
Table 1.2: Number of kinematic variables for inclusive B decays. Using the constraints on the rightcolumn we can eliminate some of the variables on the left column.
jet carrying momentum PX . Conservation of momentum implies MBv − q = PX . At the
partonic level we look at the decay as a decay of a b quark, carrying momentum mbv, into
a u quark, carrying momentum p (at tree level), and a virtual W carrying momentum q.
The W in turn decays into a lepton ` and an anti-neutrino ν` (more accurately we write
the momentum of the b quark as mbv + k where k is O(ΛQCD) and expand in powers of
k). Conservation of momentum implies mbv − q = p. If we define Λ ≡ MB −mb we find
that PX = p+Λv. Beyond tree level p would be the momentum of the jet of light partons
created in the decay.
There are generically two common choices of variables:
• Leptonic: the energy of the lepton E`, the energy of the neutrino Eν and the
invariant mass of virtual W boson q2, which is also the invariant mass of the leptonic
pair. This choice focuses on the leptons created in the decay.
• Partonic: the energy of the lepton E`, the energy of the partonic jet v · p and the
invariant mass of the partonic jet p2. This choice focuses on the partons created in
the decay.
For example we can only look at events for which P 2X < M2
D. This fact implies that
the “typical” Xu state will have large energy of order mb, since it originates from a decay
of a heavy quark and intermediate invariant mass, because of the experimental cut. Since
MD ∼√mbΛQCD we can write P 2
X ∼ mbΛQCD. This implies that some of the components
of PX are larger than others. We would like the choice of our variables to reflect that. A
pair of variables which satisfy this condition is:
P− = EX + |~PX |, P+ = EX − |~PX |, (1.45)
where EX and PX are the energy and momentum of the hadronic jet, respectively. Note
17
that P+P− = P 2, P+ + P− = 2EX and P+ < P−. The scaling of these variables will
therefore be P− ∼ mb and P+ ∼ ΛQCD. Specifying P+ and P− would determine the
energy and the invariant mass of the lepton pair, but not the individual energies of the
lepton and neutrino. We therefore have to add another variable that would distinguish
between the two:
P` = MB − 2E` (1.46)
We can determine now the phase space region in terms of P+, P` and P−. In the rest frame
of B meson, conservation of energy and momentum gives us the following equations:
E` + Eν + EX = MB (1.47)
~P` + ~Pν + ~PX = 0. (1.48)
Considering the lepton massless implies E` = |~P`| and Eν = |~Pν |. The limits of phase
space are determined by the extremal values of angles between the momenta. Because of
conservation of momentum (Eq. 1.48) we have only two independent angles.
Let θ be the angle between ~P` and ~Pν . Equation 1.48 then implies ~P 2X = E2
` + E2ν +
2EνE` cos θ. Since −1 ≤ cos θ ≤ 1, we have (E` − Eν)2 ≤ |~PX |2 ≤ (E` + Eν)
2. Using
P+ ≤ P−, the upper limits gives us P− ≤MB, and the lower limit P+ ≤ P` ≤ P−.
Let α be the angle between ~P` and ~PX . Equation 1.48 then implies E2ν = (MB −
E` − EX)2 = E2` + |~PX |2 + 2E`|~PX | cosα. Since −1 ≤ cosα ≤ 1, the upper limit gives
(MB−P+)(P−−P`) ≥ 0, and the lower limit (MB−P−)(P`−P+) ≥ 0. Another constraint
comes from the QCD spectrum: the lightest state containing a u quark is the pion, so we
must have M2π ≤ P 2
X = P+P−. Combining all of these constraints we finally have:
M2π
P−≤ P+ ≤ P` ≤ P− ≤MB. (1.49)
One of the benefits of this choice of variables (apart from the easy derivation) is that phase
space (shown in Fig. 1.4) has an extremely simple form. By examining the phase-space
plane we can find regions where the CKM favoured b → c transitions are forbidden and
therefore select cuts that can be used for the experimental measurements:
• cut on the charged lepton energy E`. If E` ≥ (M2B−M2
D)/2MB ≈ 2.31 GeV, the final
18
[GeV]-P0 1 2 3 4 5
[G
eV]
+P
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Figure 1.4: The (P+P−) phase space for B → Xu`ν. Left: The charm free region is the dark greyregion below the black hyperbola, which correspond to M2
X = P+P− = M2D The solid blue line is
q2 = (MB − P+)(MB − P−) = (MB −MD)2. The red dashed line is P+ = M2D/MB . Right: same as left,
but with the actual distribution of b → u`ν superimposed.
hadronic state will have invariant mass smaller than MD. For this cut P` ≤ 0.66 GeV,
which implies that P+ is of order or ΛQCD;
• cut on the hadronic invariant mass M2X . To eliminate charm background we need
M2X ≤M2
D. The cut M2X = M2
D is depicted as a solid hyperbola in Figure 1.4;
• cut on the leptonic invariant mass q2. Any cut of the form q2 ≥ (MB −MD)2 would
not contain charm events. The cut q2 = (MB − P+)(MB − P−) = (MB −MD)2 is
depicted as a solid line in Figure 1.4;
• cut on P+. Red line in Figure 1.4 shows P+ = M2D/MB.
The experimental measurements have to be performed in restricted region of phase
space and then theoretical prediction on the partial decay widths are needed to extrapolate
to the full phase space. From the theoretical point of view, calculating the partial decay
rate in regions of phase space where B → Xc`ν are suppressed is very challenging, as
the HQE convergence in these regions is spoiled requiring the introduction of a non-
perturbative distribution function, whose form is unknown.
The shape function is a universal property of B mesons at leading order. It has been
19
recognized for over a decade [21, 22] that the leading shape function can be measured
in B → Xsγ decays. However, sub-leading shape functions [23, 24, 25, 26, 27] arise at
each order in 1/mb, and differ in semileptonic and radiative B decays. As previously said,
the form of the shape function cannot be calculated but can be constrained by moment
relations, which relate weighted integrals over the shape function to the heavy-quark
parameters mb (b quark mass), µ2π (kinetic energy of the b quark in the B meson) and µG
(chromomagnetic moment of the b quark). The inclusive charmed semileptonic decay rate
depends on these parameters so constraints to their values and, therefore, to the shape
function, can be applied studying B → Xc`ν decays. The same arguments hold for the
“2 body” B → Xsγ decay, which is directly sensitive to mb. An alternative way is to
employ shape-function independent relations between weighted B → Xsγ and B → Xc`ν
spectra [21, 28, 29, 30, 31]. Both approaches are equivalent; yet, not all predictions that
have been obtained using the shape function independent relations are up to the standard
of present-day calculations.
A fairly complete theoretical analysis of inclusive B → Xu`ν spectra was based on
calculation described in [32, 30] and referred to as BLNP approach. It includes complete
perturbative calculations at NLO with Sudakov resummations, subleading shape functions
at three level, and kinematical power corrections at O(αs). An alternative scheme called
“Dressed Gluon Exponentiation” (DGE) [33, 34, 35] employs a renormalon-inspired model
for the leading shape function, which is less flexible in its functional form that the forms
used by BLNP. Also, no attempt is made to include subleading shape functions, which
among other things means that the predictions for more inclusive partial rates would not
be in accord with the operator product expansion beyond the leading power in ΛQCD/mb
The DGE model is therefore less rigorous than the BLNP approach, even though it leads
to numerical results that are compatible with those of BLNP. Very recently, Gambino et
al. (GGOU) [36] released a work in which authors include the recently calculated O(β0α2s)
corrections to the decay rates [37] which were not available for BLNP. They use moment
constraints to model the subleading shape function differently for the various structures
in hadronic tensor. However, no attempt is made to resum the Sudakov logarithms. The
numerical results obtained using the GGOU code are consistent with those of BLNP in
20
both their central values and error estimates. Another calculation based on pure OPE
was proposed some time ago by Bauer, Ligeti and Luke [38]; their idea presupposes the
extraction of |Vub| from inclusive semileptonic decays b → u`ν by applying a cut on the
squared lepton-neutrino invariant mass q2. Such a cut forbids the hadronic final state
from moving fast in the B rest frame, and so the light-cone expansion which gives rise
to the shape function is not relevant in this region of phase space. It is shown that the
BLL calculation is most predictive, also in terms of uncertainties, in phase space regions
defined by a combination of MX and q2 requirements.
1.3.3 Experimental Approaches
The experimental approaches commonly used to measure charmless semileptonic B decays
fall into three categories:
1. Charged lepton momentum “endpoint” measurements. In these analyses, a single
charged electron is used to determine a partial decay rate for B → Xu`ν and no
neutrino reconstruction is employed, resulting in a ∼ 50% selection efficiency. The
decay rate can be cleanly extracted for E` > 2.3 GeV, but this is deep in the shape
function region, where theoretical uncertainties are large. Recent measurements push
down to 2.0 or 1.9 GeV, but the cost is a lower (< 1/10) signal-to-background (S/B)
ratio;
2. “untagged” neutrino reconstruction measurements. In this case, both the charged
electron and the missing momentum are measured, allowing the determination of q2
and providing additional background rejection. This allows a much higer S/B∼ 0.7
at the same E` cut and a selection efficiency ∼ 5%, but at the cost of smaller
accepted phase space for B → Xu`ν decays and uncertainties associated with the
determination of the missing momentum;
3. “tagged” measurements in which one B meson is fully reconstructed. The S/B ratio
can be quite high (∼ 2%) but the selection efficiency is ∼ 10−3. The E` cut is
typically 1.0 GeV and the full range of signal-side variables (q2, MX , P+) is available
for study, each having its own pros and cons. A cut on the hadronic invariant mass
21
(region below the black hyberbola in Fig. 1.4) has the advantage to include ≈ 80%
of b→ u transition, but has a strong dependence on the shape function. The highest
cut that is possible to set on the ligth-cone momentum is P+ < 0.66 (region below
the red line in Fig. 1.4) which provides access to ≈ 70% of charmless semileptonic
b transition, but the dependence on the shape function is high as well. The q2
distribution is less sensitive to non perturbative effetcs and less dependent on the
calculation of theoretical acceptance, but only a small fraction of events is usable
with a pure q2 cut (region below the blue line in Fig. 1.4). Combined MX and q2
cuts mitigate the drawbacks of the two methods while retaining good statistical and
systematic sensitivities. The fraction of b → u event selected with these combined
cuts is ≈ 45%.
In this thesis, the tagged approach has been chosen and three different kinematic
regions are exploited, in order to compare measurementes with different sensitivies to
theoretical uncertainties; these regions are defined by pure MX cuts, pure P+ cuts and
combined (MX , q2) cuts. Table 1.3 shows a summary of the features of each kinematic
requirement. The detailed impact of the theoretical models presented above on the deter-
Kinematic region % of rate Pros ConsMX < MD ∼ 80% lots of rate depends on shape function
(and subleading corrections)P+ < M2
D/MB ∼ 70% lots of rate depends on shape function(and subleading corrections)
q2 > (MB −MD)2 ∼ 20% insensitive to shape function - very sensitive to mb
- Weak Annihilation may be substantial- effective expansion parameter is 1/mc
(MX , q2) combined ∼ 45% insensitive to shape function less rate than MX and P+ cuts
Table 1.3: Comparison of different kinematic cuts.
mination on |Vub| from the experimental measurements discussed in this thesis are shown
in Chapter 8.
22
Chapter 2
The BABAR Experiment
The BABAR experiment at PEP-II B factory [39, 40] has been optimized for CP violation
studies and searches for rare B meson decays. The PEP-II B factory is an high luminosity
(L & 3 × 1033cm−2s−1) e+e− collider operated at the center-of-mass (CM) energy of
10.58 GeV, on the Υ(4S) resonance. This resonance decays almost exclusively in a B0B0
or a B+B− pair with equal probabilities, giving a clean environment characterized by a
good signal-to-noise ratio (σbb/σtot ≈ 0.28) and low track multiplicity per event (≈ 11).
In addition, events reconstruction and background rejection benefit by the kinematic
constraint on the momentum and energy, of each B, in the CM frame.
In PEP-II, the electron beam of 9 GeV collides head-on with the positron beam of
3.1 GeV resulting in a Lorentz boost for the Υ(4S) of βγ = 0.56 in the laboratory frame.
Figure 2.1 shows the boost effect on the polar angle. The asymmetry of the machine is
Figure 2.1: Effect of the Lorentz boost on the polar angle at BABAR .
23
motivated by the need of separating the decay vertexes of the two B mesons, a crucial
point for the determination of the CP asymmetries. The boost allows the separation and
reconstruction of the decay vertexes of both B mesons, the determination of their relative
decay length measured in the center-of-mass frame, the difference of their decaying time
and thus the measurement of time dependent asymmetries. Nevertheless other stringent
requirements on the detector are placed in order to measure the very small branching
ratios of B mesons to CP eigenstates:
- large and uniform acceptance down to small polar angle relative to the boost direc-
tion;
- excellent reconstruction efficiency down to 60 MeV/c for charged particles and
20 MeV for photons;
- very good momentum resolution to separate small signals from background;
- excellent energy and angular resolution to detect photons coming from π0 and η
decays, and from radiative decays in the range from 20 MeV to 4 GeV;
- very good vertex resolution, both transverse and parallel to the beam direction;
- efficient electron and muon identification, with low misidentification probabilities for
hadrons. This feature is crucial for tagging the B flavor, for the reconstruction of
charmonium states and also important for the study of decays involving leptons;
- efficient and accurate identification of hadrons over a wide range of momenta for B
flavor-tagging and for the reconstruction of exclusive states;
- low-noise electronics and a reliable, high bandwidth, data-acquisition and control
system;
- detailed monitoring and automated calibration;
- an on-line computing and network system that can control, process and store the
expected high volume of data;
24
- detector components that can tolerate significant radiation doses and operate reliably
under high background conditions.
2.1 The PEP-II Asymmetric Collider
The PEP-II B factory is part of the accelerator complex at SLAC, shown in Fig. 2.2.
The electron beam is produced by the electron gun near the beginning of the two-mile
long linear accelerator (the “linac”). The gun consists of a thermally heated cathode
filament held under high voltage. Large numbers of electrons are “boiled off” the cathode,
accelerated by the electric field, collected into bunches, and ejected out of the gun into the
linac. The electron bunches are accelerated in the linac with synchronized radio-frequency
(RF) electromagnetic pulses generated in RF cavities through which the beam passes by a
series of 50 Megawatt klystron tubes (klystrons generate the pulses with their own lower
energy electron beams passing through resonant cavities). The steering, bending, and
focusing of the beam is carried out with magnets throughout the acceleration cycle.
Figure 2.2: A schematic depiction of the B factory accelerator complex ad SLAC.
After acceleration to an energy of approximately 1 GeV, the electron beam is directed to
a damping ring, where the beam is stored for some time. As it circulates in the ring, it loses
energy through synchrotron radiation and is continuously re-accelerated by RF cavities.
25
The radiation and careful re-acceleration has the effect of reducing the emittance, or
spatial and momentum spread of the beam, a necessary step in high-luminosity collisions.
The “damped” beam is then re-directed to the linac and accelerated to 8.9 GeV.
Half of the generated electron bunches are used for the generation of the positron
beam. They are accelerated to approximately 30 GeV, extracted from the linac and
directed onto a tungsten target, producing electromagnetic showers that contain large
numbers of electron-positron pairs. The positrons are separated electromagnetically from
the electrons, collected into bunches, accelerated, and sent through the return line to
the source end of the linac. The positron beam is then accelerated and shaped like the
electron beam through the linac and its own damping ring, culminating in an energy of
3.1 GeV.
After reaching their respective collision energies, the electron and positron beams are
extracted from the linac, and directed to the PEP-II storage rings, the High-Energy
Ring (HER) for electrons and Low-Energy Ring (LER) for the positrons, both housed
in the same tunnel of 2.2 km circumference. As they circulate, the are focused further
by a complex of magnets and accelerated by RF cavities to compensate the synchrotron-
radiation losses. In the interaction region IR-2 (one of twelve such regions), where the
BABAR detector is located, they are brought to a collision after a final-focus system
squeezes the beams to the smallest possible emittance. During data taking, each ring
contains about 1600 circulating bunches colliding every 5 ns. The collisions are then
analyzed by the BABAR detector. About 10% of the time the beams are collided at an
energy 40 MeV below the Υ(4S) resonance for calibration of the backgrounds, as no B
mesons are produced then since this energy is below the bb threshold. As data is collected,
the collision and other losses reduce the currents in the rings, necessitating re-injection
of electron and positron bunches. Initially in the life of the B factory from 1999-2002,
data was taken for about an hour or two while the currents diminished, and then addi-
tional current was injected into the rings for a few minutes. Data could not be taken
during injection due to the large backgrounds in the detector and the resulting danger to
instrumentation. (The detector would have to be put into a “safe” but non-operational
state during injection, with, for example, all high-voltage components ramped down to
26
a lower, safer potential). Starting in 2003, a new scheme for injection, called “trickle”
injection, was developed, wherein new bunches are continuously injected at a rate large
enough to replenish beam losses but low enough to not damage the detector. This has
allowed more efficient operation of the B-factory with 30% more integrated luminosity
for a given highest instantaneous luminosity.
The PEP-II collider was designed for an instantaneous luminosity of 3× 1033 cm−2s−1,
but has reached values of 1.2 × 1034 cm−2s−1 due to improvements in the RF cavities,
beam-shaping cavities and magnet systems. The increased luminosity comes from larger
beam currents (up to 3 A in the LER and 2 A in the HER) and reduced emittance.
With these specifications and trickle injection, the machine generates hundreds of pb−1
of integrated luminosity daily during normal operations and has integrated hundreds of
fb−1 throughout its operating lifetime. Fig. 2.3 shows the total (left) and daily (right)
integrated luminosity.
Figure 2.3: PEP-II delivered and BABAR recorder total (left) and daily (right) integrated luminosity inthe data taking period of 1999-2006 (Run1-Run5).
2.1.1 PEP-II Backgrounds
Different factors should be taken into account when trying to set an acceptable background
that allows a smooth and safe BABAR detector operation. Main constraints are:
27
- Radiation levels in EMC and SVT sub-detectors;
- Current tolerated by DCH;
- L1 trigger rate;
- Other subsystems occupancy.
Simulations, data analysis and dedicated measurements of the various background sources,
on their impact on data taking and on detector performance have contributed to form
a detailed knowledge of different background-related underlying phenomena and made
possible their tuning and reduction. PEP-II main background sources [41] are:
• synchrotron radiation in the proximity of the interaction region. A strong source
of background (many kW of power) is due to the beam deflections in the inter-
action region. This component is limited by channeling the radiation out of the
BABAR acceptance with a proper design of the interaction region and the beam orbits,
and placing absorbing masks before the detector components.
• interaction between beam particles and residual gas in either ring can have two dif-
ferent origins: beam-gas bremsstrahlung and Coulomb scattering. Both these two
types of interaction causes an escape of the beam particle from their orbit. This
background represents the primary source of radiation damage for the inner vertex
detector and the principal background for the other detector components.
• electromagnetic showers generated by beam-beam collisions. These showers are due
to energy degraded e+ and e− produced by radiative Bhabha scattering and hitting
the beam pipe within a few meters of the IP. This background is proportional to
the luminosity of the machine and whereas now is under control, it is expected to
increase in case of higher operation values.
2.2 The BABAR Detector
The BABAR detector is a large, multi-purpose hermetic detector with several components.
As shown in Fig. 2.4 the detector consists of two endcaps and a cylindrical barrel hugging
28
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Instrumented Flux Return (IFR))
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3-2001 8583A51
Figure 2.4: Longitudinal (top) and end (bottom) views of the BABAR detector. Units are mm.
29
the beam pipe along the z direction and roughly symmetric in the azimuth φ. The
right-handed coordinate system is defined with the z axis pointing in the e− direction, x
pointing horizontally away from the center of PEP-II rings, and y pointing upwards. The
geometrical center is offset from the beam-beam interaction point towards polar angles
to maximize the geometric acceptance for the boosted Υ(4S) decays.
The sub-detectors are arranged in layers of increasing distance from the beam pipe.
The silicon vertex tracker (SVT), the innermost detector, is used for vertexing particle
decays and is the main source of information on the polar angle of charged particles.
The Drift Chamber (DCH) is the main device for measuring charged-particle momenta
with good resolution through gaseous wire-chamber technology. A Detector of Internally
Reflected Cerenkov Light (DRC) is used to separate pions from kaons, while a crystal Elec-
tromagnetic Calorimeter (EMC) is used for energy measurement of photons and electrons
and for electron identification. These components are placed within a 1.5 Tesla solenoidal
magnet that provides the magnetic bending of charged particles needed to measure their
momenta. Outside the magnet is the Instrumental Return Flux (IFR), which is used for the
identification of muons and long-lived neutral hadrons. The detector signals are processed
through detector electronics, and examined by a trigger system that selects physically in-
teresting collision data to be stored. Various online and offline reconstruction procedures
are employed to convert the data into a format amenable to analysis for the study of
relevant B decays and other processes.
2.2.1 Silicon Vertex Tracker (SVT)
The SVT consists of five layers of double-sided silicon sensors segmented in both the z
and φ directions, designed to measure accurately the positions and decay vertexes of B
mesons and other particles. This measurement is most accurate at small distances from
the interaction point, as the trajectory of the particles farther away is affected by multiple
scattering within the detector. Thus, the first three layers are located as close to the
beam pipe as possible. The outer two layers are closer to the Drift Chamber to facilitate
matching of SVT tracks with DCH tracks. They also provide pattern recognition in track
reconstruction, and the only tracking information for charged particles with transverse
30
momenta below 120 MeV/c, as these may not reach the Drift Chamber. The SVT covers
90% of the solid angle in the CM frame. Fig. 2.5 shows schematic views of the SVT.
Figure 2.5: Schematic view of the SVT: longitudinal section (left) and transverse section (right).
The silicon sensors are 300 µm-thick high-resistivity n-type silicon wafers, with n+ and
p+ strips running orthogonally on opposite sides. As high-energy particles pass through
the sensor they displace orbital electrons, producing conducting electrons and positive
holes that then migrate under the influence of an applied depletion voltage. The resulting
electrical signal is read-off from the strips, amplified and discriminated with respect to a
signal threshold by front-end electronics. The time over threshold of the signal is related
to the charge of the signal and is read out by the data acquisition system for triggered
events. The position resolution is in the 10 µm-50 µm range, depending on the orientation
of the strip (φ or z) and the layer number.
The SVT is water-cooled and monitored for temperature, humidity and position vari-
ations. Local and global position alignment is performed frequently in the outline re-
construction software. As the SVT has to withstand a lifetime integrated radiation dose
of 2 Mrad, the sensors have a high threshold for radiation damage. Nevertheless, they
are easily damaged by high instantaneous or integrated doses and an extensive system of
radiation monitoring with PIN and diamond diodes can abort the beams if dangerous level
develop. Up to 2007 the monitoring systems have prevented any significant damage from
occurring and the SVT has performed extremely well, with an average track reconstruction
efficiency of 97%.
31
2.2.2 Drift Chamber (DCH)
The Drift Chamber is the main tracking device. It supplies high precision tracking for
charged particles with transverse momenta pT above ≈ 120 MeV/c, and provides also
particle identification by measuring track ionization losses as function of position (dE/dx),
in particular for tracks with momenta less than 700 MeV/c.
The inner wall of the Drift Chamber is placed close to the SVT outer wall to facilitate
track-matching between the two devices. The chamber is 2.8 m long and consists of 40
cylindrical layers of 12 mm by 19 mm hexagonal cells, each consisting of six field wires
at the corners and one field wire in the center as shown in Fig. 2.6 and Fig. 2.7. The
Figure 2.6: Longitudinal section of the DCH. Dimensions are in mm. The chamber center has an offsetof 370 mm from the interaction point (IP).
field wires are grounded, while the sense wire is held at high voltage, typically around
1900 V. The space around the wires is filled with gas mixture containing 80% helium and
20% isobutane. High-energy particles ionize the gas as the traverse it, and the liberated
electrons are then accelerated toward the sense wires, ionizing additional electrons, which
are in turn accelerated themselves and result in the formation of a gas avalanche of
electric charge. The avalanche collects on the sense wire with drift times of 10-500 ns
and the charge and timing information of the signal is read-off through electronic circuits
AC-coupled to the wire. The gain relative to the charge of primary ionization is about
32
0Stereo
1 Layer
0Stereo
1 Layer
0 2 0 2 0 2
0 3
0 4 0 4
45 5 45 5
47 6 47 6 47 6
48 7 48 7
50 8
-52 9
-5410
-5511
-5712
013 013
014 014
015
016
4 cm
Sense Field Guard Clearing
1-2001 8583A14
Figure 2.7: Layout of the four innermost super-layers.
33
5× 104. The grounded field wires produce a uniform electric field in the cell with evenly
distributed isochrones, or contours of equal drift time, as shown in Fig. 2.8. “Stereo”
wires in 24 of the 40 layers are placed at small angles with respect to the z direction in
order to provide longitudinal information. The chamber has a typical position resolution
of 140 µm.
Sense
Field Guard 1-2001
8583A16
Figure 2.8: Isochrones in a typical DCH cell.
Isobutane has large molecules with rotational degrees of freedom that can absorb elec-
trical energy, and its presence in the gas mixture limits the growth of the avalanche in
order to protect the chamber from damaging levels of accumulated charge. The choice
of the gas mixture is motivated by considerations of aging and avalanche size as well as
minimizing multiple scattering in the chamber, which is accomplished by choosing helium
as the primary gas component and aluminum as the lightweight material for the multiple
field wires. The gas is circulated to flush out any degraded component, with one full
volume of fresh gas (5.2 m3) added every 36 h. In addition, the water content of the gas is
maintained by a water bubbler at 3500±200 ppm and oxygen is removed with a catalytic
filter, both measures designed to prevent Malter-effect discharges in the gas that would
degrade the performance and aging behavior of the chamber.
The DCH has demonstrated excellent performance throughout the life of BABAR with
track-reconstruction efficiencies at the 95% level. This includes the effect of discon-
necting a fraction of the wires in superlayers 5 and 6 the were damaged during the
commissioning phase. The dE/dx response, with a resolution of about 7%, is shown
34
in Fig. 2.9, and a new calibration in 2006 has improved the PID potential of this ca-
pability for high-energy tracks. The achieved resolution on transverse momentum is
σpT/ pT = (0.13 ± 0.01)% × pT + (0.45 ± 0.03)% where pT is given in units of
GeV/c.
Figure 2.9: dE/dx in the DCH as a function of track momentum for different particles: protons (blue),kaons (red), pions (green), muons (black) and electrons (magenta).
2.2.3 Cerenkov Light Detector (DRC)
The DIRC (Detector of Internally Reflected Cerenkov ) is the main PID sub-detector at
BABAR , providing π−K separation of 2.5σ or more over the momentum range 700 MeV/c -
4.2 GeV/c. It is thin and light, minimizing the size and the impact on performance of
the EMC that is located outside the DRC in the radial direction. Cerenkov devices detect
light radiated by particles that move faster than the speed of light in a given medium,
with the Cerenkov angle θC of the radiated photons given by
cos(θC) =1
nβ=
c
nv, (2.1)
where n is the index of refraction of the medium and v is the particle’s velocity. For a
given momentum, particles of different mass will have different velocities, differentiating
particle-mass hypotheses for a track and thus different PID hypotheses.
35
The DRC consists of 144 bars made of fused silica running along the z direction, with
dimensions of 17 mm by 35 mm and 4.9 m in length. The silica serves as the Cerenkov
radiator, with the high index of refraction of n = 1.437 and as a waveguide, with a
low attenuation length. A charged particle passing through radiates Cerenkov photons,
which then propagate to the longitudinal end of the bar, trapped within by total internal
reflections at the flat boundaries of the bar. Each reflection preserves the original Cerenkov
angle. At the end of the bars, the photons pass through a standoff box filled with purified
water that has a similar refractive index of n = 1.346, so that refraction at the silica-
water boundary is minimized. The water must be highly transparent as the photons
pass through about one meter of water in the standoff box, so it is filtered, de-gassed,
de-ionized, exposed to UV radiation to prevent the growth of bacteria, and treated with
a reverse-osmosis unit.
The rear surface of the standoff box is instrumented with 12 sectors of 896 photo-
multiplier tubes (PMTs) each, which collect the photons, convert them to electrons with
photo-cathodes and amplify the signal using the gas-avalanche principle. As the standoff
box is located outside the solenoid magnet, it is possible to limit the magnetic field in its
volume to about 1 Gauss with a bucking coil that counteracts the field of the solenoid.
Thus, conventional PMTs, which do not tolerate high magnetic fields, can be used. To
limit the number of PMTs, there is only one standoff box, located at the backward end
of the detector to exploit the forward boost environment of the collisions. The forward
ends of the silica bars have mirrors perpendicular to the axis of the bars, so that forward-
pointing photons are reflected and reach the backward end of the bars as well. The
detector is depicted schematically in Fig. 2.10. The total photon detection efficiency is
at the 5% level, with the average number of detected photons ranging from 20 at normal
track incidence to 65 at large polar angles.
