Experimental Heavy Quark Physics
description
Transcript of Experimental Heavy Quark Physics
Experimental Heavy Quark Physics
Fabrizio Bianchi
University of Torino, Italy and INFN - Torino
F. Bianchi XXX Nathiagali Summer College
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Outline
• Lecture 1:• Big Questions in Particle Physics• Goals of Heavy Quark Physics• Tools for Heavy Quark Physics
• Lecture 2:• CP Primer• Observation of Direct CP Violation• Measurement of sin2
• Lecture 3:• Measurement of and • Measurement of |Vcb| and |Vub|
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(0,0) (0,1)
(,)
Vub Vud
Vcd Vcb
*
*
Vtd Vtb
Vcd Vcb
*
*
Measuring
B → B → B →
ubud
tbtdargVV
VV
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The Route to sin(2)Access to from the interference of a b→u decay () with B0B0 mixing ()
d
d
0B
*tbV
tdV
b
b
0Bt
t
*tdV
tbV
** // tdtbtdtb VVVVpq
B0B0 mixing
du
dd0B
ubV
*udV
b u
Tree decay
ubudVVA *
)cos()sin()( tmCtmStA dd
sin
)2sin(1 2
C
CS eff
ii
iii
eePT
eePTe
2
du
dd
0B
gb
utcu ,,
Penguin decay
tbtdVVA *
Inc. penguin contribution
0
)2sin(
C
S
222 iii eeeA
A
p
q
How can we obtain α from αeff ?
Time-dep. asymmetry :
NB : T = "tree" amplitude P = "penguin" amplitude
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Taming the Penguins: Isospin Analysis
)( 0 BAΑ
)( 00000 BAΑ
)( 00 BAΑ2|
eff|
)(~ 0 BAΑ
)(~ 00000 BAΑ
Gronau and London, Phys. Rev. Lett. 65, 3381 (1990)
The decays B are related by SU(2) Isospin relations between amplitudes A+-, A+0, A00
Central observation is that states can have I = 2 or 0, but penguins only contribute to I = 0 (I = ½ rule) is pure I = 2, so only tree amplitude |A+0| = |A-0|
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CP Asymmetries in B0 →
0 30 0.17 0 030 09 0.15 0.04
S . .C .
hep-ex/0501071
33467n
K crossfeed
(submitted to PRL)
Ignoring penguins:
deg 99 5 2
BB million 227
B0
B0
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Now we need B→
Analysis method reconstructs and fits B→and B→Ktogether
60 10)4.06.08.5()( BB
B→B→
B→KB→K
02.010.001.0)( 0 BACP
60 10)6.07.00.12()( KBB
Inserts show background components
B→hB→h
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…and B→
6000 10)10.032.017.1()( BB
06.056.012.000 C
B±→±0
3 B.F.sB0BB0
2 asymmetriesC
C
Using isospinrelations and
Isospin analysis not currently viable in the B→ system
|eff |< 35°
61±17 events in signal peak (227MBB)
Signal significance = 5.0
13167
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Comparison between BaBar and Belle
S = - 0.67 ± 0.16(stat) ± 0.06(syst)
C = - 0.56 ± 0.12(stat) ± 0.06(syst).
Belle: hep-ex/0502035
S = - 0.30 ± 0.17(stat) ± 0.03(syst)
C = - 0.09 ± 0.15(stat) ± 0.04(syst).
BaBar: hep-ex/0501071
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from B →
021.0029.0014.0978.0
Lf
P → VV decay, three possible ang mom states:•S wave (L=0, CP even)
•P wave (L=1, CP odd)
•D wave (L=2, CP even)
Blessing #1: helicity angle~100% longitudinally
polarized!
Angular analysis needed
~pure CP-even final state
22
12
41
22
12
21
2
sinsin)1(coscoscoscos
LL ff
dd
Nd
Preliminary
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from B0 →
fit in events 68703 ,M232 BB
52617)( BN
08.014.024.033.0
S
09.018.003.0 C
tags0B
tags0B
)ps(t
Preliminary
Preliminary
04.003.003.099.0
long
Lf60 10)5430()( BB
BaBar: hep-ex/0503049
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Search for B0 → : Blessing #2
Didn’t find it? Excellent!
