Next-to-leading order radiative corrections to the decay b --> ccs

We calculate the complete {\cal O}(\alpha_s) corrections to the quark decay b\to ccs taking full account of the quark masses, but neglecting penguin contributions. For a c to the b quark mass ratio m_c/m_b= 0.3 and a strange quark mass of 0.2\,GeV, we find that the next-to-leading order (NLO) corrections increase \Gamma(b\to ccs) by (32\pm 15)\% with respect to the leading order expression, where the uncertainty is mostly due to scale- and scheme-dependences. Combining this result with the known NLO and non-perturbative corrections to other B meson decay channels we obtain an updated value for the semileptonic branching ratio of B mesons, B_{SL}, of (12.0\pm 1.4)\% using pole quark masses and (11.2\pm 1.7)\% using running \overline{\mbox{MS}} masses.