As the Cerenkov angle of the emitted photons is preserved, it can be reconstructed
from the PMT signals, the timing information and the track momentum vectors obtained
by matching the signal with tracks from the DCH and SVT. The resolution on the single-
photon Cerenkov angle θC,γ is 10.2 mrad, while the resolution that can be obtained for a
36
Figure 2.10: DRC scheme: radiation area and imaging region.
track from all its radiated photons is
θC,track =θC,γ√Nγ
(2.2)
where Nγ is the number of detected photons. This yields typical track angular resolutions
of 3 mrad.
The DRC is intrinsically a three-dimensional imaging device, giving the position and
arrival time of the PMT signals. The three-dimensional vector pointing from the center
of the bar end to the center of the PMT is computed and then is extrapolated (using
Snell’s law) into the radiator bar in order to extract, given the direction of the charged
particle, the Cerenkov angle. Timing information is used to suppress background hits
and to correctly identify the track emitting the photons. Fig. 2.11 shows light rings
reconstructed by the DRC.
2.2.4 Electromagnetic Calorimeter (EMC)
The electromagnetic calorimeter has been designed to measure with excellent resolution
the energy and angular distribution of electromagnetic showers with an energy in the
range from 20 MeV (for photons from decays of slow π0 or η0) to 4 GeV (for photons and
electron from weak processes). An efficient and pure selection of electrons is necessary
37
Figure 2.11: Cerenkov light ring reconstruction using the DRC.
for B flavor tagging via semileptonic decays, for the reconstruction of vector mesons like
J/ψ, or of several exclusive final states of B and D mesons. Furthermore QED processes
like e+e− → e+e−(γ) and e+e− → γγ need to be efficiently detected because they are
useful for calibration and luminosity determination.
The EMC (Fig. 2.12) is made of 6580 CsI Tallium activated crystals (Fig. 2.13) The
transverse segmentation is at the scale of Moliere radius to optimize the angular resolution
while limiting the number of crystals and readout channels. The crystals serve as radiators
for the traversing electrons and photons, with a short radiation length of 1.85 cm. The
crystal scintillate under the influence of the showers and the light is passed through total
internal reflection to the outer face of the crystal, where it is read out by silicon PIN diodes.
As these diodes are well suited for operation in the high magnetic fields in the EMC, part
of the motivation for the crystal choice was that the frequency spectrum of CsI(Tl) is
detected by silicon PIN sensors with the high quantum efficiency of 85%. The EMC is
cooled by water and Flourinert coolant and monitored for changes in the environmental
and radiation conditions and for changes in the light response of individual crystals.
38
Figure 2.12: EMC longitudinal section (top-half only, dimension in mm) showing how the 56 crystal ringsare placed. Detector has an axial symmetry along z axis.
Figure 2.13: EMC crystal scheme.
39
The energy response of the EMC is calibrated using low-energy photons from a radioac-
tive source and high-energy photons from radiative e+e− Bhabha events. As electromag-
netic showers spread throughout several crystals, a reconstruction algorithm is used to
associate activated crystals into clusters and either to identify them as photon candidates
or to match individual maxima of deposited energy to extrapolated tracks from the DCH-
SVT tracker. Additional PID is obtained from the spatial shape of the shower. The energy
and angular resolutions are determined to be
σE
E=
(2.32± 0.30)%4√E(GeV)
⊕ (1.85± 0.12)%, (2.3)
σθ = σφ =(3.87± 0.07) mrad√
E(GeV)⊕ (0.00± 0.04) mrad. (2.4)
In both cases, the first term is due to fluctuations in the number of photons and to
electronic noise of the photon detector and electronics, while the second term arises from
the non-uniformity of light collection, leakage and absorption due to materials between
and in front of the crystals and calibration uncertainties. Fig. 2.14 shows the agreement
between data and simulation of the angular resolution of the EMC and its π0 reconstruction
performance.
Figure 2.14: Left: angular resolution in the EMC as function of photon energy. The solid curve is a fit toEq. 2.4. Right: the reconstructed diphoton peak at the π0 mass region.
40
2.2.5 Instrumented Flux Return (IFR)
The IFR is the primary muon detector at BABAR and is also used for the identification
of long-lived neutral hadrons (primarily K0L’s). The IFR is divided into a hexagonal bar-
rel, which covers 50% of the solid-angle in the CM frame, and two endcaps (Fig. 2.15).
Originally it consisted of layers of steel of varying thickness interspersed with Resistive
Figure 2.15: Overview of the original IFR Barrel sectors and forward and backward end-doors.
Plate Chambers (RPCs), 19 layers in the barrel and 18 in each endcap1. The steel serves
as a flux return for the solenoidal magnet as well as a hadron absorber, limiting pion
contamination in the muon ID. RPCs where chosen as they were believed to be a reliable,
inexpensive option to cover the 2000 m2 of instrumented area in this outermost region of
BABAR with the desired acceptance, efficiency and background rejection for muons down
to momenta of 1 GeV/c.
The RPCs detect high energy particles through gas-avalanche formation in high electric
field. The chambers consist of 2 mm-thin bakelite sheets kept 2 mm apart by an array of
spacers located every 10 cm (Fig. 2.16). The space between is filled with a non-flammable
gas mixture of 56.7% argon, 38.8% freon 134a and 4.5% isobutane, while the sheets are
held at a potential of 7600V. The inside surface of the bakelite is smoothed with a linseed-
1Additional cylindrical RPCs where placed just outside the solenoid magnet to improve the matching between IFR andEMC showers
41
Figure 2.16: Planar RPC section with HV connection scheme.
oil coating so that the electric field is uniform, thus preventing discharges in the gas and
large dark currents. The RPCs operate in streamer mode, wherein the avalanche grows
into a streamer, a mild, controlled form of electrical discharge in the gas. The streamer
charge is read out in both φ and z directions by aluminum strips located outside and
capacitively coupled to the chamber. The streamer is kept from producing electrical
breakdown of the gas by the quenching action of the freon and isobutane molecules, as
described for the DCH.
In streamer mode, the gas gain is at the 108 level. The factor 10-1000 increase in gain
over avalanche mode greatly simplifies the readout electronics. Moreover, the charge of
the streamer is independent of the primary-ionization charge, resulting in an effectively
digital signal with high efficiency. Initially, the RPCs performed over 90% efficiency as
expected geometrically from inactive space in the detector, resulting in a muon detection
efficiency of 90% for a pion misidentification rate of 6–8% in the momentum range of
1.5 < p < 3.0 GeV/c, as shown in Fig. 2.17.
Shortly after the start of data-taking with BABAR in 1999, the performance of the
RPCs started to deteriorate rapidly. Numerous chambers began drawing dark currents
and developing large areas of low efficiency. The overall efficiency of RPCs started to
drop and the number of non-functional chambers (with efficiency less than 10%) rose
dramatically (Fig. 2.18), deteriorating muon ID. The problem was traced to insufficient
42
Figure 2.17: Initial muon-identification performance of BABAR RPCs.
Figure 2.18: Deterioration with time of the average RPC efficiency (red). The green dots show thefraction of RPCs with efficiency lower than 10%.
43
curing and R&D of the linseed-oil coating and to the high temperature at which the
RPCs were operated initially. Uncured oil droplets would form columns under the action
of the strong electric field and the high temperature (up to 37 C), bridging the bakelite
gap and resulting in large currents and dead space. Various remediation measures were
attempted, including flowing oxygen through the chambers to cure the oil and introducing
water cooling of the IFR, but they did not solve the problem. Extrapolating the efficiency
trend showed a clear path towards losing muon ID capability at BABAR within a couple
of years of operations, so an upgrade of the IFR detector was deemed necessary by the
collaboration.
The forward endcap was retrofitted with new improved RPCs in 2002. The new cham-
bers were screened much more stringently with QC tests and had a much thinner linseed-
oil coating that was properly cured and tested. They have performed well since then.
The backward endcap was not retrofitted, as its acceptance in the CM frame is small.
In the barrel, the collaboration decided to upgrade the detector with Limited Streamer
Tube (LST) technology. The RPCs were removed and replaced by 12 layers of LSTs and
6 layers of brass to improve hadron absorption. (The last layer of RPCs is inaccessible,
so the old chambers there were disconnected from all utilities but kept in place). Since
the author was partially involved in this upgrade as the project was a laborious and
careful but time-sensitive project undertaken at a mature age of the experiment, it will
be described in more detail than the other components of the detector.
The LSTs consist of PVC comb of eight 15 mm by 17 mm cells about 3.5 m in length,
encased in PVC sleeve, with a 100 µm gold-plated beryllium-copper wire running down
the center of each cell (Fig. 2.19). The cells in the comb are covered with graphite, which
is grounded, while the wires are held at 5500 V and held in place by wire holders located
every 50 cm. The gas mixture consists of 3.5% argon, 8% isobutane, and 88.5% carbon
dioxide. Like the RPCs and their name implies, the LSTs are operated in streamer mode.
The signal is read off directly from the wires through AC-coupled electronics (granularity
of two wires per channel in the φ direction) and from strips running perpendicular to
the tubes and capacitively coupled to the wires (35 mm pitch in the z direction). After
the mechanical assembly, the tubes were conditioned under progressively higher applied
44
Figure 2.19: The mechanical structure of BABAR LSTs.
45
voltages to burn off dirt accumulated during construction. Only tubes that could hold
the operational voltage without drawing excessive currents were accepted.
One of the crucial performance characteristics was the “singles’-rate”, or counting-
rate, plateau. As the streamer signals are effectively digital, given a constant incident
flux of particles, the chamber should show a counting-rate plateau over a range of applied
voltage where the charge of every streamer is above the read-out threshold (Fig. 2.20).
The plateau provides operational tolerance of the applied HV, allowing operations of the
LSTs at the middle of the plateau to safeguard against fluctuations in efficiency due to
changes in the gas gain from pressure or voltage fluctuations. Defects in the surface of
the graphite or dirt accumulated on the wire can result in large discharges in the tube
(including the Malter effect) that raise the singles’ rate and spoil the plateau (Fig. 2.20
right). In addition, a short plateau is an indication of poor aging behavior. Thus, the
quality of the plateau is a powerful QC test.
Figure 2.20: Left: a singles’ rate plateau seen versus applied voltage for several LSTs. Right: defects inthe chamber can spoil the plateau.
The LSTs were constructed at PolHiTech, an Italian company located in Carsoli, out-
side Rome. The construction and QC procedures outlined above were conducted under
the supervision of BABAR personnel. After all QC tests, the tubes were held under high
voltage for a month to verify that no premature aging behavior occurred. Thereafter,
they were assembled into modules of two to three tubes at Princeton University and The
Ohio State University and then shipped to SLAC for the installation, which occurred in
two stages: two sextants of the hexagonal barrel in summer of 2004 and the remaining
46
four sextants in the Fall of 2006. QC procedures were performed at every step to make
sure that only the best tubes were installed in the detector.
The project involved the manufacture of 1500 LSTs including contingency, with more
than 1200 installed in the detector. It also necessitated the design an fabrication of custom
read-out electronics (done by INFN Ferrara in Italy), HV power supplies (The Ohio State
University) and gas system (SLAC). The project was completed successfully, safely and
ahead of schedule. After installation, the tubes have performed very well since 2005 in
two sextants and since the beginning of 2007 in all sextants, with failure rate below 0.5%
for both the tubes and z-strips. The efficiencies of all layers are at the geometrically
expected level of 90%. Regular testing of singles’-rates with cosmic rays has verified
continuing excellent behavior with long single’s-rate plateaus (Fig. 2.21). Figure 2.22
Figure 2.21: Singles’ rate measurements with cosmic rays for diagnostic of installed LST module.
shows muon tracks in the LST part of the IFR, while in Fig. 2.23 efficiency maps for all
the six barrel sextants instrumented with LST are shown.
47
Timestamp: 7f:020000:41d633/a603358b:W
The PEP-II/BaBar B-Factory
Run: 68724
HER: 8.985 GeV, LER: 3.112 GeV
Date Taken: Tue Nov 14 10:25:46.270537000 2006 PST?
Figure 2.22: Event display of a cosmic muon event as seen by LSTs.
Figure 2.23: Efficiency map: each rectangle represents one sextant.
48
2.2.6 Trigger System (TRG) and Data Acquisition (DAQ)
The basic requirements for the trigger system is the selection of events of interest with a
high, stable and well-understood efficiency while rejecting background events and keeping
the total event rate under 1 kHz. At design luminosity, beam-induced background rates
are typically about 20 kHz each for one or more tracks in the Drift Chamber with pT >
120 MeV/c or at least one EMC cluster with E > 100 MeV.
The total trigger efficiency is required to exceed 99% for all BB events and at least
95% for continuum events. Less stringent requirements apply to other event types, e.g.
τ+τ− events should have a 90-95% trigger efficiency, depending on the specific τ± decay
channels.
The BABAR trigger system is implemented as a two-level hierarchy. The Level 1 (L1) is
hardware based, consisting in several dedicated microprocessor systems that analyze data
from the front-end electronics (FEEs) of the DCH, EMC and IFR to form primitive physics
objects used to make the trigger decision. These include tracks of minimum transverse
momentum that penetrate to a particular depth into the DCH and energy clusters in
the EMC above set thresholds. The selections are optimized to maintain nearly perfect
BB efficiency while removing most of the beam-induced backgrounds in the process of
reducing the data collection rate from about 20 kHz to a few kHz, which can be processed
by the next trigger level. Some “prescaled” events of random beam-beam crossing and
special event types are also collected for efficiency, diagnostic and background studies.
The trigger decision is made and communicated within the 12.8 µs buffer limit of the
FEEs. The L1 trigger has greater than 99.5% efficiency for BB processes.
After an L1 accept decision, the L1 output is passed on to the Level 3 (L3) trigger,
which consist of software based algorithm run on a farm of PCs. The L3 triggers also
has access to the complete event data and refines the L1 decision with more sophisticated
selections, such as requirements on a track’s distance of closest approach to the interaction
point or the total invariant mass of an event. It maintains the BB selection efficiency at
more than 99% while reducing the data rate to about 200 Hz. Each event corresponds to
about 30 kB of detector information.
49
An event that results in an L3 accept decision is processed by the data-acquisition
electronics and event-building software. In this process, charged tracks are reconstructed
from DCH and SVT information and extrapolated to the outer part of the detector, in-
corporating knowledge of the distribution of material in the detector and the magnetic
field. The momentum of tracks is measured from the sagitta in the curves of the tracks.
PID is refined with DRC, EMC and IFR as well as with attempts to match objects in those
sub-detectors with tracks in the DCH. Fundamental physical objects reconstructed in the
detector are also used to assemble candidates for composite particles. Lists of particle
candidates as well as the original digitized data is stored on tape in collections that are
retrieved later for high-level analysis by individual groups of users.
Throughout event reconstruction various calibrations such as alignment constants and
energy-scale adjustments in the EMC are applied to detector information to refine recon-
struction performance. Calibration information is updated frequently during data taking
to keep it consistent with running conditions. Data-quality scripts monitor detector be-
havior and various physics processes to verify that the collected data is not compromised
by deviations from expected behavior of the detector or accelerator. A parallel system
based on the EPICS slow-control environment is used to monitor and control the detec-
tor elements for all subsystems. Detector, accelerator and environmental conditions are
recorded in another “ambient” database. The entire data-taking process is supervised
at all times by at least two BABAR shifters on the detector side and several accelerator
operators on the PEP-II side.
50
Chapter 3
Event Reconstruction
Given the low branching ratio for charmless SL decays, it is essential to reconstruct
the maximum number of signal events in order to have precise measurements. This
suggests to collect inclusive samples of B decays, where little or no requirements are
made on the rest of the event. On the other hand, the poor signal over background ratio,
and the consequent need to apply kinematic cuts in order to reduce background from
semileptonic decays with charm, calls for a detailed knowledge of decay kinematics. This
can be achieved by partially or fully reconstructing the rest of the event, which results
in a low reconstruction efficiency. However, given the high-statistics sample collected at
B Factories, it is possible to find a reasonable compromise between these two apparently
contradicting requirements.
This analysis is based on the study of the recoil of B mesons fully reconstructed in
a hadronic mode (Breco). One of the two B mesons from the decay of the Υ(4S) is
reconstructed in a fully hadronic mode (see Fig. 3.1). Then, the remaining particles of
the event are then supposed to belong to the other B (Brecoil).
Due to the exclusive reconstruction of the Breco, the properties of the recoil can be
studied in a very clean environment. As it will be shown in detail in Chapter 5, charge
conservation can be required and the missing mass of the event should be compatible
with zero. Moreover, since the kinematics is over-constrained, the resolution on the re-
constructed quantities, such as the mass MX of the hadronic system X, is improved. The
momentum of the recoiling B is also known and therefore it’s possible to apply a Lorentz
transformation to the charged lepton four-momentum and compute it in the B rest frame.
51
Figure 3.1: Semileptonic events on the recoil of a fully reconstructed B meson.
The charge of the B is known, so B0 and B+ decays can be studied separately. The flavor
of the B is known, therefore the correlation between the charge of the lepton and the
flavor of the B can be used to reject B → D → lepton cascade events, as described
in Sec. 6.1. The only drawback is that the efficiency of this method is quite low and is
dominated by the B reconstruction efficiency.
The charged and neutral particles reconstruction is described in this chapter together
with the algorithm used for the full hadronicB reconstruction, the so-called Semi-exclusive
reconstruction [42] (Sec. 3.5).
3.1 Charged Particle Reconstruction
The charged particle tracks are reconstructed by processing the information from both
tracking systems, the SVT and the DCH. Charged tracks are defined by five parameters
(d0, φ0, ω, z0, tanλ) and their associated error matrix, measured at the point of closest
approach to the z-axis. d0 and z0 are the distances between the point and the origin of
the coordinate system in the x−y plane and along the z-axis respectively. The angle φ0 is
the azimuth of the track, λ is the angle between the transverse plane and the track tangent
vector at the point of closest approach and the x-axis, and ω = 1/pt is the curvature of
the track. d0 and ω are signed variables and their sign depends on the charge of the
track. The track finding and the fitting procedures use the Kalman filter algorithm [43]
that takes into account the detailed distribution of material in the detector and the full
magnetic field map.
For what concerns this analysis, the definition of charged track is based on some specific
52
quantities:
• distance of closest approach to the beam spot measured in the x - y plane (|dxy|)and along the z axis (|dz|). A cut on those variables rejects fake tracks and back-
ground tracks not originating near the beam-beam interaction point. We require
|dxy| < 1.5 cm and |dz| < 5 cm;
• maximum momentum: to remove tracks not compatible with the beam energy we
require plab < 10 GeV/c , where plab refers to the laboratory momentum of the track,
against misreconstructed tracks;
• polar angle acceptance: the polar angle, in the laboratory frame, is required to be
0.41 < θlab < 2.54 in order to match the acceptance of the detector. This ensures a
well-understood tracking efficiency and systematics.
No restrictions on the impact parameter have been imposed for secondary tracks from
Ks decays. No cut on the minimum number of hits on track is used in order to maximize
the efficiency for low momenta tracks.
In addition, special criteria are used to reject tracks due to specified tracking errors.
Tracks with a transverse momentum p⊥ < 0.18 GeV/c don’t reach the EMC and therefore
they will spiral inside the DCH (“loopers”). The tracking algorithms of BABAR will not
combine the different fragments of these tracks into a single track. Therefore dedicated
cuts have been developed to reject track fragments compatible with originating from
looper based on their distance from the beam spot. Looper candidates are identified as
two tracks with a small difference in p⊥, φ and θ. Of such a pair only the track fragments
with the smallest distance |dz| to the beam interaction point is retained. These cuts
remove roughly 13% of all low-momentum tracks in the central part of the detector. On
average, the mean observed charged multiplicity per B meson is reduced by less than 1%.
Two tracks very closely aligned to each other are called ”ghosts”. These cases arise
when the tracking algorithms splits the DCH hits belonging to a single track in two track
fragments. If two tracks are very close in phase space only the track with the largest
number of DCH hits is retained. This ensures that the fragment with the better momentum
measurement is kept in the analysis.
53
A summary of the track selection criteria is shown in Table 3.1.
Track selection Cutdistance in x− y plane |dxy| < 1.5 cm
distance in z axis |dz| < 5 cmmaximum momentum plab < 10 GeV/cminimum momentum P⊥,lab > 0.06 GeV/c
maximum momentum for SVT-only tracks plab < 0.2 GeV/c if NDCH = 0geometrical acceptance 0.410 < θlab < 2.54 rad
Reject tracks if ∆p⊥,lab< 0.12 GeV/c (loopers)
∆p⊥,lab< 0.15 GeV/c (ghost)
loopers (∆p⊥,lab < 0.25 GeV) Same sign: |∆φ| < 0.1 & |∆θ| < 0.1(| cos θ| < 0.2) Opposite sign: |∆φ| < 0.1 & |π − |∆θ|| < 0.1
ghosts (p⊥ < 0.35GeV ) |∆φ| < 0.1 & |∆θ| < 0.1N1
DCH < 45−N2DCH
Table 3.1: Summary of track selection cuts as adopted from [44]. N1DCH and N2
DCH are the numbers ofDCH hits for ghost candidate tracks. Track 1, the one with most DCH is selected.
3.2 Particle Identification
3.2.1 Electron Identification
The EMC is crucial for electron identification. Different criteria are established to select
electrons with different level of purity and efficiency. Electrons are primarily separated
from charged hadrons by taking into account the ratio of the energy E deposited in the
EMC to the track momentum p, E/p. In addition, the dE/dx energy loss in the DCH and
the DRC Cerenkov angle are required to be consistent with the values expected for an
electron. This offers a good e/π separation in a wide range.
The track selection criteria are tightened for electrons selection to suppress background
and to ensure a reliable momentum measurement and identification efficiency. There are
requirements in addition for transverse momentum p⊥ > 0.1 GeV/c, and NDCH ≥ 12 for
the number of associated drift chamber hits. Furthermore, only electron candidates with
a laboratory momentum plab > 0.5 GeV/c are considered.
Electrons are identified using a likelihood-based selector [45], which uses a number of
discriminating variables:
• Ecal/plab, the ratio of Ecal, the energy deposited in the EMC, and plab the momentum
54
in the laboratory rest frame measured using the tracking system; LAT , the lateral
shape of the calorimeter deposit (defined by Eq. 3.3); ∆Φ, the azimuthal distance
between the centroid of the EMC cluster and the impact point of the track on the
EMC; and Ncry, the number of crystals in the EMC cluster;
• dE/dx, the specific energy loss in the DCH;
• the Cerenkov angle θC and NC , the number of photons measured in the DRC.
First, muons are rejected on the basis of dE/dx ratio value and the shower energy
relative to the momentum. For the remaining tracks, likelihood functions are computed
assuming the particle is an electron, pion, kaon, or proton. These likelihood functions are
based on probability density functions that are derived from pure particle data control
samples for each of the discriminating variables. For hadrons, we take into account the
correlations between energy and shower-shapes. Using combined likelihood functions
L(ξ) = P (E/p, LAT,∆Φ, dE/dx, θC |ξ) (3.1)
= PEMC(E/p, LAT,∆Φ|ξ) PDCH(dE/dx|ξ) PDRC(θC |ξ)
for the hypotheses ξ ∈ {e, π,K, p}, the fraction
Fe =feL(e)∑ξ fξL(ξ)
, (3.2)
is defined, where, for the relative particle fractions, fe : fπ : fK : fp = 1 : 5 : 1 : 0.1 is
assumed. A track is identified as an electron if Fe > 0.95.
The electron identification efficiency has been measured using radiative Bhabha events,
as function of laboratory momentum plab and polar angle θlab. The misidentification rates
for pions, kaons, and protons are extracted from selected data samples. Pure pions are
obtained from kinematically selected K0S → π+π− decays and three prong τ± decays.
Two-body Λ and D0 decays provide pure samples of protons and charged kaons.
The performance of the likelihood-based electron identification algorithm is summa-
rized in Fig. 3.2, in terms of the electron identification efficiency and the per track prob-
ability that an hadron is misidentified as an electron.
55
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.10.20.30.40.50.60.70.80.9
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0
0.002
0.004
0.006
0.008
0.01
- e-π - K
[GeV/c]labp
Eff
icie
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20 40 60 80 100 120 1400
0.10.20.30.40.50.60.70.80.9
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0
0.002
0.004
0.006
0.008
0.01
- e-π - K
[deg]labθ
Eff
icie
ncy
Mis
iden
tific
atio
n
Figure 3.2: Electron identification and hadron misidentification probability for the likelihood-based elec-tron selector as a function of momentum (left) and polar angle (right). Note the different scales foridentification and misidentification on the left and right ordinates, respectively.
The average hadron fake rates per track are determined separately for positive and
negative particles, taking into account the relative abundance from Monte Carlo simu-
lation of BB events, with relative systematic uncertainties of 3.5%, 15% and 20% for
pions, kaons, and protons, respectively. The resulting average fake rate per hadron track
of plab > 1.0 GeV/c, is of the order of 0.05% for pions and 0.2% for kaons.
3.2.2 Muon Identification
Muons are identified by measuring the number of traversed interaction lengths in the entire
detector and comparing it with the number of expected interaction lengths predicted for a
muon of the same momentum. Moreover, the projected intersections of a track with RPC
or LST planes are computed and, for each readout plane, all clusters (groups of adjacent
hits in one of the two readout coordinates) detected within a maximum distance from the
predicted intersection are associated with the track. An additional π/µ discriminating
power is provided by the average number and the RMS of the distribution of the RPC
and LST hits per layer. The average number of hits per layer is expected to be larger
for pions, producing an hadronic interaction, than for muons. Other variables exploiting
clusters distribution shapes are constructed and criteria, based on all these variables, are
applied to select muons. The muon selection performance has been tested on samples of
kinematically identified muons from µµee and µµγ final states and pions from three-prong
56
τ decays and K0S decays.
The muon selection procedure is as follows:
• tight criteria on tracking: p⊥ > 0.1 GeV/c, NDCH ≥ 12, 0.360 < θlab < 2.37 and
plab > 1.0 GeV/c;
• the energy deposited in the EMC is required to be consistent with the minimum
ionizing particle hypothesis, 50 MeV < Ecal < 400 MeV;
• the number of IFR layers associated with the track has to be NL ≥ 2;
• the interaction lengths of material traversed by the track has to be λmeas > 2.2;
• The number of interaction lengths expected for a muon of the measured momentum
and angle to traverse is estimated by extrapolating the track up to the last active layer
of the IFR. This estimate takes into account the IFR efficiencies which are routinely
measured and stored. The difference ∆λ = λexp − λmeas is required to be < 1.0
for tracks with momentum greater than 1.2 GeV/c. For track momenta between
0.5 GeV/c and 1.2 GeV/c, a variable limit is placed: ∆λ < [(plab − 0.5)/0.7];
• the continuity of the IFR cluster is defined as Tc = NL
L−F+1, where L and F are the last
and first layers with hits. Tc is expected to be 1.0 for muons penetrating an ideal
detector whereas is expected smaller for hadrons. We require Tc > 0.3 for tracks
with 0.3 < θlab < 1.0 (i.e. in the Forward End Cap to remove beam background);
• the observed number of hit strips in each RPC or LST layer is used to impose the
conditions on the average number of hits, m < 8, and the standard deviation, σm < 4;
• the strip clusters in the IFR layers are combined to form a track and fit to a third de-
gree polynomial, with the quality of the fit selected by the condition χ2fit/DOF < 3.
In addition, the cluster centroids are compared to the extrapolated charged track,
with the requirement χ2trk/DOF < 5.
The muon identification efficiency has been measured using µ+µ−(γ) events and two-
photon production of µ+µ− pairs. The misidentification rates for pions, kaons, and protons
are extracted from selected data samples. The performance of the muon identification
57
p [GeV/c]1 2 3 4 5
0
0.2
0.4
0.6
0.8 < 57.00θ≤Forward , 17.00
+µ−µ
p [GeV/c]1 2 3 4 5
0
0.2
0.4
0.6
0.8 < 115.00θ≤Barrel , 57.00
+µ−µ
p [GeV/c]1 2 3 4 5
0
0.2
0.4
0.6
0.8 < 155.00θ≤Backward , 115.00
+µ−µ
[Deg]θ20 40 60 80 100 120 140
0
0.2
0.4
0.6
0.8 p[GeV/c]<1.70≤Low P , 1.10
+µ−µ
[Deg]θ20 40 60 80 100 120 140
0
0.2
0.4
0.6
0.8 p[GeV/c]<5.00≤High P , 1.90+µ−µ
Figure 3.3: Muon identification efficiency for the tight muon selector as a function of momentum (top)and polar angle (bottom).
algorithm is summarized in Fig. 3.3, in terms of the muon identification efficiency. The
errors shown are statistical only, the systematic error is dominated by variations in the
performance of the IFR as a function of position and time.
3.2.3 Charged Kaon Identification
A standard selector, based only on track candidates with an associated momentum above
300 GeV/c and exploiting variables based on information from the DRC, the DCH and
the SVT, is used to identify charged kaons. Likelihood functions are computed separately
for charged particles, as products of three terms, one for each detector subsystem and
then combined, similarly to the electron algorithm previously described. Fig. 3.4 shows a
comparison of the charged kaon efficiency versus the charged pion misidentification.
