1. Search for New Physics in B decays Tadashi Yoshikawa Nagoya U. KEKPH07 3/1 – 3/3

2. We are going to next stage to search for • New physics hiding well ! Kobayashi-Maskawa Theory ( CKM matrix) are almost confirmed !! Unitarity Triangle :

3. Where are they hiding ? Where can we find them in ? direct search Indirect search VS tree loop High luminosity Exp. High energy exp. Both approach are important to understand (find) new Physics . B Physics are going to indirect search of New Physics . They will give us some useful hints and strong constraints for new Physics.

4. Example: Ishidori and Paradisi (hep-ph/0605012) Constraints for tan b and charged Higgs mass in the MFV within the MSSM. g-2 A Case: m = 1.0 TeV , Au = -1.0 TeV (Belle)

5. Main Targets are in Penguin processes . ｂ s u Bd u d d b – s(d) gluon penguin b – s(d) electro weak penguin …….. They will give us some useful hints and strong constraints for new Physics.

6. Searching for New Physics in B decays Investigating Penguin effects. How to handle these penguin processes? How to play with penguin. ｂ d π＋ u Bd u π－ d d

7. Plan of this talk: • Introduction • Status of several puzzle Scp of B f K, h’K K p puzzle Still remaining the window for NP ? • BV ll and BKp ll

8. Time-dependent CP Asymmetry : Bigi and Sanda c J/j b B B K c J/j b s B K No CP phase in diagrams cc mode S penguin s b B

9. Φ１＝　２１．２±１．０　°

10. Discrepancy of Scp between CC modes and b-s modes in the SM The EX. Data are moving to the SM direction !!

11. Almost 0!! Af direct CP violation Sf mixing CP violation : fM (phase of B-B mixing)　～f１ fＤ(phase of A(Bf) ) Comparison by CP asymmetry Time-dependent CP asymmetry:

12. New Physics window is still remaining ? 2005 2005

13. 2003 SM discrepancy

14. 2004 SM

15. 2005 SM

16. 2006 SM

17. How do you think about this situation ? Still remaining deviation. There were many many works to explain these deviations, SUSY, extra D model ……… It will give us several useful hints or constraint to build new model !! As the Next step, we should consider comparison among each decay modes even if the modes are b-s penguin. We have to investigate carefully the detail each contributions. Kim, Kwon, Lee, TY New Physics is hiding them !! SK0p0 may have some hints of New Physics. SK0pi0 = 0.31 ± 0.26 Kp puzzle

18. Present status of the Kp Puzzle Lipkin Yoshikawa( 03)., Gronau - Rosner, Buras-Fleischer et al , Li, Mishima and Yoshikawa(04) ……. Many works. What was the Puzzle ? . Discrepancies from expectations by Sum rule among the branching ratios. (Theory) (After ICHEP06) Still remaining this Problem ??

19. History of Rc- Rn 0 or not Rc – Rn Rc Rn The EX. Data are moving to the SM direction !!

20. 2006 HFAG

21. What can we learn from the K pi puzzle ?

22. Gronau, Hernandez,London, Rosner Diagram Decomposition Relation among amplitudes : Isospin relation Several Sum rules for Br and Acp .

23. B decays ：topological diagram decomposition Gronau, Hernandez,London, Rosner b b B B Ｔｒｅｅ QCDＰｅｎｇｕｉｎ b Color suppressed tree b ElectroWeak Penguin (PEW) B B Annihilation Color suppressed EWPenguin (PCEW) Singlet QCD Penguin b b b B B B

24. Hierarchy Assumption in B  Kp Naïve factorization method ＰＱＣＤ (Leading order) O(0.1) O(0.01)

25. Branching ratios under the assumption by neglecting r2terms including rC, rcEW , rA (smaller terms than O(0.01 ). )

26. Rc - Rn The difference comes from r^2 O(0.1^2) terms !!! ＝０．２１±　０．１１　　　　≠　O（０．１＾２）　　　（２００５） ＝０．１２±　０．１０　　　　O（０．１＾２）　　　（ICHEP０６）　 The Origin of Sum rule breaking is Electro Weak Penguin ?? rEW : Electro Weak Penguin Contribution

27. Maximum of Rc – Rn for delta(EW) and rew Rc – Rn rew = 0.14, 0.2, 0.3, 0.4 0.4 0.4 0.3 0.3 0.2 0.2 0.14 0.14 d(EW) Strong phase of EW penguin

28. dT + Direct CP Violation of B  K+ p- -0.093 0.015 as a function of dT with rT= 0.2 . dT should be around 15o or 155o Fleischer-Mannel bound Cos dT > 0 is favored. dT should be around 15o.

