Two-loop QCD Corrections to $b \to c$ Transitions at Zero Recoil: Analytical Results

We present analytical results for the $O(α_s ^2)$ contributions to the functions $η_A$ and $η_V$ which parameterize QCD corrections to semileptonic $b \to c$ transitions at zero recoil. Previously obtained approximate results are confirmed. The methods of computing the relevant two-loop diagrams with two mass scales are discussed in some detail.

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