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B P P ,V V decays and R parity Violating SUSY Rumin Wang Work done in collaboration with G. R.. Lu & Y. D. Yang Huazhong Normal University Henan Normal University November 15, 2005, Beijing Outline Motivation Theoretical input Polarization anomaly in B VV decays Puzzles in B PP decays Summary 2 Motivation for study To solve the polarization anomaly in B VV decays To solve the puzzles in B , K deacys 3 B VV Decay amplitude of B to VV in helicity basis: A f H i A0 A A Decay amplitudes in transversity basis: A0 A0 A ,|| ( A A ) / 2 Longitudinal polarization fraction: | A0 |2 | A0 |2 ( ~0.9 in SM ) fL 2 2 2 2 2 2 | A0 | | A | | A | | A0 | | A | | A|| | 4 B VV Surprise Tree + penguin : B , 0 and K * f L ~ 0.9 Pure penguin (Sensitive to NP): B K * , K *0 and K *0 ?? f L ~ 0.5 5 Previous study B VV 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 fL 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. 6 Motivation for study To solve the polarization anomaly in B VV decays To solve the puzzles in B , K decays 7 ? puzzle Br(Bd ) exp. Br(Bd ) SM 0 0 0 1.5x10^(-6) Br(B ) exp. d 10^(-7) 1 Br(B d ) SM 2 4.6x10^(-6) 8.3x10^(-6) ACP ( Bd ) exp . dir 0.319 0 ( B ) SM ACP d dir -0.057 8 ? K puzzle A dir CP ( Bd K ) ACP ( B K ) in SM But -0.120 dir 0 0.063 in Exp. 0 0 Br ( B K )exp. is larger than the SM prediction 11.4x10^(-6) 6.0x10^(-6) 9 B PP 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 . 10 Outline Motivation Theoretical input Polarization in B VV decays Puzzles in B PP decays Summary 11 Theoretical input The effective Hamiltonian in SM R-parity Violating SUSY QCD Factorization 12 The effective Hamiltonian in SM The effective weak Hamiltonian for B decays: GF 10 CKM H eff i Ci ( )Qi ( ) C7 ( )Q7 ( ) C8 g ( )Q8 g ( ) 2 i 1 SM Qi are local four-quark operators The decay amplitude in SM: A ( B M 1 M 2 ) M 1 M 2 H eff B SM SM ~ M 1 M 2 Qi ( ) B 13 R-parity Violating SUSY R - parity : R p (1) 3B L2 S S is the particle spin B is the baryon number L is the lepton number R-parity violating superpotential: c c c c c 1 1 ˆ W R i Lˆ i Hˆ u 2 [ij]k Lˆ i Lˆ j Eˆ k ijk Lˆ i Q j Dˆ k 2 i[ jk ]Uˆ i Dˆ j Dˆ k L 1 B 1 : Yukawa couplings i, j,k : generation indices C : charge conjugate field 14 The four fermion effective Hamiltonians due to the exchanging of the sleptons: 1 5 1 5 , PR 2 2 s (m ~f ) 2 , 0 11 n f s (mb ) 3 PL i The effective Hamiltonians due to the exchanging of the squarks: 15 R-parity Violating decay amplitude: A ( B M 1M 2 ) R M 1M 2 H B R ~ M 1M 2 Q i ( ) B R 16 The total decay amplitude: A ( B M 1 M 2 ) ASM ( B M 1 M 2 ) AR ( B M 1 M 2 ) ~ M 1 M 2 Qi B M 1 M 2 Qi B ? Naïve factorization, Generalized factorization, QCD factorization, Perturbative QCD, Light-cone QCD sum rules, Lattice QCD, Soft-collinear effective theory, etc. 17 QCD Factorization BBNS approach: PRL 83:1914-1917,1999 NPB 591:313-418, 2000 Naïve Factorization: M 1 M 2 (q2 q3 ) (V A) (b q1 ) (V A) B M 2 (q2 q3 ) (V A) 0 fM M 1 (b q1 ) (V A) B F 2 B M1 QCD Factorization: M 1 M 2 (q2 q3 ) (V A ) (b q1 ) (V A ) B M 2 (q2 q3 ) (V A ) 0 M 1 (b q1 ) (V A ) B 1 r n n s ( QCD / mb ) 18 Outline Motivation Theoretical input Polarization in B VV decays Puzzles in B PP decays Summary 19 Polarization in B VV decays Based on paper: Phys.Rev.D72:015009(2005) 20 Longitudinal polarization RPV SUSY ? B VV Polarization Anomaly !! 21 RPV effects in B K * | i23i22* | [1.5 103~Li2 ,2.1 103~Li2 ] previous bound : 2.3 103 ~ f 100 Gev 2 m ~f 2 22 RPV effects in B ρK * 23 Bounds by B K * 24 RPV effects in Β ρρ 25 The polarization anomaly could be solved by RPV effects. 26 Outline Motivation Theoretical input Polarization in B VV decays Puzzles in B PP decays Summary 27 Puzzle in B K decays Based on paper: hep-ph/0509273 28 B PP Branching ratios Puzzle !! 29 B PP ACPdir Direct CP asymmetries Br ( B f ) Br ( B f ) Br ( B f ) Br ( B f ) (B is Bd0 or B-u ) RPVPuzzle SUSY !! ? 30 The allowed parameter spaces constrained by B 31 Bounds by B 32 The allowed parameter spaces constrained by B K 33 Bounds by B K 34 B , K puzzles could be solved by RPV effects 35 Outline Motivation Theoretical input Polarization in B VV decays Puzzles in B PP decays Summary 36 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. 37 38 39 SM particles & Higgs bosons : R P 1 Squarks, sleptons & higgsinos : R P 1 [ ij ] k : ijk jik i[jk ] : ijk ikj 1 for Q i 3 1 B for u i , d i 3 B 0 for other B L 1 for L i L -1 for ei L0 for other 40 R-parity Violating decay: ~ Not d , for i[jk ] is antisymmet ric in e p 0 " j" and " k" e K 0 0 41 Ratios of branching ratios B 1.069 B u d 42 Branching ratios B VV 43