Standard Model prediction of the $B_c$ lifetime

TL;DR

This paper updates the Standard Model prediction of the $B_c$ meson lifetime using an operator product expansion, analyzing scheme dependence, renormalon cancellation, and uncertainties, but results remain inconclusive for New Physics effects.

Contribution

It provides a refined Standard Model prediction of the $B_c$ lifetime with detailed uncertainty analysis and explores scheme dependence and renormalon cancellation.

Findings

Predicted $B_c$ lifetime consistent with experiment

Uncertainties are large, limiting conclusions on New Physics

Scheme dependence affects the lifetime calculation

Abstract

Applying an operator product expansion approach we update the Standard Model prediction of the $B_c$ lifetime from over 20 years ago. The non-perturbative velocity expansion is carried out up to third order in the relative velocity of the heavy quarks. The scheme dependence is studied using three different mass schemes for the $\bar b$ and $c$ quarks, resulting in three different values consistent with each other and with experiment. Special focus has been laid on renormalon cancellation in the computation. Uncertainties resulting from scale dependence, neglecting the strange quark mass, non-perturbative matrix elements and parametric uncertainties are discussed in detail. The resulting uncertainties are still rather large compared to the experimental ones, and therefore do not allow for clear-cut conclusions concerning New Physics effects in the $B_c$ decay.