1. Rumin Wang G. R.. Lu& Y. D. Yang Work done in collaboration with G. R.. Lu & Y. D. Yang Huazhong Normal University Henan Normal University November 15, 2005, Beijing

2. 2  Motivation  Theoretical input   Summary Outline

3. 3 To solve the polarization anomaly To solve the puzzles Motivation for study

4. 4 Decay amplitude of B to VV in helicity basis: Decay amplitudes in transversity basis: Longitudinal polarization fraction: ( ~0.9 in SM )

5. 5  Tree + penguin : ( Sensitive to NP )  Pure penguin ( Sensitive to NP ) : ?? Surprise

6. 6 Previous study  Kagan show increasing nonfactorizable contribution of annihilation diagram to solve anomaly by QCDF( hep-ph/0407076 ). But H.n. Li & Mishima: annihilation contribution is not sufficient to lower f L down to 0.5 by PQCD ( PRD 71,054025 ).  Polarization anomaly might be due to large charming penguin contributions and final-state-interactions (FSI) by Colangelo et al. & Ladisa et al. ( PLB 597,291; PRD 70,115014 ). However, H. Y. Cheng et al. have found the FSI effects not able to fully account for this anomaly ( PRD 71, 014030 ).  We try to solve this anomaly including RPV SUSY effects.

7. 7 To solve the polarization anomaly To solve the puzzles Motivation for study

8. 8  1.5x10^(-6) 10^(-7)  4.6x10^(-6) 8.3x10^(-6)  0.319 -0.057 ?

9. 9  But But -0.120 0.063 in Exp.  11.4x10^(-6) 6.0x10^(-6) ?

10. 10 Previous study  Buras et al. point out B to pi pi can be nicely accommodated in the SM through nonfactorizable hadronic interference effects, whereas B to pi K system may indicate NP in the electroweak penguin sector (PRL 92,101804; NPB 697,133).  H. N. Li et al. & Y. D. Yang et al. study the next to leading order corrections by PQCD & QCDF, respectively. These higher order corrections may be important for Br(B to pi K), but the can not explain other experimental data( hep-ph/0508041;PRD72,074007 ). NP  We try to calculate RPV SUSY effects.

11. 11  Motivation  Theoretical input   Summary Outline

12. 12 Theoretical input The effective Hamiltonian in SM R-parity Violating SUSY QCD Factorization

13. 13 The effective Hamiltonian in SM The effective weak Hamiltonian for B decays: Qi are local four-quark operators The decay amplitude in SM:

14. 14 S is the particle spin B is the baryon number L is the lepton number R-parity violating superpotential: R-parity Violating SUSY : Yukawa couplings i, j,k : generation indices C : charge conjugate field

15. 15  The four fermion effective Hamiltonians due to the exchanging of the sleptons:  The effective Hamiltonians due to the exchanging of the squarks:

16. 16 R-parity Violating decay amplitude:

17. 17 The total decay amplitude: Naïve factorization, Generalized factorization, QCD factorization, Perturbative QCD, Light-cone QCD sum rules, Lattice QCD, Soft-collinear effective theory, etc.

18. 18 BBNS approach: PRL 83:1914-1917,1999 NPB 591:313-418, 2000 Naïve Factorization: QCD Factorization: QCD Factorization

19. 19  Motivation  Theoretical input   Summary Outline

20. 20 Based on paper: Phys.Rev.D72:015009(2005)

21. 21 Longitudinal polarization Polarization Anomaly !! RPV SUSY ?

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26. 26 The polarization anomaly could be solved by RPV effects.

27. 27  Motivation  Theoretical input   Summary Outline

28. 28 Based on paper: hep-ph/0509273

29. 29 Branching ratios Puzzle !!

30. 30 Direct CP asymmetries Puzzle !! RPV SUSY ?

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36. 36  Motivation  Theoretical input   Summary Outline

37. 37 Summary Employed QCDF to study RPV SUSY effects in following modes: o Polarization in B to VV. o Branching ratios & direct CP asymmetry in B to pi pi, pi K. RPV couplings can give a possible solution to the puzzles. Obtain the ranges of RPV couplings, but these are very narrow. The allowed spaces constrained by B to PP are consistent with these by B to VV decays. An explanation is need: o SM is in no way ruled out. o Existence of New Physics. o Many more measurement are in progress.

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41. 41 R-parity Violating decay:

42. 42 Ratios of branching ratios

43. 43 Branching ratios