Charm Quark Mass Dependence of QCD Corrections to Nonleptonic Inclusive B Decays

Abstract

We calculate the radiative corrections to the nonleptonic inclusive B decay mode $b\to c\bar{u}d$ taking into account the charm quark mass. Compared to the massless case, corrections resulting from a nonvanishing c quark mass increase the nonleptonic rate by (4--8)\%, depending on the renormalization point. As a by--product of our calculation, we obtain an analytic expression for the radiative correction to the semileptonic decay $b\to u\tau \bar{\nu }$ taking into account the $\tau$ lepton mass, and estimate the c quark mass effects on the nonleptonic decay mode $b\to c\bar{c}s$.

Comments: 38 pages, TUM-T31-67/94/R (to be published in Nuclear Physics) (one reference added and used for an improved phenomenological analysis)