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

Abstract

We present analytical results for the $O({\alpha }_s^2)$ contributions to the functions ${\eta }_A$ and ${\eta }_V$ 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.

19 pages, latex