High precision measurement of the form factors of the...
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
High precision measurement of the form factors ofthe semileptonic decays K± → π0l±νl (Kl3)
David LomidzeOn behalf of the NA48/2 Collaboration
Institut fur Physik, Johannes Gutenberg-Universitat
13th International Conference on Meson-Nucleon Physics and the Structure of the NucleonROME, ITALY
02 Oct 2013
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
• Motivation◦ Semileptonic Kaon Decays◦ Kl3 Form Factors◦ Form Factor Parametrizations
• The NA48/2 Experiment
• Kl3 Form Factor Analysis◦ Signal◦ Background◦ Results
◦ Summary
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
Semileptonic Kaon DecaysKl3 Form Factors
Form Factor Parametrizations
Motivation
• Unitarity of the CKM quark mixing matrix can be tested experimentally
• It is an important tool for exploring the limits of the Standard Model
• Any observed deviation from the matrix’s unitarity would either undermine thevalidity of the Standard Model or indicate existence of a fourth generation offermions. One of such unitarity constraints is:
|Vud|2 + |Vus|2 + |Vub|2 = 1 + 4CKM
• 4CKM parametrizes any possible deviations from the Standard Model inducedby new physics operators
• Whole uncertainty of the unitarity relation is dominated by uncertainty on |Vus|
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
Semileptonic Kaon DecaysKl3 Form Factors
Form Factor Parametrizations
|Vus| from Semileptonic Kaon Decays
K± → π0l±νl decays provide the most accurate and theoretical cleanest way toaccess |Vus|The master formula for Kl3 decay rates is:
Γ(Kl3(γ)) =C2KG
2Fm
5K
192π3SEW |Vus|2|f+(0)|2IlK (λ+0)(1 + δlSU(2)) + δlEM )2
Experimental Inputs
I Γ(Kl3(γ)) Branching rations and Kaon lifetime
I IlK(λ+0) Integral of form factor slopes over phase space
Theoretical Inputs
I SEW Universal short distance Electro-Weak corrections
I f+(0) Vector form factor at zero momentum transfer
I δlSU(2) Form factor correction for isospin breaking
I δlEM Long distance Electro-Magnetic effects
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
Semileptonic Kaon DecaysKl3 Form Factors
Form Factor Parametrizations
Klv From Factors
Kl3 Decays are described by two form factors f+(t) and f−(t) and matrix elementcan be expressed as:
M =GF2Vus(f+(t)(PK + Pπ)µulγµ(1 + γ5)uν + f−(t)mlul(1 + γ5)uν)
t = q2 is the squared four momentum transfer to the lepton neutrino system.
f−(t) can only be measured in the Kµ3 decay, because of me � mK .
f±(t) is the vector form factor and f0(t) the scalar form factor, they are related by:
f0(t) = f+(t) +t
m2K −m2
π
f−(t)
f+(0) can not be measured directly, to be given by theory (lattice QCD, χPT).
Both scalar and vector form factors are measured by experiment relative to f+(0):
f+(t) =f+(t)
f+(0)f0(t) =
f0(t)
f+(0)f+(0) = f0(0)
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
Semileptonic Kaon DecaysKl3 Form Factors
Form Factor Parametrizations
Kl3 Form Factor Parametrizations
Several ways are know to parametrize the Kl3 form factors
Pole Parametrization: One single resonance (vector (1-) or scalar (0+)) isassumed to be responsible for the process. The corresponding masses mV and mS
are only free parameters and can be estimated from the fit:
f+,0(t) =m2V,S
m2V.S − t
Taylor expansion Linear/quadratic expansion in the momentum transfer t = q2
f+,0(t) =
[1 + λ+,0
t
m2π
]Linear
f+,0(t) =
[1 + λ′+,0
t
m2π
+λ′′+,0
2
(t
m2π
)2]Quadratic
More free parameters to be determined =⇒ Strong correlation between parameters
Other parametrizations (Dispersive, Z-fit) are also known, but not yet used in thisanalysis.
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
The NA48/2 Experiment The Beam LineDetector
NA48/2 Experiment @ CERN
NA48/2 is a fixed target experiment in the North Area of CERN the SPS.
