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1 CKM unitarity problem: results from NA48 experiment Evgueni Goudzovski (JINR) JINR Scientific Council January 20, 2005 Slide 2 2 The CKM matrix The Cabibbo-Kobayashi-Maskawa matrix connects the eigenstates d,s,b of weak interaction with the quark flavour eigenstates d,s,b: V ud V us V ub V cd V cs V cb V td V ts V tb d s b d s b = Conservation of probability: CKM matrix has to be unitary: V CKM V CKM + =I If unitary not fulfilled: New Physics (e.g. 4 th quark generation) E. Goudzovski JINR SC January 20, 2005 Slide 3 3 CKM unitarity problem CKM unitarity requires for the 1 st row: |V ud | 2 +|V us | 2 + |V ub | 2 = 1 (PDG) Particle Data Group (PDG) 2004 review: |V ub |=(3.67 0.47)10 -3 [negligible contribution into unitarity relation, ~10 -5 ] |V ud |=0.9738 0.0005 [well measured, e.g. neutron lifetime] |V us |= 0.2200 0.0026 (sin Cabibbo ) [old measurements: semileptonic kaon decays] |V ud | 2 +|V us | 2 +|V ub | 2 = 1 (4.31.9)10 -3 (2.2 deviation from unitarity) E. Goudzovski JINR SC January 20, 2005 Slide 4 4 CKM unitarity: |V us | measurement Best way to determine |V us |: semileptonic (neutral and charged) kaon decays K e (K e3 ); A few recent measurements of BR(K e3 ) lead to |V us | values significantly above PDG 2004 values; New measurements of |V us | are desirable. E. Goudzovski JINR SC January 20, 2005 Slide 5 5 Determination of |V us | from BR(K e3 ) where Br(K e3( ) ) experimentally measured value; K kaon lifetime, measured by other experiments; f + (0) form-factor, evaluated theoretically; S EW =1.0232 short distance enhancement factor; I K phase space integral; C 2 =1 for K 0, C 2 =1/2 for K . |V us |= 128 3 Br(K e3( ) )/ K C 2 G F 2 M K 5 S EW I K 1 f + K (0) f + K 0 + (0) = 0.981 0.010 f + K + 0 (0) = 1.002 0.010 Form-factor calculation (Cirigliano, Neufeld, Pichl, EPJC35,53,2004) (evaluated with 1% precision) Precisions Kaon lifetimes: (K L )/ (K L )=0.8%; (K )/ (K )=0.2%; Desirable BR(K e3 ) precision: BR/BR0.93 for 1 track; 6.8 mln candidates selected. Data sample and selection E. Goudzovski JINR SC January 20, 2005 Slide 13 13 Background to K e3 sample: K 3 /K 3 with misidentified as e Estimated from K e3 data with identified e (E/p>1): Prob( e)=5.810 -3 Electron/pion separation E. Goudzovski JINR SC January 20, 2005 Quality of electron ID can be estimated from the data itself! Inefficiency of electron ID: Estimated from data with identified (0.3 Slide 14 14 Monte Carlo simulation To determine acceptances, Monte Carlo simulation of 5 significant 2-track modes involved (radiative corr. included): Decay channelBR (PDG04)Acceptance K L e 38.8%0.2599 K L 27.2%0.2849 KL+-0KL+-0 12.6%0.0975 KL+-KL+- 2.110 -3 0.5229 KL000DKL000D 7.610 -3 0.0001 For average 2-track acceptance use ratios of BR: averages from PDG + KTeV (B 3 /B e3, B 3 /B e3, ) Absolute BRs are not used! Acceptance(2-track events) = 0.2412 0.0004 Small normalization uncertainty: A/A=0.16% E. Goudzovski JINR SC January 20, 2005 Slide 15 15 Errors on R= (K e3 )/ (2-track) Statistical errors are negligible; Dominating systematic uncertainty: due to inexact knowledge of beam energy spectrum; Summary of systematic errors: R/R, % Energy spectrum0.67 Normalization (input BR)0.16 E/P cut (electron ID)0.05 Trigger efficiency0.05 DCH overflows0.05 Magnet polarity0.07 E. Goudzovski JINR SC January 20, 2005 Slide 16 16 Data/Monte Carlo comparison Profiles at drift chamber Kaon energy spectrum: major uncertainty E. Goudzovski JINR SC January 20, 2005 Slide 17 17 Br(K L e ): result Experimental result: R = (K L e ) (K L all two-track) = 0.4978 0.0035 To compute Br(K L e ) we use Br(K L 3 0 ): PDG 04: 0.2105 0.0023 KTeV 04 prel.: 0.1945 0.0018 Br(K L 3 0 )=0.1992 0.0070 Result on K e3 branching ratio: Br(K L e ) = 0.4010 0.0028(exp) 0.0035(norm) = 0.4010 0.0045 (inconsistent data; scale factor applied to error) E. Goudzovski JINR SC January 20, 2005 Phys.Lett. B602 (2004) 41 Slide 18 18 From BRs to unitarity test Br(K ) = (5.14 0.06)% Br(K L ) = 0.4010 0.0045 K : f + (0)|V us | = 0.2245 0.0013 K L : f + (0)|V us | = 0.2146 0.0016 K : |V us | = 0.2241 0.0026 K L : |V us | = 0.2187 0.0028 (PDG: 0.2200 0.0026) |V us |f + (0) ~ Br(K e3 )/ K [accuracy 1.1%] [1.1%] [0.6%] [0.7%] [1.3%] [1.2%] E. Goudzovski JINR SC January 20, 2005 Slide 19 19 Results on |V us |f + (0) 0.2 0.21 0.22 0.23 0.24 0.25 0.26 |V us |f + (0) NA48: K L NA48/2: K (preliminary) (2003) E. Goudzovski JINR SC January 20, 2005 PL B602 (2004) 41 Slide 20 20 Conclusions Values of |V us | obtained by experiments before 2003 are in poor agreement with CKM unitarity; Recent NA48 measurements of |V us |: From K : In agreement with new BNL result and CKM unitarity; In disagreement with the old measurements; From K L : In agreement with new KTeV and KLOE measurements; In better agreement with CKM unitarity than the old measurements. More precise calculations of f + (0) are desirable. E. Goudzovski JINR SC January 20, 2005