1. 1 CKM unitarity problem: results from NA48 experiment Evgueni Goudzovski (JINR) JINR Scientific Council January 20, 2005

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

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  (4.3±1.9)∙10 -3 (2.2  deviation from unitarity) E. Goudzovski  JINR SC  January 20, 2005

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

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/BR<1% E. Goudzovski  JINR SC  January 20, 2005

6. 6 NA48 experiment at CERN SPS Main detector components: Magnetic spectrometer (4 DCHs) redundancy  high efficiency; Δp/p = 0.5% + 0.009%*p [GeV/c]. Hodoscope high granularity multiplicity trigger; precise time measurement (150ps). Liquid Krypton EM calorimeter (LKr) High granularity, quasi-homogenious; ΔE/E = 3.2%/√E + 9%/E + 0.42%; electron/pion discrimination;  registration. E. Goudzovski  JINR SC  January 20, 2005 DCH LKr HOD

7. 7 |V us | measurements by NA48 NA48/2 NA48/2: Semileptonic K ± decays: K ±  0 e (K e3 ) Data: 90k events in 8 hours of low intensity run 2003; Loose hodoscope trigger (1 charged track); NA48 NA48: Semileptonic K L decays: K L   e (K e3 ) Data: 6.8 mln events in 2 days of special run 1999; Trigger on 2 charged particles in DCH or hodoscope; NA48/1 NA48/1: Semileptonic  0 decays:  0  + e Data: whole high intensity run 2002 (6.2k events); Approach different to the one for kaon decays; These preliminary results are not discussed in this talk. E. Goudzovski  JINR SC  January 20, 2005

8. 8 Measurement method: normalize K e3 events to K     0 events (Br=0.2113  0.0014); Signal practically background free; Statistics selected from the minimum bias run: Br(K   0 e ) measurement DecayStatistics K +  + e 59∙10 3 K    e 33∙10 3 K +  +  0 468∙10 3 K     0 260∙10 3 E. Goudzovski  JINR SC  January 20, 2005

9. 9 K   0 e : Data/MC comparison Without radiative corrections With radiative corrections E. Goudzovski  JINR SC  January 20, 2005 Data/MC Data/MC

10. 10 Br(K   0 e ): result  Br Detector acceptance0.038% Trigger efficiency0.004% BR (K     0 ) 0.034% Radiative events0.006% MC statistics0.022% Total systematics0.056% Statistic uncertainty0.017% Preliminary NA48/2 result: Br(K   0 e ) = (5.14  0.02 stat  0.06 syst )% Main systematics: PDG 2004 NA48/2 BNL E865 K+K+ KK KK … confirms the deviation from PDG observed by BNL E865! … the most precise measurement of Br(K e3 )! E. Goudzovski  JINR SC  January 20, 2005 Branching ratio

11. 11 Measurement method: Use minimum bias trigger to collect K L  2-track events; Normalization to Br(2-track) = 1.0048  Br(3  0 ) Best input precision: ΔBr(2-track)/Br(2-track)<0.9% Exactly the same selection for signal (K e3 ) and normalization events, but electron identified by energy deposit in the LKr calorimeter; Measured quantity: Br(K L   e ) measurement R=  (K L  e )  (K L  all two-track) = N(K e3 )/acceptance(K e3 ) N(2-track)/acceptance(2-track) E. Goudzovski  JINR SC  January 20, 2005 Phys.Lett. B602 (2004) 41

12. 12 Data sample: ~80 million 2-track triggers taken during 2 days of minimum bias run with pure K L beam; Selection criteria: Conditions on track geometry and kinematics; Leave a sample of 12.6 million 2-track events; Additional criterion for K e3 : Electron ID: E(LKr)/P>0.93 for 1 track; 6.8 mln candidates selected. Data sample and selection E. Goudzovski  JINR SC  January 20, 2005

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)=5.8·10 -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<E/p<0.7): Prob(e  )=4.9·10 -3

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+- 2.1·10 -3 0.5229 KL000DKL000D 7.6·10 -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 BR’s are not used! Acceptance(2-track events) = 0.2412  0.0004 Small normalization uncertainty: ΔA/A=0.16% E. Goudzovski  JINR SC  January 20, 2005

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

16. 16 Data/Monte Carlo comparison Profiles at drift chamber Kaon energy spectrum: major uncertainty E. Goudzovski  JINR SC  January 20, 2005

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

18. 18 From BR’s 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

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

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