Theoretical status of $B_s$-mixing and lifetimes of heavy hadrons

Abstract

We review the theoretical status of the lifetime ratios $\tau_{B^+} / \tau_{B_d}$, $\tau_{B_s} / \tau_{B_d}$, $\tau_{\Lambda_b} / \tau_{B_d}$ and $\tau_{B_c}$ and of the mixing quantities $\Delta M_s$, $\Delta \Gamma_s$ and $\phi_s$. $\Delta M_s$ and $\Delta \Gamma_s$ suffer from large uncertainties due to the badly known decay constants, while the ratio $\Delta \Gamma_s / \Delta M_s$ can be determined with almost no non-perturbative uncertainties, therefore it can be used perfectly to find possible new physics contributions in the mixing parameters. We suggest a very clear method of visualizing the bounds on new physics and demonstrate this by combining the latest experimental numbers on the mixing quantities quantities with theory - one already gets some hints for new physics contributions, but more precise experimental numbers are needed to draw some definite conclusions. We conclude with a ranking list of all the discussed quantities according to their current theoretical uncertainties and point out possible improvements.