CP asymmetries in $B\to \varphi K_S$ and $B\to {\eta }^{\prime }{K}_S$ in MSSM

Abstract

We study the $B\to \varphi K_S$ and $B\to \ep K_S$ decays in MSSM by calculating hadronic matrix elements of operators with QCD factorization approach and including neutral Higgs boson (NHB) contributions. We calculate the Wilson coefficients of operators including the new operators which are induced by NHB penguins at LO using the MIA with double insertions. We calculate the ${\alpha }_s$ order hadronic matrix elements of the new operators for $B\to \varphi K_s$ and $B\to {\eta }^{\prime }{K}_s$. It is shown that the recent experimental results on the time-dependent CP asymmetries in $B\to \varphi K_S$ and $B\to \ep K_S$, $S_{\varphi K}$ is negative and $S_{{\eta }^{\prime }K}$ is positive, which can not be explained in SM, can be explained in MSSM if there are flavor non-diagonal squark mass matrix elements of 2nd and 3rd generations whose size satisfies all relevant constraints from known experiments ($B\to X_S\gamma ,B_s\to {\mu }^{+}{\mu }^{-},B\to X_s{\mu }^{+}{\mu }^{-},B\to X_{s}g,\Delta M_s$, etc.). In particular, we find that one can explain the experimental results with a flavor non-diagonal mass insertion of any chirality when ${\alpha }_s$ corrections of hadronic matrix elements of operators are included, in contrast with the claim in the literature. At the same time, the branching ratios for the two decays can also be in agreement with experimental measurements.

21 pages, 23 figures. Some changes have been made, which include comments on contributions to $B\to \varphi K_S$ and $B\to {\eta }^{\prime }{K}_S$ from RR and RL insertion and some typing errors

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