3.3 Neutral Particles Reconstruction
Neutral particles (photons, π0, neutral hadrons) are detected in the EMC as clusters of
close crystals where energy has been deposited. They are required not to be matched to
58
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0.02
0.04
0.06
0.08
0.1 - K + K-π +π
[GeV/c]labp
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20 40 60 80 100 120 1400
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0.02
0.04
0.06
0.08
0.1- K+ K-π +π
[deg]labθ
Eff
icie
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Mis
iden
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atio
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Figure 3.4: Charged kaon identification and pion misidentification probability for the tight kaon microselector as a function of momentum (left) and polar angle (right). The solid markers indicate the efficiencyfor positive particles, the empty markers the efficiency for negative particles. Note the different scales foridentification and misidentification on the left and right ordinates, respectively.
any charged track extrapolated from the tracking volume to the inner surface of the EMC.
For this analysis a neutral particle is selected by its local maximum energy depositions
in the EMC. These energy clusters originate mostly from photons, thus momenta and
angles are assigned to be consistent with photons originating from the interaction region.
The list of neutrals is also used to reconstruct the neutral pions. In Sec. 3.4.1 is described
the selection of the π0 candidates used in the Breco reconstruction.
Photon candidates are required to have an energy Eγ > 30 MeV in order to reduce the
impact of the sizeable beam-related background of low energy photons. Some additional
backgrounds, due to hadronic interactions, either by KL or neutrons, can be reduced by
applying requests on the shape of the calorimeter clusters.
The variable LAT , used to discriminate between electromagnetic and hadronic showers
in the EMC, is defined as
LAT =
N∑i=3
Eir2i
∑Ni=3Eir2
i + E1r20 + E2r2
0
, (3.3)
where N is the number of crystals associated with the electromagnetic shower, r0 is
the average distance between two crystals, which is approximately 5 cm for the BABAR
calorimeter, Ei is the energy deposited in the i-th crystal, numbering them such that
E1 > E2 > . . . > EN and ri, φi are the polar coordinates in the plane perpendicular to
59
the line pointing from the interaction point to the shower center centered in the cluster
centroid. Considering that the summations start from i = 3, they omit the two crystals
containing the highest amounts of energy. Since electrons and photons deposit most of
their energy in two or three crystals, the value of LAT is small for electromagnetic showers.
Multiplying the energies by the squared distances enhances the effect for hadronic showers,
compared with electromagnetic ones.
Another useful shape variable is the so-called S9S25, that is the ratio of the energy
deposited in the 9 closest crystals from the cluster centroid over the energy deposited in
the 25 closest clusters. Are assigned to the neutral particles all the local energy maxima,
not matching with charged tracks, and stored in a list the relative parameters, determined
by assuming that the particle is a photon.
Clusters, which are considered as neutral candidates, although they are close to tracks,
need to be rejected. These unmatched clusters are due to inefficiencies in the matching
algorithms and lead to double counting of their energies. In order to study them, the
distance in φ(dφ) and θ(dθ) with respect to all the tracks which do not have a matched
cluster, were considered. In this analysis, a cut on the 3-D angle
α = cos−1 [cos θcl cos θtr + sin θcl sin θtr cos(φcl − φtr)] (3.4)
was considered, where θcl,tr and φcl,tr are the polar coordinates for clusters and tracks
respectively. Clusters which satisfy α < 0.08 with the closest track that is not matched
to another EMC cluster are considered unassociated clusters and not used in the further
analysis [44].
Tab. 3.2 shows a detailed summary of the selection criteria applied on the neutral
candidates.
Cut Selection criteriaNumber of crystals Nc Nc > 2Cluster energy Eclus Eclus > 50 MeV
LAT LAT < 0.6Geometrical acceptance θclus 0.32 < θclus < 2.44
unmatched clusters α > 0.08
Table 3.2: Summary of the photon selections.
60
3.4 Meson Reconstruction
This section describes the reconstruction of the mesons used in the full reconstruction
of the B. A number of control samples have been employed to perform all the relevant
studies; in most cases, the optimizations have been obtained by using only part of the
available data, and it has been assumed that the results are valid for the entire sample as
well.
3.4.1 π0 Reconstruction
A wide energy spectrum of π0’s ranging from particles almost at rest up to several GeV
is needed in this analysis. For instance, lowest energy π0’s are used to reconstruct the
D∗0 → D0π0 decays while the decay products in the B → Dππ0 channel have quite large
momentum.
The π0’s are reconstructed using pairs of neutral clusters with a lower energy at 30 MeV
and applying a cut on the LAT variable. The π0 candidate has to have an energy above
200 MeV. A mass windows of 110-155 MeV/c2, corresponding to (−4σ, +3σ), is required.
In Fig. 3.5 the invariant masses distributions for simulated events and data are shown.
Mgg (GeV)
Simulation
mean = 0.13520 +/- 0.00003
sigma = 0.00640 +/- 0.00002
Mgg (GeV)
Data
mean = 0.13440 +/- 0.00003
sigma = 0.00686 +/- 0.00002
Figure 3.5: Distribution of the invariant mass of the π0 candidates for simulated events and for data.
61
3.4.2 K0S Reconstruction
K0S are reconstructed in the channel K0
S → π+π− by pairing all possible tracks of opposite
sign and looking for the 3D point (vertex) which is more likely to be common to the two
tracks. The algorithm is based on a χ2 minimization and uses as starting point for the
vertex finding the point of closest approach of the two tracks in 3D. No constraint is
applied on the invariant mass of the pair, but a ±3σ cut around the nominal value is
imposed: 0.486 < mπ+π− < 0.510 GeV/c2. The invariant mass distribution of the π+π−
obtained from data is shown in Fig. 3.6. A comparison between data and Monte Carlo
for the K0S momentum and polar angle is shown in Fig. 3.7. The channel K0
S → π0π0 is
not reconstructed in this analysis.
MKs(GeV)0.4750.480.4850.490.495 0.5 0.5050.510.5150.520
1000
2000
3000
4000
5000
6000
7000
8000
9000
2x10
mean = (497.305 +/- 0.005) 10-3
sigma1 = ( 1.924 +/- 0.021) 10-3
sigma2 = ( 4.349 +/- 0.031) 10-3
Figure 3.6: Mass distributions for K0S → π+π− on data. The distribution is fitted with a sum of a double
Gaussian and a first order polynomial function.
3.4.3 D Reconstruction
The reconstruction of the B mesons in hadronic modes utilizes charmed D mesons decay-
ing in a variety of channels. These channels and their branching fractions are summarized
in Tab. 3.3.
The D0 is reconstructed in the modes D0 → Kπ, D0 → K3π, D0 → Kππ0 and
62
[GeV]labp0 0.5 1 1.5 2 2.5 3
En
trie
s/B
in
0
50
100
150
200
250
300
[deg]labθ0 20 40 60 80 100 120 140 160
En
trie
s/B
in
0
20
40
60
80
100
120
140
160
180
Figure 3.7: K0S momentum (left) and polar angle (right) distributions in data (solid markers) and Monte
Carlo simulation (hatched histogram), normalized to the same area.
D0 → K0Sππ. The charged tracks originating from a D meson are required to have a
minimum momentum of 200 MeV/c for the channel D0 → Kπ and 150 MeV/c for the
remaining three modes. The D0 candidates are required to lie within ±3σ of the nominal
D0 mass. All D0 candidates must have momentum greater than 1.3 GeV/c and lower
than 2.5 GeV/c in the Υ(4S) frame. The lower bound is needed to reduce combinatorics,
the upper one is the kinematic endpoint of the D0 coming from a B → D0X decay or
B → D∗+X with D∗+ → D0π+. A vertex fit is performed and a χ2 probability greater
than 0.1% is required. The selection criteria are summarized in Tab. 3.4.
D+ candidates are reconstructed in the modes D+ → K−π+π+, D+ → K−π+π+π0,
D+ → K0Sπ
+, D+ → K0Sπ
+π0, D+ → K0Sπ
+π+π+. We require that the kaon used in
the K−π+π+ and K−π+π+π0 modes have a minimum momentum of 200 MeV/c while
the pions are required to have momentum greater than 150 MeV/c. For the K0Sπ
+X
modes, the minimum charged track momentum is required to be 200 MeV/c. D+ can-
didates are required to have an invariant mass within ±3σ, calculated on an event-by-
event basis, of the nominal D+ mass. The D+ candidates must have momentum greater
than 1.0 GeV/c in the Υ(4S) frame for the three cleanest modes (D+ → K −π+π+,
D+ → K0Sπ
+ and D+ → K0Sπ
+π0) and greater than 1.6 GeV/c for the two remaining
ones (D+ → K−π+π+π0 and D+ → K0Sπ
+π+π+). Moreover, all D+ candidates must
have momentum lower than 2.5 GeV/c in the Υ(4S) frame, as the D0 case. A vertex fit
is performed and a χ2 probability greater than 0.1% is required. The selection criteria
63
Decay mode Branching Fraction(%)D∗ → D0 π; D0 → Kπ 2.55± 0.06D∗ → D0 π; D0 → K3π 5.0± 0.2D∗ → D0 π; D0 → Kππ0 8.8± 0.6D∗ → D0 π; D0 → K0
S ππ (K0S → π+π−) 1.35± 0.08
D+ → Kππ 9.5± 0.3D+ → K0
S π (K0S → π+ π− ) 0.94± 0.06
D+ → Kπππ0 5.5± 2.7D+ → K0
S πππ (K0S → π+ π− ) 2.38± 0.31
D+ → K0S ππ0 (K0
S → π+ π− ) 3.5± 1.0D∗0 → D0 π0 ; D0 → Kπ 2.35± 0.12D∗0 → D0 π0 ; D0 → K3π 4.6± 0.3D∗0 → D0 π0 ; D0 → Kππ0 8.1± 0.7D∗0 → D0 π0 ; D0 → K0
S ππ (K0S → π+π−) 1.2± 0.1
D∗0 → D0 γ; D0 → Kπ 1.44± 0.19D∗0 → D0 γ; D0 → K3π 2.82± 0.18D∗0 → D0 γ; D0 → Kππ0 5.0± 0.4D∗0 → D0 γ; D0 → K0
S ππ (K0S → π+π−) 0.7± 0.1
D0 → Kπ 3.80± 0.07D0 → K3π 7.72± 0.28D0 → Kππ0 14.1± 0.5D0 → K0
S ππ 2.03± 0.12
Table 3.3: D mesons decays used in the Semi-exclusive B reconstruction.
D0 → Kπ D0 → Kππ0 D0 → K3π D0 → K0S ππ
mD invariant mass window ± 15 MeV/c2 ± 25 MeV/c2 ± 15 MeV/c2 ± 20 MeV/c2
Charged Tracks : lower p∗ cut > 200 MeV/c > 150 MeV/cD0 upper p∗ cut < 2.5 GeV/cD0 lower p∗ cut > 1.3 GeV/c
Vertex Fit χ2 > 0.01
Table 3.4: Summary of criteria applied for the D0 selection.
64
are summarized in Tab. 3.5.
D+ → Kππ D+ → K0S π D+ → K0
S ππ0 D+ → Kπππ0 D+ → K0S πππ
mD invariant mass window ± 20 MeV/c2 ± 20 MeV/c2 ± 30 MeV/c2 ± 30 MeV/c2 ± 30 MeV/c2
D+ lower p∗ cut > 1.0 GeV/c > 1.6 GeV/cD+ upper p∗ cut < 2.5 GeV/c
Charged Tracks : lower p∗ cut > 200 MeV/cVertex fit χ2 > 0.01
Table 3.5: Summary of criteria applied for the D+ selection.
D∗+ candidates are formed by combining a D0 with a pion which has momentum
greater than 70 MeV/c. Due to the limited phase space available from the D∗−D0 mass
difference ∆m, the pion coming from the D∗ has a low momentum, below 450 Mev/c,
and is referred to as soft pion (see Fig. 3.8). Only the reconstruction of the D∗+ → D0π+
channel is discussed here, since D∗+ → D+π0 events enter in the B → D+X category
of the Semi-exclusive reconstruction, as explained in Sec. 3.5. A vertex fit for the D∗+
is performed using a constraint to the beam spot to improve the angular resolution for
the soft pion. A fixed σy = 30 µm is used to model the beam spot spread in the vertical
direction, to avoid bias in the D∗+ vertex fit. The fit is required to converge, but no cut
is applied on the probability of χ2. After fitting, selected D∗+ candidates are required to
have ∆m within ±3σ of the measured nominal value (see Fig. 3.8). ∆m distribution is
fitted with a double Gaussian distribution. The width is taken to be a weighted average
of the core and broad Gaussian distributions. The selection criteria are summarized in
Tab. 3.6.
Criteria CutD∗+ → D0 π+
Vertexing and χ2 beam spot constraint (σy = 30 µm), convergencem(Dπ+)−m(D0) ±3σ MeV/c2
p∗(π+) [70,450] MeV/c
Table 3.6: Summary of criteria applied for the D∗+ selection.
D∗0 candidates are reconstructed by combining a selected D0 with a either a π0 or a
photon having a momentum less than 450 MeV/c in the Υ(4S) frame. The minimum
momentum for the π0 corresponds to 70 MeV while the photons are required to have an
energy greater than 100 MeV. ForD∗0 → D0π0 decay, selectedD∗0 candidates are required
to have ∆m within 4 MeV/c2 of the nominal value while a wider window, 127 MeV/c2 <
65
0
10
20
30
40
50
60
70
80
0 0.05 0.1 0.15 0.2 0.25 0.3
Soft pion momentumSoft pion momentumSoft pion momentump(π))_soft
Soft pion momentum
Signal MCData
0
50
100
150
200
250
0.136 0.138 0.14 0.142 0.144 0.146 0.148 0.15
D*-D0 Mass DifferenceD*-D0 Mass DifferenceD*-D0 Mass Difference∆M (GeV)
D*-D0 Mass Difference
Signal MCData
Figure 3.8: Distribution of soft pion momentum in the Υ(4S) frame (left) and m(D∗+π−)−m(D0) massdistribution for D∗+ candidates in the B → D∗+π−, D0 → Kπ mode. Units in both plots are GeV.Vertical lines indicate the signal windows used in the selection.
∆m < 157 MeV/c2, is used for D∗0 → D 0γ. The selection criteria are summarized in
Tab. 3.7.
Criteria CutD ∗0 → D 0π0
m(D 0π0)−m(D 0) ±4 MeV/c2
p∗(π0) [70 , 450] MeV/cp∗(D ∗0) 1.3 < p∗ < 2.5 GeV/c
D ∗0 → D 0γm(D 0γ)−m(D 0) [127 , 157] MeV/c2
E∗(γ) [100 , 450] MeVp∗(D ∗0) 1.3 < p∗ < 2.5 GeV/c
Table 3.7: Summary of criteria applied for the D∗0 selection.
3.5 Semi-exclusive Reconstruction Method
The aim of the Semi-exclusive reconstruction is to get as many as possible B mesons
in fully hadronic modes in order to study the properties of the recoiling B meson in
Υ(4S) → BB transitions.
The sum of a few, very pure exclusive modes ensures very high purity but low efficiency.
66
Decay mode Branching Fraction (%)B → D∗±Y 22.5± 1.5B → D±Y 22.8± 1.4
B → D∗0/D∗0Y 26.0± 2.7B → D0/D0Y 64.0± 3.0
B → D+s Y 10.1± 3.1
B → D−(∗)D(∗)s 4.9± 1.2
B → D(∗)D(∗)K 7.1+2.3−1.7
B0 → D−(∗)D+(∗) ∼ 1.0
Table 3.8: Inclusive and Exclusive branching fractions relevant to this analysis as measured in [46].
On the other hand a fully inclusive approach with high multiplicities is not feasible since
the level of combinatoric background would be too high. A compromise has been set up,
where only favored modes are considered and an algorithm which combines the final state
particles neglecting the intermediate states as inclusive as possible is used.
Since B0 mesons mostly decay into charged D(∗) mesons while B− mesons decay into
the neutral D0(∗) mesons, only B− → D0(∗)Y , B0 → D+(∗)Y modes are considered.
Tab. 3.8 shows the relevant branching fractions for B mesons decaying predominantly
into fully hadronic final states.
The Semi-exclusive reconstruction approach comprises the following steps:
• reconstruct all possible decay modes B → DY , where the D refers to a charm meson
(D0, D+, D∗0, D∗±), and Y system is a combination of π+, π0, K+ and K0S, with
total charge equal to ±1, and composed of n1π± + n2K
± + n3K0S + n4π
0, where
n1 + n2 < 6, n3 < 3 and n4 < 3;
• study the structure of the Y system looking for resonances in the signal and studying
the shape of the background (Sec. 3.5.2);
• identify submodes and create sub-categories according to the their multiplicity and
to the structure of the Y system (e.g. Dππ0, mππ0 < 1.5 GeV/c2). For each mode,
the most relevant parameter is the apriori-purity of the mode: the ratio S/√S +B,
where S and B are the signal and combinatorial background respectively, as esti-
mated from a mES fit on data (Sec. 3.5.2);
• determine a mode by mode combinatorial background rejection, in order to account
67
for different background levels depending on the number of charged tracks and, above
all, on the number of π0s in the reconstructed mode (Sec. 3.5.3);
• rank the submodes according to their purity and yields and study the significance as a
function of the number of used modes in order to maximize the statistical significance
of the sample (Sec. 3.5.4);
• group the submodes with similar purity;
• resolve the multiple candidates (Sec. 3.5.4).
The starting point of the Semi-exclusive selection is the D0, D+, D∗, D∗0 meson
reconstruction, described in Sec. 3.4.3. Charged pions, kaons, π0 and K0S candidates are
then combined to the D meson to form the B candidate.
3.5.1 Definition of ∆E and mES
Two main variables are used to select B candidates, to extract the yields and to define a
sideband region to study the background: ∆E and mES.
The energy difference ∆E is defined as:
∆E = E∗B −
√s/2, (3.5)
where E∗B is the energy of the B candidate in the Υ(4S) rest frame (CM) and
√s is the
total energy of the e+e− system in the CM rest frame. The resolution of this variable
is affected by the detector momentum resolution and by the particle identification since
a wrong mass assignment results in a shift in ∆E. Due to the energy conservation,
signal events are Gaussian distributed in ∆E around zero. Continuum and part of the bb
background have a ∆E distribution that can be modeled with a polynomial distribution.
Instead, some other bb background, due to misidentification, gives shifted Gaussian peaks.
The resolution of this variable depends essentially on the reconstructed B mode and π0
multiplicity and it can varies from 20 to 40 MeV.
The beam energy-substituted mass mES is defined as
mES =√
(√s/2)2 − p∗2B , (3.6)
68
mes(GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28
Eve
nts
/ (
0.00
0523
485
)
0
200
400
600
800
1000
1200
1400
= 0.94262χ
mes(GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28
Eve
nts
/ (
0.00
0523
485
)
0
200
400
600
800
1000
1200
1400
UDS+CCBAR MC
-2
0
2
-2
0
2
Figure 3.9: Left: fit of the Argus function (Eq. 3.7) to the mES distributions for candidates in thecontinuum background (udsc).
where p∗B is the B candidate momentum in the CM rest frame. It is clear that, since |p∗B| ¿√s/2, the experimental resolution on mES is dominated by beam energy fluctuations. To
an excellent approximation, the shapes of themES distributions for B meson reconstructed
in a final states with charged tracks only are Gaussian and practically identical. Otherwise
the presence of neutrals in the final states, in case their showers are not fully contained
in the calorimeter, can introduce tails.
It is important to notice that, since the sources of experimental smearing are uncorre-
lated (beams energy for mES and detector momentum resolution for ∆E), mES and ∆E
also are basically uncorrelated.
The background shape in mES is parametrized using the Argus function [47]:
dN
dmES
= N ·mES ·√
1− x2 · exp(−χ · (1− x2)
)(3.7)
where x = mES/mmax and χ is a free parameter determined from the fit. The mmax,
that represents the endpoint of the Argus distribution, is fixed in the fit to Monte Carlo
mES distributions. The Argus function provides a good parametrization of the continuum
(uuddccss), as Fig. 3.9 shows.
69
)2 (GeV/cESm5.22 5.24 5.26 5.28
2E
ntri
es /
0.5
MeV
/c
0
2000
4000
6000
8000(a)
)2 (GeV/cESm5.22 5.24 5.26 5.28
2E
ntri
es /
0.5
MeV
/c
0
2000
4000
6000
8000
)2 (GeV/cESm5.24 5.26 5.28
(b)
)2 (GeV/cESm5.24 5.26 5.28
Figure 3.10: The mES distribution for data (points with statistical errors) is shown together with theresults of the fit (solid line) for selected semileptonic decays from B+B− events (a) and B0B0 events (b).The dashed line shows the contribution from combinatorial and continuum background.
The signal component is fitted using a modified Gaussian function [48], which will be
described in detail in Chapter 5. The total fit (Argus and signal function) to the data
sample is shown in Fig. 3.10. The radiative tail of this function can take into account
cases where the energy of the neutral candidates is not fully deposited in the EMC crystals.
The left tail of the distribution depends on the reconstructed B mode and in particular
on the number of π0.
The maximum total number of floating parameters in the mES fits is 7. Two of them
refer to the Argus shape, while the remaining five parameters belong to the signal function.
In the following the number of signal and background events (indicated as S and B in
the plots) are estimated as the area of the signal and the Argus functions integrated for
mES > 5.27 GeV.
3.5.2 Study of the Y System
The choice of the submodes is crucial in the reconstruction method. The identification of
the clean modes allows to set up the most efficient and pure selection among the multiple
candidates in different modes. A detailed study of the Y system, looking for resonances
in the signal and background shape is performed.
As an example, the invariant mass of the Y = ππ0 system in the B → D∗ππ0 mode is
shown in Fig. 3.11. There is a large contribution below 1.5 GeV/c2 due to the ρ resonance,
but there is also a small amount of signal at ∼ 2.4-2.6 GeV/c2, but not clear enough for
70
Figure 3.11: Mass distribution of the Y system ππ0 in data for the B → D∗ππ0 decay mode. Thenormalized background, as evaluated from sidebands, is overlaid.
a specific selection. Therefore two sub-modes are defined depending on whether mππ0
is smaller than 1.5 Gev/c2 or greater than 1.5 GeV/c2, without requiring the sub-mode
belonging to a precise resonance structure. In this way the clean B → D∗ππ0 sub-mode
(mππ0 < 1.5 GeV/c2) has been separated from the low purity ones (mππ0 > 1.5 GeV/c2).
Finally, the total number of the reconstructed B decay modes are 52 and 53 for the D0
and D+ seeds, respectively. The total number of the decay modes is 1097. A summary is
shown in Tab. 3.9.
3.5.3 ∆E Selection
Once all possible reconstruction modes are identified, a window in ∆E is applied in order
to pick up among several candidates in a given submode.
The ∆E resolutions are determined from the ∆E distributions before the best candi-
date selection; they depend essentially on the number of charged tracks and, above all,
on the number of π0s in Y system (since the reconstructed D is mass constrained). For
the modes without π0s a fit with a linear background and a Gaussian is performed and
71
Channel pre-seed mode number of B modes total number of modesB± → D0Y D0 → Kπ 52 208
D0 → Kππ0 52D0 → K0
Sππ 52D0 → Kπππ 52
B → D+Y D+ → Kππ 53 265D+ → Kπππ0 53D+ → K0
Sπ 53D+ → K0
Sππ0 53B± → D∗0 D∗0 → D0π0, D0 → Kπ 52 416
D+0 → D0π0, D0 → Kππ0 52D ∗0 → D0π0, D0 → K0
Sππ 52D ∗0 → D0π0, D0 → Kπππ 52
D∗0 → D0γ, D0 → Kπ 52D∗0 → D0γ, D0 → Kππ0 52D∗0 → D0γ, D0 → K0
Sππ 52D∗0 → D0γ, D0 → Kπππ 52
B0 → D∗+Y D∗+ → D0π, D0 → Kπ 52 208D∗+ → D0π, D0 → Kππ0 52D∗+ → D0π, D0 → K0
Sππ 52D∗+ → D0π, D0 → Kπππ 52
Total 1097
Table 3.9: Summary of the number of Semi-exclusive modes.
2σ symmetric windows are taken. In the case of modes with at least a π0, the situation
is worse. First of all there are too many candidates per event. Requiring that only the 10
candidates with the smallest |∆E| are taken, can create a bias in the ∆E distribution. Due
to studies of the decay modes, the chosen windows are: |∆E| < 45 MeV for candidates
without π0 and K0S, |∆E| < 50 MeV for candidates with up to one π0 and two K0
S and
−90 < ∆E < 60 MeV for all the others.
3.5.4 Multiple Candidates and Definition of Purity
Multiple candidates can be reconstructed in the same submode; candidates reconstructed
in different submodes per event are also possible.
If there are multiple candidates in the same submode only the one with lowest ∆E is
chosen and one candidate per submode is selected.
The selection of the best B decay among different submodes cannot use ∆E because
the modes with higher combinatoric background would be privileged with respect to the
clean ones. An unbiased criterion for choosing a signal event is based on an a-priori
72
Figure 3.12: Dependence of the quality factor S/√
S + B as a function of the yield when adding modesfor the B0 → D+Y case. Statistic corresponds to 80 fb−1.
probability. The a-priori probability here is given by the purity of the mode, determined
by fitting the mES distribution and determining the signal and background contributions
in the signal region (mES > 5.27 GeV). The selection of the best B in the event is based
on the choice of the reconstructed mode with the highest purity.
The decay modes are ranked according to their purity and are added to the sample of
reconstructed B one at a time. At each addition of a mode the yield increases and the
purity mostly decreases. This method is very useful once the composition of the modes has
to be optimized for the analysis of the recoil. The significance S/√S +B is computed as
a function of the number of added modes and the best composition is chosen. An example
for the B0 → D+Y case is shown in Fig. 3.12.
The final yields depend on the cut on the purity. The yields for different levels of
purity on the Breco sample are shown in Tab. 3.10.
The study of the recoiling B can improve the purity of the sample, since the application
of selection criteria on the recoil, for instance the request of an hard lepton, removes
most of the non bb events without changing the mES shape above the signal threshold
(5.27 GeV/c2) and allows to use most of the Semi-exclusive modes.
73
Decay mode a-priori pur.> 80% a-priori pur.> 50% a-priori pur.> 10%B+ → D0 X 75524 ± 322 213774 ± 684 376055 ± 1316B0 → D+ X 43726 ± 258 101594 ± 518 220528 ± 948B+ → D∗0 X 73470 ± 337 174866 ± 665 297632 ± 1161B0 → D∗+ X 81646 ± 335 198685 ± 676 219462 ± 768Total B+ 148994 ± 477 388640 ± 1010 673712 ± 1752Total B0 125372± 414 300279 ± 871 439990 ± 1232Total 274366 ± 631 688919± 1308 1113702 ± 2116
Table 3.10: Yields from Semi-exclusive reconstruction for different levels of purity for 316 fb−1 of data.
74
Chapter 4
Data and Monte Carlo Samples
4.1 Data
The total dataset used in this analysis correspond to an integrated on-peak luminosity
of 347.4 fb−1, recorded by BABAR in the years 1999-2006. They correspond to about 383
million of BB pairs. Table 4.1 summarizes data event samples divided by run period.
Data Set integrated luminosity on peak NBB(106)Run 1 20.4 fb−1 22.4Run 2 61.1 fb−1 67.5Run 3 32.3 fb−1 35.6Run 4 100.3 fb−1 110.5Run 5 133.3 fb−1 147.2
Table 4.1: Data event samples.
4.2 Monte Carlo Samples
The Monte Carlo samples used in this analysis are summarized in Table 4.2.
Data Set 1’ B mode 2’ B mode equiv. lumin.B0 generic Generic Generic 1080 fb−1
B± generic Generic Generic 1095 fb−1
|Vub| pure res. generic b → u`ν exclusive Generic 3689 fb−1
|Vub| pure non-res. generic b → u`ν inclusive Generic 1743 fb−1
Table 4.2: Monte Carlo event samples used in this analysis.
75
4.2.1 Generic bb Monte Carlo
Generic bb Monte Carlo represents the full simulation of all possible decays of the B meson
and it should represent the data and an unbiased event sample. This sample is actually
used to model the data.
4.2.2 Resonant Models for B → Xu`ν
Exclusive charmless semileptonic B → Xu`ν decays are simulated as a combination of
three-body decays to narrow resonances, Xu = π, η, ρ, ω, η′.
These decays are simulated using the ISGW2 model [49]. To be consistent with the
latest measurements, generation values of branching ratios (detailed in Table 4.3) have
been adjusted in a reweighting procedure to match the current PDG values [46] (see also
Tab. 4.4). The hadronic invariant mass spectrum at the generator level for these decays
is shown in Fig. 4.1 (left).
mode BR hadron mass [GeV] mode BR hadron mass [GeV]B0 → π−`+ν 180 · 10−6 0.1396 B+ → π0`+ν 90 · 10−6 0.135
B+η`+ν 30 · 10−6 0.5488B0 → ρ−`+ν 260 · 10−6 0.7669 B+ → ρ0`+ν 130 · 10−6 0.77
B+ → ω`+ν 130 · 10−6 0.782B+ → η′`+ν 60 · 10−6 0.9575
B0 → a−0 `+ν 14 · 10−6 0.983 B+ → a00`
+ν 7 · 10−6 0.983B0 → a−1 `+ν 165 · 10−6 1.26 B+ → a0
1`+ν 82 · 10−6 1.26
B0 → a−2 `+ν 14 · 10−6 1.318 B+ → a02`
+ν 7 · 10−6 1.318B0 → b−1 `+ν 102 · 10−6 1.233 B+ → B0
1`+ν 48 · 10−6 1.233B+ → f0
0 `+ν 4 · 10−6 1.00B+ → f ′00 `+ν 4 · 10−6 1.4B+ → f0
1 `+ν 41 · 10−6 1.283B+ → f ′01 `+ν 41 · 10−6 1.422B+ → f0
2 `+ν 4 · 10−6 1.274B+ → f ′02 `+ν 4 · 10−6 1.525B+ → h0
1`+ν 24 · 10−6 1.17
B+ → h′01 `+ν 24 · 10−6 1.41exclusive 735 · 10−6 exclusive 730 · 10−6
inclusive 1365 · 10−6 inclusive 1365 · 10−6
total 2100 · 10−6 total 2095 · 10−6
Table 4.3: Branching fractions and hadron masses used in the generator for b → u`ν decay.
