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 ${\varphi }_s$. $\Delta M_s$ 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.

Comments: 6 pages, invited talk at Hadron Collider Physics Symposium 2007, La Biodola, Isola d'Elba, Italy, misprints in Note added corrected