Next-to-next-to-leading order relation between $R(e^+e^-\to b\bar b)$ and $\Gamma_{\rm sl}(b\to cl\nu_l)$ and precise determination of $|V_{cb}|$

Abstract

We present the next-to-next-to-leading order relation between the moments of the $\Upsilon$ system spectral density and the inclusive $B$-meson semileptonic width. The perturbative series for the width as an explicit function of the moments is well convergent in three consequent orders in the strong coupling constant that provides solid and accurate theoretical estimate. As a result, the uncertainty of the value of $|V_{cb}|$ Cabibbo-Kobayashi-Maskawa matrix element is reduced.