We calculate the complete ${cal O}(alpha_s)$ corrections to the quark decay $bto ccs$ 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 $Gamma(bto ccs)$ by $(32pm 15)%$ 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 $(12.0pm 1.4)% $ using pole quark masses and $(11.2pm 1.7)% $ using running $overline{mbox{MS}}$ masses.
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