Three loop calculations and inclusive $V_{cb}$

Abstract

We discuss the impact of the recent $\mathcal{O}(\hat{I}{\pm }_s^3)$ 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 $|V_{cb}|=42.16(51)10^{-3}$.

6 pages, 1 figure