76
)2 (GeV/cXM0 1 2 3 4 50
1000
2000
3000
4000
5000
6000
resonantXM
)2 (GeV/cXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
200
400
600
800
1000
1200
1400
1600
1800
Non resonantXM
Figure 4.1: MX distributions at generator-level for pure resonant (left) and pure non-resonant (right)b → u`ν Monte Carlo.
4.2.3 Non-Resonant Model for B → Xu`ν
The BABAR simulation code models the inclusive charmless semileptonic B decays into
hadronic states with masses larger than 2mπ using a prescription by De Fazio and Neubert
(DFN) [50]; other theoretical models, like the ones described in Sec. 1.3.2 are not yet
implemented. However, predictions from the DFN model in this analysis are used only
to calculate the detector reconstruction efficiency for events in restricted phase-space
regions. In this respect, differences with the more detailed theoretical models shown in
Chapter 1 are negligible and indeed, as it will be shown in Chapter 7, the systematic
uncertainties due to the limited knowledge of the parameters involved in the definition
of the signal model, are among the smallest ones. The most recent theoretical models
are nevertheless used to compute the acceptances needed to relate the partial charmless
semileptonic branching fraction to |Vub| (see Chapter 8).
The DFN model calculates the triple-differential decay rate, d3Γ / dq2 dE` dsH
(sH = M2X), up to O(αs) corrections. The non perturbative corrections to this ob-
servable (the S function in Eq. 1.35) can be associated with the motion of b quark inside
the B meson, and are commonly referred as “Fermi motion”.
Fermi motion effects are included in the heavy-quark expansion by re-summing an
infinite set of leading-twist correction into a shape function F (k+), which governs the
light-cone momentum distribution of the heavy quark inside the B meson [21, 22]. The
77
physical decay distributions are obtained from a convolution of parton model spectra with
this function.
As already mentioned in Chapter 1, the shape function is a universal characteristic
of the B meson governing inclusive decay spectra in processes with mass-less partons in
the final state, such as B → Xu`ν and B → Xsγ. The convolution of the parton spectra
with this function is such that in the perturbative formulae for the decay distributions the
b-quark mass mb is replaced by the momentum dependent mass mb +k+ and similarly the
parameter Λ = MB −mb is replaced by Λ− k+. Here k+ takes values between −mb and
Λ, with a distribution centered around k+ = 0 and with a characteristic width of O(Λ).
Several functional forms for the shape function have been suggested in the literature
but they are all subject to constraints on the moments of this function, An = 〈kn+〉, which
are related to the forward matrix elements of local operator on the light cone [21]. The
first three moments must satisfy
A0 =
∫F (k+)dk+ = 1 (4.1)
A1 =
∫k+F (k+)dk+ = 0 (4.2)
A2 =
∫k2
+F (k+)dk+ =µ2
π
3(4.3)
where µ2π is the average momentum squared of the b quark inside the B meson [51]. The
form of the shape function is unknown and usually is adopted the simple form [52]
F (k+) = N(1− x)ae(1+a)x; x =k+
Λ≤ 1 (4.4)
which is such that A1 = 0 by construction (neglecting exponentially small terms in mb/Λ),
whereas the condition A0 = 1 fixes the normalization N . The parameter a can be related
to the second moment, yielding A2 = µ2π/3 = Λ2/(1 + a). Thus the b quark mass (or Λ)
and the quantity µ2π are the two parameters of the function.
In the simulation the hadron Xu is produced with a non-resonant and continuous
invariant mass spectrum according to the DFN model. Finally, the fragmentation of the
Xu system into final state hadrons is performed by JETSET [53]. Invariant hadronic mass
spectrum for pure non-resonant charmless semileptonic B decays at the generator level is
shown in Fig. 4.1 (right).
78
Figure 4.2: ∆χ2 = 1 contour plot in the (mb, µ2π) plane for the combined fit to all moments (solid line),
the fit to hadron and leptons moment only (dashed lines), and the fit to photon moments only (dottedline).
A reweighting of the Fermi motion distribution is used to obtain distributions for
different values of Λ and µ2π. Several experimental measurements of these heavy quark
parameters are available. In this thesis, the determination from the B → Xsγ spectrum
as measured by Belle, CLEO and BABAR and from b→ c`ν moments measured by several
experiments and extracted by Flacher and Buchmuller [11]
mb = 4.590± 0.039 GeV (4.5)
µ2π = 0.401± 0.040 GeV2,
and also comprehensively presented by the HFAG group [54], has been used. In Figure 4.2
a fit to the heavy quark parameters using constraints from different measurements are
displayed.
4.2.4 BABAR Hybrid Model for B → Xu`ν
Neither the resonant, or the non-resonant models alone are adequate for a proper simu-
lation of charmless semileptonic decays. The non-resonant generator for instance is not
able to produce hadronic final states with masses below 2mπ and it does not produce
any resonant structure in the hadron mass. Therefore the resonant and non-resonant
79
components are combined such that the total branching fraction is consistent with the
measured value [55, 56] and that the fraction of events below a given threshold in MX
is similar to the non-resonant case (except local discontinuity due to the resonant struc-
ture). This requirement is imposed in order to minimize theoretical uncertainties related
to the hadronization in the charmless decay and to ensure that the OPE is valid. This
reweighting procedure is common among the other |Vub| analyses performed in BABAR .
4.2.5 Reweighting Hybrid Model for B → Xu`ν
The hybrid model described in the previous paragraph considers the non-resonant model
only above 1.264 GeV/c2, while it is in principle possible to go down to the allowed
kinematic limit. So the non-resonant events have been reweighted in the hybrid model
in order to have a better agreement between the model and the measured fraction of
resonant and non-resonant events.
The (MX , q2, E`) phase space is dived into an 8×8×8 grid; the number of non-resonant
(resonant) events in each bin is denoted as N inr (N i
r), then the weights w are determined
in the following way:
• the ratio between the number of non-resonant and resonant events after reweighting
is equal to the imposed one∑
iwi ·N inr
Nr
= R =B(b→ u)− B(Xu`ν resonant)
B(Xu`ν resonant)(4.6)
• the fraction of hybrid events in a given bin Hybi/Hyb is the same as the fraction of
non-resonant events form the reference sample in that bin Ref i/Ref :
Hybi
Hyb=
wi ·N inr +N i
r
Nr +∑
iwi ·N inr
=N i
nr
Nnr
=Ref i
Ref(4.7)
where Hyb = Nr +Nnr = Nr +∑
iwi ·N inr.
Solving these two equations the weights are
wi =Ref i −Nr
N inr
(4.8)
• if the wi is negative, is set to zero. To preserve the overall normalization between the
reference sample and the hybrid, a global weight is applied to the inclusive component
80
of the hybrid corresponding to and the weights for the inclusive is recomputed. The
correct weight corrwi it then
corrwi = wiGlobalW · T − E
Y(4.9)
where GlobalW is the ratio Reference Inclusive/sum of Hybrid, T is the branching
ratio of the total hybrid, E (Y ) is the branching ratio of exclusive (inclusive) part of
the hybrid model. This preserves not only the normalization between the reference
inclusive and the hybrid but also the exclusive/inclusive BRs.
Since the generation values are not updated to the latest measurements, inclusive and
exclusive branching ratios are reweighted to the measured values as reported in Table 4.4.
The experimental errors on these measurements are one of the sources of the systematic
uncertainties.
All branching fractions and theory parameters involved in this reweighting technique
are varied within their errors in the evaluation of the associated uncertainty. The uncer-
tainty due to the specific parametrization given in Equation 4.4 has also been evaluated
by using other two empirical parametrization (see Sec. 7.3).
Decay mode generation value new value with error generation value new value with error(B0) (B0) (B+) (B+)
B → π`ν 1.80 1.36± 0.08 0.90 0.77± 0.12B → η`ν 0.30 0.84± 0.36B → ρ`ν 2.60 2.14± 0.59 1.30 1.16± 0.32B → ω`ν 1.30 1.30± 0.54B → η′`ν 0.60 0.84± 0.84
other resonant 2.95 0.00 (see note *) 2.90 0.00 (see note *)non-resonant 13.65 22.20 (see note **) 13.65 23.04 (see note **)Total sample 21.00 25.70± 3.83 20.95 27.95± 4.17
Table 4.4: Comparison between the BABAR generated branching fraction and the latest measurementswith corresponding errors (in 10−4) to which they are rescaled. *: Since there are no measurements forother resonances (a,b,f ,. . . ), these BR are set to 0.**: The fraction for inclusive events is adjusted topreserve the correct overall normalization of the hybrid sample.
Figure 4.3 shows the comparison, for charged and neutralB, between pure non-resonant
signal Monte Carlo and its rescaled component in the hybrid model along with the rescaled
resonant component. The hybrid model is represented by the black line.
81
05000
100001500020000250003000035000400004500050000
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
B0 decays
HybridResonant (hybrid)Inclusive (hybrid)Inclusive only
mass of Xu (GeV)
05000
100001500020000250003000035000400004500050000
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
B+ decays
HybridResonant (hybrid)Inclusive (hybrid)Inclusive only
mass of Xu (GeV)
Figure 4.3: MX distribution for the resonant (“exclusive”), the pure non-resonant (“inclusive”) b → u`νMC and for the reweighted combination of exclusive and non-resonant MC (“hybrid”) for B0 (top) andB+ (bottom) decays.
82
Chapter 5
Event Selection
In this thesis, the Υ(4S) → BB process is used to study semileptonic decays of the
B meson recoiling against a B meson whose decay into hadronic final states is fully
reconstructed. Compared with to untagged analyses, where little information on the
companion B is used, this tagging technique offers many advantages:
• the Brecoil decay products consist of particles that are not used to reconstruct the
Breco meson; in other terms, it is possible to assign particles to the Brecoil in an
inclusive and unambiguous way, and compute the relevant hadronic variables;
• it is possible to require charge conservation in the event and impose the missing mass
of the event (due to the undetected neutrino) to be compatible with zero;
• the momentum of the recoiling B is known and therefore it is possible to apply
a Lorentz transformation and compute the relevant kinematic variables in the rest
frame of the decaying B;
• charge and flavor of the B mesons are known, and the correlation between the charge
of the lepton and flavor of the Breco can be exploited to reject B → DX → `Y
background events.
The only disadvantage of this technique is a low reconstruction efficiency, typically in the
0.1− 0.4% range.
The idea to isolate B → Xu`ν decays in regions where the b → c transitions are
forbidden is conceptually simple (see Fig. 5.1 left plots), but the measurement of kine-
83
)2 gen (GeV/cXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Arb
itra
ty U
nit
s
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
u generated→ for bXM
)2 rec (GeV/cXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Arb
itra
ty U
nit
s
0
0.005
0.01
0.015
0.02
0.025
0.03
u reconstructed→ for bXM
)2 rec (GeV/cXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Arb
itra
ty U
nit
s
0
0.1
0.2
0.3
0.4
0.5
c generated→ for bXM
)2 rec (GeV/cXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Arb
itra
ty U
nit
s
0
0.005
0.01
0.015
0.02
0.025
0.03
c reconstructed→ for bXM
Figure 5.1: Generation-level distribution (left set of plots) of the invariant mass of the hadronic recoilsystem in semileptonic b → u`ν (top) and b → c`ν (bottom). The invariant mass distribution after theevent reconstruction are shown on the right.
matic variables is not trivial. Undetected particles and reconstruction errors distort the
measured distribution (see Fig. 5.1 right plots) and lead to a large background from the
dominant b → c`ν transition . The data samples are divided in two event sub-samples,
one that is enriched in b→ u transitions by a veto on the presence of kaons in the recoil
system, and one that is enriched in b → c transitions by requiring the detection of at
least one charged or neutral kaon. The latter can be used as a control sample to check
the agreement between data and Monte Carlo for background, so that the remaining
background in the b → u enriched sample in the phase space region under study can be
obtained by extrapolation from the b→ c dominated region.
5.1 Reconstruction of the Recoil System
Events containing a B meson decaying in a fully reconstructed hadronic final state are
selected by the Semi-exclusive reconstruction technique (see Sec. 3.5). The following steps
84
are employed to identify and study semileptonic decays in the recoil system:
- charged particles and neutral clusters are selected according to the criteria of Sec. 3.1
and 3.3;
- leptons are identified using standard BABAR algorithms for electrons and muon (see
Sec. 3.2.1 and 3.2.2);
- charged and neutral kaons are used to separate B → Xu`ν from the dominant
B → Xc`ν decays (see Sec. 3.2.3 and 3.4.2);
- the hadronic system X, the charged lepton ` and the undetected neutrino ν make
up the rest of the event (except for lost particles) recoiling against the Breco.
The hadronic system X is reconstructed from charged tracks and energy depositions in
the calorimeter that are not associated with the Breco candidate or the identified lepton.
The measured four-momentum pmX of the X system can be written as
pmX =
Nch∑i=1
pchi +
Nγ∑j=1
pγj (5.1)
where p are four-momenta and the indices ch and γ refer to the selected number of charged
tracks, and photons. Care is taken to eliminate fake charged tracks (see Section 3.1), as
well as low-energy beam-generated photons and energy depositions in the calorimeter
(Section 3.3) due to charged particles. The reconstruction of K0S mesons is used for veto
purposes only, without applying any mass constraints.
The neutrino four-momentum pν is estimated from the missing momentum four-vector
pmiss = pΥ(4S) − pmBreco
− pmX − pm
` = QCM − pmreco − pm
X − pm` (5.2)
where all momenta are measured in the laboratory frame, pΥ(4S) refers to the Υ(4S) meson
and QCM is the four-momenta of the colliding beams. The measured invariant mass
squared, m2miss = p2
miss, is an important estimator of the quality of the reconstruction
of the total recoil system. Undetected particles and measurement uncertainties affect
the determination of the four-momenta of the X system and neutrino, and lead to a
85
large leakage of B → Xc`ν background from the high MX into the low MX region and,
similarly, in other kinematic regions which would otherwise be background-free. Likewise
any sizable energy loss of the leptons via bremsstrahlung or internal radiation will impact
the measurement of these two quantities. However, the effect of initial state radiation is
small, due to the fact that the width of the Υ(4S) resonance is rather small.
5.2 Selection of Semileptonic Decays
The following requirements have been optimized to select a sample of Nmeassl semileptonic
B decays:
- cut on the purity per seed for reconstructed B modes. The Semi-exclusive
reconstruction allows to select samples of a given purity; clearly, the higher is the
purity, the smaller is the sample. The impact of the purity selection on the statistical
error was studied on the basis of data. The ratio S/(S + B), for events passing all
selection criteria as a function of the purity for the four charm seeds is shown in
Figure 5.2, while in Table 5.1 the optimal cuts are summarized, as a function of the
Semi-exclusive reconstruction decay channel.
- Lepton with a momentum in the B rest frame p∗` > 1 GeV/c. Semileptonic
B decays are identified by the presence of a high momentum electron or muon. A
minimum lepton momentum, in the B rest frame, is required to reduce background
leptons from secondary charm or τ± decays, and fake leptons. It is possible to boost
the lepton momentum to the rest frame of the recoiling B since the momenta of
the Υ(4S) and the reconstructed B are known. The cut p∗` > 1 GeV/c removes
Seed Mode Cut on Purity S B
B0 → D∗X 24% 228± 18 51± 12B0 → D+X 9% 510± 31 357± 26B± → D0X 9% 615± 33 470± 27B± → D∗0X 8% 307± 23 172± 19
Total 1660± 54 1050± 44
Table 5.1: Signal yield S and background B per seed, for the 81.9 fb−1 data sample, as obtained fromfits to the mES distribution for the optimum choice of the purity of the sample.
86
single mode purity0 10 20 30 40 50 60 70
0
2
4
6
8
10
12
14
s/sqrt(s+b) vs int purity D*
D*
single mode purity0 10 20 30 40 50 60 70
0
2
4
6
8
10
12
14
s/sqrt(s+b) vs int purity Dc
D+
single mode purity0 10 20 30 40 50 60 70
0
2
4
6
8
10
12
14
16
18
s/sqrt(s+b) vs int purity D*0
D*0
single mode purity0 10 20 30 40 50 60 70
0
2
4
6
8
10
12
14
16
18
s/sqrt(s+b) vs int purity D0
D0
Figure 5.2: Statistical significance S/(S + B) as a function of the purity (in %) for the four charm seedsof the reconstructed B sample after all cuts: clockwise (starting from the upper left plot) the seeds areB0 → D∗+X, B0 → D+X, B± → D0X, B+ → D∗0X.
about 10% of the fraction of signal events, as shown in Figure 5.3. The theoretical
uncertainty in the small fraction of the spectrum lost by this cut is small.
- Lepton Charge and B Flavor Correlation. In semileptonic decays of B mesons
the lepton charge is correlated with the B flavor. This leads to the relation
QBrecoilQ` > 0 for primary leptons and QBrecoil
Q` < 0 for secondary leptons (here
QBrecoilrefers to the b quark charge and Q` to the lepton charge in the semileptonic
decay). The former condition is imposed on charged B decays. No requirements
are made on neutral B decays, due to flavor oscillations; this implies a small mixing
correction to be applied on the results (see Sec. 6.1).
5.2.1 Selection of Charmless Semileptonic Decays
Further requirements refine the previously selected sample, enrich it with charmless
semileptonic decays, and reject as much charm background as possible. The relevant
87
lepton momentum (GeV/c)0 0.5 1 1.5 2 2.5 30
100
200
300
400
500
600
ν ul→b ν ul→b
lepton momentum (GeV/c)0 0.5 1 1.5 2 2.5 30
1000
2000
3000
4000
5000
6000
7000
ν cl→b ν cl→b
lepton momentum (GeV/c)0 0.5 1 1.5 2 2.5 30
1000
2000
3000
4000
5000
6000
7000
8000
lepp
ν Xl→B νlu X→B
lepp
Figure 5.3: The momentum p∗` of the lepton in the recoiling B rest frame after all analysis cuts. Top leftplot shows the spectrum for b → u`ν transitions, bottom left for b → c`ν. Right plot shows spectra fortotal and charmless semileptonic decays.
variables involved are:
- Number of Leptons, N` = 1. In b → c`ν transitions it is possible to find out a
second lepton originated in cascade decays of the charm particles, whereas secondary
leptons coming from b→ u`ν decays are very rare. Therefore, charmless decays can
be isolated by requesting one and only one lepton with p∗` > 1 GeV/c in the event.
On the other hand, additional leptons are accepted when measuring Nmeassl , which is
a quantity dominated by b → c`ν transitions. The number of detected leptons per
event is shown in Fig. 5.4. A cut at 1 GeV/c offers a reasonable compromise be-
tween the uncertainties due to available statistics, lepton identification, background
estimate and theoretical models.
- Total Charge of the event, Qtot = 0. The reconstructed kinematical variables
of the recoil system are distorted if one or more charged particles are lost, therefore
charge conservation Qtot = QBreco +QBrecoil= 0 is imposed. This requirement rejects
not only events with missing reconstructed charged particles, but also those with an
additional charged particle due to γ → e+e− conversions or tracking errors. This cut
is also important to reject B → Xc`ν events, that are more prone to inefficiencies in
88
Number of leptons-0.5 0 0.5 1 1.5 2 2.5 3 3.50
2000
4000
6000
8000
10000
ν ul→b ν ul→b
Number of leptons-0.5 0 0.5 1 1.5 2 2.5 3 3.50
20
40
60
80
100
310×ν cl→b ν cl→b
Number of leptons-0.5 0 0.5 1 1.5 2 2.5 3 3.50
20
40
60
80
100
310×lN
ν Xl→B νlu X→B
lN
Figure 5.4: Number of identified leptons per event with p∗` > 1 GeV/c after all analysis cuts. Top leftplot shows the distribution for b → u`ν transitions, bottom left for b → c`ν. Right plot shows spectrafor total and charmless semileptonic decays.
particle detection, due to their higher charged multiplicity. As an example, a sizeable
fraction of decays with low momentum pions coming from D∗ decays are rejected by
a requirement on the total charge of the event. Figure 5.5 shows the distributions of
Qtot.
- Missing mass squared, m2miss < 0.5 GeV2/c4. The only undetected particle in a
semileptonic B decay should be the neutrino. Therefore a cut on the missing mass
of the recoil is a powerful tool to reject events in which one or more particles are
undetected or poorly measured. As illustrated in Fig. 5.6, the m2miss distribution
is much wider and extends to higher values for b → c`ν decays. A cut in this
variable results in a valuable background suppression, due to higher multiplicities
and/or the presence of an additional neutrino or KL in charm decays. The optimal
requirement m2miss < 0.5 GeV2/c4 is chosen because a tighter cut introduces large
systematic uncertainties due to differences in m2miss resolution in data and Monte
Carlo simulations, and a looser cut results in poor signal-to-background ratio and
thus unacceptable statistical and systematic errors due to background subtraction.
89
Total event charge-4 -3 -2 -1 0 1 2 3 40
2000
4000
6000
8000
10000
ν ul→b ν ul→b
Total event charge-4 -3 -2 -1 0 1 2 3 40
20
40
60
80
100
310×ν cl→b ν cl→b
Total event charge-4 -3 -2 -1 0 1 2 3 40
20
40
60
80
100
310×totQ
ν Xl→B νlu X→B
totQ
Figure 5.5: total charge of events selected after all analysis cuts. Top left plot shows the distributionfor b → u`ν transitions, bottom left for b → c`ν. Right plot shows spectra for total and charmlesssemileptonic decays.
)4/c2Missing mass squared (GeV-4 -2 0 2 4 6 8 100
200
400
600
800
1000
1200
1400
1600
ν ul→b ν ul→b
)4/c2Missing mass squared (GeV-4 -2 0 2 4 6 8 100
2000
4000
6000
8000
10000
12000
14000
ν cl→b ν cl→b
)4/c2Missing mass squared (GeV-4 -2 0 2 4 6 8 100
2000
4000
6000
8000
10000
12000
14000
16000
2mm
ν Xl→B νlu X→B
2mm
Figure 5.6: Missing mass squared after all analysis cuts. Top left plot shows the distribution for b → u`νtransitions, bottom left for b → c`ν. Right plot shows spectra for total and charmless semileptonictransitions.
90
- Partially-Reconstructed Missing Mass Squared, m2miss,PR < −3 GeV2/c4.
One of the dominant backgrounds (∼ 50% of the entire B → Xc`ν) decays is due to
B0 → D∗`ν decays, with D∗ → D0π. This decay can be identified exploiting the
fact that the mass difference between the D∗ and the D0 is close to the pion mass
and therefore the pion produced in the D∗ decay is soft and basically collinear with
the D∗. Using the approximation that the direction of flight of the pion is the same
as the D∗ one, and taking into account that the soft pion energy in the D∗ rest frame
is fixed (E′π = 145.0 MeV), the pion energy in the laboratory frame is
Eπ = γ(E′π − βP
′π) (5.3)
where β and γ refer to the D∗ boost and P′π = 39.0 MeV/c is the soft pion momentum
in the D∗ frame. The D∗ energy in the laboratory frame can be computed, by
)4/c2PR Missing mass squared (GeV-45 -40 -35 -30 -25 -20 -15 -10 -5 0 50
10
20
30
40
50
60
70
80
90
ν ul→b ν ul→b
)4/c2PR Missing mass squared (GeV-45 -40 -35 -30 -25 -20 -15 -10 -5 0 50
200
400
600
800
1000
1200
1400
1600
1800
ν cl→b ν cl→b
)4/c2PR Missing mass squared (GeV-45 -40 -35 -30 -25 -20 -15 -10 -5 0 50
200
400
600
800
1000
1200
1400
1600
1800
2PR mm
ν Xl→B νlu X→B
2PR mm
Figure 5.7: m2miss,PR after all analysis cuts for neutral B meson decays with a positively identified soft
pion. Top left plot shows the distribution for b → u`ν transitions, bottom left for b → c`ν. Right plotshows spectra for total and charmless semileptonic decays.
neglecting the second term in equation 5.3, as
ED∗ = γMD∗ = EπMD∗
E ′π
. (5.4)
91
Given that the 4-momentum PD∗ of the D∗ is now known, the missing invariant mass
can be computed as
m2miss,PR = |Precoil − PD∗ − Plepton|2. (5.5)
Its distribution peaks at zero for background and varies smoothly for signal, as it
can be seen in Figure 5.7.
- Number of Kaons, NK± = NKS= 0. Since kaons are produced in nearly all
charm semileptonic decays, whereas they are highly suppressed in B → Xu`ν decays,
rejecting events where a kaon has been detected in the recoil system reduces the
background from B → Xc`ν decays. Both the number of identified charged kaons and
the number of detected KS are therefore required to be zero (see Figure 5.8). Studies
performed show that EMC and IFR information does not permit the identification of
KL and KS → π0π0 with a sufficient degree of purity. Charged kaons are identified
[40] with an efficiency varying between 60% at the highest and almost 100% at the
lowest momenta. The KS → π+π− decays are reconstructed with an efficiency of
80% from pairs of oppositely charged tracks with an invariant mass between 486 and
510 MeV/c2.
Number of Kaons-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
2000
4000
6000
8000
10000
ν ul→b ν ul→b
Number of Kaons-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
20
40
60
80
100
120
140
310×ν cl→b ν cl→b
Number of Kaons-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
20
40
60
80
100
120
140
310×KN
ν Xl→B νlu X→B
KN
Figure 5.8: Number of identified charged kaons after all analysis cuts. Top left plot shows the distributionfor b → u`ν transitions, bottom left for b → c`ν. Right plot shows spectra for total and charmlesssemileptonic decays.
92
The criteria for the selection of semileptonic events, after having found a Breco can-
didate, and of the final sample enriched in b → u`ν signal events are summarized in
Table 5.2.
Semileptonic selection at least one leptonp∗` > 1 GeV/c
correlation between lepton charge and B flavorFinal selection only one lepton
mm2 < 0.5 GeV2/c4
Sum of all charged particles equal to zeroReject events with kaons in Brecoil
Reject events with partially reconstructed D∗±`∓ν
Table 5.2: Selection criteria for semileptonic events and final selection.
5.3 Fit to the mES Distribution
As mentioned in Section 3.5.1, the kinematic consistency of reconstructed Breco candidates
with actual B decays and the subtraction of combinatorial backgrounds are determined
by performing a fit to mES distributions. In this thesis, a large number of fits to mES
distributions are performed, on samples of very different statistical power and signal
purity. It is therefore important to properly subtract combinatorial backgrounds and
insure that the parametrization of the fitting function used in the mES fits is accurate,
reproduces well the data and keeps systematic uncertainties to a minimum.
In other BABAR analyses [57], the only combinatorial background generally considered
is due to random associations of tracks and neutral clusters in BB and continuum events.
This background does not peak in mES and is subtracted by performing an unbinned like-
lihood fit to the mES distribution. In this fit, the combinatorial background is described
by an Argus function and the signal is described by a Crystal Ball function [58] peaking
at the B meson mass. This parametrization works quite well for moderate data samples,
but its shortcomings are visible in some regions of the mES distribution when using larger
datasets.
In principle, a B meson can be reconstructed in a different decay mode (defined in
the Semi-exclusive reconstruction algorithm) than is actually decaying into. Daughters
of the two B mesons can be lost or assigned to the wrong B in the reconstruction. The
93
mES distribution of these events exhibits a broad peaking component, which is referred
to as “peaking background”. A typical example is due to the swapping of charged and
neutral soft pions from D∗ decays, which have nearly the same kinematic properties, give
an incorrect charge assignment to the reconstructed B mesons and a peaking background
in mES. Since it is not possible to include this peaking component in the Argus back-
ground function, new functions describing the mES distributions have been studied and
are presented in the next sections.