1233)( 2220
000 BN
C.L.%90101.1
10)19.054.0()(6
636.032.0
000
BB
)M227( BB000 B
B (B→= 30 x 106
c.f. B→
B.F.= 4.7 x 106
and B→
B.F.= 1.2 x 106
BaBar: Phys.Rev.Lett.94:131801,2005
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Taking the world average
and thanks to
we apply the isospin analysis to B→ The small rate of means
|eff | is small[er] P/T is small in the B→ system
(…Relative to B→ system)
Isospin analysis using B→
61.64.6
0 10)4.26()(
BB
1 longLf
000 B
|eff |< 11°
)(11.)(4.)(1096 penguinsyststat
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Combined Measurements of
Isospin analyses in and , time-dep Dalitz analysis in
From combined results
from B0 → (
6113 2717
α = (106 ± 8)o U (170 ± 9)o
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(0,0) (0,1)
(,)
Vub Vud
Vcd Vcb
*
*
Vtd Vtb
Vcd Vcb
*
*
Measuring
cbcd
ubudargVV
VV
B± → D(*)K(*)
GLW, ADS and D0-Dalitz methods
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Measuring in B → DK
BB
CP
r
DKBDKB
DKBDKBA
sinsin
)()(
)()(
cbV
*usVIn general: need ≥ 2 amplitudes with
different weak and strong phases leading to the same final state
ubV
*csV
fDD 00 , where decays Choose
Relative amplitude rB, weak phase and strong phase B
Use additional dof in D decay to determine simultaneously
rB, , B
•Three methods on the market:
GLW, ADS, D0 Dalitz
Critical parameter:)(
)(
cbA
ubArB
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The GLW Method: choose D → fCP
( ) ( ) 2 sin sin
( ) ( )CP CP
CP CPCP
CP
B BB D K B D K
B D K B D K
rAR
02( ) ( )
1 2 cos cos( )
CB B B
P PCP
CB D K B D K
B D Kr rR
,0 KKDCP
000 SCP KD
KDB CP0
0CPDB
214 M BB
95 15CPN 76 13CPN
•Theoretically clean
•B → D background
•Limited statistics
4 observables (ACP+-,RCP+-)
to determine rB, , B
07.017.021.0
08.015.040.0
08.014.080.0
06.014.087.0
CP
CP
A
A
R
R
KDCP0
)()10.015.0(
07.034.033.0
06.020.009.0
06.029.076.0
12.037.077.1
CPCP
CP
CP
AA
A
A
R
R
KDCP0
03.004.0
*
*
23.010.0
007.0021.0086.0
CP
CP
A
R
KDCP0
BBM123BBM227BBM214
No useful constraints yet. Need more data!
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The ADS method: choose D → K
KDB 0
0
0
| ( ) |0.060 0.003
| ( ) |D
A D K
A Dr
K
2 2([ ] ) ([ ] )2 cos( )cos
([ ] ) ([ ] ) D B DD D BA S BR r r rBr K K Br K K
Br K K Br K Kr
([ ] ) ([ ] )
2 sin( )sin /([ ] ) ([ ] ) BADS ADSD D B
Br K K Br K K
Br Kr
K Br Kr
KA R
Phys.Rev.Lett.91:171801,2003
K
KDB 0
favored
suppressed
K
KDB 0favored
suppressed
Interference
Strong phase D
unknown
→ scan all values
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The ADS Method: results = no signal!
0B D K
0 0*[ ]DB D K
0*[ ]DB D K
0.0110.009
4.03.2
0.01
4 7
3
.
ADSR
N
1.3
0.0100.006
0.80.2
0.001ADSR
N
0.0190.013
2.11.4
0.01
1 2
1
.
