1. 20 May 2006E. Blucher Kaons and the CKM Matrix Ed Blucher University of Chicago Kaons and the Unitarity Triangle V us and related measurements Conclusions

2. 1964 observation of K L     demonstrated CP violation and presented problem for the electroweak theory with 2 generations Kobayashi and Maskawa recognized that 3 generation theory allowed CP violation, with a single CP-violating quantity. Until 1999, however, there was only one measured CP violating parameter, . K L ~ K odd +  K even  “Direct” in decay process “Indirect” from asymmetric mixing  Kaons and the CKM Matrix

3. KTeV Detector K L +  K S KLKL NA48 Detector

4. NA48 LKr CalorimeterKTeV CsI Calorimeter

5. NA48 KTeV Calorimeter Performance

6. World average: Re(  ) = (16.6   6)    (confidence level = 10%) Measurements of Re(  )

7. Calculations of Re(  ) Re(  )  , but large hadronic uncertainties currently make it impossible to convert measurement of Re(  ) into a meaningful CKM constraint. Bertolini, Sozzi

8. B(K L   ) and B(K +  + ) can be used to determine ( ,  ) with little systematic uncertainty. K decays and the Unitarity Triangle

9. Combined E787/E949 Result: Standard Model: ~0.8  1   BNL E787 (95-98) observed 2 K +  + events. E949 involved modest detector upgrades and more data; goal 5-10 evts … but, run ended after 20% of proposed exposure. Measurement allows clean determination of |V td | (~5% th. error) Analysis underway for p  <195 MeV/c

10. Pure direct CP violation - clean measurement of  (~1% th. error) SM: Signature: Single unbalanced  0 Backgrounds: K L  , K L  3  , neutron interactions, etc. Best limit came from KTeV using    ee  E391 (KEK), the first experiment dedicated to began taking data in 2004. Model-independent limit (Grossman, Nir):

11. E391a Experimental Method

12. E391a Experiment

13. E391a Preliminary Limit Preliminary result from 1 week of data during first run: Goal with run III: Single event sensitivity near Grossman-Nir bound. Severe cuts required to reduce background from membrane. Resulting acceptance ~ 0.75%, an order of magnitude lower than design. Runs II and III will have higher acceptance lower background.

14. Isidori Current Constraints on  and  Planned experiments with goal of ~100 SM events in 2-3 year run JPARC: P326-aka NA48/3 (CERN) :

15. Unitarity Tests of CKM Matrix: Uncertainty on  j V ij 2 0.2% 2.7% 30 % For first row, PDG quotes 2.2  deviation from unitarity: New Determinations of |V us |

16. |V ud | = 0.9734  0.0008 from 0 +  0 + nuclear  decays, neutron decay |V us | = 0.2196  0.0023 from K +, K 0 decays to  e (  not used by PDG because of large uncertainties in form factor measurements). |V ub | = (3.6  0.7)  10  3 from semileptonic B decay Interesting to revisit K 0 measurements (PDG fit values based on averages of many old experiments with large errors) 2003 K + measurement from BNL E865 consistent with unitarity. 2002 PDG |V ux | Evaluations

17. Determination of |V us | in Semileptonic K Decays Experiment: B(K  e ) and B(K  ),  Experiment: form factors needed to calculate phase space integrals Rad. Corrections (theory) Form factor at t=0 (theory) |V us | 2 SU2 corr. for K + (theory)

18. 2003: BNL E865 Measurement of B(K +   e + ) Using 70,000 K + e3 decays normalized to K +    , K +    , K +      , they found B(K + e3 ) 5% higher than PDG. Result consistent with CKM unitarity at 1% level. Assumes other K + branching ratios are correct; B(K + e3 ) is only 5%. Data/MC comparison for e + momentum from    e + e   decay for signal and normalization decay modes.