5.3.1 Modeling of mES Distribution with 3 PDFs
The parametrization of the two backgrounds to be considered when fitting the mES dis-
tribution has been determined following the studies of [48]. An Argus shape is used for
non-peaking backgrounds, originating from both continuum (e+e− → qq, q = (u, d, s, c))
and BB events. The shape of BB background peaking in mES can be determined by using
Monte Carlo truth matching and selecting events where the generated and reconstructed
decays do not match. Figure 5.9 shows the mES distribution from BB Monte Carlo events
with incorrect truth-matching. The shape can be in principle described by the sum of an
Argus and a Crystal Ball function
fcb(x) =
{Ncbe
− 12
(x−xc)2
σ2 , x ≥ xc − ασ
Ncbe− 1
2α2(nσ
α)n 1
(xc−ασ+ nσα −x)n x < xc − ασ
(5.6)
However this function does not model the sharp cutoff at the endpoint, leading to prob-
lems in the last bins when trying to fit this function to the total mES distribution. To
model this endpoint region a “cutoff” Crystal Ball function is used:
fccb(x) =
{0 x > xmax
fcb − e−500(xmax−x)ffcb(2xmax − x) x < xmax(5.7)
which by construction drops down to 0 at x = xmax. The factor e−500(xmax−x) ensures this
behavior and confine it to the endpoint region. The value 500 is found empirically. The
fit results are shown in Table 5.3.
Decays with correct truth-matching, where the B meson is reconstructed in the same
mode that is decaying into, are defined as signal candidates. The mES distribution of
these candidates is displayed in Fig. 5.10, showing an almost gaussian shape with a slight
94
mes(GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28
Eve
nts
/ (
0.00
0691
)
0
2000
4000
6000
8000
10000
12000
14000
= 2.67402χ
mes(GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28
Eve
nts
/ (
0.00
0691
)
0
2000
4000
6000
8000
10000
12000
14000
MC Comb. Background: ccb+Argus
-5
0
-5
0
Figure 5.9: Fit of the Argus and “cutoff” Crystal Ball function to mES distribution of Breco candidateswith incorrect truth-matching. The semileptonic selection criteria of Table 5.2 have been applied on therecoiling B. The fitted function is plotted in blue and the single contributions from Argus and “cutoff”Crystal Ball are plotted in yellow and red. The bottom plot shows the pull distribution, namely thedifference between the fit and the points, divided by the statistical error for each bin.
Parameter Fitxc − 5279 MeV [MeV] 0.90± 0.04
σ [MeV] 5.10± 0.09α 0.465± 0.020n 20± 17
xcut − 5289 MeV [MeV] 0.90± 0.09
Table 5.3: Results from fitting “cutoff” Crystal Ball function to B-background Monte Carlo.
tail to the left. Usually such a distribution is modeled by a Crystal Ball function (Fig 5.10
left), which is however inadequate when the data sample to be fitted exceeds some tens
of thousand events. A three region function is then built starting from a Crystal Ball
function. The right side of the function is described by the sum of the derivative of
tanh(x)
ftanh′(x) =e−x
(1 + e−x)2(5.8)
and a gaussian function
fsigR(x) = Nr
σR1
ftanh′(x− xc
σR1
) +N1− r
σR2
fgauss(x− xc
σR2
) (5.9)
The left side of the function is described by a modified Crystal Ball function, where the
95
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-5
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10
Figure 5.10: Left: fit of a Crystal Ball function to the mES distribution of Breco candidates with correcttruth-matching from BB Monte Carlo for run period Run1-4. Right: fit of Eq. 5.12 to the mES distribu-tion of the same Breco candidates but for Run1-5 data period. We see that the fit of the 3-wise functionhas a better agreement with the mES distribution resulting in better χ2. The semileptonic selectioncriteria of Table 5.2 have been applied on the recoiling B.
gaussian part has been substituted by ftanh′(x):
fsigL(x) =
Ncb
exp(−x−xcσL
)
(1+exp(−x−xcσL
))2x ≥ xc − αsigσL
NcbB
(A+xc−x)nsig x < xc − αsigσL
(5.10)
with
A = −2αsigσL
1− eαsig, B =
eαsig
(1 + eαsig)2(A+ αsigσL)nsig . (5.11)
Both functions fsigR(x) and fsigL(x) are combined into the final signal function:
fsig(x) = N ×{CfsigL(mES, xc, σL, αsig, nsig) x ≤ xc
fsigR(mES, xc, r, σr1, σr2) x > xc(5.12)
with
C = fsigR(xc)/fsigL(xc). (5.13)
Figure 5.10-right shows the result of fitting the signal function fsig(x), with all parameters
floating free, to the mES distribution using only signal candidates. The function fits well
in all three regions (left tail, peak, right tail). Table 5.4 shows the results of the fit.
A function that is the sum of an Argus function for non-peaking (continuum and B)
backgrounds, a “cutoff” Crystal Ball function for the peaking B-background and the
signal function fsig is used to describe the mES distribution on data:
fmES= Nagfag(mES) +Ncbfccb(mES) +Nsigfsig(mES) (5.14)
96
Parameter Fitxc − 5279 MeV [MeV] 0.50± 0.01
σL [MeV] 0.00202± 0.00005αsig 4.20± 0.01nsig 1.27± 0.01
σR1 [MeV] 1.59± 0.03σR2 [MeV] 2.30± 0.10
r 0.94± 0.03
Table 5.4: Results from fitting the signal function to signal candidates from Monte Carlo.
Studies show that all the parameters of the peaking background function need to be fixed
in order to get a converging fit. In addition, the parameters αsig, nsig, σR2 and r of the
signal function fsig(x) need to be fixed. Table 5.5 shows the results of the fit on Monte
Carlo (Fig. 5.11). As the endpoint is fixed in Monte Carlo, the corresponding parameters
also have been fixed for the Argus and “cutoff” Crystal Ball.
Component Parameter Fitxc − 5279 MeV [MeV] 0.75± 0.02
σL [MeV] 0.00192± 0.00009αsig 4.20 (fixed)
Signal nsig 1.27 (fixed)σR1 [MeV] 1.58± 0.02σR2 [MeV] 2.30 (fixed)
r 0.94 (fixed)xc − 5279 MeV [MeV] 0.90 (fixed)
σ [MeV] 5.10 (fixed)Peaking background α 0.465 (fixed)
n 20 (fixed)xcut − 5289 MeV [MeV] 0.90 (fixed)
Non-peaking background χ −22.6± 0.02xmax − 5289 MeV [MeV] 0.10 (fixed)
Table 5.5: Results from fitting the mES function to BB Monte Carlo.
Figure 5.12 shows the mES distribution in data. Due to variations in the beam energy,
the endpoint of the mES distribution is not constant over time. Hence xmax cannot be
assumed constant and is left free in the fit. To extract the number of signal B’s, we
fit Eq. 5.14 to the observed mES distribution with the normalizations Nag, Ncb and Nsig
being free parameters. The peaking background shape is taken from Monte Carlo and
fixed. The signal shape is also taken from Monte Carlo but only a few parameters are
fixed, as indicated in Table 5.6.
97
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MC: Argus+ccb+Thorsten sig
-5
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-5
0
Figure 5.11: Fit to the mES function (Eq. 5.14) to the mES distribution of Breco candidates from BBMonte Carlo. The semileptonic selection criteria of Table 5.2 have been applied on the recoiling B. Thefitted function is plotted in blue and the single contributions from Argus, “cutoff” Crystal Ball and signalfunction are plotted in yellow, red and green.
)2 (GeV/cESm5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
2E
ntri
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eV/c
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-10
0
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3-20
-10
0
Figure 5.12: Fit of the mES function (Eq. 5.14) to the mES distribution of Breco candidates in data. Thesemileptonic selection criteria of Table 5.2 have been applied on the recoiling B.
98
Component Parameter Fitxc − 5279 MeV [MeV] 0.62± 0.13
σL [MeV] 0.0016± 0.0001αsig 4.20 (fixed)
Signal nsig 1.27 (fixed)σR1 [MeV] 1.90± 0.56σR2 [MeV] 2.30 (fixed)
r 0.94 (fixed)xc − 5279 MeV [MeV] 0.90 (fixed)
σ [MeV] 5.10 (fixed)Peaking background α 0.465 (fixed)
n 20 (fixed)xcut − 5289 MeV [MeV] 0.31± 0.05
Non-peaking background χ −22.1± 0.4xmax − 5289 MeV [MeV] 0.10± 0.03 (fixed)
Table 5.6: Results from fitting the mES function to data.
The parametrization of the mES distribution with 3 PDFs is accurate for high statistics
data samples, hence adequate to calculate the number of semileptonic decays Nmeassl .
However, severe instabilities show up in low statistics samples, such as the ones selected
to measure b → u transitions, Nmeasu . This is mainly due to the shape of the signal and
peaking background being very similar in the B mass region of the mES distribution.
Studies have been performed to determine whether fixing the ratio S/P , where S is the
number of signal events and P is the number of peaking background events, can help to
stabilize the fit. This was certainly the case, but large systematic uncertainties due to the
knowledge of S/P were also introduced. Therefore the 3 PDF model has been eventually
dropped.
5.3.2 Modeling of mES Distribution with 2 PDF
As already shown, the main problem when modeling the mES distribution for high statis-
tics samples is the presence of the peaking background due to errors in the association of
daughter particles to the reconstructed B. Simply neglecting peaking background events
can potentially introduce a bias in the high MX end of the spectrum, where larger particle
multiplicity makes it more likely for particles to be swapped between the two B mesons.
This possibility has been studied by selecting a sample of well-reconstructed B mesons
and looking for biases and changes in resolution after adding increasing amounts of peak-
99
ing background. Figure 5.13 shows a comparison of the MX resolution achieved, where
the amount of peaking background varies according to the truth-matching algorithms
described in Sec. 5.3.3. It is evident that small contamination due to peaking background
still provides a good resolution. Therefore the “cutoff” Crystal Ball function for modeling
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
0.1
0.2
0.3
0.4
0.5
0.6
Figure 5.13: Comparison between the MX resolution obtained by selecting only well-reconstructed Bmesons (black points) and by allowing some peaking background contamination. The contamination isdefined by the truth-matching algorithms described in Table 5.9, where the points relative to codes 1 to4 are, respectively, in red, green blue and yellow.
the peaking background has been dropped and the fit includes the Argus and the signal
functions described in the previous section; in this case part of the peaking background
is taken into account by the Argus function, the rest is considered as signal.
Figure 5.14 (left) shows an example of the result of fitting the signal and continuum
background to the mES distribution for a generic Monte Carlo sample. To allow the con-
vergence of the fit, the parameters α, n, σR2 and r of the signal function fsig(x) (Eq. 5.12)
need to be fixed. Table 5.7 shows the result of the fit. These values are used as starting
values for all subsequent fits in the analysis.
Figure 5.14 (right) shows the mES distribution in data. The fitted function describes
the distribution well over the full range. The results of the fit is shown in Table 5.8
Clearly, a good mES parametrization is not sufficient per se to avoid any biases in the
event yields and analysis results, due to the neglection of peaking backgrounds. However,
it is expected that the criteria applied on the recoiling B, when going from the semileptonic
100
to the final selection, do not modify substantially the fraction of peaking background.
Since all measurements shown in the next chapter are normalized to the semileptonic
event selection, it is expected that any bias due to the peaking backgrounds should be
small. This is indeed the case, as demonstrated in Section 5.3.4.
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allMC_enr_SL_haspi0-1.intp0.00 = 2.26702χ
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allMC_enr_SL_haspi0-1.intp0.00
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Figure 5.14: Example of a fit of 2-PDF model to mES distribution of Breco candidates in BB MonteCarlo (left) and data (right). The semileptonic selection criteria of Table 5.2 have been applied on therecoiling B.
5.3.3 Study of Truth-Matching Criteria
Up to now, the standard BABAR truth-matching algorithm has been used to determine
whether a B meson is correctly reconstructed or not. It is well known that several truth-
matching criteria can be defined. Generally speaking, truth-matching algorithms are less
efficient and accurate for soft particles and in dense environments. The Semi-exclusive
reconstruction is particularly challenging from this point of view, being based on the
reconstruction of high multiplicity modes and low momentum particles. Ideally, truth-
matching should be tailored to each single Breco mode, which is an unpractical task, given
that about 1000 modes are reconstructed.
An alternative approach to check the reliability of truth-matching and its impact on
final results involves a looser definition of well-reconstructed Breco decays, which can be
adopted as basis of a pseudo-truth-matching algorithm; as in standard truth-matching,
the peaking background component can be estimated from Monte Carlo and subtracted
from the signal yields obtained in data.
101
The signal sample is defined based on the shape of the resulting mES distribution.
The number of generated ngen and reconstructed nreco daughter particles of the Breco are
subdivided according to their charge (nchggen, nchg
reco, nneugen , nneu
reco); the number of reconstructed
daughter particles that are truth-matched, nchgtm , and nneu
tm , are also split according to their
charge, i.e. to whether they are coming from the Breco according to simulation information.
The following quantities can be defined: mchg = nchgreco − nchg
tm , mneu = nneureco − nneu
tm , lneu =
nchggen − nchg
tm and lneu = nneugen − nneu
tm .
Different choices for mneu, lneu, mchg, lchg lead to differences in the identification of
the signal component. An example is shown in Fig. 5.16 and 5.17, where, using generic
Monte Carlo samples, the truth-matched signal and background components are shown
for different truth-matching algorithms (see Table 5.9), and the result of the fit to the full
mES distribution in Figure 5.18 is overlaid.
It can be noticed that no truth-matching algorithm actually reproduces the fit results,
but it is possible to estimate the bias that is introduced and correct for it. The choice
mneu < 3, lneu < 3 and mchg = lchg = 0 gives the best agreement for the resulting “signal”
mES distribution with the modified Crystal Ball function.
Truth-matching algorithms can be used on generic Monte Carlo to estimate the peak-
ing background contamination both for semileptonic and for signal selection. For each
selection and for each Breco reconstructed charge, the ratio Stm/Sfit can be computed,
where Stm is the number of signal events that satisfy the truth-matching criteria, and Sfit
is the number of signal events obtained by fitting the mES distribution. This ratio can be
used to correct the signal yields of mES fits on data where, by definition, it is not possible
to apply any kind of truth-matching. The statistical uncertainty on the ratio Stm/Sfit is
computed by taking into account the correlation between the yields from mES fits and
the ones from truth-matching, which are obtained on the same Monte Carlo sample.
5.3.4 Strategy for mES Fits
The fitting strategy chosen for mES distributions represents a compromise between the
accuracy of the final measurements and the practical implementation of more detailed
techniques aimed at subtracting peaking backgrounds.
102
Parameter Fitxc - 5279 MeV [MeV] 0.92± 0.03σL [MeV] 2.24± 0.01α 4.64± 0.02n 1.55± 0.02σR1 [MeV] 1.19± 0.02σR2 [MeV] 1.55± 0.07r 0.95± 0.01χ −24.18± 0.63xmax - 5289 MeV [MeV] 0.28± 0.01
Table 5.7: Results from fitting the mES function toBB Monte Carlo. The parameters α, n, σR1 andxmax are kept fixed in the fit, but their uncertaintiesare used in the evaluation of the systematic uncer-tainties due to the fitting technique.
Parameter Fitxc - 5279 MeV [MeV] 0.92± 0.03σL [MeV] 2.14± 0.01α 4.64± 0.02n 2.08± 0.01σR1 [MeV] 1.31± 0.02σR2 [MeV] 3.25± 0.07r 0.71± 0.01 (fixed)χ −21.28± 1.29xmax - 5289 MeV [MeV] 0.24± 0.01
Table 5.8: Results from fitting the mES function todata. The parameters α, n, σR1 and xmax are keptfixed in the fit, but their uncertainties are used inthe evaluation of the systematic uncertainties dueto the fitting technique.
CODE mneu lneu mchg lchg
1 0 0 0 02 < 3 0 0 03 < 3 < 2 0 04 < 3 < 3 0 05 < 3 < 3 < 2 06 < 3 < 3 < 2 < 27 < 2 < 2 < 2 < 28 mchg + mneu < 2 lchg + lneu < 39 reconstructed Breco mode equals generated Breco mode
Table 5.9: Truth-matching algorithms.
103
In the following, the measurements of partial branching fractions subject of this thesis
work and further detailed in the next chapter, are compared in two different scenarios for
the mES fits:
• a parametrization with 2 PDFs, without peaking background subtraction;
• a parametrization with 2 PDFs, where peaking background is subtracted by using
the truth-matching algorithm which gives the smallest bias (see previous section).
The systematic uncertainty associated to the peaking background subtraction in the
latter scenario has been evaluated by randomizing 100 times the peaking background
correction according to a gaussian distribution whose mean and sigma are the central
value and the statistical error of the ratio Stm/Sfit, respectively, and by performing the
measurements of partial branching fractions on the Monte Carlo sample for each ran-
domization. The RMS of the distribution of the 100 results thus obtained (see Fig. 5.15)
is taken as systematic error and added in quadrature to the other uncertainties. The
resulting error is optimistic, since it neglects any additional systematic uncertainty in
Stm/Sfit and refers to the truth-matching algorithm that gives the smallest bias in the
event yields. Nevertheless, it can be compared to the uncertainty due to the bias intro-
duced by neglecting peaking background completely. As shown in Table 5.10, the bias
on the analysis results determined by fitting all mES distributions without subtracting
peaking backgrounds corresponds to an uncertainty which, summed in quadrature with
the others, is comparable to the optimistic one that comes from the peaking background
subtraction procedure. For this reason, a 2-PDF model without peaking background
subtraction will be used in the following to fit the mES distributions, the resulting biases
will be corrected for and a systematic uncertainty equal to the bias will be assumed. Nev-
ertheless, the model where peaking background is subtracted according to truth-matching
will be used as a validation of the results.
5.3.5 Binned vs. Unbinned Fits
Due to the large number of events that survive the semileptonic selection, it is not very
practical to perform every fit as an unbinned maximum likelihood fit. On the other
104
Entries 100
Mean 0.02152
RMS 0.0007613
Constant 1.67± 11.95
Mean 0.00008± 0.02147
Sigma 0.000077± 0.000723
BRBR0.018 0.019 0.02 0.021 0.022 0.023 0.024 0.0250
2
4
6
8
10
12
Entries 100
Mean 0.02152
RMS 0.0007613
Constant 1.67± 11.95
Mean 0.00008± 0.02147
Sigma 0.000077± 0.000723
xRun 1-5: MEntries 100
Mean 0.0214
RMS 0.0008636
Constant 1.342± 9.564
Mean 0.00010± 0.02143
Sigma 0.0000968± 0.0008859
BRBR0.018 0.019 0.02 0.021 0.022 0.023 0.024 0.0250
2
4
6
8
10
12
14Entries 100
Mean 0.0214
RMS 0.0008636
Constant 1.342± 9.564
Mean 0.00010± 0.02143
Sigma 0.0000968± 0.0008859
+Run 1-5: P
Entries 100
Mean 0.02132
RMS 0.001006
Constant 1.213± 8.584
Mean 0.00013± 0.02125
Sigma 0.000115± 0.001003
BRBR0.018 0.019 0.02 0.021 0.022 0.023 0.024 0.0250
2
4
6
8
10
12Entries 100
Mean 0.02132
RMS 0.001006
Constant 1.213± 8.584
Mean 0.00013± 0.02125
Sigma 0.000115± 0.001003
2/qxRun 1-5: M
Figure 5.15: Distribution of the 100 ratio of branching ratio (Ru/sl) measurements obtained by randomlyvarying the Stm/Sfit according to a gaussian distribution whose RMS is the Monte Carlo statistical erroron Stm/Sfit (see text). The top left, top right and bottom plots refer to MX , P+ and (MX , q2) analyses,respectively. The generation value for Ru/sl is 0.0215.
Ru/sl (10−4) Ru/sl (10−4) Ru/sl (10−4)generation value truth-matching + sys fit mES
MX analysis 215 215± 11± 12 220± 12± 11P+ analysis 215 215± 12± 13 219± 12± 12
(MX , q2) analysis 215 214± 15± 16 222± 16± 16
Table 5.10: Comparison among the partial ratio of branching fractions generated on Monte Carlo (firstcolumn), fitted on Monte Carlo using the truth-matching approach and adding the systematic error onpeaking background evaluation (second column), and fitted using the mES fit approach without subtract-ing the peaking background (third column). In the last column, a systematic uncertainty correspondingto 100% of the observed bias has been added in quadrature to the other uncertainties.
105
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Figure 5.16: Truth-matched distributions for the signal component in Run4 BB Monte Carlo, afterall analysis cuts have been applied, according to the various truth-matching algorithms described inTable 5.9. The signal PDF, as determined from the mES fit in Figure 5.18 has been overlaid in eachsub-plot.
side, the unbinned fit is needed when fitting low statistics samples. These are either
single bins in MX , P+ and (MX , q2) or small data samples, e. g. the b→ u`ν Monte Carlo
sample. Datasets with less than Nt = 20000 events are fitted using an unbinned maximum
likelihood fit, all other datasets are fitted using a binned one. With this threshold most
of the fits are unbinned. The Nt threshold has been varied from 10000 up to 100000 and
removed it entirely. No appreciable differences in the fitted yields and the ratio of partial
branching ratios have been found.
5.4 Data/Monte Carlo Comparison
A good description of the relevant variables by the Monte Carlo simulation is important
for this inclusive analysis. Distributions showing data and Monte Carlo agreement for
Run5 are shown in Figures 5.19 to 5.28, according to event type (signal-enriched or -
depleted) for the full running period. The distributions for other run periods are very
106
similar.
Since b → u`ν events are basically free of kaons, the total number of kaons (neutral
or charged) in the recoil system is a powerful tool to discriminate between signal and
background. On the basis of this kaon veto, two data samples are defined:
1. the signal-enriched sample (events with NK± = NK0S
= 0), and
2. the signal-depleted sample with (NK± > 0 or NK0S> 0).
The plots for each variable were produced using data and generic Monte Carlo samples.
All the selection cuts were applied, except the one on the plotted variable. All spectra
were background-subtracted with the appropriate mES sideband distribution after having
performed a binned mES fit for each bin of the observed variable. Error on data points
is the fit error on yields. Data and Monte Carlo were normalized to equal area; each pair
of histograms was then tested for compatibility by calculating the χ2/d.o.f..
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Eve
nts
/ (
0.00
0666
667
)
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A RooPlot of "mes (GeV)" = 86.05132χ
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nts
/ (
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A RooPlot of "mes (GeV)"
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nts
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A RooPlot of "mes (GeV)" = 82.18172χ
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
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nts
/ (
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A RooPlot of "mes (GeV)"
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
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nts
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A RooPlot of "mes (GeV)" = 47.10252χ
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
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A RooPlot of "mes (GeV)"
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
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nts
/ (
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A RooPlot of "mes (GeV)" = 33.43512χ
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
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nts
/ (
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A RooPlot of "mes (GeV)"
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Eve
nts
/ (
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)
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A RooPlot of "mes (GeV)" = 45.25102χ
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Eve
nts
/ (
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A RooPlot of "mes (GeV)"
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Eve
nts
/ (
0.00
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)
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A RooPlot of "mes (GeV)" = 27.59472χ
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Eve
nts
/ (
0.00
0666
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)
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A RooPlot of "mes (GeV)"
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Eve
nts
/ (
0.00
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)
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A RooPlot of "mes (GeV)" = 30.58282χ
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Eve
nts
/ (
0.00
0666
667
)
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A RooPlot of "mes (GeV)"
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Eve
nts
/ (
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)
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A RooPlot of "mes (GeV)" = 26.62792χ
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Eve
nts
/ (
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A RooPlot of "mes (GeV)"
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Eve
nts
/ (
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A RooPlot of "mes (GeV)" = 33.17982χ
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Eve
nts
/ (
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)
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A RooPlot of "mes (GeV)"
Figure 5.17: Truth-matched distributions for the background component in Run4 BB Monte Carlo, afterall analysis cuts have been applied, according to the various truth-matching algorithms described inTable 5.9. The background PDF, as determined from the mES fit in Figure 5.18 has been overlaid ineach sub-plot.
107
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Eve
nts
/ (
0.00
0666
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)
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3000
4000
5000
6000
7000
A RooPlot of "mes (GeV)" = 3.25582χ
mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Eve
nts
/ (
0.00
0666
667
)
0
1000
2000
3000
4000
5000
6000
7000
A RooPlot of "mes (GeV)"
-5
0
5
-5
0
5
Figure 5.18: Fit to mES distribution for Run4 BB Monte Carlo, after all analysis cuts have been applied.The two PDF functions for signal and background that have been determined on this plot are overlaidto the truth-matched signal and background events in Figure 5.16 and 5.17.
108
The overall data-Monte Carlo agreement is good; differences between data and Monte
Carlo considered as systematic uncertainties are discussed in Chapter 7.
The following observations can be made:
• Figure 5.19 illustrates the multiplicities of charged particles. The charged multiplicity
observed in data has a good agreement with the Monte Carlo distributions. The
signal-depleted distributions start only with a minimum of two tracks, since at least
one charged kaon is required in the event selection (in addition to the lepton). The
structure in the signal-enriched distribution is from B+ decays with two tracks in
addition to the lepton.
• The charged lepton momentum distribution (Figure 5.21) shows a good data-Monte
Carlo agreement in both the signal enriched and depleted sample
• Good agreement is observed for the total charge distribution (Figure 5.23).
• Good agreement is also observed for the missing mass squared distribution for the
partial D∗ reconstruction (Figure 5.25) and the reconstructed hadronic recoil mass
MX (Figure 5.26).
• The q2 distributions (Figure 5.27) agree very well.
109
500
1000
1500
2000
2500
3000
nchg data events after all cuts: enriched h400000Entries 10
Mean 3.665
RMS 1.12
Underflow 0
Overflow 0Integral 4967
= 1.80322χ
nchg data events after all cuts: enriched
0 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 100.5
1
1.5
1000
2000
3000
4000
5000
6000
nchg data events after all cuts: depleted d400000Entries 10
Mean 4.452
RMS 1.093
Underflow 0
Overflow 0
Integral 1.067e+04
= 3.93282χ
nchg data events after all cuts: depleted
0 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 100.5
1
1.5
Figure 5.19: Charged track multiplicity (side-bandsubtracted) in data and generic Monte Carlo forb → u`ν enhanced (top row) and depleted (bottomrow) event samples.
200
400
600
800
1000
nneu data events after all cuts: enriched h400000Entries 15
Mean 5.435
RMS 2.554
Underflow 0
Overflow 0Integral 4952
= 1.12802χ
nneu data events after all cuts: enriched
0 2 4 6 8 10 12 140 2 4 6 8 10 12 140.5
1
1.5
500
1000
1500
2000
2500
nneu data events after all cuts: depleted d400000Entries 15
Mean 4.198
RMS 2.119
Underflow 0
Overflow 0
Integral 1.063e+04
= 1.94092χ
nneu data events after all cuts: depleted
0 2 4 6 8 10 12 140 2 4 6 8 10 12 140.5
1
1.5
Figure 5.20: Photon multiplicity (side-band sub-tracted) in data and generic Monte Carlo for b →u`ν enhanced (top row) and depleted (bottom row)event samples.
110
200
400
600
800
1000pcms data events after all cuts: enriched h400000
Entries 15
Mean 1.658
RMS 0.3234
Underflow 0
Overflow 0
Integral 4980
= 1.28532χ
pcms data events after all cuts: enriched
1 1.21.41.61.8 2 2.22.42.62.8 31 1.21.41.61.8 2 2.22.42.62.8 30.5
1
1.5
200400600800
100012001400160018002000
pcms data events after all cuts: depleted d400000Entries 15
Mean 1.589
RMS 0.3104
Underflow 0
Overflow 0
Integral 1.063e+04
= 0.56132χ
pcms data events after all cuts: depleted
1 1.21.41.61.8 2 2.22.42.62.8 31 1.21.41.61.8 2 2.22.42.62.8 30.5
1
1.5
Figure 5.21: Charged lepton momentum distribu-tion in the CM frame (side-band subtracted) in dataand generic Monte Carlo for b → u`ν enhanced (toprow) and depleted (bottom row) event samples.
500
1000
1500
2000
2500
3000
mm2 data events after all cuts: enriched h400000Entries 40
Mean 2.78
RMS 2.87
Underflow 0
Overflow 0
Integral 2.082e+04
= 1.63932χ
mm2 data events after all cuts: enriched
-4 -2 0 2 4 6 8 101214-4 -2 0 2 4 6 8 1012140.5
1
1.5
1000
2000
3000
4000
5000
6000mm2 data events after all cuts: depleted d400000
Entries 40
Mean 0.7529
RMS 1.715
Underflow 0
Overflow 0
Integral 1.765e+04
= 1.15352χ
mm2 data events after all cuts: depleted
-4 -2 0 2 4 6 8 101214-4 -2 0 2 4 6 8 1012140.5
1
1.5
Figure 5.22: Missing mass squared distribution(side-band subtracted) in data and generic MonteCarlo for b → u`ν enhanced (top row) and depleted(bottom row) event samples.
111
1000
2000
3000
4000
5000
6000
qtot data events after all cuts: enriched h400000Entries 9
Mean 0.03677
RMS 0.7495
Underflow 0
Overflow 0
Integral 8810
= 1.51032χ
qtot data events after all cuts: enriched
-4 -3 -2 -1 0 1 2 3 4-4 -3 -2 -1 0 1 2 3 40.5
1
1.5
2000
4000
6000
8000
10000
12000
14000
qtot data events after all cuts: depleted d400000Entries 9
Mean -0.0001751
RMS 0.6564
Underflow 0
Overflow 0
Integral 1.69e+04
= 1.56592χ
qtot data events after all cuts: depleted
-4 -3 -2 -1 0 1 2 3 4-4 -3 -2 -1 0 1 2 3 40.5
1
1.5
Figure 5.23: Total charge distribution (side-bandsubtracted) in data and generic Monte Carlo forb → u`ν enhanced (top row) and depleted (bottomrow) event samples.