ADSR
N
227 M BB
hep-ex/0408028 It’s a hard road ahead…
7348
20 D
1Dr
)CL %90( 23.0Br
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0D
2m202 )(
SKmm202 )(
SKmm
KDCS
0D
2m
Interference
Use the phase information across the
Dalitz plane to determine rB, , B
from B → D(*)0K, D0 → KS
0D
2m
2m
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The D0→KS Dalitz model
Determine on clean, high statistics sample of 81500 D*→D0 events ASSUME no D-mixing or CP violation in D decays Build model from 15 known resonances (+2 unidentified scalar resonances)
d.o.f. = 3824/(3054-32) = 1.27
2m
2m 2
m
K
KDCS
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D0 Dalitz method : B→D(*)0K (227 MBB)
KDB 0
KDB D0
282 ± 20
44 ± 8
KDB 0
B+
B+
B+
B
B2m
2m
2m
202 )( SKmm
2m
B2m
K
DCS
KDB D
00
89 ± 11
Maximum likelihood fit extracts rB(*),,
(*) from a fit to mES, E, Fisher and the D0→KS Dalitz model.
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D0 Dalitz method : B→D(*)0K : result
DK : rB < 0.19
D*K : rB = 0.155
(90% C.L.)
+0.0700.077 ± 0.040 ± 0.020
B = 114°±41°±8°±10° (+n)
B = 303°±34°±14°±10° (+n)
BaBar: hep-ex/0408088 γ = (70 ± 26 ± 10 ± 10)o
Belle: hep-ex/0504013B+→D0K*+
γ = (112 ± 35 ± 9 ± 11 ± 8)o
Belle: hep-ex/0411049
γ = (68 ± 15 ± 13 ± 11)o
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Combined measurement of
3rd error is due attributed to the Dalitz model
Measurement of : twofold ambiguity in extraction
γ = 64.0 ± 18.2 ([30.1,99.8] @ 95% CL)
γ = -116.0 ± 18.2 ([-149.7,-80.4] @ 95% CL)
Belle B+→D0K*+
γ = (112 ± 35 ± 9 ± 11)not used
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Putting the Angles Together…
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Measuring the sides of the UT Sides of Unitarity Triangle related to CKM matrix elements.
|Vub| and |Vcb| constrain the distance of the apex of the triangle from the origin.
Vub| and |Vcb| measurement complementary to sin2
|Vub| and |Vcb| measured in semileptonic B decays
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Semileptonic B decays Inclusive: B → Xcℓv or Xuℓv
Tree-level rates are
QCD corrections must be calculated Operator Product Expansion (OPE)
How do we separate Xu from Xc? c = 50 × u Much harder problem for |Vub|
Exclusive: B → D*ℓv, Dℓv, ℓv, ℓv, etc. Need form factors to relate the rate to |Vcb|, |Vub|
B
X
22 5
2( )
192F
u ub b
Gb u V m
22 2 3
2( ) ( )
192F
c cb b b c
Gb c V m m m
|Vcb| , |Vub|
plep
q
Mx
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Understanding inclusive SL decays
The Operator Product Expansion provides a systematic method of separating perturbative from non-perturbative scales
OPE + Heavy Quark symmetry HQE Heavy Quark Expansion now calculated to αs
2, mB-3
Essentially all we need to know for bcℓν Coefficients of operators calculated perturbatively (EW and
QCD); non-perturbative physics enters through matrix elements of operators
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Inclusive bcℓν Measure electron momentum spectrum and mass of hadronic
system in SL decay Determine moments to allow comparison with parton-level
calculations (duality assumed) Calculations exist for the following:
Strategy: measure spectrum + as many moments as possible Fit for HQE parameters and |Vcb|
),,,,,,( 33220
00LSDGcbnE
nlBEE
nl mmEfdEE
l
),,,,,,( 33220
00LSDGcb
xnE
nXBEE
nx mmEfdMM
l
Mass of hadronic system
Lepton energy spectrum
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Observables Define 8 moments from inclusive Eℓ and mX spectra
Integrations are done for Eℓ > Ecut, with Ecut varied in 0.6–1.5 GeV
0B
dM
1
E dM
d
1( 2,3)
i
i
E M dM i
d
( 1,2,3,4)iXX
i
m dM i
d
Partial branching fraction
Lepton energymoments
Hadron massmoments
