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

Abstract

We review the theoretical status of the lifetime ratios $τ_{B^+} / τ_{B_d}$, $τ_{B_s} / τ_{B_d}$, $τ_{Λ_b} / τ_{B_d}$ and $τ_{B_c}$ and of the mixing quantities $ΔM_s$, $ΔΓ_s$ and $ϕ_s$. $ΔM_s$ and $ΔΓ_s$ suffer from large uncertainties due to the badly known decay constants, while the ratio $ΔΓ_s / ΔM_s$ 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.

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