1000
2000
3000
4000
5000
6000
nks+nkp data events after all cuts: enriched h400000Entries 10
Mean 0.5
RMS 0
Underflow 0
Overflow 0Integral 4976
= 0.00002χ
nks+nkp data events after all cuts: enriched
0 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 100.5
1
1.5
2000
4000
6000
8000
10000
nks+nkp data events after all cuts: depleted d400000Entries 10
Mean 1.753
RMS 0.5304
Underflow 0
Overflow 0
Integral 1.066e+04
= 0.73982χ
nks+nkp data events after all cuts: depleted
0 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 100.5
1
1.5
Figure 5.24: Sum of charged and neutral kaons(side-band subtracted) in data and generic MonteCarlo for b → u`ν enhanced (top row) and depleted(bottom row) event samples. Please note that thisquantity is used to define the enriched/depletedsample hence the enriched sample shows zeros only.
112
100
200
300
400
500
600
700
800
wdeltam data events after all cuts: enriched h400000Entries 40
Mean -21.81
RMS 26.46
Underflow 0
Overflow 0Integral 4942
= 0.84212χ
wdeltam data events after all cuts: enriched
-140-120-100-80-60-40-20 0-140-120-100-80-60-40-20 00.5
1
1.5
200400600800
1000120014001600180020002200
wdeltam data events after all cuts: depleted d400000Entries 40
Mean -23.62
RMS 27.93
Underflow 0
Overflow 0
Integral 1.063e+04
= 1.10892χ
wdeltam data events after all cuts: depleted
-140-120-100-80-60-40-20 0-140-120-100-80-60-40-20 00.5
1
1.5
Figure 5.25: Missing mass squared distributionfor the partial D∗+ reconstruction (side-band sub-tracted) in data and generic Monte Carlo for b →u`ν enhanced (top row) and depleted (bottom row)event samples selecting neutral B s only.
200
400
600
800
1000
1200
1400
1600mxhad data events after all cuts: enriched h400000
Entries 20
Mean 1.954
RMS 0.5654
Underflow 0
Overflow 0
Integral 4949
= 1.43822χ
mxhad data events after all cuts: enriched
0 0.5 1 1.5 2 2.5 3 3.5 40 0.5 1 1.5 2 2.5 3 3.5 40.5
1
1.5
500
1000
1500
2000
2500
3000
3500
mxhad data events after all cuts: depleted d400000Entries 20
Mean 2.171
RMS 0.4466
Underflow 0
Overflow 0
Integral 1.062e+04
= 0.79592χ
mxhad data events after all cuts: depleted
0 0.5 1 1.5 2 2.5 3 3.5 40 0.5 1 1.5 2 2.5 3 3.5 40.5
1
1.5
Figure 5.26: Hadronic recoil invariant mass spec-trum (side-band subtracted) in data and genericMonte Carlo for b → u`ν enhanced (top row) anddepleted (bottom row) event samples.
113
100
200
300
400
500
600
q2 data events after all cuts: enriched h400000Entries 20
Mean 5.786
RMS 3.975
Underflow 0
Overflow 0Integral 4966
= 1.16632χ
q2 data events after all cuts: enriched
0 2 4 6 8 10121416180 2 4 6 8 10121416180.5
1
1.5
200
400
600
800
1000
1200
1400
1600q2 data events after all cuts: depleted d400000
Entries 20
Mean 4.628
RMS 3.188
Underflow 0
Overflow 0
Integral 1.065e+04
= 0.78282χ
q2 data events after all cuts: depleted
0 2 4 6 8 10121416180 2 4 6 8 10121416180.5
1
1.5
Figure 5.27: q2 distribution (side-band subtracted)in data and generic Monte Carlo for b → u`ν en-hanced (top row) and depleted (bottom row) eventsamples.
200
400600800
10001200
140016001800
pplus data events after all cuts: enriched h400000Entries 20
Mean 1.033
RMS 0.5071
Underflow 0
Overflow 0Integral 4965
= 0.55552χ
pplus data events after all cuts: enriched
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.5
1
1.5
500
1000
1500
2000
2500
3000
3500
4000
pplus data events after all cuts: depleted d400000Entries 20
Mean 1.173
RMS 0.457
Underflow 0
Overflow 0
Integral 1.064e+04
= 0.63072χ
pplus data events after all cuts: depleted
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.5
1
1.5
Figure 5.28: P+ distribution in the CM frame (side-band subtracted) in data and generic Monte Carlofor b → u`ν enhanced (top row) and depleted (bot-tom row) event samples.
114
Chapter 6
Partial Charmless BranchingFraction Measurements
6.1 Measurement Technique
Inclusive charmless semileptonic branching ratios are determined in phase space regions
defined by the MX , P+ and (MX , q2) kinematic variables. Rather than perform direct
measurements of the ∆B(B → Xu`ν), a measurements of the partial branching ratios
relative to the inclusive semileptonic one B(B → X`ν) allows to cancel out relevant
contributions to the systematic uncertainties.
To derive partial charmless semileptonic branching ratios, the observed number of
events, corrected for background and efficiency, is normalized to the total number of
semileptonic decays b → q`ν (here q stands for c or u) in the Brecoil event sample. The
measurement of a ratio of branching ratios offers at least three experimental advantages:
1. the efficiency of the Semi-exclusive reconstruction is not needed. This is very impor-
tant because the Semi-exclusive reconstruction efficiency is affected by large uncer-
tainties due to the fact that many of the reconstructed modes are not well described
in Monte Carlo;
2. most of the systematics, due to charged lepton identification, are removed since they
are present in both numerator and denominator of the ratio, and they vanish;
3. the normalization to the number of semileptonic events, that is extracted from a fit
to the mES distribution, is less affected by biases, which affect in almost the same
115
way the numerator and the denominator of this ratio.
The number of observed Brecoil events which survive the semileptonic event selection (Ta-
ble 5.2) is denoted as Nmeassl . It can be related to the true number of semileptonic decays,
N truesl = N true
c +N trueu , and the remaining background BGsl which is to be subtracted,
Nmeassl = εc`ε
ctN
truec + εu` ε
utN
trueu +BGsl = εsl` ε
slt N
truesl +BGsl, (6.1)
thus
N truesl =
Nmeassl −BGsl
εsl` εslt
=Nsl
εsl` εslt
. (6.2)
Here εsl` refers to the efficiency of the semileptonic selection on a semileptonic B decay in
an event tagged with efficiency εslt . As already discussed, additional selection criteria are
imposed to select b → u`ν decays. If we denote as Nmeasu the number of events fitted in
the sample after all requirements, with BGu the background coming from semileptonic
decays other than the signal, the measured number of events can be expressed in terms
of N trueu , the true number of signal events, as
Nu = Nmeasu −BGu = εuselε
ukinε
u` ε
utN
trueu (6.3)
where εusel is the efficiency for detecting B → Xu`ν decays after applying all cuts but the
one on the kinematical variables, relative to the semileptonic event selection, and εukin is
the efficiency for B → Xu`ν decays when cutting on the kinematic variables MX , P+ or
(MX , q2).
To determine Nu, the background (BGu) is subtracted by performing a χ2 fit on the
P+, MX or (MX , q2) distributions, where the background shape is computed from Monte
Carlo simulation, and its normalization is floating. An example of such a χ2 fit is shown in
Fig. 6.1. The P+, MX or (MX , q2) distributions in data and Monte Carlo are determined
by mES fits in individual P+, MX or (MX , q2) bins. For charged B mesons, the charge of
the direct lepton from a semileptonic decay is exactly correlated with the charge of the
flavor of the b quark. For neutral B mesons, the effect of B0 − B0 mixing needs to be
taken into account.
If the sample were made only of direct cascade leptons from neutral B decays, the right
(rs) and wrong (ws) sign events would be related to the direct (B → X`ν) and cascade
116
/ GeVXm0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
500
1000
1500
2000
2500
3000
/ GeVXm0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
500
1000
1500
2000
2500
3000 ν l uB -> Xν l cB -> X
OtherData
/ GeVXm0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
500
1000
1500
2000
2500
3000
/ GeVXm0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
500
1000
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2000
2500
3000ν l uB -> Xν l cB -> X
OtherData
/ GeVXm0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-50
0
50
100
150
200
250
/ GeVXm0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-50
0
50
100
150
200
250
MCν l uB -> X
Data bkgd subtr.
Figure 6.1: χ2 fit to the MX distribution. Left: fit result with ”other” background (red), b → c`ν (yellow)and signal (green) shapes superimposed. Middle: same as in the left plot with finer binning. Right: MX
distribution subtracted of the backgrounds (binning as in the middle plot).
(D → X`ν) decays by
Nrs = (1− χd)NB + χDND (6.4)
Nws = χdNB + (1− χd)ND (6.5)
where χd = 0.188± 0.003 [46] is the neutral Bd mixing parameter. The contribution from
cascade would be subtracted in an exact way by computing
NB =1− χd
1− 2χd
Nrs − χd
1− 2χd
Nws (6.6)
Actually there are events which do not contain any leptons and events that contain two
D mesons and can therefore have a right sign lepton even if it is not direct. These
components are very small and neglected.
In order to have Monte Carlo distributions as much similar as possible to data, the
ratio of the charged to neutral B yields in Monte Carlo is reweighted to be the same
observed in data.
Monte Carlo and data distribution are divided into 3 flavor subsamples, corresponding
to charged B mesons, right-sign and wrong-sign neutral B mesons. The mES distribution
of events surviving the semileptonic selection is fitted for each subsample in order to deter-
mine the number of semileptonic B decays and subtract the combinatorial backgrounds.
To get convergence, the parameters α, n, r and σR2 of the signal function are fixed in these
fits. The mixing correction of Eq. 6.6 is applied to data and Monte Carlo subsamples,
charge reweighting is applied to Monte Carlo only.
117
The distributions of the kinematic variables (MX , P+, (MX , q2)) are divided into bins
and for each bin a mES fit is performed on events surviving the signal selection, again for
each of the 3 flavor subsamples. In these fits, all parameters of the signal function are
fixed to the values fitted in the semileptonic selection samples; only the shape of the Argus
function and the signal and background normalizations are free to float. The number of
events in each bin of the kinematical variable under study is obtained after applying the
mixing correction and charge reweighting. The remaining background is due to b → c`ν
transitions and to “other” components such cascade decays and non semileptonic decays
that survive the selection criteria; this background is subtracted with a χ2 fit described
further on.
The ratio between the partial branching fraction for the signal decays in a given phase
space region and B → X`ν decays is given by
∆Ru/sl =B(signal)
B(B → X`ν)=N true
u
N truesl
=(Nmeas
u −BGu)/(εuselε
ukin)
(Nmeassl −BGsl)
× εsll εslt
εul εut
. (6.7)
The efficiency ratio (last term of Eq. 6.7) is expected to be close to, but not equal to
unity. Due to the difference in multiplicity and the different lepton momentum spectra,
the tag efficiency εt and lepton efficiency εl are expected to be different for the two classes
of events.
Partial branching fractions for charmless decays in the regions of interest are then
obtained from ∆Ru/sl using the semileptonic branching ratio determined by the HFAG
group by averaging over several experiments [54]
B(B → X`ν) = (10.75± 0.16)%. (6.8)
In order to extract the partial charmless semileptonic branching ratio ∆B(B → Xu`ν)
in a given region of the MX , (MX , q2) or P+ distributions, signal events are defined as
the ones with true values of the kinematic variables in the chosen region. The b → u`ν
events with true values of the kinematic variables outside the signal region are treated as
background. This means that in applying Eq. 6.7, the b→ u`ν events outside the signal
region are included in BGu and the quoted efficiencies refer only to events with true
values of the kinematical variables in the chosen kinematic region. These efficiencies are
118
computed on Monte Carlo, and therefore are based on the DFN model. The associated
theoretical uncertainty on the final result is small compared to the extrapolation error to
the full phase space.
The binned kinematic distribution obtained is fitted with a χ2 minimization which
extracts Nu and BGu as defined by Eq. 6.7 using signal and background shapes taken
from simulation, and by determining their relative normalizations with respect to the
experimental distribution. The distribution of the kinematic variable(s) on data (Nu measi )
is fitted to the sum of three distributions, the b→ u`ν events inside the signal region (N inu i),
the b→ u`ν events outside the signal region (N outu i ), and the sum of b→ c`ν and “other”
backgrounds (N bkgi )
µi = CinNin MCu i + CoutN
out MCu i + CbN
bkg MCi . (6.9)
The χ2 function is:
χ2(Cin, Cout, Cbkg) = −∑
i
Nu meas
i − µi√δNu meas
i2 + δN in MC
u i2
2
(6.10)
where the sum runs over the bins, Nu measi is the number of observed events in bin i,
δNu measi and δN in MC
u i are the corresponding statistical errors coming from the mES fits
for data and Monte Carlo respectively. Cin, Cout and Cbkg are the normalizations of the
three components which are free parameters of the fit. The constraint Cin = Cout is
applied. When fitting the MX and P+ distributions, the first bin is chosen to contain all
events within the phase space being considered for the calculation of the partial branching
fraction. In this way, the number of fitted signal events is Nu = N in measu 1 − CoutN
out MCu 1 −
CbkgNbkg MC1 . For the (MX , q
2), Nu is determined by summing over the appropriate q2
bins.
6.2 Monte Carlo Fits
The measurement technique described above has been extensively tested using Monte
Carlo samples.
Generic Monte Carlo was used to study the b → c`ν component, signal Monte Carlo
119
for the b → u`ν component; both were properly reweighted to reproduce the currently
measured values of branching fractions, heavy quark parameters, form factors, and de-
tector effects. Generic and signal Monte Carlo are summed by taking into account their
relative luminosities.
The two approaches described in 5.3.4 were followed. In the approach without peaking
background corrections, all quantities including efficiencies were determined by measuring
yields with mES fits. For the other approach, all the efficiency calculations were performed
by counting truth-matched events surviving the cuts, and the peaking component was
corrected for when determining the number of semileptonic events and the shapes of the
kinematical distributions. For the latter, the peaking background evaluation was done
in bins of the kinematic variable under study. As an example, figures 6.2 to 6.5 show
the Stm/Sfit ratio as a function of MX for the three flavour subsamples in different run
periods. The ratio Stm/Sfit is approximately constant and well behaved for every run
period, regardless of the charge of the reconstructed B meson.
The fit results are shown for the different analyses in tables 6.1 to 6.7, divided in run
periods. A very good agreement can be noticed between the two mES fit approaches
and the generated values. The small biases observed in the approach without peaking
background subtraction will be corrected for in data fits, and a systematic uncertainty
corresponding to 100% of the correction will be assigned.
6.3 One Dimensional MX Fit and Results
The MX data distribution, obtained by following the procedure outlined in Section 6.1,
is fitted by using the two mES fit approaches outlined in Section 5.3.4 and Nu and BGu,
as defined by Eq. 6.7, are determined.
Fits to theMX distribution have been performed for phase space regions defined byMX
smaller than 1.55 GeV/c2 and 1.7 GeV/c2 on data for different run periods, and for the
entire sample. Results for MX < 1.55 GeV/c2 are shown in Table 6.8 and Figure 6.6 for
the approach without peaking background subtraction, and in Table 6.9 and Figure 6.7 for
the approach based on truth-matching. The results for MX < 1.7 GeV/c2 are presented
120
/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
fitt
ed/S
tru
thm
atch
edS
0.8
0.9
1
1.1
1.2
1.3
= 0.70832χRun 1-2 charged
/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
fitt
ed/S
tru
thm
atch
edS
0.2
0.4
0.6
0.8
1
1.2
1.4
= 0.82922χRun 1-2 neutrals Same Sign
/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
fitt
ed/S
tru
thm
atch
edS
0.4
0.6
0.8
1
1.2
1.4
= 0.38802χRun 1-2 neutrals Opposite Sign
Figure 6.2: Left: Stm/Sfit in MX bins for Run1-2 B± (right), unmixed B0 (left), mixed B0 (bottom).The red line represents Stm/Sfit calculated.
Run Period gen. Nsl Nsl
Run1-2 106963 106901Run3 39339 39318Run4 138185 137724Run5 172373 171981
Run1-5 456858 457014
Table 6.1: Generated and fitted values for Nsl in all the analyses.
Run Period gen. Ru/sl Ru/sl (truth-matching) Ru/sl
Run1-2 215× 10−4 (216± 23± 16)× 10−4 (219± 22± 20)× 10−4
Run3 215× 10−4 (216± 35± 25)× 10−4 (215± 35± 30)× 10−4
Run4 215× 10−4 (216± 21± 15)× 10−4 (219± 21± 19)× 10−4
Run5 215× 10−4 (216± 20± 16)× 10−4 (221± 21± 18)× 10−4
Run1-5 215× 10−4 (215± 11± 9)× 10−4 (220± 12± 10)× 10−4
Table 6.2: Generated and fitted values for Ru/sl in the MX analysis. The first fitted value is obtainedwith the truth-matching based approach, the second with the approach based on fits to all data andMonte Carlo mES distributions.
121
/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
fitt
ed/S
tru
thm
atch
edS
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
= 0.29032χRun 3 charged
/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
fitt
ed/S
tru
thm
atch
edS
0.5
1
1.5
2
2.5
3
= 0.13812χRun 3 neutrals Same Sign
/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
fitt
ed/S
tru
thm
atch
edS
0.5
1
1.5
2
2.5
3
= 0.62902χRun 3 neutrals Opposite Sign
Figure 6.3: Left: Stm/Sfit in MX bins for Run3 B± (right), unmixed B0 (left), mixed B0 (bottom).
Run Period gen. Nu Nu gen. εuselε
ukin εu
selεukin gen. εsll εslt
εul εu
t
εsll εslt
εul εu
t
Run1-2 517± 13 518± 54± 13 0.371 0.371 1.22 1.22± 0.05Run3 192± 8 193± 31± 8 0.389 0.389 1.17 1.17± 0.08Run4 630± 15 629± 61± 15 0.346 0.346 1.23 1.23± 0.05Run5 706± 15 706± 65± 15 0.321 0.321 1.20 1.20± 0.04
Run1-5 2045± 26 2046± 109± 26 0.347 0.347 1.21 1.21± 0.02
Table 6.3: Generated and fitted values for Nu, the efficiencies product εuselε
ukin and εsll εslt
εul εu
tin the MX
analysis.
Run Period gen. Ru/sl Ru/sl (truth-matching) Ru/sl
Run1-2 215× 10−4 (215± 23± 17)× 10−4 (220± 23± 21)× 10−4
a Run3 215× 10−4 (214± 37± 18)× 10−4 (223± 39± 34)× 10−4
Run4 215× 10−4 (215± 22± 17)× 10−4 (220± 22± 20)× 10−4
Run5 215× 10−4 (215± 20± 16)× 10−4 (221± 21± 19)× 10−4
Run1-5 215× 10−4 (214± 12± 9)× 10−4 (219± 12± 11)× 10−4
Table 6.4: Generated and fitted values for Ru/sl in the P+ analysis. The first fitted value is obtained withthe truth-matching based approach, the second with the approach based on fits to all data and MonteCarlo mES distributions.
122
/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
fitt
ed/S
tru
thm
atch
edS
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
= 0.28842χRun 4 charged
/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
fitt
ed/S
tru
thm
atch
edS
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
= 0.39972χRun 4 neutrals Same Sign
/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
fitt
ed/S
tru
thm
atch
edS
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
= 0.83862χRun 4 neutrals Opposite Sign
Figure 6.4: Left: Stm/Sfit in MX bins for Run4 B± (right), unmixed B0 (left), mixed B0 (bottom).
Run Period gen. Nu Nu gen. εuselε
ukin εu
selεukin gen. εsll εslt
εul εu
t
εsll εslt
εul εu
t
Run1-2 477± 13 476± 52± 13 0.367 0.367 1.14 1.14± 0.05Run3 180± 7 179± 31± 7 0.391 0.391 1.10 1.10± 0.08Run4 582± 14 590± 59± 14 0.345 0.345 1.15 1.15± 0.04Run5 680± 15 679± 64± 15 0.328 0.328 1.13 1.13± 0.04
Run1-5 1920± 26 1919± 106± 26 0.348 0.348 1.15 1.14± 0.02
Table 6.5: Generated and fitted values for Nu, the efficiencies product εuselε
ukin and εsll εslt
εul εu
tin the P+ analysis.
Run Period gen. Ru/sl Ru/sl (truth-matching) Ru/sl
Run1-2 215× 10−4 (211± 31± 23)× 10−4 (216± 30± 27)× 10−4
Run3 215× 10−4 (213± 49± 37)× 10−4 (210± 47± 42)× 10−4
Run4 215× 10−4 (208± 27± 20)× 10−4 (225± 28± 26)× 10−4
Run5 215× 10−4 (224± 26± 20)× 10−4 (220± 27± 24)× 10−4
Run1-5 215× 10−4 (214± 23± 12)× 10−4 (222± 16± 14)× 10−4
Table 6.6: Generated and fitted values for Ru/sl in the (MX , q2) analysis. The first fitted value is obtainedwith the truth-matching based approach, the second with the approach based on fits to all data and MonteCarlo mES distributions.
123
/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
fitt
ed/S
tru
thm
atch
edS
0.6
0.7
0.8
0.9
1
1.1
= 0.83742χRun 5 charged
/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
fitt
ed/S
tru
thm
atch
edS
0.4
0.6
0.8
1
1.2
1.4
1.6
= 0.46842χRun 5 neutrals Same Sign
/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
fitt
ed/S
tru
thm
atch
edS
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
= 0.41132χRun 5 neutrals Opposite Sign
Figure 6.5: Left: Stm/Sfit in MX bins for Run5 B± (right), unmixed B0 (left), mixed B0 (bottom).
Run Period gen. Nu Nu gen. εuselε
ukin εu
selεukin gen. εsll εslt
εul εu
t
εsll εslt
εul εu
t
Run1-2 362± 11 357± 52± 11 0.390 0.390 1.16 1.16± 0.05Run3 131± 6 129± 30± 6 0.373 0.372 1.19 1.19± 0.09Run4 469± 13 453± 160± 13 0.387 0.388 1.17 1.17± 0.04Run5 517± 13 539± 63± 13 0.355 0.355 1.13 1.13± 0.04
Run1-5 1479± 22 1467± 106± 22 0.375 0.374 1.15 1.15± 0.02
Table 6.7: Generated and fitted values for Nu, the efficiencies product εuselε
ukin and εsll εslt
εul εu
tin the (MX , q2)
analysis.
124
in Tables 6.10 and 6.11, and Figures 6.8 and 6.9.
The value for ∆Ru/sl obtained by using the full Run1-Run5 dataset and
MX < 1.55 GeV/c2 is
∆Ru/sl(MX < 1.55 GeV/c2) = (109± 8± 4± 10)× 10−4 (6.11)
where the first error is statistical, the second is due to Monte Carlo statistics and the
third is systematic.
Using the above result and the measurement of the inclusive semileptonic branching
fraction (Eq. 6.8), the partial branching fraction for charmless semileptonic B decays is
measured to be
∆B(B → Xu`ν,MX < 1.55 GeV/c2) = (1.18± 0.09stat. ± 0.07sys. ± 0.01SF)× 10−3
(6.12)
where the first error is statistical, the second systematic and the third is due to the
uncertainties of the shape function parameters.
Systematic uncertainties will be discussed in Chapter 7.
6.4 One Dimensional P+ Fit and Results
The P+ data distribution, obtained by following the procedure outlined in Section 6.1, is
fitted by using the two mES fit approaches outlined in Section 5.3.4 and Nu and BGu, as
defined by Eq. 6.7, are determined.
Reference [32] suggests that the region defined by P+ < 0.66 GeV/c2 is optimal for a
reliable calculation of the theoretical phase space acceptance.
Fits to the P+ distribution have been performed for different run periods, and on the
full data sample. Results are shown in Table 6.12 and in Figure 6.10 for the mES fit
approach without peaking background subtraction, and in Table 6.13 and in Figure 6.11
for the algorithm based on truth-matching.
The value for ∆Ru/sl obtained by using the full dataset is
∆Ru/sl(P+ < 0.66 GeV/c2) = (88± 9± 4± 10)× 10−4 (6.13)
125
Parameters Run1-Run2 Run3 Run4 Run5 Run1-Run5Nsl 43031± 574 17544± 344 53097± 393 66458± 520 181074± 706
BGsl 2659± 35 1296± 25 3708± 27 4376± 34 12187± 48Nsl −BGsl 40372± 538 16249± 319 49389± 366 62082± 486 168888± 659
N inu 214± 29 105± 19 205± 32 282± 36 803± 60
Noutu 5± 1 2± 0 7± 1 11± 2 27± 2
Nbkg 208± 9 79± 6 276± 11 362± 14 923± 21εusel 0.409 0.437 0.403 0.376 0.397
εukin 0.858 0.846 0.826 0.827 0.834
(εut εu
` )/(εslt εsl
` ) 1.29± 0.06 1.29± 0.10 1.31± 0.04 1.31± 0.06 1.31± 0.03∆Ru/sl(10−4) 117± 16± 7 135± 24± 11 96± 15± 7 112± 14± 6 110± 8± 4
Table 6.8: Summary of the fit to the MX distribution and results for MX < 1.55 GeV/c2 for the fullsample and for various subsamples. The approach fully based on mES fits without any attempt tosubtract peaking backgrounds has been used. N in
u is the number of signal events in the signal region(MX < 1.55 GeV/c2). The first error on ∆Ru/sl(MX < 1.55 GeV/c2) is statistical, the second is due toMonte Carlo statistics. The non-resonant component in the Monte Carlo has been reweighted accordingto the shape function parameters from the HFAG combination using B → Xc`ν and B → Xsγ decays asdescribed in Section 4.2.5.
Parameters Run1-Run2 Run3 Run4 Run5 Run1-Run5Nsl 37577± 512 15196± 293 46058± 340 57332± 442 156252± 603
BGsl 2221± 30 1056± 20 3210± 24 3849± 30 10352± 40Nsl −BGsl 35355± 481 14141± 273 42848± 316 53483± 412 145900± 563
N inu 194± 26 94± 17 187± 30 254± 32 724± 54
Noutu 5± 1 2± 0 6± 1 9± 1 24± 2
Nbkg 194± 8 73± 5 262± 10 322± 12 850± 18εusel 0.423 0.442 0.423 0.390 0.412
εukin 0.871 0.868 0.837 0.852 0.853
(εut εu
` )/(εslt εsl
` ) 1.31± 0.05 1.27± 0.08 1.32± 0.05 1.30± 0.04 1.31± 0.03∆Ru/sl(10−4) 114± 15± 6 137± 25± 9 94± 15± 5 110± 14± 5 108± 8± 3
Table 6.9: Summary of the fit to the MX distribution and results for MX < 1.55 GeV/c2 for the fullsample and for various subsamples. The mES fit approach based on Monte Carlo truth-matching wasused. N in
u is the number of signal events in the signal region (MX < 1.55 GeV/c2). The first error on∆Ru/sl(MX < 1.55 GeV/c2) is statistical, the second is due to Monte Carlo statistics. The non-resonantcomponent in the Monte Carlo has been reweighted according to the shape function parameters from theHFAG combination using B → Xc`ν and B → Xsγ decays as described in Section 4.2.5.
126
(GeV)xM
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
500
1000
1500
2000
2500
3000
3500
INν ul→b + othν cl→b OUTν ul→b
data
(GeV)xM
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
200
400
600
800
scaled MC
data subtr.
Figure 6.6: One-dimensional MX < 1.55 GeV/c2 analysis: 2-parameter χ2 fit to the MX distributionfor Run1-Run5 data The approach fully based on mES fits without any attempt to subtract peakingbackgrounds has been used. Left: Points are data, the blue, magenta and yellow histograms representrespectively the fitted contributions from b → u`ν events with true MX < 1.55 GeV/c2, the rest of theb → u`ν events, and background events. The signal box is defined by MX < 1.55 GeV/c2. Right: MX
distribution subtracted of the backgrounds. χ2 per degree of freedom = 17.6/8.
(GeV)xM
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
500
1000
1500
2000
2500
3000
INν ul→b + othν cl→b OUTν ul→b
data
(GeV)xM
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
200
400
600
800
scaled MC
data subtr.
Figure 6.7: One-dimensional MX < 1.55 GeV/c2 analysis: 2-parameter χ2 fit to the MX distribution forRun1-Run5 data. The mES fit approach based on Monte Carlo truth-matching was used. Left: Pointsare data, the blue, magenta and yellow histograms represent respectively the fitted contributions fromb → u`ν events with true MX < 1.55 GeV/c2, the rest of the b → u`ν events, and background events.The signal box is defined by MX < 1.55 GeV/c2. Right: MX distribution subtracted of the backgrounds.χ2 per degree of freedom = 12.8/8.
