Kaons and the CKM Matrix

1. Kaons and the CKM Matrix Ed Blucher University of Chicago • Kaons and the Unitarity Triangle • Vus and related measurements • Conclusions

2. Kaons and the CKM Matrix • 1964 observation of KL 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, . KL~ Kodd + Keven  “Indirect” from asymmetric mixing “Direct” in decay process 

3. KTeV Detector NA48 Detector KL KL + KS

4. KTeV CsI Calorimeter NA48 LKr Calorimeter

5. Calorimeter Performance KTeV NA48

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

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

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

9. Measurement allows clean determination of |Vtd| (~5% th. error) 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. Combined E787/E949 Result: Standard Model: ~0.81 Analysis underway for p<195 MeV/c

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

11. E391a Experimental Method

12. E391a Experiment

13. E391a Preliminary Limit Preliminary result from 1 week of data during first run: 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. • Goal with run III: Single event sensitivity near Grossman-Nir bound.

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

15. New Determinations of |Vus| Unitarity Tests of CKM Matrix: Uncertainty on j Vij2 0.2% 2.7% 30 % For first row, PDG quotes 2.2  deviation from unitarity:

16. 2002 PDG |Vux| Evaluations |Vud| = 0.9734  0.0008 from 0+0+ nuclear  decays, neutron decay |Vus| = 0.2196  0.0023 from K+, K0 decays to e ( not used by PDG because of large uncertainties in form factor measurements). |Vub| = (3.6  0.7)  103 from semileptonic B decay 2003 K+ measurement from BNL E865 consistent with unitarity. Interesting to revisit K0 measurements (PDG fit values based on averages of many old experiments with large errors)

17. Determination of |Vus| in Semileptonic K Decays |Vus|2 Experiment: form factors needed to calculate phase space integrals Experiment: B(Ke) and B(K),  SU2 corr. for K+ (theory) Form factor at t=0 (theory) Rad. Corrections (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. New Measurements since 2003 (“the kaon revolution” – Marciano) • KTeV measured 6 largest KL branching fractions and KL • semileptonic form factors (Ke3 and K3) + Ke3, K3 • NA48 measured KLe/charged fraction, B(KL), • Ke3 FF, B(K+e3) + Ke3, K3 • KLOE measured main KL branching fractions, KL lifetime, • B(KSe), B(K+), and recently, B(KL+). • ISTRA+ has measured K+e3 branching fraction and FF

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

21. Simple event reconstruction and selection may be used to distinguish different decay modes with very little background. KLOE NA48 Dmp = Minimum cPmiss - Emiss for  hypothesis

22. KTeV Particle Identification

23. Note: branching fractions include inner bremsstrahlung contributions for all decay modes with charged particles. KTeV: Data – MC Comparison for Radiative Photon Candidates It is critical to include radiation properly in Monte Carlo simulation. E.g., for KTeV, radiation changes Ke3 acceptance by 3%; effect on other modes is < 0.5%. Both KTeV and NA48 have published new measurements of B(Ke3) and B(K3)

24. KTeV Measured Partial Width Ratios

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

26. How could PDG averages be so far off? Comparison with Individual Experiments • 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.

27. + data KLOE KL Lifetime Measurements • “Indirect method” – from branching fraction measurement. • Detector acceptance depends on L. Comparison of B(KLi) + small with 1 can be used to determine  L= (50.720.140.33) ns 2. “Direct method” using using KL000 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 Events/0.3 ns t*= LK/c (ns)

28. Determination of |+| Using B(KL) KL-KS Interference

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

30. KL Form Factor Results

31. Input to Calculate “Recent” |Vus| (on next page) B(KLe3): KTeV, KLOE, NA48 B(KL3): KTeV, KLOE B(KSe3): KLOE B(K+e3): E865, NA48, KLOE, ISTRA+ L: KLOE+PDG average S: KTeV, NA48 average +: PDG K0: 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 Average of all “recent” results accounting for correlations:  theory Uses updated |Vud| = 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3measurements result in +3% shift in |Vus| compared to PDG 2002, and are consistent with CKM unitarity (depending on f+(0)) • Other methods (K2/2, ) give somewhat lower |Vus|; new measurements of 0+0+ nuclear  decays in progress. • 5-8% shifts observed in main KL branching fractions. Value in repeating old measurements with modern, high statistics experiments. • First results from dedicated KL experiment E391a. • Next generation of rare K decay experiments hold promise of precision determination of ,  to compare with B system.