LEP/LHC
SPS
CERN
NA48
Main purpose was the search of direct CP violation in the K3π by measuringcharge asymmetry in charged Kaon decays:
K± → π±π0π0
K± → π±π+π−
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
The NA48/2 Experiment The Beam LineDetector
The NA48/2 Beam Line
I Simultaneous K+ and K− beams with pK = (60 ± 1.8) GeV/c
K+
K−
K+
K−
KABES 3
Kev
lar
win
dow
1000
1 cm
0.36 mrad
50 200
10 cmHe tank +
Ho
do
LK
rH
AC
MU
V
DCH 1Protectingcollimator
Quadropol
ACHROMAT
Target
Defining
2nd
collimator Final
collimator Cleaning
250 m
Spectrometertank
Vacuum
focused beams
Decay volume
MagnetDCH 4
KABES 2
KABES 1
Z
collimator
Y
ACHROMAT1ST
Momentum Selection
BeamSelection
2~3 x 10Kaons/spill
6
I 3 days of dedicated run with minimum trigger requirements for the Kl3measurement
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
The NA48/2 Experiment The Beam LineDetector
The NA48/2 Detector
Main Sub-Detectors:
• Magnetic spectrometer4 sets of drift chambers: ∆p/p ≈ 0.45%for typical momentum of 20 GeV/c
• Charged and Neutral Hodoscopesσt = 150 ps
• Liquid Krypton Calorimeter∆E/E = 1.0% GeV/c for typical energy of20 GeV
• Hadron calorimeter, photon vetos, muoncounters
Kevlar window
Drift chamber 1
Anti counter 6Drift chamber 2
Magnet
Drift chamber 3
Helium tank
Anti counter 7Drift chamber 4
Hodoscope
Liquid krypton calorimeterHadron calorimeter
Muon veto sytem
Trigger Condition:Hodoscope space point + ELkr > 10 GeV
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
SignalBackgroundRadiative CorrectionsForm Factor extraction
K±l3 Data-MC
SystematicsResultsSummary
Kl3 Event Selection
K±
γ
γ
ν
µ±/e±
π0
• 1 good trackMuon identification using muon counter and E/pElectron identification using E/p
• 1 good π0 → γγ
Pion mass cut: |mγγ −mPDGπ0 | < 10 MeV2
• Event reconstructionLkr clusters and muon track consistent in time.Missing mass cut using calculation with K±l3 hypothesis
(Mmiss)2Kl3 = (PK − Pl − Pπ0 )
2 < 10 MeV2.Kaon energy reconstruction under the assumption of amissing undetected neutrino within the range of:55 GeV < EK± < 65 GeV
2.5× 106K±µ3 events selected
4.0× 106K±e3 events selected
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
SignalBackgroundRadiative CorrectionsForm Factor extraction
K±l3 Data-MC
SystematicsResultsSummary
K± → π±π0 (K2π0) Background rejection
K±µ3 :
Main Background: K± → π±π0 with π± → µ± mis-ID can fake signal:
I Without suppression, K± → π±π0 bkg at thelevel of 20%
I Cut in the invariant π±π0 - mass and thetransverse momentum of the pion:
• Background contamination reduced to 0.5%.• about 24% loss of K±µ3 events.
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
SignalBackgroundRadiative CorrectionsForm Factor extraction
K±l3 Data-MC
SystematicsResultsSummary
K± → π±π0 (K2π0) Background rejection
K±e3 :
Main Background: K± → π±π0 with π± → e± mis-ID can fake signal:
I π± with E/p > 0.95 can fake a Ke3 decay
I Cut in transverse momentum of the event
• Background contamination reduced < 0.5%.• K±e3 acceptance loss ≈ 3%.
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
SignalBackgroundRadiative CorrectionsForm Factor extraction
K±l3 Data-MC
SystematicsResultsSummary
K± → π±π0π0 (K3π0) Background
K±µ3 :
• π± → µ± decay with one lost photons from π0
decays.
• Small but introduces slope in the Dalitz plot.
• No dedicated cut to reduce the background.
• A correction is applied to take the backgroundinto account.
• Without the correction result shifts by ≈ 0.5 σstat.
K±e3 :
• K± → π±π0π0 is negligible.
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
SignalBackgroundRadiative CorrectionsForm Factor extraction
K±l3 Data-MC
SystematicsResultsSummary
Radiative Effects
K±µ3:
Kl3 decay rate including first order radiativecorrections can be written as:
ΓKl3 = Γ0Kl3
+ Γ1Kl3
= Γ0Kl3
(1 + 2δKlEM )
Simulation code provided by KLOE (C. Gatti)(EPJ C45 (2006) 417).
Parameters used for the normalization(JHEP 11 (2008) 006).