127
Parameters Run1-Run2 Run3 Run4 Run5 Run1-Run5Nsl 43031± 574 17544± 344 53097± 393 66458± 520 180418± 701
BGsl 2659± 35 1296± 25 3708± 27 4376± 34 11480± 45Nsl −BGsl 40373± 538 16249± 319 49390± 366 62082± 486 168937± 657
N inu 259± 36 132± 24 211± 41 303± 47 914± 76
Noutu 5± 1 4± 1 5± 1 9± 2 25± 2
Nbkg 346± 16 135± 10 480± 19 600± 24 1548± 36εusel 0.396 0.419 0.382 0.358 0.381
εukin 0.869 0.843 0.875 0.869 0.867
(εut εu
` )/(εslt εsl
` ) 1.27± 0.06 1.32± 0.11 1.30± 0.05 1.29± 0.04 1.29± 0.05∆Ru/sl(10−4) 147± 21± 9 174± 31± 15 99± 19± 9 121± 19± 9 128± 11± 5
Table 6.10: Summary of the fit to the MX distribution and results for MX < 1.7 GeV/c2 for the fullsample and for various subsamples. The approach fully based on mES fits without any attempt tosubtract peaking backgrounds has been used. N in
u is the number of signal events in the signal region(MX < 1.7 GeV/c2). The first error on ∆Ru/sl(MX < 1.7 GeV/c2) is statistical, the second is due toMonte Carlo statistics. The non-resonant component in the Monte Carlo has been reweighted accordingto the shape function parameters from the HFAG combination using B → Xc`ν and B → Xsγ decays asdescribed in Section 4.2.5.
Parameters Run1-Run2 Run3 Run4 Run5 Run1-Run5Nsl 37577± 512 15196± 293 46058± 340 57332± 442 156252± 603
BGsl 2221± 30 1056± 20 3210± 24 3849± 30 10352± 40Nsl −BGsl 35355± 481 14141± 273 42848± 316 53483± 412 145900± 563
N inu 236± 33 122± 22 193± 38 265± 42 821± 69
Noutu 6± 1 2± 0 4± 1 7± 1 19± 2
Nbkg 321± 15 125± 9 446± 17 543± 21 1431± 32εusel 0.404 0.429 0.402 0.373 0.394
εukin 0.890 0.861 0.887 0.881 0.883
(εut εu
` )/(εslt εsl
` ) 1.30± 0.06 1.29± 0.09 1.31± 0.05 1.28± 0.04 1.29± 0.03∆Ru/sl(10−4) 144± 20± 8 182± 32± 13 97± 19± 7 117± 19± 7 125± 11± 4
Table 6.11: Summary of the fit to the MX distribution and results for MX < 1.7 GeV/c2 for the fullsample and for various subsamples. The mES fit approach based on Monte Carlo truth-matching wasused. N in
u is the number of signal events in the signal region (MX < 1.7 GeV/c2). The first error on∆Ru/sl(MX < 1.7 GeV/c2) is statistical, the second is due to Monte Carlo statistics. The non-resonantcomponent in the Monte Carlo has been reweighted according to the shape function parameters from theHFAG combination using B → Xc`ν and B → Xsγ decays as described in Section 4.2.5.
128
(GeV)xM
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
500
1000
1500
2000
2500
3000
INν ul→b + othν cl→b OUTν ul→b
data
(GeV)xM
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
200
400
600
800scaled MC
data subtr.
Figure 6.8: One-dimensional MX < 1.7 GeV/c2 analysis: 2-parameter χ2 fit to the MX distributionfor Run1-Run5 data. The approach fully based on mES fits without any attempt to subtract peakingbackgrounds has been used. Left: Points are data, the blue, magenta and yellow histograms representrespectively the fitted contributions from b → u`ν events with true MX < 1.7 GeV/c2, the rest of theb → u`ν events, and background events. The signal box is defined by MX < 1.7 GeV/c2. Right: MX
distribution subtracted of the backgrounds. χ2 per degree of freedom = 17.5/8.
(GeV)xM
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
500
1000
1500
2000
2500
3000
INν ul→b + othν cl→b OUTν ul→b
data
(GeV)xM
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
200
400
600
800scaled MC
data subtr.
Figure 6.9: One-dimensional MX < 1.7 GeV/c2 analysis: 2-parameter χ2 fit to the MX distribution forRun1-Run5 data The mES fit approach based on Monte Carlo truth-matching was used. Left: Pointsare data, the blue, magenta and yellow histograms represent respectively the fitted contributions fromb → u`ν events with true MX < 1.7 GeV/c2, the rest of the b → u`ν events, and background events. Thesignal box is defined by MX < 1.7 GeV/c2. Right: MX distribution subtracted of the backgrounds. χ2
per degree of freedom = 12.6/8.
129
where the first error is statistical, the second is due to Monte Carlo statistics and the
third is systematic.
Using the result of the fit, the partial branching fraction for charmless semileptonic B
decays, in the phase space region P+ < 0.66 GeV/c2, is measured to be
∆B(B → Xu`ν, P+ < 0.66 GeV/c2) = (0.95± 0.10stat. ± 0.08sys. ± 0.01SF)× 10−3
(6.14)
where the measurement of the inclusive semileptonic branching fraction reported in Eq. 6.8
has been used. The first error is statistical, the second is systematic and the third is due
to the uncertainties of the shape function parameters.
6.5 Two Dimensional (MX , q2) Fit and Results
The (MX , q2) two-dimensional distribution for data, obtained by following the procedure
outlined in Section 6.1, is fitted by using the two mES fit approaches outlined in Sec-
tion 5.3.4 and Nu and BGu, as defined by Eq. 6.7, are determined.
Previous studies [59] have shown that the phase space region defined by
MX < 1.7 GeV/c2 and q2 > 8 GeV2/c4 is optimal for a good measurement of the
partial branching ratio.
Fits to the (MX , q2) distribution have been performed for different run periods, and on
the full data sample. Results are shown in Table 6.14 and in Figure 6.12 for the approach
without peaking background subtraction, and in Table 6.15 and in Figure 6.13 for the
algorithm based on truth-matching.
In the signal region defined by MX < 1.7 GeV/c2 and q2 > 8 GeV2/c4, the value for
∆Ru/sl obtained by using the full dataset is
∆Ru/sl(MX < 1.7 GeV/c2, q2 > 8 GeV2/c4) = (75± 7± 3± 10)× 10−4 (6.15)
where the first error is statistical, the second is due to Monte Carlo statistics and the
third is systematic.
Using the result of the fit, the partial branching fraction for charmless semileptonic B
decays, for the phase space region defined by (MX < 1.7 GeV/c2, q2 > 8 GeV2/c4), is
130
Parameters Run1-Run2 Run3 Run4 Run5 Run1-Run5Nsl 43031± 574 17544± 344 53097± 393 66458± 520 181074± 706
BGsl 2659± 35 1296± 25 3708± 27 4376± 34 12187± 48Nsl −BGsl 40373± 538 16249± 319 49389± 366 62082± 486 168887± 659
N inu 212± 30 65± 20 164± 35 194± 38 633± 63
Noutu 13± 2 5± 2 14± 3 13± 3 48± 5
Nbkg 245± 12 115± 8 360± 15 459± 18 1183± 27εusel 0.414 0.428 0.395 0.383 0.399
εukin 0.874 0.879 0.862 0.858 0.865
(εut εu
` )/(εslt εsl
` ) 1.21± 0.06 1.21± 0.10 1.22± 0.06 1.23± 0.05 1.23± 0.03∆Ru/sl(10−4) 120± 17± 7 88± 26± 14 80± 17± 8 77± 15± 7 88± 9± 4
Table 6.12: Summary of the fit to the P+ distribution and results for P+ < 0.66 Gev/c2 for the fullsample and for various subsamples. The approach fully based on mES fits without any attempt tosubtract peaking backgrounds has been used. N in
u is the number of signal events in the signal region(P+ < 0.66 GeV/c2). The first error on ∆Ru/sl(P+ < 0.66 GeV/c2) is statistical, the second is due toMonte Carlo statistics. The non-resonant component in the Monte Carlo has been reweighted accordingto the shape function parameters from the HFAG combination using B → Xc`ν and B → Xsγ decays asdescribed in Section 4.2.5.
Parameters Run1-Run2 Run3 Run4 Run5 Run1-Run5Nsl 37577± 512 15196± 293 46058± 340 57332± 442 156252± 603
BGsl 2221± 30 1056± 20 3210± 24 3849± 30 10352± 40Nsl −BGsl 35355± 481 14141± 273 42848± 316 53483± 412 145900± 563
N inu 193± 28 56± 18 146± 32 170± 34 560± 58
Noutu 13± 2 5± 2 13± 3 12± 3 43± 5
Nbkg 232± 11 109± 7 336± 13 422± 16 1100± 24εusel 0.421 0.446 0.414 0.396 0.412
εukin 0.886 0.882 0.871 0.880 0.879
(εut εu
` )/(εslt εsl
` ) 1.23± 0.05 1.18± 0.08 1.23± 0.04 1.23± 0.04 1.23± 0.02∆Ru/sl(10−4) 118± 17± 6 84± 27± 12 77± 17± 7 74± 15± 6 87± 9± 4
Table 6.13: Summary of the fit to the P+ distribution and results for P+ < 0.66 GeV/c2 for the fullsample and for various subsamples. The mES fit approach based on Monte Carlo truth-matching wasused. N in
u is the number of signal events in the signal region (P+ < 0.66 GeV/c2). The first error on∆Ru/sl(P+ < 0.66 GeV/c2) is statistical, the second is due to Monte Carlo statistics. The non-resonantcomponent in the Monte Carlo has been reweighted according to the shape function parameters from theHFAG combination using B → Xc`ν and B → Xsγ decays as described in Section 4.2.5.
131
(GeV)+P
0 1 2 3 4 5
0
1000
2000
3000
4000
5000
6000 INν ul→b + othν cl→b OUTν ul→b
data
(GeV)+P
0 1 2 3 4 5
0
100
200
300
400
500
600
700
scaled MC
data subtr.
Figure 6.10: One-dimensional P+ analysis: 2-parameter χ2 fit to the P+ distribution for Run1-Run5 data.The approach fully based on mES fits without any attempt to subtract peaking backgrounds has beenused. Left: Points are data, the blue, magenta and yellow histograms represent respectively the fittedcontributions from b → u`ν events with true P+ < 0.66 GeV/c2, the rest of the b → u`ν events, andbackground events. The signal box is defined by P+ < 0.66 GeV/c2. Right: P+ distribution subtractedof the backgrounds. χ2 per degree of freedom = 5.5/5.
(GeV)+P
0 1 2 3 4 5
0
1000
2000
3000
4000
5000
6000
INν ul→b + othν cl→b OUTν ul→b
data
(GeV)+P
0 1 2 3 4 5
0
100
200
300
400
500
600
scaled MC
data subtr.
Figure 6.11: One-dimensional P+ analysis: 2-parameter χ2 fit to the P+ distribution for Run1-Run5data (truth-matching based approach for mES fits). Left: Points are data, the blue, magenta andyellow histograms represent respectively the fitted contributions from b → u`ν events with true P+ <0.66 GeV/c2, the rest of the b → u`ν events, and background events. The signal box is defined byP+ < 0.66 GeV/c2. Right: P+ distribution subtracted of the backgrounds. χ2 per degree of freedom= 6.4/5.
132
measured to be
∆B (B → Xu`ν, MX < 1.7 GeV/c2, q2 > 8 GeV2/c4) =
=(0.81± 0.08stat. ± 0.07sys. ± 0.02SF)× 10−3 (6.16)
where the measurement of the inclusive semileptonic branching fraction reported in
Eq. 6.8 has been used. The first error is statistical, the second is systematical and the
third is due to the uncertainties of the shape function parameters.
133
Parameters Run1-Run2 Run3 Run4 Run5 Run1-Run5Nsl 43031± 574 17544± 344 53097± 393 66458± 520 181074± 706
BGsl 2658± 35 1295± 25 3708± 27 4376± 34 12185± 48Nsl −BGsl 40373± 538 16249± 319 49390± 366 62083± 486 168889± 659
N inu 165± 26 82± 16 125± 30 189± 33 562± 55
Noutu 10± 1 2± 0 7± 1 11± 1 32± 2
Nbkg 181± 4 70± 3 239± 5 299± 6 789± 9εusel 0.415 0.415 0.399 0.377 0.400
εukin 0.869 0.858 0.871 0.913 0.881
(εut εu
` )/(εslt εsl
` ) 1.24± 0.05 1.32± 0.16 1.27± 0.06 1.25± 0.05 1.26± 0.04∆Ru/sl(10−4) 91± 14± 6 107± 20± 10 57± 13± 6 71± 12± 5 75± 7± 3
Table 6.14: Summary of the fit to the (MX , q2) distributions and results for MX < 1.7 GeV/c2 andq2 > 8 GeV2/c4 for the full sample and for various subsamples. The approach fully based on mES
fits without any attempt to subtract peaking backgrounds has been used. N inu is the number of signal
events in the signal region (MX < 1.7 GeV/c2, q2 > 8 GeV2/c4). The first error on ∆Ru/sl(MX <1.7 GeV/c2, q2 > 8GeV2/c4) is statistical, the second is due to Monte Carlo statistics. The non-resonantcomponent in the Monte Carlo has been reweighted according to the shape function parameters from theHFAG combination using B → Xc`ν and B → Xsγ decays as described in Section 4.2.5.
Parameters Run1-Run2 Run3 Run4 Run5 Run1-Run5Nsl 37577± 512 15196± 293 46058± 340 57332± 442 156252± 603
BGsl 2221± 30 1056± 20 3210± 24 3849± 30 10352± 40Nsl −BGsl 35355± 481 14141± 273 42848± 316 53483± 412 145900± 563
N inu 157± 24 75± 15 111± 27 176± 29 516± 50
Noutu 9± 1 1± 0 6± 1 10± 1 28± 2
Nbkg 161± 4 64± 2 225± 4 260± 5 711± 8εusel 0.423 0.439 0.427 0.400 0.417
εukin 0.874 0.829 0.889 0.916 0.891
(εut εu
` )/(εslt εsl
` ) 1.27± 0.05 1.27± 0.09 1.27± 0.05 1.23± 0.04 1.25± 0.03∆Ru/sl(10−4) 95± 14± 5 115± 22± 9 54± 13± 4 73± 11± 4 76± 7± 3
Table 6.15: Summary of the fit to the (MX , q2) distributions and results for MX < 1.7 GeV/c2 and q2 >8 GeV2/c4 for the full sample and for various subsamples. The mES fit approach based on Monte Carlotruth-matching was used. N in
u is the number of signal events in the signal region (MX < 1.7 GeV/c2,q2 > 8 GeV2/c4). The first error on ∆Ru/sl(MX < 1.7 GeV/c2, q2 > 8 GeV2/c4) is statistical, the secondis due to Monte Carlo statistics. The non-resonant component in the Monte Carlo has been reweightedaccording to the shape function parameters from the HFAG combination using B → Xc`ν and B → Xsγdecays as described in Section 4.2.5.
134
)2 (
GeV
2 q
05
1015
2025
050100
150
200
250
300
350
400
450
< 1
.70
X0.
00 <
M INν
ul
→b
+ot
hν
cl
→b
OU
Tν
ul
→b da
ta
)2 (
GeV
2 q
05
1015
2025
0
200
400
600
800
< 2
.20
X1.
70 <
M INν
ul
→b
+ot
hν
cl
→b
OU
Tν
ul
→b da
ta
)2 (
GeV
2 q
05
1015
2025
0
100
200
300
400
500
600
< 2
.80
X2.
20 <
M INν
ul
→b
+ot
hν
cl
→b
OU
Tν
ul
→b da
ta
)2 (
GeV
2 q
05
1015
2025
050100
150
200
250
300
350
< 5
.00
X2.
80 <
M INν
ul
→b
+ot
hν
cl
→b
OU
Tν
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→b da
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Fig
ure
6.12
:T
wo-
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ensi
onal
(MX
,q2)
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ysis
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ES
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wit
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akin
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ckgr
ound
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nts
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enta
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ons
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ith
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135
) 2 (G
eV2
q
05
1015
2025
0 50
100
150
200
250
300
350
400
< 1.70
X0.00 <
M IN
ν ul
→b
+oth
ν cl
→b
OU
Tν
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b data
) 2 (G
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05
1015
2025
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200
400
600
800
< 2.20
X1.70 <
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→b
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→b
OU
Tν
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) 2 (G
eV2
q
05
1015
2025
0
100
200
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400
500 <
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100
150
200
250
300
350
< 5.00
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ν ul
→b
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Tν
ul→
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Figure
6.13:T
wo-dim
ensional(M
X,q
2)analysis:
2-parameter
χ2
fitto
the(M
X,q
2)distribution
forR
un1-Run5
data(tru
th-m
atchin
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Sfits).
Points
aredata,the
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histograms
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contributionsfrom
b→u`ν
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ithtrue
MX
<1.7
GeV
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q2
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2/c4,
therest
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The
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X<
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2/c4.
χ2
perdegree
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=40.2/29.
136
Chapter 7
Systematic Uncertainties
Theoretical uncertainties appearing when extrapolating measurements of partial branch-
ing fraction for charmless semileptonic decays to the full phase space are taken from theory
papers, and shown in the next chapter. The other systematic uncertainties are extremely
similar to the one described in previous BABAR inclusive semileptonic branching fraction
measurements [57, 60, 61]. Since a ratio of branching fractions is measured, most of them
cancel. The sources of systematic uncertainties on the (partial) ratio of branching fraction
are summarized in Tables 7.5 and 7.6, and can be divided into categories, as described
below.
7.1 Detector-related Effects
7.1.1 Charged Particle Tracking
Any difference between data and Monte Carlo simulation can potentially lead to a distor-
tion in the distribution of the kinematical variables under study, as well as in the efficiency
calculations.
The tracking efficiencies are well reproduced by the Monte Carlo simulations and, as
shown in Figure 5.19, the charged track spectrum is in good agreement between data
and Monte Carlo. A similar agreement has been obtained on other control samples. For
high momentum tracks, e+e− → τ+τ− events, where one τ decaying leptonically and the
other to three charged hadrons (plus an arbitrary number of neutrals), are used. They
are a good control sample for this purpose because the e+e− → τ+τ− cross section is
137
0.94 nb and the branching fraction to ` + 3 hadrons is 11% so this sample allows high
statistics tests. Moreover, the momentum distribution of tracks from τ decays is similar
to the one from B decays. Data and Monte Carlo efficiencies are in good agreement
within the statistical errors. To assign a systematic uncertainty on the charged particle
tracking, a common prescription within BABAR measurements has been followed and no
correction has been applied to Monte Carlo tracks, but a systematic uncertainty per track
has been assigned depending on the run period. The Monte Carlo has been reweighted by
randomly eliminating tracks with probabilities detailed in Table 7.1, and the difference
observed with respect to the default measurements is taken as the systematic uncertainty.
Run period syst. uncertainty (%)Run 1 0.44Run 2 0.32Run 3 0.18Run 4 0.54Run 5 0.65
Table 7.1: Systematic uncertainty per track used in the calculation of tracking systematic uncertainties,divided by run period.
7.1.2 Neutral Reconstruction
Differences between data and Monte Carlo simulation in the photon detection efficiency
and resolution, as well as additional energy depositions in the EMC, can impact the dis-
tributions of the kinematic variables used in this analysis.
Two different control samples are used to check for disagreements between data and
Monte Carlo simulation in efficiency and energy resolution. The study is performed using
the τ hadronic decays that represent an abundant source of neutral pions. The τ → eνν
decay is identified in e+e− → τ+τ− events. The ratio R = N(τ → h±π0 ντ )/N(τ →h±π0 π0 ντ ) is computed both for data and Monte Carlo as a function of the π0 energy in
order to evaluate possible differences in efficiency. The agreement has been found to be
good and the ratio is compatible with the unity in the full range. A systematic uncertainty
of 1.8% per photon is assigned, due to uncertainties in the hadronic interactions in the
EMC, to the photon background being not perfectly modeled in the Monte Carlo, and to
138
the uncertainty in the τ branching fractions in πντ and ρντ final states. The corresponding
systematic uncertainty is about 0.1% for all analyses.
The resolution has been studied taking π0s from both τ → h±π0 ντ and τ → h±π0 π0 ντ
decays. The π0 mass is fitted in energy bins and the resolution (corresponding to the σ
of a Gaussian fit) is then compared between data and Monte Carlo. The Monte Carlo
resolution is changed by applying a smearing factor such to be identical to data. Similar
corrections are applied on Monte Carlo to take into account differences in the energy scale
and effects due to energy deposits close to crystal boundaries and to the edges between
the barrel and the endcap of the EMC. These factors are determined as well with control
samples such as µµγ and B → K∗(K+π−)γ decays. All corrections turn out to be small.
The systematic uncertainty due to the reconstruction of neutral particles has been ob-
tained by repeating the analysis without applying the corrections and taking the difference
with respect to the default measurements.
7.1.3 KL Reconstruction
Systematic uncertainties in the simulation of KL interactions have been estimated accord-
ing to the results shown in [62]. Several corrections are applied on the Monte Carlo in
order to reproduce data. The energy deposition of calorimeter clusters truth-matched to a
KL are corrected by ad-hoc factors. The KL detection efficiency is corrected by rejecting
neutral clusters truth-matched to a KL with a probability, which is a function of the true
KL momentum.
A correction due to the differences between data and simulation for the KL production
rate is also applied, based on studies detailed in [63]. Given that such a correction can
not be accomplished by eliminating neutral clusters, a different approach, also described
in [64], has been employed. Clusters truth-matched to KL’s are randomly transformed
into “pseudo-photons” and in this way the energy and momentum balance in the event
are restored. This is achieved by rescaling the measured energy and momentum of the KL
cluster to the true KL momentum, assuming zero mass. The probability of the correction
depends on the KL momentum: 22% for momenta between 0 and 0.4 GeV/c, 1% for
momenta between 0.4 and 1.4 GeV/c, 9% for momenta larger than 1.4 GeV/c.
139
The systematic uncertainty due toKL reconstruction has been determined by repeating
the measurements without applying the above corrections in the Monte Carlo, and taking
the difference with respect to the default measurements.
7.1.4 Lepton Identification
The systematic uncertainties related to lepton identification efficiencies and misidentifi-
cation probabilities are derived from control samples. For electron efficiency, radiative
Bhabha events are used. For pions, samples of K0S → π+π− and three-prong τ decays
are used. A control sample of kaons is obtained by selecting D ∗+ → D 0π+, D 0 → Kπ
decays, where only kinematic information is used to identify the kaon. Muons with a mo-
mentum spectrum covering the range of interest are extracted from the e+e− → µ+µ−γ
and e+e− → e+e−µ+µ− channels.
The statistical and systematic errors from the data-Monte Carlo comparison in bins
of momentum and polar angle are used to compute the systematic uncertainties due
to particle identification. Each bin is shifted by ±2% for efficiency and by ±15% for
misidentification and the analysis is repeated. The difference in the results is taken
as the systematic uncertainty. The effect of the time dependence (especially in muon
identification) has been investigated by using efficiency corrections depending on run
periods.
7.1.5 Charged Kaon Identification
The systematic uncertainty associated with kaon identification efficiency and misidenti-
fication probabilities (shown in Figure 3.4) are obtained with the same technique used
for lepton identification. Kaon and pion samples are selected from the D∗+ → D0 π+ ,
D0 → Kπ decay chain. Each bin (as a function of the momentum and polar angle) is
shifted by ±2% for efficiency and by ±15% for misidentification.
7.2 Uncertainties Related to the mES Fits
In the fits to the mES distributions, some parameters of the signal function (α, n, σR1, r)
are kept fixed to values determined from high-statistics data sample or simulation. The
140
systematic uncertainty due to the choice of these parameters has been determined by
varying their values within the statistical errors. The small bias introduced in the mES
fitting approach, where the peaking background is not taken into account, is corrected for
and an error of 100% on this bias is assumed as systematic uncertainty.
7.3 Signal Knowledge
Our limited knowledge of the shape function parameters determined from other measure-
ments affects the experimental efficiencies (εsel, εkin). The corresponding uncertainty on
the measurement of partial branching fractions is expected to be small. This uncertainty
is estimated by varying the heavy quark parameter along the ellipse in the (mb,µ2π) plane
corresponding to ∆χ2 = 1 (Figure 7.1 and Table 7.2) and taking the maximum positive
and negative fit deviations from the central point.
/ GeVbm4.6 4.62 4.64 4.66 4.68 4.7 4.72 4.74
2 /
GeV
2 πµ
0.35
0.4
0.45
0.5
0.55
0.6
Figure 7.1: ∆χ2 = 1 contour plot in the (mb, µ2π) plane in the Kagan-Neubert Scheme [11]. The points
around the ellipse are the values used in the evaluation of systematic uncertainties (see also Tab. 7.2).
Systematic effects due to the form of the shape function have been studied by using
alternative parametrization, such as a Gaussian (Eq. 7.1) and a Roman form (Eq.7.2),
shown in Figure 7.2, both of them satisfying the same moments constraints as the original
form of Eq. 4.4.
F (k+; c) = N(1− k+/Λ)ce−b(1−k+/Λ)2 , b =
(Γ
(c+ 2
2
)/Γ
(c+ 1
2
))2
(7.1)
141
Point mb (GeV/c2) µ2π (GeV2/c4)
Central 4.6586 0.49661 4.6184 0.51322 4.6232 0.47533 4.6359 0.44534 4.6591 0.42575 4.6874 0.43786 4.6983 0.46977 4.6978 0.50958 4.6891 0.54359 4.6732 0.570410 4.644 0.580211 4.6253 0.556
Table 7.2: mb and µ2π values for the ∆χ2 = 1 contour plot shown in Fig. 7.1.
Figure 7.2: Left: Functional forms used for the Shape Function. Right: cumulative distribution for eachform.
F (k+; ρ) = Nκ√π
exp
(−1
4
(1
κ
ρ
1− k+/Λ− κ(1− k+/Λ)2
)2), κ =
ρ√πeρ/2K1(ρ/2)
(7.2)
Other effects due to the modeling of charmless semileptonic decays have been evaluated
by varying the branching fractions for the exclusive charmless semileptonic decays within
their known uncertainties (Table 4.4).
Signal Monte Carlo contains events where a gluon splits in an ss pair, resulting in
decays of the heavy Xu states into KK pairs. This happens both in the resonant and
142
the non-resonant contributions. In the hybrid model the fractions of events with gluon
splitting in ss for B+ (B0) are 10.7% (0.1%) for the resonant component and 12.0%
(11.3%) for the non-resonant one. The resonant contribution is almost entirely due to the
f′1 and h
′1 decays that produce only KK pairs. The non-resonant contribution is modeled
using JETSET. The parameter which sets gluon splitting in ss in JETSET is also known
as γs and it is set to γs = 0.30 in Monte Carlo. This parameter has been measured by two
experiments at center of mass energies between 12 and 36 GeV as γs = 0.35 ± 0.05 [65],
γs = 0.27 ± 0.06 [66]. Reference [66] shows how the scaling to lower energies (to 3 GeV,
equivalent to the energies involved in the Xu decays for MX ∼ 1.5 GeV/c2) works fine
compared to [67].
In order to calculate the systematic uncertainty, the fraction of events where a gluon
splits in an ss pair has been varied by ±30%. For non-resonant events this corresponds
to taking as 1σ interval the sum of the intervals from the two experiment.
7.4 Background Knowledge
Exclusive semileptonic branching fractions for B → Xc`ν are known with a certain pre-
cision. Moreover, the individual branching fractions in the Monte Carlo simulations are
known to differ from the current world averages. This difference is corrected by re-
weighting simulated events to match the world averages, shown in Table 7.3. Here D∗∗
refers to either non-resonant or broad D∗∗ states and the corresponding branching frac-
tion is taken as the difference between the total semileptonic rate and the other measured
branching fractions. The systematic uncertainty due to the limited knowledge of the
exclusive semileptonic branching fractions is computed by varying them randomly within
one standard deviation of their world averages, repeating the measurements, iterating the
procedure 100 times, and taking the RMS of the resulting distribution of results.
A similar procedure was followed to estimate the uncertainty, which turns to be negli-
gible, due to the branching ratios of charm mesons (Table 7.4) Uncertainties in the form
factors in the B → D∗`ν decays are also taken into account, by repeating the analyses
after varying the form factors within their experimental error [68].
143
B Decay mode best average (%) Monte Carlo (%)B0 → D−lν 2.13 ±0.14 2.07B0 → D∗−lν 5.53±0.25 5.70B0 → D−
1 lν 0.50±0.08 0.52B0 → D∗−
2 lν 0.39±0.07 0.23B0 → Xclν 10.14±0.38 10.2B+ → D0lν 2.30±0.16 2.24B+ → D∗0lν 5.95 ±0.24 6.17B+ → D0
1lν 0.54±0.06 0.56B+ → D∗0
2 lν 0.42± 0.08 0.30B+ → Xclν 10.92± 0.37 11.04
Table 7.3: Branching fractions for B → Xc`ν decays, current best averages and values used in MonteCarlo simulation, plus shift of the results due to the adjustments of the BR. The non resonant B → D`νXis obtained by difference of the inclusive rate and the other 4 components.
