$B_s-{\bar{B}}_s$ Mixing and Its Implication for $b\to s$ Transitions in Supersymmetry

Abstract

We investigate the effect of the current measurement of the neutral $B_s$ meson mass difference, $\hat{I}”M_{B_s}$, on SUGRA models which have non-zero values of the soft breaking terms $(m_{LL,RR}^2{)}_{23}$ and $A_{23}^{u,d}$ at the GUT scale. We use non-zero values of these parameter to explain the $B\to K\ddot{I}€$ puzzle and find that even after satisfying the experimental result on $\hat{I}”M_{B_s}$ and the branching ratio (BR) of $b\to s{\hat{I}}^3$ we still can explain the puzzle. Further we show that in this parameter space it is possible to accommodate the large BR of $B\to \hat{I}{\cdot }^{\prime }K$ and the current experimental data for CP asymmetries of $B\to \hat{I}{\cdot }^{\prime }{K}^0$ and $B\to \ddot{I}•K^0$. The predicted value of $\sin (2β^{\rm eff})_{η' K^0}$ is about $0.52-0.67$.

13 pages, 5 figures