Mode δKµ3EM (%)
K0µ3 0.700 ± 0.110
K±µ3 0.008 ± 0.125
For K±µ3 small effect on the acceptance.∼ 1% effect on the Dalitz plot slope.
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
SignalBackgroundRadiative CorrectionsForm Factor extraction
K±l3 Data-MC
SystematicsResultsSummary
Radiative Effects
K±e3 :
Kl3 decay rate including first order radiativecorrections can be written as:
ΓKl3 = Γ0Kl3
+ Γ1Kl3
= Γ0Kl3
(1 + 2δKlEM )
Simulation code provided by KLOE (C. Gatti)(EPJ C45 (2006) 417).
Parameters used for the normalization(JHEP 11 (2008) 006).
Mode δKe3EM (%)
K0e3 0.495 ± 0.100
K±e3 0.495 ± 0.100
For K±e3 the effect on the acceptance are bigger.∼ 10% effect on the Dalitz plot slope.
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
SignalBackgroundRadiative CorrectionsForm Factor extraction
K±l3 Data-MC
SystematicsResultsSummary
Form Factor Fitting Procedure
To extract form factors, a fit to the Dalitz plot density is applied
ρ(E∗l , E∗π) =
d2N(E∗l , E∗π)
dE∗µdE∗π∝ Af2
+(t) +Bf+(t)(f0 − f+)m2K −m2
π
t+ C
[(f0 − f+)
m2K −m2
π
t
]2
E∗l and E∗π are the energy of the lepton and the pion in the Kaonrest frame.
Cells which are outside or crossing the border of thephysical region of Dalitz plot are not used in the fit.
A, B and C are kinematic terms. The fit is performed on cells of 5 × 5 MeV2.
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
SignalBackgroundRadiative CorrectionsForm Factor extraction
K±l3 Data-MC
SystematicsResultsSummary
K±l3 Data-MC Comparison
=⇒ Data-MC difference mostly below the 0.1% level.
=⇒ Remaining differences taken into account by systematics.
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
SignalBackgroundRadiative CorrectionsForm Factor extraction
K±l3 Data-MC
SystematicsResultsSummary
Study of Systematic Errors
=⇒ K±µ3 is dominated by statistics.Main error from K2π background.
=⇒ K±e3 is dominated by systematics.
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
SignalBackgroundRadiative CorrectionsForm Factor extraction
K±l3 Data-MC
SystematicsResultsSummary
Preliminary Results for the NA48/2
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
SignalBackgroundRadiative CorrectionsForm Factor extraction
K±l3 Data-MC
SystematicsResultsSummary
Preliminary Results for the NA48/2 (Combined)
Statistical and systematic uncertainties combined:
K0l3 results from KLOE, KTeV
and NA48, K−l3 from ISTRA.
NA48/2 is the firstmeasurement which usesK±µ3 and K±e3.
NA48/2 preliminary resultshave smallest errors.
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
SignalBackgroundRadiative CorrectionsForm Factor extraction
K±l3 Data-MC
SystematicsResultsSummary
Summary and Outlook
I 4 millions of Ke3 and 2.5 millions of Kµ3 events analysed
− First measurement with K+ and K−
− Very small background
− Good agreement between Ke3 and Kµ3 results
− Preliminary results competitive with the world avarage
I ∼10 times larger Ke3 and Kµ3 data-samples are recorded in 2007 by theNA62 experiment. Analysis of Ke3 data is ongoing. First results are expectedsoon.
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
SignalBackgroundRadiative CorrectionsForm Factor extraction
K±l3 Data-MC
SystematicsResultsSummary
Thanks for your attention!
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)
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OutlineMotivation
The NA48/2 ExperimentKl3 Form Factor Analysis
SignalBackgroundRadiative CorrectionsForm Factor extraction
K±l3 Data-MC
SystematicsResultsSummary
Dispersive Parametrization:
Uses dispersive techniques and known low energy K-π phases toparametrize vector and scalar form factors:
f+(t) = exp
[t
m2π
(Λ+ +H(t))
];
f0(t) = exp
[t
m2K −m2
π
(ln(C)−G(t))
];
Λ+ is slope of the vector form factor
ln(C) = ln[f0(m2K −m2
π)] is the logarithm of the scalar form factor atthe Callan-Treiman point
Accurate polynomial approach for the dispersive integrals H(t) andG(t) are available.
David Lomidze High precision measurement of the form factors of the semileptonic decays K± → π0l±νl (Kl3)