19. KTeV measured 6 largest K L branching fractions and K L semileptonic form factors (K e3 and K  3 ) + K e3 , K  3  NA48 measured K L  e /charged fraction, B(K L       ), K e3 FF, B(K + e3 ) + K e3 , K  3  KLOE measured main K L branching fractions, K L lifetime, B(K S  e ), B(K +   ), and recently, B(K L  +   ). ISTRA+ has measured K + e3 branching fraction and FF New Measurements since 2003 (“the kaon revolution” – Marciano)

20. These six decay modes account for 99.93% of K L decays, so ratios may be combined to determine branching fractions. Ke3 K3K3 3030 +-0+-0 K L Branching Ratio Measurements KTeV measures the following 5 ratios: NA48 measures: KLOE (e + e   K + K , K L K S ) can tag one kaon and measure branching fractions using accompanying kaon; they measure branching fractions for 4 main K L decay modes assuming  B(K L  i)=1  small These may be combined to measure B(K e3 ).

21. Simple event reconstruction and selection may be used to distinguish different decay modes with very little background.    Minimum cP miss - E miss for  hypothesis KLOE NA48

22. KTeV Particle Identification

23. KTeV: Data – MC Comparison for Radiative Photon Candidates E.g., for KTeV, radiation changes K e3 acceptance by 3%; effect on other modes is < 0.5%. Note: branching fractions include inner bremsstrahlung contributions for all decay modes with charged particles. It is critical to include radiation properly in Monte Carlo simulation. Both KTeV and NA48 have published new measurements of B(K e3  ) and B(K  3  )

24. KTeV Measured Partial Width Ratios

25. Value based on PDG-style fit to all new measurements (KTeV, KLOE, NA48) Comparison of KTeV, NA48, KLOE, PDG K L Branching Fractions

26. PDG fit combined different width ratios from many (~40) experiments. It’s likely that many (most?) experiments did not treat radiation adequately, particularly for electron modes. These potentially large correlated systematic errors were not taken into account in the PDG fit. Comparison with Individual Experiments How could PDG averages be so far off?

27. KLOE K L Lifetime Measurements 1.“Indirect method” – from branching fraction measurement. Detector acceptance depends on  L. Comparison of  B(K L  i) +  small with 1 can be used to determine   L = (50.72  0.14  0.33) ns 2. “Direct method” using using K L  0  0  0 + data Events/0.3 ns t*= L K /  c (ns)  L =(50.87  0.16  0.26) ns Combining both KLOE results:  L =(50.81  0.23)ns PDG Average:  L =(51.5  0.4)ns New average:  L =(50.98  0.21)ns

28. Determination of |  +  | Using B(K L  ) K L -K S Interference

29. Semileptonic Form Factor Measurements (to determine I K integrals) I K depends on the two independent semileptonic FFs: f + (t), f  (t)

30. K L Form Factor Results

31. Input to Calculate “Recent” |V us | (on next page) B(K L e3): KTeV, KLOE, NA48 B(K L  3): KTeV, KLOE B(K S e3): KLOE B(K + e3): E865, NA48, KLOE, ISTRA+  L : KLOE+PDG average  S : KTeV, NA48 average  + : PDG K 0 : KTeV quadratic FF (including 0.7% model dep.) K + : ISTRA+ quadratic FF (including 0.7% model dep.) SEW (short-distance rad. corr) = 1.023 (Sirlin) Long-distance radiative corrections: (Andre, Cirigliano et al.)  e =0.0104  0.002 (was ~2% from Ginsberg)   =0.019  0.003  e + =0.0006  0.002  SU2 =0.046  0.04 (Cirigliano) f + (0)= 0.961  0.008 (Leutwyler – Roos) + recent calculations

32. Comparison with Unitarity  theory Average of all “recent” results accounting for correlations: Uses updated |V ud | = 0.9739  0.0003 (Hardy, Towner; Marciano,Sirlin -- Kaon 2005) Using f + (0)= 0.961  0.008 (Leutwyler – Roos), Assuming unitarity, = 0.227  0.001.

33. Conclusions New K 3 measurements result in +3% shift in |V us | compared to PDG 2002, and are consistent with CKM unitarity (depending on f + (0)) Other methods (K  2 /   2,  ) give somewhat lower |V us |; new measurements of 0 +  0 + nuclear  decays in progress. 5-8% shifts observed in main K L branching fractions. Value in repeating old measurements with modern, high statistics experiments. First results from dedicated K L  experiment E391a. Next generation of rare K decay experiments hold promise of precision determination of ,  to compare with B system.