29. What can we expect 1) 2) No strong phase difference between tree and EW(Z) penguin under SU(3) symmetry. Because the diagrams are topologically same. z K W b b Neubert-Rosner, Buras and Fleischer u B s B K EW Penguin tree

30. If the strong phases of tree and EW penguin should be same, small discrepancy is still remaining!! Rc – Rn rew = 0.14, 0.2, 0.3, 0.4 0.4 0.4 If Rc – Rn keep the positive value, EW penguin should have extra (new) phase. 0.3 0.3 0.2 0.2 0.14 0.14 New Physics window ? d(EW) Strong phase of EW penguin

31. New Physics solution Consider a case that EW Penguin including NP with New CP Phase. New Phase rew = 0.14, 0.2, 0.3, 0.4 The maximum bound of Rc – Rn for qEW at d( EW) = d(T) and rT = 0.2 and under constraint Acp. 0.40 Rc - Rn 0.30 0.40 q(EW)around 270o is favored 0.20 0.30 0.14 0.20 q(EW)

32. Relaxing the hierarchy assumption= keeping r2C terms in Kp. rC rC Allowed Allowed Need 3 times larger rEW rEW prediction prediction Large rc solution in NLO PQCD -- Li, Mishima and Sanda PRD72:114005

33. 2) Direct CP asymmetry : theoretically、　 1 >r_T ~ r_{EW} > r_C > r_A expectation BUT different!! Experimental data, New Physics ? In rEW EW penguin ? or Large rc contribution ?

34. Direct CP asymmetries in B  Kp 0.025 Relation among the CP asymmetries : (SUM rules) Consistent ? Large EW Penguin ? Or Still early ?

35. Direct CP asymmetries in B  Kp 0.025 Relation among the CP asymmetries : (SUM rules) Still depend on Acp00 . Need more precise data!!

36. If EW Penguin : ( Z penguin ) : should include new phase, the effect will appear in semi-leptonic decays . But to investigate the effects in C10 process is slightly difficult !! CP asymmetry of B ll or B Xs ll final states are both CP odd and even . tiny Br Need angular analysis of B  K pi ll . Let’s consider semi-leptonic decays

37. BK* l l decay matrix element Z penguin b-s g Tiny contribution in SM l^- K qK B K* ql l^+ B (K* K p) + l l p Forward-Backward Asymmetry l^+ l^+ - B K* B K*

38. How to detect the evidence of New Phys. by B K* ll . We need to remove the hadronic uncertainty !! We should use some asymmetries : V, Ti, Ai : B-K* Form Factors Using Forward-Backward asymmetry: The zero of FB asymmetry is rather insensitive to hadron uncertainty . AFB AFB B K* ll C7 ~ + 4 Depend on C7 and C9. -C7 z = (pl^+ + pl^-)^2 How about BK pi l l decay ? Dilepton invariant mass

39. -C7 C7

40. The angular distribution : definition of the angles φ K l+ qk θl K* γ z B π l- θl：　angle between l+ momentum direction and z axis at CM system of (l+ l- ) FB asymmetry q K：　angle between π direction and - z axis at CM of (K pi ) φ：　angle between ２　decay planes There are 3 angles. Can not we use them ?

41. Using angle between decay planes: An Example: Kim, Kim, Lu and Morozumi, PRD62:034013 hep-ph/0001151 Grossman and Pirjol, JHEP0006: 029 hep-ph/0005069 in B K pi ll decay Points: Using small-q^2 region, ( q^2 ~ 0 ) We can neglect 1) local interactions with O9, O10 2) longitudinal modes, A0 One can investigate B　Vγby using polarization analysis or angular distribution A : CP-even A⊥ : CP-odd = From angular distribution analysis Time dependent CP

42. After integrating angles and q^2 at small region, approximately, Angler analysis where Small contribution in SM From the distribution for angle φ + B->V γ、one can extract C7 C7’ which may be including new physics info.

43. B  K p l l mode Kruger,Sehgal, Shinha, Shinha Kruger, Matias The branching ratios is After integrating all angles, G1 remains as the decay rate. The other terms shown the angular distribution. CP: odd CP: odd CP: even CP: odd CP: even CP: odd

44. If Possible, we would like to extract these contributions by using FB asymmetries. FB asymmetry for l^+ CP: odd Triple FB asymmetry CP: even An asymmetry for f CP: odd Triple FB asymmetry CP: odd Double FB asymmetry for f and qk CP: odd CP: even

45. CP Asymmetries Direct CPA CP phase Strong phase difference Need strong phase difference !! の　imaginary part (Buchalla 00) C9 is including strong phase comes from CC resonances However no phase in low q^2 region !!

46. FB asymmetry for l^+ FB2 Acp C10 i |C10| C7 -C7

47. If C7’ with CP phase exists, the effect will appear in FB4. FB4 C9 i |C9| C7’ not =0 If C7’ with CP phase exists, the effect will appear in FB4 and Acp .

48. Triple FB asymmetry If C7’ with CP phase exists, the effect will appear in FB5. FB5 C7’ not =0

49. Double FB asymmetry for f and qk FB6 C10 i |C10| C7’ not =0 -C7 C7

50. C10 i |C10|