Inclusive decay of B mesons into $D_s$ or $D_s^{\ast }$

Abstract

We compute the inclusive decay rates $b\to D_s^{-}(D_s^{\ast -})c$ including lowest order QCD corrections on the quark legs, and compare with existing data. Unlike the short distance QCD corrections, that are of higher order, these corrections are of order ${\alpha }_s$. In the on-shell renormalization scheme and for ${\alpha }_s(m_b)\cong 0.2$ we find a correction of -10% to the inclusive rate computed using factorization. This gives a total rate $BR(b\to D_s^{-}(D_s^{\ast -})c)\cong 8$ consistent within $1\sigma$ with the measured value $BR(B\to D_s^{\pm }X)=(10.0\pm 2.5)$. The general formulae given here include the case of vanishing mass for the final quark $b\to D_s^{-}(D_s^{\ast -})u$. The radiative correction to this rate is -17%. We show in another place that this process can be useful for the measurement of the CKM matrix element $V_{ub}$. We also give the renormalized vertex at the interesting values $q^2=0$ and $q^2=q_{max}^2$, and compare with existing literature.

Comments: 30 pages, LaTeX