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

TL;DR

This paper reviews the theoretical understanding of heavy hadron lifetimes and mixing parameters, highlighting uncertainties, proposing visualization methods for new physics bounds, and emphasizing the need for more precise experimental data.

Contribution

It provides a comprehensive review of heavy hadron lifetime ratios and mixing quantities, and introduces a visualization method for constraining new physics contributions.

Findings

Decay constants cause large uncertainties in mixing quantities.

The ratio ΔΓ_s/ΔM_s is nearly free of non-perturbative uncertainties.

Current data hints at possible new physics, but more precise measurements are needed.

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.