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Rumin Wang Work done in collaboration with G. R.. Lu & Y. D. Yang

Rumin Wang Work done in collaboration with G. R.. Lu & Y. D. Yang. Huazhong Normal University Henan Normal University November 15 , 200 5 , Beijing. Outline. Motivation Theoretical input Summary. Motivation for study. To solve the polarization anomaly To solve the puzzles.

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Rumin Wang Work done in collaboration with G. R.. Lu & Y. D. Yang

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  1. Rumin Wang Work done in collaboration with G. R.. Lu& Y. D. Yang Huazhong Normal University Henan Normal University November15, 2005, Beijing

  2. Outline • Motivation • Theoretical input • Summary

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

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

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

  6. Previous study Kagan show increasing nonfactorizable contribution of annihilation diagram to solve anomaly by QCDF(hep-ph/0407076). ButH.n. Li & Mishima: annihilation contribution isnot sufficient to lower fLdown 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. Motivation for study • To solve the polarization anomaly • To solve the puzzles

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

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

  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. Outline • Motivation • Theoretical input • Summary

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

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

  14. R-parity Violating SUSY S is the particle spinB is the baryon numberL is the lepton number R-parity violating superpotential: : Yukawa couplingsi, j,k :generation indicesC :charge conjugate field

  15. The four fermion effective Hamiltonians due to the exchanging of thesleptons: • The effective Hamiltonians due to the exchanging of thesquarks:

  16. R-parity Violating decay amplitude:

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

  19. Outline • Motivation • Theoretical input • Summary

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

  21. Longitudinal polarization RPV SUSY ? Polarization Anomaly !!

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

  23. Outline • Motivation • Theoretical input • Summary

  24. Based on paper: hep-ph/0509273

  25. Branching ratios Puzzle !!

  26. Direct CP asymmetries RPV SUSY ? Puzzle !!

  27. Outline • Motivation • Theoretical input • Summary

  28. Summary • Employed QCDF to study RPV SUSY effects in following modes: • Polarization in B to VV . • 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: • SM is in no way ruled out. • Existence of New Physics. • Many more measurement are in progress.

  29. Thanks!

  30. R-parity Violating decay:

  31. Ratios of branching ratios

  32. Branching ratios

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