DPG - Dortmund Dominant K L Branching Ratios, K L Lifetime and V us at KLOE  Introduction - CKM and V us - DA  NE and KLOE  K L physics - Branching Ratios - Lifetime - Form Factor - V us  f + (0)  Conclusions Paolo Beltrame IEKP University of Karlsruhe

DPG - Dortmund CKM Matrix and V us 95%5% % V ub V us V ud 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 |V ud | 2 + |V us | 2 + |V ub | 2 ~ |V ud | 2 + |V us | 2  1 –  Determination of V us K 0   e ,  K l3 )  semileptonic decays K0K0 s  + u veve ee V us dd

DPG - Dortmund The  – Factory  (1020) – Factory: electron-positron-collider at  s = M   = MeV BR(   K + K  ) = 49.1% BR(   K S K L ) = 34.1%  – Factory  K – Factory  KSK+KSK+ KLK-KLK-  The  decay at rest provides monochromatic and pure beams of kaons  Tagging: observation of K L (K S ) signals presence of K S (K L )  -  precision measurements of absolute BR’s  K L and K S are well separated: - c  (K S ) = 6 mm, K S decays near to the interaction point - c  (K L ) = 3.4 m, large detector to keep reasonable acceptance for K L decays

DPG - Dortmund The DA  NE  – Factory  s = M   = MeV L design = 5  cm -2 s pb pb pb pb -1 Analysis nearly complete  Data taking at  peak finished in 2005 L peak = 1.3 × cm  s  L tot  2.4 fb -1  Off-peak run  s = 1 GeV finished in March L tot  250 pb -1

DPG - Dortmund The KLOE detector Magnetic Field of 0.52 T Superconducting coil Track momentum resolution  p / p  0.4% (  > 45 ° ) Vertex resolution  xy  150  m,  z  2 mm Drift chamber sense wires wires in total 90% He + 10% C 4 H 10 Energy resolution  E / E = 5.7% /  E(GeV) Time resolution  T = 54 ps /  E(GeV)  50 ps Electromagnetic calorimeter Electromagnetic calorimeter Lead/Scint fibres 4880 PM

DPG - Dortmund The Tagging method KS  KS  KS  KS   KL  2KL  2KL  2KL  2 K L tagged by K S      vertex at IP Efficiency ~70% (mainly geometrical) K L angular resolution: ~1° K L momentum resolution: ~2 MeV Tagging of K S, K L 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  TB Tag bias: carefully measured using MC, and data control samples, typically O(1%)

DPG - Dortmund Dominant K L Branching Ratios High momentum resolution of KLOE DC  Ke3, Kµ3,       vertex  Tag K L by decay K S       Charged decays selected by closing the kinematics at the vertex: lesser of P miss - E miss  Fit data with linear combination of three MC shapes  Radiative corrections included in MC Data: 328 pb -1 From PDG‘04 Rare K L decays: K L Lifetime: ns BR(  e  +  +       + 3    KLOE + BR(     +     ) PDG’04 =  Imposing  (BR  x) = 1  K L = (50.72  0.14 stat   0.36 syst  ns (P miss  E miss ) in  or  hyp Data  e    (MeV)

DPG - Dortmund BR(K L  e ) =  stat  syst BR(K L  ) =  stat  syst BR(K L  3   ) =  stat  syst BR(K L        ) =  stat  syst Dominant K L Branching Ratios results (328 pb -1 ) Reasonable agreement with KTeV and NA48 The new results go in the same direction respect to the PDG older values Phys. Lett. B632 (2006) 43

DPG - Dortmund K L Lifetime: direct measurement  + + I.P.  0 0 L LL LKLK Measure the mean decay path L/  c (ns) ns cm 0.37 L × 10 2 Events/0.3 ns P K = 110 MeV Excellent lever arm for lifetime measurement  K L       tagged by K S      L  and L K obtained from t cl  At least three  ’s required   (L K ) ~99% uniform in L  1.3% residual background   L (K L ) ~2 cm Average with result from K L BR’s:   L  = (50.84  0.23) ns Time resolution of KLOE EmC  K L       Phys. Lett. B626 (2005) 15   L  = (50.92  0.17 stat  0.17 syst ) ns

DPG - Dortmund K e3 Form Factor slopes  Parametrizations: f  (t) = f  (0) [1   t] or f  (0) [1   t    t 2 / 2] t = (p K - p  ) 2 / m 2  +  Signal selection: - K L   e decays tagged by K S      - Two tracks in fiducial volume forming vertex - Kinematic cuts + ToF PID to reduce background  Fit t distribution +  10  3    KTeV ISTRA NA48 KLOE 1  contours Linear fit (  2 /dof ~ 330/363): + = (28.6  0.5  0.4)   Quadratic fit (  2 /dof ~ 325/362): + = (25.5  1.5  1.0)    + = (1.4  0.7  0.4)   hep-ex/ Submitted to Phys. Lett. B

