1. Systematic Analysis of B  Ｋ πll decays Tadashi Yoshikawa Nagoya U. ３ｒｄ International Workshop on “B factories and New Measurements” Jan. 24 – 26, 2008 Atami, Japan This talk is based on : C.S. Kim and T. Yoshikawa arXiv:0711.3880[hep-ph]

2. In Penguin processes as the loop effects. ｂ s u u d d BdBd b – s(d) gluon penguin b – s(d) electro weak penguin …….. They will give us some useful hints and strong constraints for new Physics. New Physics is hiding very well in B decays!! Important modes to find NP

3. New Physics is hiding very well in B decays!! The new physics may be hiding in EW Penguin!! Where ? Why ? If you can think K  puzzle is still remaining, One of the solutions is the contribution as an EW penguin with the new CP phase which may be induced by new physics. “K  puzzle” in B  K  decays. = 0 ( should be 0 within the SM) POINT!!

4. What can we learn from the K pi puzzle ? We should investigate pure EW penguin processes to find some evidences of New Physics (new CP phase ). (Direct or indirect ) CP asymmetries of EW processes ( b->s gamma, b->s ll ) BUT Tiny strong phase difference ・ Including both CP odd and even states ・ Small interference term and X 2 ∝ 1/k Slightly difficult to investigate the CP asymmetries !!

5. CP Asymmetries Direct CPA Strong phase difference CP phase Need strong phase difference !! Has imaginary part C9 is including strong phase comes from CC resonances However no phase in low k^2 region !! Z ＝ k^2 Im[C9]

6. 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  s gamma, B  Xs ll tiny Br final states are both CP odd and even. Need angular analysis of B  K pi ll. Let’s consider semi-leptonic decays Small strong phase.

7. 1.New measurements using External Photon Conversion at a High Luminosity B Factory 2.Systematic analysis of B  Kπ ｌｌ decays Ishino,Hazumi,Nakao, T.Y. hep-ex/0703039 C.S. Kim and T.Y, arXiv:0711.3880[hep-ph] At Low invariant mass region, z = (p+ + p-)^2 ~ 0 investigate CP phase in b->s  ll ] 2 methods At large invariant mass region, Investigate the CP asymmetries or FB asymmetry in B  K  ll.

8. 2. Systematic Analysis of B  Kπll decays C.S.Kim and T.Y. arXiv:0711.3880[hep-ph] Investigate the contributions of the new CP phase by using angular analysis and the CP asymmetries for B  Kπll 4 body decays. We defined several partial angle integration asymmetries, like Forward-Backward asymmetry (FB) and the CP asymmetries. Points: 1.There are 3 angles so that we can have many observables by angular decompositions. 2.Tiny CPV is enhanced by strong phases from cc resonance effects. 3.We may use the strong phase from K^*, K-scalar … resonances.

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

10. The branching ratios is After integrating all angles,   remains as the decay rate. The other terms shown the angular distribution. B  K  l l mode CP: odd CP: even CP: odd CP: even Kruger,Sehgal, Shinha, Shinha Kruger, Matias Kim,Kim,Lu,Morozumi Kim, T.Y. Angular decomposition

11. B  K* l l decay matrix element b-s  Tiny contribution in SM Z penguin B  (K*  K  ) + l l l^- l^+ ll    KK Forward-Backward Asymmetry    l^+ For example

12. How to detect the evidence of New Phys. by B  K* ll. Using Forward-Backward asymmetry: The zero of FB asymmetry is rather insensitive to hadron uncertainty. We need to remove the hadronic uncertainty !! We should use some asymmetries : C7C7 -C 7 A FB z = (pl^+ + pl^-)^2 Dilepton invariant mass A FB  V, Ti, Ai : B-K* Form Factors B  K* ll How about B  K pi l l decay ? Depend on C7 and C9.

