Three loop calculations and inclusive $V_{cb}$

TL;DR

This paper evaluates how recent three-loop QCD calculations influence the precision of the inclusive $V_{cb}$ determination, resulting in a reduced uncertainty and a refined value of $|V_{cb}|$.

Contribution

It incorporates recent $ ext{O}( ext{α}_s^3)$ calculations into the $V_{cb}$ extraction, improving the precision of the inclusive determination.

Findings

Reduced uncertainty in $|V_{cb}|$ to 0.51e-3

Updated $|V_{cb}|$ value: 42.16e-3

Enhanced theoretical understanding of heavy quark masses

Abstract

We discuss the impact of the recent $\mathcal{O}(\alpha_s^3)$ calculations of the semileptonic width of the $b$ quark and of the relation between pole and kinetic heavy quark masses by Fael et al. on the inclusive determination of $|V_{cb}|$. The most notable effect is a reduction of the uncertainty. Our final result is $|V_{cb}|=42.16(51)\, 10^{-3}$.