1. Electroweak B Decays T. Yoshikawa ( Nagoya ) Possibility of Large EW Penguin contribution FPCP2004 Oct. 4 – 9, EXCO, Daegu, Korea This talk is based on S. Mishima and T.Y. hep-ph/0408090 and T.Y. Phys.Rev. D68, 054023 (2003). and T.Y. Phys.Rev. D68, 054023 (2003).

2. B decays Ｔｒ ｅｅ QCD Ｐｅｎｇ ｕｉｎ Color suppressed tree ElectroWeak Penguin (P EW ) Annihilation Singlet QCD Penguin Color suppressed EW Penguin (P C EW ) Gronau, Hernandez,London, Rosner b

3. B decays Ｔｒ ｅｅ QCD Ｐｅｎｇ ｕｉｎ Color suppressed tree ElectroWeak Penguin (P EW ) Anihilation Color suppressed EW Penguin (P C EW ) Main Contributions T, P usually Negligible Contributions P C EW, A How should we treat P EW, C ?

4. Discrepancies between TH and EX K - Puzzle The direct CPVs are almost zero !! BUT the indirect CPV Ss are How about the differences among these b-s penguin modes ? Relations among the branching ratios Relation among Direct CP asymmetries Large B  Branching ratio CP asymmetries : B  K 0 (b-s penguin type modes ) vs B  J/ K 0 We discuss what happens in B  and decays. Fleischer-Mannel, Neubert-Rosner, Lipkin, Buras, … T.Y., Gronau - Rosner, Buras-Fleischer et al, Li, ……. Many works.

5. K  -  Puzzle Experimental data do not satisfy several relations among the branching ratios.    Before ICHEP04  TheoryExperimental There were quite large discrepancies.

6. Before ICHEP04 After ICHEP04 What changed ?

7. K  -  Puzzle 1) Experimental data do not satisfy several relations among the branching ratios.    After ICHEP04 Still remaining the discrepancies !!

8. K  -  Puzzle direct CP asymmetries of B  K . 2) There seems to be a discrepancy in direct CP asymmetries of B  K . After ICHEP04 Theoretically, Exeimental data, Is the relation among the A cp s violated ?

9. We have to know what makes the discrepancies! Do we still need large EW Penguin contribution ?

10. Diagram Decomposition of B  K  and 

11. Hierarchy in B  K  Ｔｒ ｅｅ QCD Ｐｅｎｇ ｕｉｎ Color suppressed tree EW Penguin (P EW ) Annihilation (Exchange) Color suppressed EW Penguin (P C EW ) Gronau, Hernandez,London, Rosner b Large Small

12. They are rewritten as follows: where r is the ratio of each diagram with QCD Penguin, and  X is the strong phase difference. where r is the ratio of each diagram with Tree contribution, and  X is the strong phase difference. A (Exchange) and P C EW are neglected here.

13. Hierarchy Assumption ＰＱＣ Ｄ in B  K  O(0.1) O(0.01)

14. Hierarchy Assumption in B   O(0.1) negligible

15. Branching ratios under the assumption by neglecting r 2 terms including r C, r c EW, r A (smaller terms than O(0.01 ). )

16. Fleischer-Mannel bound We can find several relations among them.

17. Some relations among the branching ratios These relation seems to be proportional to r 2 so that they should be O(0.01) quantities. =0 or not ?

18. Branching ratios Rough estimation under assumption ~ 1 ?

19. Experimental data > 0.1 1.04 + = 2 - = 0 - = 0

20. = = =    Do we need large EW penguin contribution ? Relations

21. 1  0.14 From the 1  bound of R c -R n, S, R + -2 with r T =0.2 We may still need slightly large EW penguin contribution. To discuss more detail, we need the information about strong phases. If flavor SU(3) sym. is good,    EW and    will be constrained by A CP. Consider about direct CP asymmetries !!

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

23. Direct CP asymmetries in B  K  Relation among the CP asymmetries : Large EW Penguin ? Or Still early ?

24. Cos  T > 0 is favored.  T should be around 20 o. Fleischer-Mannel bound -0.114  0.020 as a function of  T with r T = 0.2.  T should be around 20 o or 150 o  T +

25. Maximum bound of Rc-Rn under constraints from A CP and R with r T = 0.2. We still need large EW penguin contribution and large strong phase difference. is disfavored.

26. How about B   ? where. It seems to be difficult to explain by only EW penguin because it will be sub-leading contribution. because it will be sub-leading contribution. To explain the large ratios, we need 1) To suppress the denominator.        with     2) Larger r P < < 00

27. Large may be possible if there is SU(3) breaking effect between b-s P and b-d Penguins. BUT the magnitude will be constrainted from B  KK (pure b-d penguin ) modes. d s s K K Pure b-s penguin Pure b-d penguin At largest, P  is 1.5 times larger. We can not take so large.

28. How about B   ? where. It seems to be difficult to explain by only EW penguin because it will be sub-leading contribution. because it will be sub-leading contribution. To explain the large ratios, we need 1) To suppress the denominator.        with     2) Larger r P 3) Larger (color suppressed tree ) New Physics ?? Or New Physics ?? with new CP phase Before considering about New Physics, review the contribution from r C.

29. An example:        EW      C =  

30. Relaxing the hierarchy assumption= keeping r 2 C terms Relaxing the hierarchy assumption = keeping r 2 C terms in  The lower bound of r C to satisfy Rc-Rn, S, R + -2 at 1  bound.  s are free parameters 2)    EW  case If large is allowed, it may explain the discrepancies. Chiang - Gronau-Rosner-Suprum too large But it seems to be too large though it is color suppressed tree-type contribution. The usual estimation is 0.02. Charn ｇ -Li

31. Conclusion The allowed region of r EW should be larger than about 0.2. The allowed region of r EW should be larger than about 0.2. Still remaining the discrepancies ! Still remaining the discrepancies ! Large strong phase differences are needed. Large strong phase differences are needed. SU(3) breaking ? SU(3) breaking ? As a possibility, we need to consider Large r c case also. As a possibility, we need to consider Large r c case also. Direct CP asymmetries will be more important to understand Direct CP asymmetries will be more important to understand which is the origin of the discrepancies. which is the origin of the discrepancies. To keep, need new CP phase in Penguin type diagrams. Or Large r c case. To keep, need new CP phase in Penguin type diagrams. Or Large r c case. If P EW is including New CP Phase, the effect must appear in CP asymmetries, Acp 00 and S K 0   

32.    or + + Large    SU(3) breaking Possibility of New Physics ? or