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Electron Energy Spectrum BABAR data, 47.4 fb-1 at (4S) + 9.1 fb-1 off-peak Select events with an electron
having p*>1.4 GeV; study spectrum of 2nd electron for p* > 0.5 GeV as f n of charge Unlike-sign events dominated by
B Xcev Like-sign events from D Xev,
B0 mixing As done by ARGUS, CLEO…
BABAR PR D69:111104
Unlike-sign
Like-sign
BABAR
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Electron Energy Spectrum
Determine Ee spectrum
Subtract B Xueυ Correct for efficiency Correct for the detector
material (Bremsstrahlung) Move from (4S) to B rest frame Correct for the final state radiation using PHOTOS
Calculate 0th-3rd Ee moments for Ecut = 0.6 … 1.5 GeV
BABAR
BABAR PR D69:111104
All but ~few % can be measured
Ee (GeV)
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Hadron Mass Moments BABAR data, 81 fb-1 on U(4S) resonance Select events with a fully-reconstructed B meson
Use ~1000 hadronic decay chains Rest of the event contains one “recoil” B
Flavor and momentum known Find a lepton with E > Ecut in the recoil-B
Lepton charge consistent with the B flavor mmiss consistent with a neutrino
All left-over particles belong to Xc Improve mX with a kinematic fit = 350 MeV
4-momentum conservation; equal mB on both sides; mmiss = 0
BABAR PR D69:111103
Fully reconstructedB hadrons
lepton
v
Xc
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Hadron Mass Moments Unmeasured particles
measured mX < true mX
Calibrate using simulation Depends (weakly) on decay
multiplicity and mmiss
Validate in MC after applyingcorrection
Validate on data using partiallyreconstructed D*± D0 ±, tagged by the soft ± and lepton
Calculate 1st-4th mass moments with Ecut = 0.9 … 1.6 GeV
BABAR
BABAR PR D69:111103
Validation:
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Inputs to OPE Fit
mX moments
Eℓ moments
BABAR
BABAR PRL 93:011803
Error bars are stat. & syst.with comparable sizes
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OPE Fit Parameters Calculation by Gambino & Uraltsev (hep-ph/0401063,0403166)
Kinetic mass scheme to Eℓ moments
mX moments 8 parameters to determine
8 moments available with several E0
Sufficient degrees of freedom to determineall parameters without external inputs
Fit quality tells us how well OPE works
cbV bm cm 2
2G
3D
3LS( )cB X B
kinetic
chromomagnetic
Darwin
spin-orbit
2(1/ )bmO
3(1/ )bmO
3(1/ )bmO2( )sO
( )sO
BABAR PRL 93:011803
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Fit Results
mX moments
Eℓ moments
● = used, ○ = unusedin the nominal fit
Red line: OPE fitYellow band: theory errors
BABAR
2/ndf = 20/15
BABAR PRL 93:011803
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Fit Results
Impressive agreement between data and theory ≈ identical results obtained in another renorm. scheme: Bauer,
Ligeti, Luke, Manohar, Trott in hep-ph/0408002
s
s
s
3exp HQE th
exp HQE
exp HQE
exp HQE
2 2exp HQE
2exp HQE
(41.4 0.4 0.4 0.6 ) 10
(10.61 0.16 0.06 )%
(4.61 0.05 0.04 0.02 )GeV
(1.18 0.07 0.06 0.02 )GeV
(0.45 0.04 0.04 0.01 )GeV
(0.27 0.06 0.03 0.0
cb
c
b
c
G
V
m
m
B
s
s
s
2
3 3exp HQE
3 3exp HQE
2 )GeV
(0.20 0.02 0.02 0.00 )GeV
( 0.09 0.04 0.07 0.01 )GeV
D
LS
kinetic mass scheme with μ=1 GeV
Fitted values consistent with
external knowledge
2/ndf = 20/15
Uncalculatedcorrections to
BABAR PRL 93:011803
precision on mb = 1.5%
precision on |Vcb| = 2%
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Inclusive |Vcb| in Perspective
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Inclusive |Vub|
|Vub| can be measured from
The problem: b → cℓv decay
Use mu << mc difference in kinematics Maximum lepton energy 2.64 vs. 2.31 GeV First observations (CLEO, ARGUS, 1990)
used this technique Only 6% of signal accessible
How accurately do we know this fraction?
