$B_s - \bar B_s$ 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, $ΔM_{B_s}$, on SUGRA models which have non-zero values of the soft breaking terms $(m^2_{LL,RR})_{23}$ and $A^{u,d}_{23}$ at the GUT scale. We use non-zero values of these parameter to explain the $B\to Kπ$ puzzle and find that even after satisfying the experimental result on $ΔM_{B_s}$ and the branching ratio (BR) of $b\to sγ$ we still can explain the puzzle. Further we show that in this parameter space it is possible to accommodate the large BR of $B\to η' K$ and the current experimental data for CP asymmetries of $B\to η' K^0$ and $B\to ϕK^0$. The predicted value of $\sin (2β^{\rm eff})_{η' K^0}$ is about $0.52-0.67$.