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MSSM Anatomy of the Polarization Puzzle in B --> phi K* Decays

We analyze the $B \to ϕK^{*}$ polarization puzzle in the Minimal Supersymmetric Standard Model (MSSM) including the neutral Higgs boson (NHB) contributions. To calculate the non-factorizable contributions to hadronic matrix elements of operators, we have used the QCD factorization framework to the $α_s $ order. It is shown that the recent experimental results of the polarization fractions in $B\to ϕK^{*}$ decays, which are difficult to be explained in SM, could be explained in MSSM if there are flavor non-diagonal squark mass matrix elements of 2nd and 3rd generations, which also satisfy all relevant constraints from known experiments ($B\to X_sγ, B_s\to μ^+μ^-, B\to X_s μ^+μ^-, B\to X_s g, ΔM_s$, etc.). We have shown in details that the experimental results can be accommodated with the flavor non-diagonal mass insertion of chirality RL, RL+LR, RR, or LL+ RR when the NHB contributions as well as $\mathcal{O}(α_s)$ corrections of hadronic matrix elements of operators are included. However the branching ratios for the decay are smaller than the experimental measurements.