13. C7C7 -C 7

14. 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 tiny Br final states are both CP odd and even. Need angular analysis of B  K pi ll. Let’s consider semi-leptonic decays

15. The branching ratios is After integrating all angles,   remains as the decay rate. The other terms shown the angular distribution. B  K  l l mode CP: odd CP: even CP: odd CP: even Decomposition by using 3 angle distribution

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

17. Here we are using and start from most general 4-fermi interaction C 9, C 10, C 7 : SM parameters C 9 ’, C 10 ’, C 7 ’ : L-R model et.al. R current C ss, C As, C sA, C AA : scalar type interactions C T, C TE : tensor type interactions

18. Usual FB asymmetry Double FB asymmetry for  and  Proportional (C 9 * C 10 )

19. Double FB asymmetry for  and  Appear Im ( C 10 C 7 )Imaginary part of C10 Note: s = q^2 = (Pk + Pπ)^2 z = k^2 = (P+ + P- )^2 Proportional Im(C 10 * C 7 )

20. An asymmetry for  Triple FB asymmetry Proportional Im(C 9 * C 7 ) Im(C 7 * C 7 ’ ) Im(C 7 * C 7 ’ )

21. CP Asymmetries Direct CPA Strong phase difference CP phase Need strong phase difference !! has imaginary part C9 is including strong phase comes from CC resonances Z ＝ k^2 Im[C9] no phase in low q^2 region !! And CP odd and even interference effect is also existing in the new FBs. Important points to use new FBs

22. The definition of direct and time-dependent CP asymmetries: s, z distributions  ＝ －  （ＣＰ odd) +1 (CP even) direct CPV of FB asymmetry direct CPV of FB asymmetry time-dependent CPV FB asymmetry

23. FB asymmetry for l^+ FB 2 C 10  i |C 10 | Acp C7 = C7 SM, C7’ = 0    /2   

24. FB 4 C 9  i |C 9 | C7 = C7 SM, C7’ = 0  ９   /2   

25. FB 5 Triple FB asymmetry FB 5 C7 = C7 SM, C7’ = 0  ９   /2   

26. C 10  i |C 10 | FB 6 Double FB asymmetry for  and  FB 6

27. Sensitive to the phase of C10 and C7 FB 7 C 10  i |C 10 |

28. An Example FB2 The CP phase of C_9 are ０ π/ ４ π/2 FB2 － Sin2φ １

29. We need more strong phases. How about interferences between K^* and scalar resonance as intermediated states ？ We may get many fruitful information from B  K pi ll decay modes. Angular analysis CP asymmetries  l l  S (scalar) K 0 *(800)   We can define new FB like asymmetries!! There is another strong phase source by the resonance effects. We used Im parts Descotes-Genon, Moussallam EPJ C8, 553

30. Here we are using and start from most general 4-fermi interaction C 9, C 10, C 7 : SM parameters C 9 ’, C 10 ’, C 7 ’ : L-R model et.al. R current C ss, C As, C sA, C AA : scalar type interactions C T, C TE : tensor type interactions

31. Br

32. With scalar resonance We can define new type FBs.

33. K meson FB asymmetry L-R asymmetry for angle  UP-Down asymmetry for angle  Triple asymmetry L-R for phi, FB asymmetry for lepton K K*(l+ l- ) 

34. If there is such scalar resonance effects, these new FBs will appear!! π/ ８ ０ π/ ４ π/2 CP Phase of C9 UP-Down asymmetry for angle  FB ４＾ｓ FB ２ ＾ｓ K meson FB asymmetry

35. Summary There are several discrepancies between Ex. and theory in B decays. But some ones seem to be moving to SM prediction. Still remaining the region for New Physics in EW penguin as the new CP phases. To understand and find the evidence of NP, we should investigate semi-leptonic rare decays. At Low invariant mass k^2 ~ 0 region Using photon conversions technique C 7 ’ and the CP phase Angular analysis and the CP asym. C10 or C9 CP phase With Scalar resonance effectNew information