Uncertainties in the Determination of $|V_{cb}|$

Abstract

I discuss the theoretical uncertainties in the extraction of $|\,V_{cb}|$ from semilep\-to\-nic decays of $B$ mesons, taking into account the most recent theoretical developments. The main sources of uncertainty are identified both for the exclusive decay mode $B\to D^*\ell\,\bar\nu$ and for the inclusive channel $B\to X\,\ell\,\bar\nu$. From an analysis of the available experimental data, I obtain $|\,V_{cb}|_{\rm excl} = 0.041\pm 0.003_{\rm exp}\pm 0.002_{\rm th}$ from the exclusive mode, and $|\,V_{cb}|_{\rm incl} = 0.040\pm 0.001_{\rm exp}\pm 0.005_{\rm th}$ from the inclusive mode. I also give a prediction for the slope of the form factor ${\cal{F}}(w)$ at zero recoil, which is $\widehat\varrho^2=0.8\pm 0.3$.