Dominant KL Branching Ratios,

1
Dominant KL Branching Ratios, KL Lifetime and Vus
at KLOE

• Introduction
• - CKM and Vus
• - DAFNE and KLOE
• KL physics
• - Branching Ratios
• - Lifetime
• - Form Factor
• - Vus ? f(0)
• Conclusions

Paolo Beltrame IEKP University of Karlsruhe
2
CKM Matrix and Vus
Couplings parameters between quarks in Weak
Interactions, mixing Mass and Weak Eigenstates.
Wolfenstein parametrization four free parameters
(?, A, ?, ?). Standard Model does not predict the
value of any of them.
CKM matrix unitarity first row Vud2 Vus2
Vub2 Vud2 Vus2 ? 1 ?
Determination of Vus K0 ? ?e????, (Kl3)
semileptonic decays
3
The f Factory
f(1020) Factory electron-positron-collider at
?s Mf 1019.4 MeV
BR(? ? KK-) 49.1 BR(? ? KSKL) 34.1
f Factory ? K Factory

• The f decay at rest provides monochromatic and
  pure beams of kaons
• Tagging observation of KL(KS) signals presence
  of KS(KL)
• - precision measurements of absolute BRs
• KL and KS are well separated
• - ct (KS) 6 mm, KS decays near to the
  interaction point
• - ct (KL) 3.4 m, large detector to keep
  reasonable acceptance for KL decays

4
The DAFNE f Factory

• ?s Mf 1019.4 MeV
• Ldesign 5 ? 1032 cm-2 s-1

2001 170 pb-1 2002 280 pb-1 Analysis nearly
complete
2004 750 pb-1 2005 1250 pb-1

• Data taking at ??peak finished in 2005
• Lpeak 1.3 1032 cm??s??
• Ltot ?2.4 fb-1
• Off-peak run ?s 1 GeV finished in March
• Ltot ?250 pb-1

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The KLOE detector
Superconducting coil
Drift chamber
Magnetic Field of 0.52 T

• Track momentum resolution
• sp/p ?0.4 (q gt 45)
• Vertex resolution
• sxy ?150 mm, sz ?2 mm

12582 sense wires 52140 wires in total 90 He
10 C4H10
Electromagnetic calorimeter
Energy resolution sE/E 5.7/?E(GeV) Time
resolution sT 54 ps/?E(GeV) ? 50 ps
Lead/Scint fibres 4880 PM
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The Tagging method
Tagging of KS, KL and K? beams allows absolute
Branching Ratios measurement

• Relies on capability of selecting a tagging
• kaon independently on the decay mode
• of the other kaon in the other hemisphere
• In fact some dependence on signal
• mode exists tag bias aTB
• Tag bias
• carefully measured using MC, and data
• control samples, typically O(1)

KL tagged by KS ? ???? vertex at IP Efficiency
70 (mainly geometrical) KL angular resolution
1 KL momentum resolution 2 MeV
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Dominant KL Branching Ratios
High momentum resolution of KLOE DC ? Ke3, Kµ3,
pp-p0 vertex

• Tag KL by decay KS?? pp-
• Charged decays selected by closing the kinematics
  at the vertex
• lesser of Pmiss- Emiss
• Fit data with linear combination of three MC
  shapes
• Radiative corrections included in MC

• 2001-2002 Data 328 pb-1
• From PDG04
• Rare KL decays 0.0036
• KL Lifetime 51.50 ns
• BR(?e? ??? ?????? 3????KLOE
• BR(???? ????) PDG04
• 1.0104 ??0.0076
• Imposing S(BR ? x) 1
• tKL (50.72 ? 0.14stat ? 0.36syst) ns

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Dominant KL Branching Ratios results (328 pb-1)
BR(KL? ?e?(?) ) 0.4007 ? 0.0006stat ?
0.0014syst BR(KL? ???(?) ) 0.2698 ? 0.0006stat
? 0.0014syst BR(KL? 3??) 0.1997 ? 0.0005stat
? 0.0019syst BR(KL? ??????(?) ) 0.1263 ?
0.0005stat ? 0.0011syst
Phys. Lett. B632 (2006) 43

• Reasonable agreement with KTeV and NA48
• The new results go in the same direction respect
  to the PDG older values

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KL Lifetime direct measurement
Time resolution of KLOE EmC ? KL ? p0p0p0
102
Events/0.3 ns
PK 110 MeV Excellent lever arm for lifetime
measurement
6 - 24.8 ns 40-165 cm 0.37 lL

• KL ? p0p0p0 tagged by KS ? pp-
• Lg and LK obtained from tcl
• At least three gs required
• e(LK) 99 uniform in L
• 1.3 residual background
• sL(KL) 2 cm

L/bgc (ns)
?KL (50.92 ? 0.17stat ? 0.17syst) ns
Phys. Lett. B626 (2005) 15
Average with result from KL BRs ?KL
(50.84 ? 0.23) ns
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Ke3 Form Factor slopes

