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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

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2 Motivation Theoretical input Summary Outline

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

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

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

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6 Previous study Kagan show increasing nonfactorizable contribution of annihilation diagram to solve anomaly by QCDF( hep-ph/ ). But H.n. Li & Mishima: annihilation contribution is not sufficient to lower f L down to 0.5 by PQCD ( PRD 71, ). 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, ). However, H. Y. Cheng et al. have found the FSI effects not able to fully account for this anomaly ( PRD 71, ). We try to solve this anomaly including RPV SUSY effects.

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

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

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

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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/ ;PRD72, ). NP We try to calculate RPV SUSY effects.

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11 Motivation Theoretical input Summary Outline

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

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

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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

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

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16 R-parity Violating decay amplitude:

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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.

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18 BBNS approach: PRL 83: ,1999 NPB 591: , 2000 Naïve Factorization: QCD Factorization: QCD Factorization

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19 Motivation Theoretical input Summary Outline

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

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21 Longitudinal polarization Polarization Anomaly !! RPV SUSY ?

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26 The polarization anomaly could be solved by RPV effects.

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27 Motivation Theoretical input Summary Outline

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28 Based on paper: hep-ph/

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29 Branching ratios Puzzle !!

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30 Direct CP asymmetries Puzzle !! RPV SUSY ?

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36 Motivation Theoretical input Summary Outline

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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 R-parity Violating decay:

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42 Ratios of branching ratios

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43 Branching ratios

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