Systematic Analysis of B  Ｋ πll decays

1. Systematic Analysis of B  Ｋπll decays Tadashi Yoshikawa Nagoya U. International Workshop “Towards the Precise Prediction of CP violation” Oct. 22 – 25, 2007 YITP, Kyoto University

2. To investigate CP phase is very important ! In SM and In New Physics !! and One of the most important aims of B factories and super B factory. It is very important to investigate by using B meson decays (or τdecays ).

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

4. Where are they hiding ? Where can we find them in ? direct search Indirect search VS tree loop B factory　→super B factory →　super-super B … 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.

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. As you know. A few years ago, We had several excitingly large discrepancies between the experimental data and theoretical expectations. 1) In CP asymmetries in b-sqq penguin decays, ex) B fK, h’K …. ( = 0 in SM) 2) In BKp decays, which are called “Kp puzzle”. = 0 Direct CP = 0 Time-dependent CP = 0

7. 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

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

9. Present status of the Kp Puzzle Lipkin, Atwood-Soni 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 LP07) Still remaining this Problem ??

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

11. As you know. A few years ago, We had several excitingly large discrepancies between the experimental data and theoretical expectations. 1) In CP asymmetries in b-sqq penguin decays, ex) B fK, h’K …. OK ? ( = 0 ) 2) In BKp decays, which are called “Kp puzzle”. = 0.14 ±0.10 Still remaining small windows.

12. 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 !! New Physics is hiding in them !! Where ? The several relations comes from main contribution, which is QCD penguin. The new contribution to explain these situations may be in EW penguin, because it is the sub-leading contribution. A possibility is new physics with new CP phase in EW Penguin!!

13. 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

14. What can we learn from the K pi puzzle ? We should be 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 strongphase difference ・Including both CP odd and even states ・Small interference termand X2 ∝ 1/q Slightly difficult to investigate the CP asymmetries !!

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

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

17. In this talk, I am going to introduce the following works: • New measurements using External Photon Conversion at a High Luminosity B Factory • Systematic analysis of BKπｌｌ　decays Ishino,Hazumi,Nakao, T.Y. hep-ex/0703039 Low invariant mass region, z = (p+ + p-)^2 ~ 0 C.S. Kim and T.Y, preparing now

18. Using Photon Conversion Ishino,Hazumi,Nakao, T.Y. hep-ex/0703039 Using photon conversions in detector, we may measure • Time –dependent CP asymmetry of Bp0p0 • BVg photon polarization At Super B factory

19. Using Photon Conversion • Time –dependent CP asymmetry of Bp0p0 : Sp0p0 To find Sp0p0 ,we need know the vertex position. But it is difficult to find Bp0p0decay vertex because the final states are neutral pions which go to 2 photons. Dt g g p0 g B p0 g B Tag side m Can not trace to a vertex from 4 photons !

20. Using Photon Conversion • Time –dependent CP asymmetry of Bp0p0 : Sp0p0 Conversion : g + X  ｌ+ｌ- Detector etal, e e Dt g g g p0 B p0 g B m Tag side Photon change to 2 leptons by conversion with some material inside so that can trace to vertex!!

21. Sp0p0 +- +0 00 Can get one more information to understand Bpp system ! Br(Bp+p-), Br(Bp+p0), Br(Bp0p0) Acp, Sp+p-, Acp, Acp, Sp0p0 New 6 measurements + 1+1  8 measurements For Tree, Penguin, Color-suppressed tree , EW-Penguin, strong phase differences (2 + 1), weak phase f2 After neglecting EW-penguin contribution, 6 measurements + 1 more vs 6 parameters

22. ?? We have several Questions. Is the isospin relation (triangle) exact one ? 1) Is Isospin triangle closed ? or 0 ? or 2) How is EW Penguin dependence ? PEW 3) Can we remove the discrete ambiguity for the solution ? which depend on how to use the 2 triangles X = qpp - qpp orqpp + qpp B decay A B decay A

23. B  V g using photon conversion By photon conversion : B  (K*Kp) + (g  l+ l- ) Semi-leptonic decaythrough Real photon, We can do angular analysisby f . φ K l+ qk θl K* γ z B π l- Can get information of Photon Polarization !!

24. Using Photon Conversion 2. BV gamma photon polarization Conversion : g + X  ｌ+ｌ- Detector etal, e e Dt g K B K* p B m Tag side Real Photon change to 2 leptons by conversion with some material inside so that can trace to vertex!!

25. 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 ?

26. NEGLIGIBLE b-s g Tiny contribution in SM　∝　ms/mb 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 Grossman and Pirjol, JHEP0006: 029 (2000) Kim, Kim, Lu and Morozumi, PRD62: 034013 (2000) Q^2 ～０ Grinstein and Pirjol, PRD73 014013 (2006) ｑ＾２

27. 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.

28. Atwood, Gershon, Hazumi and Soni, PRD71:076003 (2005) Combining with time dependent CP asymmetry : Where f+ is a phase of decay amplitude C7 or C7’ We can extract NEW CP Phase of EM penguins !! After finding R and f+ We should investigate the phase of C10 or C9 as Z penguin .

29. 2. Systematic Analysis of BKπlldecays Kim and T.Y. To be appear soon. 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).

30. 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 ?

31. Kruger,Sehgal, Shinha, Shinha B  K p l l mode Angular decomposition Kruger, Matias Kim,Kim,Lu,Morozumi Kim, T.Y. 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

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

33. 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

34. -C7 C7

35. 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

36. B  K p l l mode Decomposition by using 3 angle distribution 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

37. 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

38. Proportional (C9* C10) Usual FB asymmetry Double FB asymmetry for f and qk

39. Double FB asymmetry for f and qk Appear Im ( C10 C7 ) Imaginary part of C10 Note: s = q^2 = (Pk + Pπ)^2 z = k^2 = (P+ + P- )^2

40. An asymmetry for f Triple FB asymmetry

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

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

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

44. FB4 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 .

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

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

47. FB7 Sensitive to the phase of C10 and C7 C10 i |C10|

48. An Example FB2 The CP phase of C_9 are ０ π/８ π/４ π/2 FB2 －Sin2φ１

49. We need more strong phases . How about interferences between K^* and scalar resonance as intermediated states？ K K* l B S (scalar) l K0*(800) π We used Im parts Descotes-Genon, Moussallam EPJ C8, 553 We may get many fruitful informationfrom B  K pi lldecay modes. Angular analysis CP asymmetries We can define new FB like asymmetries!! There is another strong phase source by the resonance effects.

50. Here we are using and start from most general 4-fermi interaction C9, C10, C7 : SM parameters C9’, C10’, C7’ : L-R model et.al.Rcurrent Css, CAs, CsA, CAA : scalar type interactions CT, CTE : tensor type interactions