DPG - Dortmund V us  f + (0) at KLOE Quadratic Form Factor parametrization: KTeV + ISTRA  + =   +    0 =  K L Lifetime: from KLOE Average between K L BR’s and direct measurement   L = 50.84(23) ns Kaon Semileptonic Branching Ratios: all of them from KLOE KLe3KLe3 KL3KL3 KSe3KSe3Ke3Ke3 K3K3 BR  BR

DPG - Dortmund Conclusions KLOE can determine the absolute K L Branching Ratios tagging the K L pure beam by means of K S →     decaying in the other detector hemisphere Using 328 pb -1 of 2001 and 2002 data, KLOE has measured the main K L Branching Ratios with relative errors of 0.5% - 1% Using 400 pb -1 of data collected in 2001 and 2002, ~10 6 K L →       events, KLOE has performed a direct measurement of K L Lifetime at the level of 0.5% KLOE has measured the K –  vector current parameters using 328 pb -1 of data collected in 2001 and 2002, corresponding to ~2  10 6 of K L →  e events Using Form Factor parameters from KTeV and ISTRA, K L Lifetime determined by KLOE (average between direct and K L BR’s measurements), main K L Branching Ratios (K L e3, K L  3, K S e3, K  e3, K   3): KLOE has extracted V us  f + (0) value with a relative error, on the average, of 0.2%

DPG - Dortmund Backup slides... In jeden Quark begäbt er seine Nase

DPG - Dortmund Ademollo Gatto theorem 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.” More theory Electromagnetic correction  Virtual corrections  Real Bremsstrahlung changes (in addition) significantly the accpetance Acceptance 100% KLOE MC

DPG - Dortmund K L physics at KLOE: determination of V us  Kl3 Partial Decay width – Experiment  Kl3 = BR(K L →  l ) /  K L S EW Short ElectroWeak Radiative corrections – Theory Included in Monte Carlo  EM Electromagnetic corrections and SU(2) corrections – Theory Included in Monte Carlo f + (0) Form Factor at t=0 – Theory f + (0) theoretical calculations I Kl (  ) Integral over the momentum dependence of the Form Factor – Experiment I Kl (  ) determined by KLOE and other experiments 0.5%0.4% experimental 0.8% theoretical

DPG - Dortmund Form Factor parameterizations Linear Quadratic Pole Fit on t spectrum A ij Smearing matrix (MC)  j Reconstruction efficiency  j “Bare” K e3 decay density F j FSR FSR correction KTeV K e3 - phase space Ed Blucher t dN/dt phase space + FF

DPG - Dortmund Shapes Lesser of P miss  E miss in  or  hypotesis (MeV)

DPG - Dortmund V us compared with unitarity and V ud The value considered for V ud is  taken from A. Czarnecki, W. J. Marciano, A. Sirlin, Phys. Rev. D70 (2004) Unitarity Band (1-|V ud | 2 )·f + (0) Leutwyler-Roos FF conf. by Lattice New V ud value from 0 +  ± Unitarity Band (1-|V ud | 2 )·f + (0) Bijnens-Talavera FF New V ud value from 0 +  ± |V us |  f + Kπ (0) PDG02

DPG - Dortmund  PT  Leutwyler-Roos (1984) f + (0) =    PT + Quark Model (Bijnens-Talavera, 2003) f + (0) = 1 + f p4 + f p6 loop + f p6 LR = ±   PT + Dispersion Relations (Jamin-Oller-Pich, 2004) f + (0) =    PT + Large N C (Cirigliano-Eidemuller-Kaiser-Pich-Portoles, 2005) f + (0) =  0.012Lattice-QCD  (Becirevic-Isidori-Lubicz-Martinelli-Simula-Tarantino-Villadoro) f + (0) = 1 + f p4 + f p6 q = ± stat ± syst Kaon Form Factor at zero momentum transferred

DPG - Dortmund Perspectives with 2.5 fb  of collected data: Limit on K S   0  0  0 at 10 –8 level Competitive measurement of K S   +  -  0 K s semileptonic asymmetry to 4  Fractional accuracy of < 1% on the BR for K S   e and for K  ℓ3 Form factors of K L and K  semileptonic decays First direct measurement of BR(K S   ), accuracy < 2% Studies of K S K L system with interference: exploit KLOE’s capability to CP,CPT mmts Future