Bottom quark pole mass and $|V_{cb}|$ matrix element from $R(e^+e^-\to b\bar b)$ and $\Gamma_{sl}(b\to cl\nu_l)$ in the next-to-next-to-leading order

Abstract

We present a consistent analysis of $\Upsilon$ sum rules and $B$-meson semileptonic width in the next-to-next-to-leading order in the strong coupling constant. The analysis is based on the analytical result for the heavy quark vector current correlator near threshold in the second order in perturbative and relativistic expansion around the nonrelativistic Coulomb approximation.