• Parametrizations
• f?(t) f?(0) 1 ???? t
• or f?(0) 1 ? ??? t ???? t2 / 2
• t (pK - pp)2 / m2p
• Signal selection
• - KL ? ?e? decays tagged by KS ? ????
• - Two tracks in fiducial volume forming vertex
• - Kinematic cuts ToF PID to reduce background
• Fit t distribution

Quadratic fit (?2/dof 325/362)
Linear fit (?2/dof 330/363)
l? (25.5 ? 1.5 ? 1.0) ? 10-3? l? (1.4 ? 0.7
? 0.4) ? 10-3?
l (28.6 ? 0.5 ? 0.4) ? 10-3?
hep-ex/0601038 Submitted to Phys. Lett. B
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Vus ? f(0) at KLOE

• Quadratic Form Factor
• parametrization KTeV ISTRA
• l? 0.0221?? 0.0011
• l? 0.0023 ? 0.0004
• l0 0.0154 ? 0.0008
• KL Lifetime from KLOE
• Average between KL BRs
• and direct measurement
• tKL 50.84(23) ns
• Kaon Semileptonic Branching Ratios all of them
  from KLOE

KLe3 KLm3 KSe3 K?e3 K?m3
BR 0.4007 0.2698 0.00709 0.0505 0.0331
dBR 0.0018 0.0012 0.00009 0.0004 0.0005
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Conclusions

• KLOE can determine the absolute KL Branching
  Ratios tagging the KL pure beam by means of KS
  ?pp- decaying in the other detector hemisphere
• Using 328 pb-1 of 2001 and 2002 data, KLOE has
  measured the main KL Branching Ratios with
  relative errors of 0.5 - 1
• Using 400 pb-1 of data collected in 2001 and 2002
  , 106 KL ?p0p0p0 events, KLOE has performed a
  direct measurement of KL Lifetime at the level of
  0.5
• KLOE has measured the K p vector current
  parameters using 328 pb-1 of data collected in
  2001 and 2002, corresponding to 2?106 of KL ?pen
  events
• Using Form Factor parameters from KTeV and ISTRA,
  KL Lifetime determined by KLOE (average between
  direct and KL BRs measurements), main KL
  Branching Ratios (KLe3, KLm3, KSe3, K? e3, K?m3)
  KLOE has extracted Vus ? f(0) value with a
  relative error, on the average, of 0.2

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Backup slides
... In jeden Quark begäbt er seine Nase
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More theory
The Ademollo Gatto theorem for
strangeness-violating leptonic decays of baryons
and mesons the vector coupling constants (i.e.,
the limit of the vector amplitudes for vanishing
momentum transfer) are uniquely predicted up to
first order in symmetry breaking.
Electromagnetic correction

• Virtual corrections
• Real Bremsstrahlung changes (in addition)
  significantly the accpetance

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KL physics at KLOE determination of Vus
GKl3 Partial Decay width Experiment
GKl3 BR(KL?pln)/tKL SEW Short
ElectroWeak Radiative corrections
Theory Included in Monte Carlo dEM
Electromagnetic corrections and SU(2) corrections
Theory Included in Monte Carlo f(0)
Form Factor at t0 Theory f(0) theoretical
calculations IKl(lI) Integral over the
momentum dependence of the Form Factor
Experiment IKl(lI) determined by KLOE and other
experiments
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Form Factor parameterizations
Linear
Quadratic
Pole
Fit on t spectrum
Aij Smearing matrix (MC) ?j Reconstruction
efficiency ?j Bare Ke3 decay density FjFSR FSR
correction
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Shapes
Lesser of Pmiss ? Emiss in ?? or ?? hypotesis
(MeV)
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Vus compared with unitarity and Vud
The value considered for Vud is 0.9740 ? 0.0005
taken from A. Czarnecki, W. J. Marciano, A.
Sirlin, Phys. Rev. D70 (2004) 093006
Vus ? fKp(0)
PDG02
PDG02
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Kaon Form Factor at zero momentum transferred

• cPT
• Leutwyler-Roos (1984) f(0) 0.961 ? 0.008
• cPT Quark Model (Bijnens-Talavera, 2003)
• 
  f(0) 1 fp4 fp6loop fp6LR 0.976
  0.010
• cPT Dispersion Relations (Jamin-Oller-Pich,
  2004)
• 
  f(0) 0.974 ? 0.011
• cPT Large NC (Cirigliano-Eidemuller-Kaiser-Pich
  -Portoles, 2005)
• 
  f(0) 0.984 ? 0.012
• Lattice-QCD
• (Becirevic-Isidori-Lubicz-Martinelli-Simula-Taran
  tino-Villadoro)
• f(0) 1 fp4
  fp6q 0.960 0.005stat 0.007syst

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Future

• Perspectives with 2.5 fb?? of collected data
• Limit on KS? ?0?0?0 at 10 8 level
• Competitive measurement of KS? ??-?0
• Ks semileptonic asymmetry to 4 ? 10-3
• Fractional accuracy of lt 1 on the BR for KS ?
  ?e? and for K?l3
• Form factors of KL and K? semileptonic decays
• First direct measurement of BR(KS ? ???),
  accuracy lt 2
• Studies of KSKL system with interference
  exploit KLOEs capability to
• CP,CPT mmts