2
2
( ) 1
( ) 50ub
cb
Vb u
b c V
E
b c
b u
22 5
2( )
192F
u ub b
Gb u V m
How can we suppress50× larger background?
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b → uℓv Kinematics There are 3 independent variables in B → Xℓv
Take Eℓ, q2 (lepton-neutrino mass2), and mX (hadronic mass)
6%20%
70%
E
2q Xm
Technique Efficiency Theoretical Error
Eℓ Straightforward Low Large
q2 Complicated Moderate Moderate
mX Complicated High Large
Where does it come from?
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Starting point: HQE Just like bcℓν…, and with similar accuracy
…until limited expt’l acceptance is considered Poor convergence of OPE in region where bcℓν decays
are kinematically forbidden Non-perturbative Shape Function must be used to calculate
partial rates
= scale which separates effects from long- and short-distance dynamics
AEW = EW corrections; Apert = pert. corrections (sj , s
k0)
32
2
52
22
32
3
52 12))(1(
21)(1||
1921)(
bb
Gpert
b
Gpertub
bFEWu m
Om
Am
AVmG
AXB
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Shape Function – what is it? light-cone momentum distribution of b quark: F(k+) Property of a B meson; universal...but new “sub-leading”
SFs arise at each order in 1/mb
Consequences: changes effective mb, smears spectra
kB bM m
Rough features (mean Λ, r.m.s. λ1) are known
Detailed shape, and especially the low tail, are not constrained
0
kF
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Shape Function – What to Do?
Measure: Same SF affects (to the first order) b → sg decays
Caveat: whole Eg spectrum is needed Only Eg > 1.8 GeV has been measured Background overwhelms lower energies
Compromise: assume functional forms of f(k+)
Example:
Fit b → sg spectrum to determine the parameters Try different functions to assess the systematics
Measure E
spectrum inb → s
Extract f(k+) Predict Eℓ
spectrum inb → uℓv
E1.8
(1 )( ) (1 ) ;a a x kf k N x e x
2 parameters( and a) to fit
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SF from b → s CLEO and Belle has measured the b → sg spectrum
BABAR result on the way
CLEO hep-ex/0402009
Belle hep-ex/0407052
Belle
Fit
E
( )f k 3 models tried
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Theory input for |Vub|
At present, all |Vub| measurements based on inclusive SL decays use fully differential SL rate calculated to O(αS, mb
-2) (DeFazio and Neubert, JHEP 06:017 (1999)) Input required includes values for the mean and r.m.s. of
the Shape Function. In what follows we use as input the parameters determined
by a fit (hep-ex/0407052) to the Belle bsγ spectrum:Λ = 0.66 GeV, λ1 = -0.40 GeV2 + associated covariance; δΛ ~ δmb ≈ 80 MeV
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Measurements
BABAR has measured |Vub| using four different approaches
Statistical correlations are small Different systematics, different theoretical errors
Technique Reference
Eℓ > 2.0 GeV hep-ex/0408075
Eℓ vs. q2 hep-ex/0408045
mX < 1.55 GeVhep-ex/0408068
mX vs. q2
Inclusive B → Xev sample.High statistics, low purity.
Recoil of fully-reconstructed B.High purity, moderate statistics.
