Next-to-leading Order Radiative Corrections to the Decay $b\to ccs$

Abstract

We calculate the complete $\mathcal{O}({\alpha }_s)$ 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.

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