D0 Decay mode PDG MC D+ Decay mode PDG MCD0 → Kπ 0.0380± 0.0070 0.0383 D+ → K0π 0.0294± 0.0012 0.0282D0 → K0π0 0.0228± 0.0024 0.0212 D+ → Kππ 0.0951± 0.0034 0.0920D0 → K0ππ 0.0580± 0.0038 0.0540 D+ → K0ππ0 0.1400± 0.0100 0.1082D0 → Kππ0 0.1410± 0.0050 0.1390 D+ → K0πππ0 0.0550± 0.0270 0.0681D0 → K0π0π0 0.0210± 0.0020 0.0161 D+ → K0πππ 0.0622± 0.0042 0.0716D0 → Kπππ 0.0772± 0.0028 0.0787 D+ → Kππππ 0.0058± 0.0006 0.0075D0 → K0πππ0 0.1060± 0.0120 0.0973 D+ → Kπππ0π0 0.0220± 0.0470 0.0084D0 → Kππ0π0 0.1500± 0.0500 0.1056 D+ → K0ππππ0 0.0540± 0.0300 0.0252D0 → Kππππ0 0.0410± 0.0040 0.0433 D+ → K0πππππ 0.0008± 0.0007 0.0000D0 → ππ 0.00136± 0.00003 0.00150 D+ → Kπππππ0 0.0020± 0.0018 0.0045D0 → π0π0 0.00079± 0.00008 0.0008 D+ → K0K0K 0.0094± 0.0042 0.0100D0 → πππ0 0.0131± 0.0006 0.0159 D+ → ππ0 0.00128± 0.00009 0.0027D0 → ππππ 0.0073± 0.0003 0.0073 D+ → πππ 0.00331± 0.00022 0.0031D0 → πππππ0 0.0041± 0.0005 0.0177 D+ → ππππ0 0.0118± 0.0009 0.0119D0 → ππππππ 0.0004± 0.0001 0.0000 D+ → πππππ 0.00168± 0.00017 0.00210
D+ → ππππππ0 0.0029± 0.0029 0.0007
Table 7.4: D branching ratios, current best measurements and values used in the Monte Carlo.
7.5 Summary
Table 7.5 shows the relative uncertainties (in percent) involved in the MX analyses for the
two kinematic cuts under study. In Table 7.6 the relative systematics uncertainties (also in
percent) for the P+ and (MX , q2) analyses are reported. Statistical errors are slightly larger
than the total systematic uncertainties for all analyses. Systematic uncertainties due to
detector, fit procedure and signal knowledge contribute roughly equally. The approach
to mES fits based on truth-matching seems slightly better than the other one. However
144
Source σ(∆B(B → Xu`ν)) σ(∆B(B → Xu`ν))MX < 1.55 GeV/c2 MX < 1.7 GeV/c2
truth-matching fit all truth-matching fit allStatistical error 7.41 7.27 8.59 8.80Monte-Carlo statistics 2.74 3.22 3.23 3.85Tracking efficiency 0.75 0.71 0.56 0.65Neutral efficiency 1.85 1.42 2.76 2.21PID eff. & misID 1.16 0.86 1.95 1.84KL 0.53 0.51 0.72 0.69
Fit-related:mES fit parameters 2.68 2.99 3.59 4.16peaking background 2.20 2.20
Signal knowledge:SF parameters +0.95
−1.15+0.71−1.01
+2.27−1.77
+1.86−1.67
SF form 0.66 0.56 0.70 0.97Exclusive b → u`ν 2.12 2.08 1.79 1.82Gluon splitting 1.49 1.62 2.04 2.43
Background knowledge:KS veto 0.40 0.44 0.84 0.77B SL branching ratio 0.81 0.87 2.07 1.76D decays 0.38 0.44 0.35 0.41B → D∗ `ν from factor 0.30 0.21 0.31 0.27Total systematics: +5.85
−5.89+6.05−6.09
+7.66−7.52
+7.98−7.94
Total error: +9.54−9.56
+9.63−9.65
+11.43−11.34
+11.59−11.56
Table 7.5: Relative uncertainties in percent for the MX < 1.55 GeV/c2 and the MX < 1.7 GeV/c2
analyses, for the two approaches to the mES fits.
it should be kept in mind that the systematic uncertainties for the former approach are
underestimated, as mentioned in Section 5.3.4. The best measurement in terms of overall
uncertainty is the one in the phase space region defined by MX < 1.55 GeV/c2.
145
Source σ(∆B(B → Xu`ν)) σ(∆B(B → Xu`ν))P+ < 0.66 GeV/c2 MX < 1.7 GeV/c2, q2 > 8 GeV2/c4
truth-matching fit all truth-matching fit allStatistical error 10.34 10.11 9.72 9.72Monte-Carlo statistics 4.08 4.62 3.44 4.29
Detector-related:Tracking efficiency 0.40 0.49 1.32 1.07Neutral efficiency 2.99 2.88 2.90 2.45PID eff. & misID 1.45 1.52 2.84 2.51KL 0.77 0.61 0.85 1.02
Fit-related:mES fit parameters 3.32 3.55 1.86 4.14peaking background 1.80 3.10
Signal knowledge:SF parameters +0.60
−1.16+0.42−1.25
+2.83−1.71
+1.65−2.26
SF form 1.30 1.25 1.37 1.78Exclusive b → u`ν 2.27 2.22 1.94 2.71Gluon splitting 1.23 1.47 0.87 1.02
Background knowledge:KS veto 1.73 1.34 0.40 0.40B SL branching ratio 2.93 2.80 1.41 1.17D decays 0.70 0.73 0.79 0.79B → D∗ `ν from factor 0.40 0.39 0.55 0.55Total systematics: +7.90
−7.97+8.34−8.42
+7.83−7.50
+8.74−8.88
Total error: +13.02−13.06
+13.03−13.08
+12.42−12.21
+13.13−13.22
Table 7.6: Relative uncertainties in percent for the P+ and the (MX , q2) analyses, for the two approachesto the mES fits.
146
Chapter 8
Measurement of |Vub|
The partial branching fractions ∆B(B → Xu`ν) determined in Chapter 7 are translated
into |Vub| values by means of theoretical calculations. These calculations use heavy quark
input parameters which are extracted from data.
8.1 Input Parameters
Moment measurements from B → Xsγ and B → Xc`ν transitions are used in or-
der to extract the non–perturbative input parameters needed to compute |Vub| from
∆B(B → Xu`ν). Different choices are possible. The values of |Vub| quoted in the fol-
lowing correspond to the set of input parameters obtained by fitting simultaneously both
B → Xsγ and B → Xc`ν moments [11].
The values of the input parameters extracted for the different theoretical calculations
are shown in Table 8.1.
BLL BLNP DGEmb(1S) mb(SF ) µ2
π(SF ) mb(MS)B → Xsγ and B → Xc`ν moments 4.73 4.60± 0.04 0.20± 0.04 4.20± 0.04
Table 8.1: Non–perturbative parameters as computed for BLL, BLNP and DGE theoretical schemes.
The fit to the B → Xsγ and B → Xc`ν moments was performed by Flacher and
Buchmuller [11] in the kinetic scheme and then translated to other schemes, except the
1S scheme, for which the result in the MS scheme was converted by using the expres-
sions in Ref. [69].
147
8.2 |Vub| Extraction
The measured values of ∆Ru/sl are converted in ∆B(B → Xu`ν), and finally |Vub| is
determined.
As there is no agreement on the theoretical calculation to be used to determine |Vub|,all currently available computations have been tried, similarly to what is done by the
HFAG [54]. The theoretical uncertainties have been computed as suggested by theory
papers.
In the BLL approach, see [38], the relation between ∆B(B → Xu`ν) and |Vub| is given
by:
|Vub| =√
192π3
τBG2Fm
5b
∆B(B → Xu`ν)
G(8.1)
where τB is the B hadron lifetime from 2007 update of the PDG [70], averaged between
charged and neutral mesons, and G is the ratio of the decay width between the phase
space we are using and all the phase space.
The value of G in Ref. [71], obtained with mb(1S) = 4.70 GeV, is 1.21 × G =
0.324 ± 0.048. The 15% error on G, resulting in a 7% error on |Vub|, is the sum in
quadrature of uncertainties due to: residual shape function effects (6%), higher order
terms in the αs perturbative expansion (6%), a 50 MeV/c2 uncertainty on the b quark
mass (9%), and O(Λ3QCD/m
3) terms in the OPE expansion (8%). The latter two sources
dominate, contributing almost 10% each to the uncertainty on G. To compute G for a
given b quark mass and given (MX , q2) cuts, a linear interpolation [72] is used to rescale
the value for G as computed by BLL [71] for (MX , q2)=(1.7-8.0) to the b quark mass
measured in the 1S scheme (see Table 8.1 for the b-quark mass values). The values
obtained for mb(1S) = 4.73 GeV and mb(1S) = 4.69 GeV, as presented in Table 8.1, are
1.21×G = 0.341± 0.050 and 1.21×G = 0.318± 0.047, respectively.
BLNP give results and uncertainties in terms of the reduced decay rate Γthy, defined
in units of |Vub|2 ps−1:
Γthy =∆Γthy
|Vub|2 (8.2)
where ∆Γthy is the partial width of the B → Xu`ν decay into the phase space of
148
interest predicted by the theory.
|Vub| is given by
|Vub| =√
∆B(B → Xu`ν)
Γthy · τB(8.3)
where τB is the B meson lifetime. The reduce decay rate Γthy is computed by a Math-
ematica notebook, given to BABAR by the authors of BLNP. The value of Γthy depends
on the analyzed phase space. The corresponding values of Γthy for the current analyses
are shown on Table 8.2 with the corresponding error due to the SF parameters (SF ), the
error due to the sub–leading shape functions (ssf), the choice of the intermediate scale
(scale), and finally the error contribution due to the Weak Annihilation (WA).
Γ%(MX , q2) 24.4± 2.0SF ± 0.4ssf ± 2.1scale ± 1.3WA
MX ≤ 1.55 GeV/c2 40.7± 4.3SF ± 1.0ssf ± 2.9scale ± 1.3WA
MX ≤ 1.70 GeV/c2 47.4± 4.3SF ± 0.6ssf ± 3.3scale ± 1.3WA
P+ 39.7± 4.7SF ± 1.2ssf ± 2.5scale ± 1.3WA
Table 8.2: Values of Γ, from the BLNP method, used in the analyses.
Finally, the partial branching fraction can be translated to |Vub| using the DGE calcu-
lation (see Ref. [35]). DGE stands for Dressed Gluon Exponentiation and is a recent new
addition to the phenomenology landscape of inclusive B meson decays. In this framework,
the on-shell b quark calculation, converted into hadronic variables, can be directly used
as an approximation to the meson decay spectrum, without need of a leading-power non–
perturbative function i.e. no shape function. The on-shell mass of the b quark within the
B meson is required as an input (mb). |Vub| is given by
|Vub| =√
∆B(B → Xu`ν)
R · ω · τB (8.4)
where ω is the B → Xu`ν total rate, as computed by DGE [35], and R is the fraction of
phase space selected by the kinematic cuts.
Theoretical uncertainties are assessed by varying the inputs of: mb (in the minimal
subtraction scheme), and the strong coupling constant (αs), the number of light fermion
flavours (NF ), and the method and scale of the matching scheme intrinsic to the approach.
Finally, a contribution to the uncertainties due to weak annihilation, so far missing in
149
DGE, has been added similarly to what has been done for BLNP [73]. See Table 8.3 for
details for the values of R and its error.
R
(MX , q2) 0.3579±1.03mb± 0.20αs ± 1.41NF ± 1.91scale ± 0.90WA
MX ≤ 1.55 GeV/c2 0.5369±4.21mb± 0.04αs ± 2.74NF
± 4.01scale ± 0.90WA
MX ≤ 1.70 GeV/c2 0.5667±4.78mb± 0.12αs
± 1.64NF± 2.27scale ± 0.90WA
P+ 0.6367±3.36mb± 0.07αs
± 1.33NF± 3.94scale ± 0.90WA
Table 8.3: Values of R, from the DGE method, used in the analyses with the corresponding errors.
8.2.1 (MX , q2)
Results on |Vub| obtained from the (MX , q2) analysis by using the three above theoretical
calculations are shown in Table 8.4. The result based on BLL is somewhat higher than
the other two. The uncertainty is also larger, due to a more conservative estimate by BLL
of weak annihilation effects, which are dominant at high q2 regions.
|Vub| for the (MX , q2) analysisCalculation |Vub|(10−3)BLL 4.93± 0.24(stat)± 0.20(syst)± 0.36(theo)BLNP 4.57± 0.22(stat)± 0.19(syst)± 0.30(theo)DGE 4.64± 0.23(stat)± 0.19(syst)± 0.25(theo)
Table 8.4: Results on |Vub| from the (MX , q2) analysis obtained with the three theoretical calculationsdescribed in the text.
8.2.2 MX
By construction, the BLL computations make sense only in phase space regions where
shape function effects are small, so they cannot be used for regions defined by pure
MX cuts. Results on |Vub| obtained with BLNP and DGE are shown in Table 8.5. It is
interesting to notice that the results based on DGE are comparable to the ones obtained in
the (MX , q2) analysis, whereas those based on BLNP are somewhat lower. The theoretical
uncertainty on the measurement with MX ≤ 1.55 GeV/c2 is higher than the one based
on MX ≤ 1.70 GeV/c2, since the latter is less sensitive to shape function effects.
150
|Vub| for the MX analysisCalculation |Vub|(10−3)BLNP (MX ≤ 1.55 GeV/c2) 4.27± 0.16(stat)± 0.13(syst)± 0.30(theo)BLNP (MX ≤ 1.70 GeV/c2) 4.28± 0.18(stat)± 0.17(syst)± 0.25(theo)DGE (MX ≤ 1.55 GeV/c2) 4.56± 0.17(stat)± 0.14(syst)± 0.32(theo)DGE (MX ≤ 1.70 GeV/c2) 4.53± 0.19(stat)± 0.18(syst)± 0.25(theo)
Table 8.5: Results on |Vub| obtained for the MX analysis with by using the BLNP and DGE calculations.
8.2.3 P+
Again, BLL cannot be applied to determine |Vub| from measurements based on regions
delimited by P+ requirements. Results on |Vub| obtained with BLNP and DGE are shown
in Table 8.6. These results are somewhat lower than the others, and closer to the range
determined with measurements of exclusive charmless semileptonic decays [54].
|Vub| for the P+ analysisComputation |Vub|(10−3)BLNP 3.88± 0.19(stat)± 0.16(syst)± 0.28(theo)DGE 3.99± 0.20(stat)± 0.16(syst)± 0.24(theo)
Table 8.6: Results on |Vub| obtained for the P+ analysis by using the BLNP and DGE calculations.
8.3 Compatibility of the |Vub| Determinations
The different |Vub| determinations obtained so far can be compared and checked for com-
patibility, but also to determine whether the features predicted by the theoretical models
for different phase space regions are observed in the experimental results.
However, the phase space regions considered above are not independent but highly
overlapping. Strong correlations among the different determinations of theoretical ac-
ceptances are also expected. Consequently, the |Vub| measurements are not independent
between each other.
Theoretical correlation have been calculated for the BLNP framework in the following
way. Since the theoretical uncertainties are dominated by the knowledge of the heavy
quark parameters, the correlation coefficients among the acceptances in different phase
space regions have been determined by computing the fractions of b → u events corre-
sponding to the three kinematic signal regions in a grid of 50 points in the (mb, µ2π) plane.
151
The resulting correlation coefficients ρ are displayed in Table 8.7.
Correlation coefficient ρ MX < 1.55 GeV/c2 P+ < 0.66 GeV/c2 MX < 1.7GeV/c2
q2 > 8 GeV2/c4
MX < 1.55 GeV/c2 1 0.98020 0.97253P+ < 0.66 GeV/c2 0.98020 1 0.97474MX < 1.7GeV/c2 0.97253 0.97474 1q2 > 8 GeV2/c4
Table 8.7: Correlation coefficients ρ for the different phase space acceptances in the BLNP model.
Taking the values of Γthy from Table 8.2, the ratio of theoretical acceptances between
two different phase space regions can be computed as
ΓMX
ΓMX ,q2
= 1.67± 0.05 (8.5)
ΓP+
ΓMX
= 0.98± 0.03 (8.6)
ΓP+
ΓMX ,q2
= 1.63± 0.05 (8.7)
The statistical correlation can be computed by rewriting Equation 8.4 as
|Vub| =√
1
Γthy · τBN in
u
Nsl
1
εuselεukin
· εsl` ε
slt
εu` εu`
(8.8)
where N inu comes from the χ2 fit described in Section 6.1. The statistical correlation has
been calculated by taking into account the statistical correlation between the number
of measured b → u transitions, Nmeasu , the number of b → u events migrating into the
signal region N outMCu and the number of background events N bkgMC and propagating the
uncertainties accordingly. A 100% correlation has been assumed for all other systematic
uncertainties.
The ratios of partial branching ratios determined in different phase space regions are
then:
∆B(B → Xu`ν)MX
∆B(B → Xu`ν)MX ,q2
= 1.46± 0.13 (8.9)
∆B(B → Xu`ν)P+
∆B(B → Xu`ν)MX
= 0.81± 0.07 (8.10)
∆B(B → Xu`ν)P+
∆B(B → Xu`ν)MX ,q2
= 1.18± 0.14 (8.11)
152
These experimental ratios are in good agreement with the same measurements performed
by the Belle Collaboration [74]. Due to the lack of information about experimental cor-
relations in the Belle paper, only the central values can be quoted:
∆B(B → Xu`ν)MX
∆B(B → Xu`ν)MX ,q2
= 1.47 [74] (8.12)
∆B(B → Xu`ν)P+
∆B(B → Xu`ν)MX
= 0.89 [74] (8.13)
∆B(B → Xu`ν)P+
∆B(B → Xu`ν)MX ,q2
= 1.31 [74] (8.14)
The double ratios between theoretical acceptances and experimental measurements in
different phase space regions should be compatible with unity within errors. Using BLNP
calculations:
theo
exp
∣∣∣∣MX/MX ,q2
= 1.14± 0.14 (8.15)
theo
exp
∣∣∣∣P+/MX
= 1.21± 0.08 (8.16)
theo
exp
∣∣∣∣P+/MX ,q2
= 1.38± 0.15 (8.17)
The MX and (MX , q2) analyses give therefore compatible results, while there is a dis-
agreement at the order of 2.5σ in the P+ analysis, which is confirmed also by the Belle
results.
8.4 Conclusion
The experimental results presented in this thesis work are used to determine the CKM
matrix element |Vub| by resorting to various theoretical models currently available. While
measurements based on MX and (MX , q2) are compatible with theory calculations, there
is a suggestive hint that results based on P+ are somewhat lower than theory predictions
and closer to |Vub| determinations which use exclusive charmless semileptonic decays.
The measurement shown in this thesis are currently the most precise on this subject and
contribute substantially to increase the precision on |Vub| determination by using inclusive
charmless semileptonic decays.
153
The dominant uncertainty is currently due to theory when extrapolating the experi-
mental measurements in restricted regions of phase space to |Vub|. As an outlook, more
efforts should be done on the theory side to reach consensus on a viable model to be used,
a better assessment of theory uncertainties and their reduction. A systematic program of
measurements in several regions of phase space, on final datasets from the B Factories,
will be extremely helpful to increase confidence in the reduction of the theoretical errors.
154
Bibliography
[1] B. Abuert et al., BABAR Collaboration, [arXiv:0708.3702 [hep-ex]], submitted to PRL.
[2] S.L. Glashow, Nucl. Phys. 22, 579 (1961); S. Weinberg, Phys. Rev. Lett. 19, 1264
(1967); A. Salam, in Proc. 8th Nobel Symp., ed. N. Swartholm, Almquist and Wiksells,
Stockholm (1968).
[3] P.W. Higgs, Phys. Lett. 12, 132 (1964).
[4] N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963).
[5] S.L. Glashow, J. Iliopoulos and L. Maiani, Phys. Rev. D 2, 1285 (1970).
[6] M. Kobayashi and T. Maskawa, Prog. Th. Phys. 49, 652 (1973).
[7] L. Wolfenstein, Phys. Lett. 51, 1945 (1983).
[8] A. J. Buras, M. E. Lautenbacher and G. Ostermaier, Phys. Rev. D 50, 3433 (1994)
[arXiv:hep-ph/9403384].
[9] M. Bona et al., UTfit Collaboration [arXiv:hep-ph/0606167], [http://www.utfit.org].
[10] J. Charles et al., CKMfitter Collaboration, Eur. Phys. J. C 41, 1-131 (2005)
[http://ckmfitter.in2p3.fr].
[11] O. Buchmuller and H. Flacher, Phys. Rev. D 73, 073008 (2006) [arXiv:hep-
ph/0507253].
[12] J. Chay, H. Georgi and B. Grinstein, Phys. Lett. B 247, 399 (1990); M. Voloshin and
M. Shifman, Sov.J.Nucl.Phys. 41, 120 (1985) and Sov.J.Nucl.Phys. 45, 292 (1987).
[13] M. Neubert, Phys. Rev. D 46, 2212 (1992) .
155
[14] T. Mannel Nucl. Phys. B 413, 396 (1994)[arXiv:hep-ph/9308262].
[15] C.W. Bauer, S. Fleming, D. Pirjol and I.W. Stewart, Phys. Rev. D 63, 114020 (2001)
[arXiv:hep-ph/0011336].
[16] C.W. Bauer, D. Pirjol, and I.W. Stewart, Phys. Rev. D 65, 054022 (2002) [arXiv:hep-
ph/0109045].
[17] M. Beneke, A.P. Chapovsky, M. Diehl and T. Feldmann, Nucl. Phys. B 643, 431
(2002) [arXiv:hep-ph/0206152].
[18] R.J. Hill and M. Neubert, Nucl. Phys. B 657, 229 (2003) [arXiv:hep-ph/0211018].
[19] A.V. Manohar and M.B. Wise, Cambridge Monogr. Part. Phys. Nucl. Phys. Cosmol.
10, 1 (2000); I. Bigi, M.A. Shifman and N. Uraltsev, Ann. Rev. Nucl. Part. Sci. 47,
591 (1997) [arXiv:hep-ph/9703290]; Z. Ligeti, eConf C020805 L02 (2002) [arXiv:hep-
ph/0302031].
[20] T. van Ritbergen, Phys. Lett. B 454, 353 (1999) [arXiv:hep-ph/9903226].
[21] M. Neubert, Phys. Rev. D 49, 3392 (1994) [arXiv:hep-ph/9311325]; Phys. Rev. D
49, 4623 (1994).
[22] I. Bigi et al., Int. J. Mod. Phys. A 9, 2467 (1994):
[23] C.W. Bauer, M. Luke and T. Mannel, Phys. Rev. D 68, 094001 (2003).
[24] C.W. Bauer, M. Luke and T. Mannel, Phys. Lett. B 543, 261 (2002).
[25] S.W. Bosch, M. Neubert and G. Paz, JHEP 0411, 073 (2004) [arXiv:hep-
ph/0409115].
[26] A.W. Leibovich, Z. Ligeti and M. Wise Phys. Lett. B 539, 242 (2002) [arXiv:hep-
ph/0205048].
[27] M. Neubert, Phys. Lett. B 543, 269 (2002).
[28] A.K. Leibovich, I. Low and I.Z. Rothstein, Phys. Rev. D 61, 053006 (2000).
156
[29] A.K. Leibovich, I. Low and I.Z. Rothstein, Phys. Lett. B 486, 86 (2000) [arXiv:hep-
ph/0005124].
[30] B.O. Lange, M. Neubert and G. Paz, JHEP 0510, 084 (2005) [arXiv:hep-
ph/0508178].
[31] B.O. Lange, JHEP 0601, 104 (2006) [arXiv:hep-ph/0511098].
[32] S.W. Bosch, B.O. Lange, M. Neubert and G. Paz, Nucl. Phys. B 699, 335 (2004)
[arXiv:hep-ph/0402094].
[33] E. Gardi, JHEP 0404, 049 (2004) [arXiv:hep-ph/0403249].
[34] J.R. Andersen and E. Gardi, JHEP 0506, 030 (2005) [arXiv:hep-ph/0502159].
[35] J.R. Andersen and E. Gardi, JHEP 0601, 097 (2006) [arXiv:hep-ph/0509360].
[36] P. Gambino, P. Giordano, G. Ossola and N. Uraltsev, JHEP 0710, 058 (2007)
[arXiv:0707.2493 [hep-ph]].
[37] P. Gambino, E. Gardi and G. Ridolfi, JHEP 0612, 036 (2006) [arXiv:hep-
ph/0610140].
[38] C.W. Bauer, Z. Ligeti and M. Luke, Phys. Rew. D 64, 113004 (2001) [arXiv:hep-
ph/0107074].
[39] BABAR Technical Design Report, SLAC-R-457 (1995).
[40] B. Abuert et al., (BABAR Collaboration), Nucl. Instrum. Meth., A 479, 1-116 (2002)
[arXiv:hep-ex/0105044].
[41] B. Abuert et al. (BABAR Collaboration), The First Year of the BABAR experiment at
PEP-II, BABAR-CONF-00/17, Contribution to XXXth International Conference on
High Energy Physics, Osaka (Japan) (2000).
[42] D. del Re et al., “Semi-exclusive B reconstruction”, BABAR Analysis document #271.
[43] P. Billior, Nucl. Instr. Meth. A 225, 225 (1984).
157
[44] M.A. Mazur and J. Richman, “Measurement of the exclusive branching fractions
B → D(∗)τν”, BABAR Analysis document #1111.
[45] T. Brandt, “Likelihood Based Electron Identification”, BABAR Analysis Document
#396.
[46] W.-M. Yao et al., (Particle Data Group), J. Phys. G 33, 1 (2006) and 2007 partial
update [http://pdg.lbl.gov/].
[47] H. Albrecth et al., ARGUS Collaboration, Z. Phys. C 48, 543 (1990).
[48] B. Abuert et al., (BABAR Collaboration) Phys. Rev. D 74, 091105 (2006).
[49] N. Isgur and D. Scora, Phys. Rev. D 52, 2783 (1995).
[50] F. De Fazio and M. Neubert, JHEP 9906, 017 (1999).
[51] A.F. Falk and M. Neubert, Phys. Rev. D 47, 2965 (1993) [arXiv:hep-ph/9209268].
[52] A.L Kagan and M. Neubert, Eur. Phys. Jour. C 7, 5 (1999) [arXiv:hep-ph/9805303].
[53] T. Sjœstrand, Comput. Phys. Commun. 82, 74 (1994).
[54] Heavy Flavour Averaging Group, Semileptonic B-decays, Winter 2006 average,
[http://www.slac.stanford.edu/xorg/hfag/semi/winter06/winter06.shtml].
[55] B. Abuert et al. (BABAR Collaboration) Phys. Rev. Lett. 95, 111801 (2005).
[56] D. Fortin et al., “Measurement of |Vub| from semileptonic B decays using the lepton
energy and q2”, BABAR Analysis Document #664.
[57] B. Abuert et al., ”Study of b→ u`ν Decays on the Recoil of Fully Reconstructed B
Mesons with the BaBar Experiment”, BABAR Analysis Document #1255. Submitted
to the XXII Intenational Symposium on Lepton-Photon Interactions at High Energy,
Uppsala, Sweden. [arXiv:hep-ex/0507017].
[58] Crystal Ball Collaboration, DESY F31-86-02.
[59] R. Faccini et al. “Determination of |Vub| with inclusive semileptonic B decays”,
BABAR Analysis Document #540.
158
[60] B. Abuert et al. “Study of b → u`ν Decays on the Recoil of Fully Reconstructed B
Mesons with the BABAR Experiment”, BABAR Analysis Document #976. Submitted
to the 32nd International Conference on High-Energy Phyics, ICHEP 04, Beijing,
China. [arXiv:hep-ph/0408068].
[61] B. Abuert et al., BABAR Collaboration, Phys. Rev. Lett. 92, 071802 (2004)
[arXiv:hep-ph/0307062].
[62] M. Bona et al., “Study of K0L efficiency and reconstruction using data samples”,
BABAR Analysis Document #1191.
[63] H.W. Wulsin and J.C. Dingfelder, “Ks Production Spectra”, BABAR Analysis Docu-
ment #1642.
[64] J.C. Dingfelder et al., “Study of exclusive charmless semileptonic decays B → π`ν
and B → ρ`ν”, BABAR Analysis Document #1520.
[65] M. Althoff et al., TASSO Collaboration, Z. Phys. C 27, 27 (1985).
[66] W. Bartel et al., JADE Collaboration, Z. Phys. C 20, 187 (1983).
[67] V. Luth et al., Phys. Lett. B 70, 120 (1977).
[68] B. Abuert et al., BABAR Collaboration, Phys. Rev. D 77, 032002 (2008)
[arXiv:0705.4008 [hep-ex]].
[69] M. Battaglia, A.J. Buras, P. Gambino, A. Stocchi (eds.) Proceedings of the “The
CKM Matrix and the Unitarity Triangle Workshop on the CKM Matrix and the
Unitarity Triangle CKM02”, CERN Yellow Report CERN-2003-002-corr. [arXiv:hep-
ph/0304132].
[70] Heavy Flavour Averaging Group, Semileptonic B-decays, PDG 2007 average
[http://www.slac.stanford.edu/xorg/hfag/osc/PDG 2007/].
[71] Talk given by Z. Ligeti at Vxb workshop in December 2004 at SLAC.
[72] Z. Ligeti, private communication.
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[73] E. Gardi, private communication.
[74] I. Bizjak et al., Belle Collaboration, Phys. Rev. Lett. 95, 241801 (2005) [arXiv:hep-
ex/0505088].
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