Resummation of Running Coupling Effects in Semileptonic B Meson Decays and Extraction of $|V_{cb}|$

Abstract

We present a determination of $|V_{cb}|$ from semileptonic B decays that includes resummation of supposedly large perturbative corrections, originating from the running of the strong coupling. We argue that the low value of the BLM scale found previously for inclusive decays is a manifestation of the renormalon divergence of the perturbative series starting already in third order. A reliable determination of $|V_{cb}|$ from inclusive decays is possible if one either uses a short-distance b quark mass or eliminates all unphysical mass parameters in terms of measured observables, such that all infra-red contributions of order $1/m_b$ cancel explicitly. We find that using the $\overline{\rm MS}$ running mass significantly reduces the perturbative coefficients already in low orders. For a semileptonic branching ratio of $10.9\%$ we obtain $|V_{cb}|(τ_B/1.50\,{\rm ps})^{1/2}= 0.041\pm 0.002$ from inclusive decays, in good agreement with the value extracted from exclusive decays.