What if the Mass Difference $\Delta M_s$ is around 18 Inverse Picoseconds?

Abstract

Present experiments in pursuit of the mass difference in the Bs-Bs(bar) system have put a lower bound on this quantity of $\Delta M_s > 14.9 ps^{-1}$ (at 95% C.L.). The same experiments also yield a local minimum in the log-likelihood function around $\Delta M_s = 17.7 ps^{-1}$, which is $2.5\sigma$ away from being zero. Motivated by these observations, we investigate the consequences of a possible measurement of $\Delta M_s = 17.7 \pm 1.4 ps^{-1}$, in the context of both the standard model and supersymmetric models with minimal flavor violation. We perform a fit of the quark mixing parameters in these theories and estimate the expected ranges of the CP asymmetries in B decays, characterized by $\alpha$, $\beta$ and $\gamma$, the interior angles of the CKM-unitarity triangle. Based on this study, we argue that, if indeed $\Delta M_s$ turns out to be in its currently-favored range, this would disfavor a large class of supersymmetric models. Indeed, of all the models examined here, the best fit to the data occurs for the standard model.