high precision measurement of the form factors of the...

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)

OutlineMotivation


• Motivation◦ Semileptonic Kaon Decays◦ Kl3 Form Factors◦ Form Factor Parametrizations

• The NA48/2 Experiment

• Kl3 Form Factor Analysis◦ Signal◦ Background◦ Results

◦ Summary


OutlineMotivation


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|


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|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


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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)


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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.


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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−


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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


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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


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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


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K±l3 Data-MC


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.


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K±l3 Data-MC


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%.


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K±l3 Data-MC


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.


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K±l3 Data-MC


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.


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K±l3 Data-MC


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.


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K±l3 Data-MC


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.


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K±l3 Data-MC


K±l3 Data-MC Comparison

=⇒ Data-MC difference mostly below the 0.1% level.

=⇒ Remaining differences taken into account by systematics.


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K±l3 Data-MC


Study of Systematic Errors

=⇒ K±µ3 is dominated by statistics.Main error from K2π background.

=⇒ K±e3 is dominated by systematics.


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K±l3 Data-MC


Preliminary Results for the NA48/2


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K±l3 Data-MC


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.


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K±l3 Data-MC


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.


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K±l3 Data-MC


Thanks for your attention!


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K±l3 Data-MC


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.


high precision measurement of the form factors of the...

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