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

We calculate the ${\cal O}(α_s^2 β_0 )$ corrections to the decay rate $b\rightarrow c\bar c s$. 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 $R_τ$, the $B$ semileptonic branching fraction and the charm multiplicity.