1. 1 A New Physics Study in B  K  & B  K*  Decays National Tsing Hua University, October 23, 2008 Sechul OH ( 吳世哲 ) ( 오세철 ) C.S. Kim, S.O., Y.W. Yoon, PLB665, 231 (2008) C.S. Kim, S.O., C. Sharma, R. Sinha, Y.W. Yoon, PRD76, 074019 (2007)

2. 2  The puzzle  The B  K  puzzle  A model-independent analysis of B  K  reparametrization invariance  -- reparametrization invariance -- how to extract New Physics effects  -- how to extract New Physics effects  A model-independent analysis of B  K*   -- interesting observables sensitive to New Physics  effects   Summary

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6. 6  Cabibbo-Kobayashi-Maskawa (CKM) matrix Unitarity: Unitarity triangle:   

7. 7 Direct CP violation in decay occurs when  Direct CP violation  Time-dependent CP violation = J/  K s

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9. 9 q q - The dominant quark level subprocesses are loop (penguin) processes  b  s penguin is sensitive to NP The 4 decay channels (& antiparticle decay channels)

10. 10 Large Smal l Conventional Hierarchy in B → Kπ strong penguin EW penguin color-suppressed tree

11. 11 Branching Ratios Fleischer Hep-ph/0701217 March 2007: Rc = 1.11 ± 0.07 Rn = 0.97 ± 0.07 = 0SM :

12. 12 CP Asymmetries SM :

13. 13 Amplitude parameterization Hierarchy between the parameters q q -

14. 14 Final form We neglect We set the strong phase of P to be zero  all phase is relative to it We hold 7 unknown parameters We use  value given by other analyses are real and positive, are phases of their amplitude

15. 15 NP term is absorbed into SM term: “Reparametrization invariance” of decay amplitudes Botella and Silva

16. 16 Original Form does not change: If there is NP,

17. 17 Analytic Solution

18. 18 4 different solutions for  We reject “Cases 1 & 3” due to predictions different from data  The SM estimate  Case 2: Large C  Case 4: Large EW ( 4-fold discrete ambiguity )

19. 19 Find solutions for NP term 4 real equations vs 7 unknowns: Need at least 3 additional inputs to fix NP terms

20. 20 Additional inputs from flavor SU(3) symmetry From B   decays Assuming no NP in B   Additional inputs

21. 21 B   parametrization with 5 parameters   -fitting with 5 measurements 3 Br’s, Gronau, Pirjol, Yan (1999)

22. 22 Li, Mishima, Sanda, PRD72, 114005 (2005) Additional inputs from PQCD result

23. 23 Solution for NP term with additional inputs Defining With inputs from SU(3) symmetry With inputs from PQCD results Cases 2 & 4 are suitable and consistent each other between two methods. Determining NP parameters

24. 24 Dependance on

25. 25  Due to the Reparametrization Invariance(RI), the NP terms can be absorbed into the SM terms C & P EW in pair.  In order to extract NP parameters, we need at least 3 additional inputs.  We could pin down each hadronic parameter under four-fold discrete ambiguity using analytic method. And also NP parameter for given additional inputs.  The result shows that there should be quite large NP contribution with a maximal weak phase ~  /2.

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27. 27 B → V V decays by angular momentum conservation B ! V 1 V 2 Spin: 0 ! 1 + 1 ) L = 0, 1, 2 or S, P, D waves S z : 0 ! 1 + (-1) (-1) + 1 0 + 0 helicity: decay amplitudes: In the B rest frame, the momenta of V 1 and V 2 are equal and opposite.  the helicities of both vector mesons are same.

28. 28 ♦ The most general covariant amplitude for B  V V Helicity basis Transversity basis paralleltransverselongitudinal

29. 29 Total decay rate (in the B rest frame) Longitudinal & Transverse polarization fractions Standard model estimation:

30. 30 Time dependent measurement For B  V V decay modes, ( g depend purely on angles describing the kinematics )

31. 31 35 independent observables (18 magnitudes + 17 relative phases) Time dependent measurement: Observables Observables

32. 32 Observables for B  K  [ Example of B  P P case ] Observables for B  K  [ Example of B  P P case ] Only 9 observables

33. 33 An example of New Physics study beyond the Standard Model by using B  V V decays B  K* 

34. 34 q q - B  K*  is a vector version (B  V V) of B  K  (B  P P) The dominant quark level subprocesses are loop (penguin) processes  b  s penguin is sensitive to NP We expect that NP contribution to B  K*  has the same nature as that of B  K  B  K*  (B  V V) provides enormously many observables

35. 35 Large Smal l Conventional Hierarchy in B  K*  strong penguin EW penguin color-suppressed tree

36. 36 Parameterization of decay amplitudes Parameterization of decay amplitudes Isospin relations: Hierarchy relation in the SM:

37. 37 Investigate how much sensitive to possible NP effects each observable for decays could be. Assume that NP contributing via the EW penguins. For simplicity, further assume that the SM amplitudes and are known (by additional information from somewhere, e.g. from future theoretical estimates). Thus, the SM amplitude is the only one modified by NP. (SM part)(NP part)

38. 38 Procedure: (i) In order to determine the theoretical parameters, adopt the   minimization technique & use the  currently available experimental data as constraints on the parameters. (HFAG) : longitudinal polarization fraction

39. 39 (ii) [number of data] < [number of parameters] Try to fit the dominant strong penguins and their phases with, first. (iii) Assume that the SM amplitudes ( ) follows the conventional hierarchy as in within the SM: in PQCD, (iv) Using the parameters determined, calculate all the 35 observables in the SM. (v) To investigate the possible NP effects, consider two different cases. (SM part)(NP part)

40. 40 For illustration: Very sensitive to NP:

41. 41 For illustration: Very sensitive to NP:

42. 42 For illustration: Very sensitive to NP:

43. 43 For illustration: Very sensitive to NP:

44. 44  B  K*  decays: useful for New Physics study certain observables are expected to be very sensitive to NP effects.  B  V V measurements B factories: Belle (KEK), BaBar (SLAC, closed), LHC-b (CERN), Tevatron (Fermi Lab), Super-B (?)