Higher Order QCD Corrections to $b\to c\overline{c}s$

Abstract

We calculate the $\mathcal{O}({\alpha }_s^2{\beta }_0)$ corrections to the decay rate $b\to c\bar{c}s$. For reasonable values of $m_c/m_b$ this term is of the same order as both the one-loop and $\CO(α_s^2 \log^2 m_W/m_b)$ corrections to the decay rate. For $m_c/m_b=0.3$ the $\CO(α_s^2β_0)$ corrections enhance the rate by $\sim 18\%$ . We also discuss the $\CO(α_s^2β_0)$ corrections to $R_{\tau }$, the $B$ semileptonic branching fraction and the charm multiplicity.

LaTex, 14 pages, 2 eps figures. Added one reference, changed some comments