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Lepton Endpoint BABAR data, 80 fb-1 on U(4S) resonance Select electrons in 2.0 < Eℓ < 2.6 GeV
Push below the charm threshold Larger signal acceptance Smaller theoretical error
Accurate subtraction of backgroundis crucial! Data taken below the 4S resonance
for light-flavor background Fit the Eℓ spectrum with b → uℓv,
B → Dℓv, B → D*ℓv, B → D**ℓv,etc. to measure
Data (eff. corrected)MC
Data (continuum sub)MC for BB background
BABAR hep-ex/0408075
4stat sys( , 2.0GeV) (4.85 0.29 0.53 ) 10u eB X e E B
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Lepton Endpoint
Translate B into |Vub|
Compare results with different Eℓ cut
Theoretical error reduced with lower Eℓ cut
Eℓ (GeV)
(10-4) |Vub| (10-3)
BABAR 2.0–2.6 4.85 ± 0.29stat ± 0.53sys 4.40 ± 0.13stat ± 0.25sys ± 0.38theo
CLEO 2.2–2.6 2.30 ± 0.15exp ± 0.35sys 4.69 ± 0.15stat ± 0.40sys ± 0.52theo
Belle 2.3–2.6 1.19 ± 0.11exp ± 0.10sys 4.46 ± 0.20stat ± 0.22sys ± 0.59theo
BABAR hep-ex/0408075
CLEO PRL 88:231803
BELLE-CONF-0325
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Inclusive |Vub| Results
Summary of BABAR |Vub| results
Statistical correlation between the mX andmX-q2 results is 72%. Others negligible
Theoretical error of the mX-q2 result is different from the rest Negligible SF dependence
Technique |Vub| × 103 D(SF) × 103
Eℓ > 2.0 GeV 4.40 ± 0.13stat ± 0.25sys ± 0.38theo 0.46
Eℓ vs. q2 4.99 ± 0.23stat ± 0.42sys ± 0.32theo 0.42
mX < 1.55 GeV 5.22 ± 0.30stat ± 0.31sys ± 0.43theo 0.45
mX vs. q2 4.98 ± 0.40stat ± 0.39sys ± 0.47theo 0.06
How much |Vub| moves if the SF is determined by the CLEO data
BABAR hep-ex/0408075
BABAR hep-ex/0408045
BABAR hep-ex/0408068
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mX vs. q2
Inclusive |Vub| in Perspective
Eℓ endpoint
mX fit
Eℓ vs. q2
Results have been re-adjusted by the Heavy Flavor Averaging Group
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Exclusive |Vub|
Measure specific final states, e.g., B → ℓv Good signal-to-background ratio Branching fraction in O(10-4) Statistics limited
So far B → ℓv and ℓv have been measured Also seen: B(B → ℓv) = (1.3±0.5)×10−4 [Belle hepex/0402023]
B(B → ℓv) = (0.84±0.36)×10−4 [CLEO PRD68:072003]
Need Form Factors to extract |Vub|
e.g.
How are they calculated?
22 223
2 3
( )
24( )F
ub
Gd BV f
dqqp
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Form Factors Form Factors are calculated using:
Lattice QCD (q2 > 16 GeV2) Existing calculations are “quenched” ~15% uncertainty
Light Cone Sum Rules (q2 < 16 GeV2) Assumes local quark-hadron duality ~10% uncertainty
Unquenched LQCD starts to appear Preliminary B →ℓv FF from FNAL+MILC (hep-lat/0409116), HPQCD
(hep-lat/0408019) All of them have uncontrolled uncertainties
LQCD and LCSR valid in different q2 ranges No crosscheck Extrapolation to full q2 range introduces model dependent uncertainties Necessary measurement of partial rates in different q2 bins
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B ℓ with Reconstruction
5 q2 bins
427 68 - ℓ147 23 0 ℓ
Data
Signal MC
Comb. Sig.
Crossfeed
bcl
(B0 - ℓ ) = 2(B+ 0 ℓ )
82 fb-1
F. Bianchi XXX Nathiagali Summer College
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B ℓ ResultsBF(B0 - ℓ ) = (1.38 ± 0.10stat ± 0.16syst ± 0.08FF)10-4 (from BK)
BF(B0 - ℓ ) = (2.14 ± 0.21stat ± 0.48syst ± 0.28FF)10-4 (from LCSR)
|Vub| = (3.82 ± 0.14stat ± 0.22syst ± 0.11theo ± 0.72FF) 10-3 82 fb-1
F. Bianchi XXX Nathiagali Summer College
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|Vub| and |Vcb| Summary Inclusive |Vcb| measurement:
- error 2%, HQE validation
Inclusive |Vub| measurements:
- error 10%, different approaches, still room from improvements
New |Vub| result from B ℓ n untagged better FF knowledge necessary
|Vcb| = (41.4 ± 0.4exp ± 0.4HQE ± 0.6theo) 10-3
|Vub| = (4.70 ± 0.44exp+syst) 10-3
|Vub| = (3.82 ± 0.14stat ± 0.22syst ± 0.11theo ± 0.72FF) 10-3
F. Bianchi XXX Nathiagali Summer College
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Putting Everything Together…