====== TTP96-05 Two-loop QCD corrections to $b\to c$ transitions at zero recoil ====== Complete two-loop QCD corrections to $b\to c$ transitions are presented in the limit of zero recoil. Vector and axial-vector coefficients $\eta_{A,V}$ are calculated analytically in the limit of equal beauty and charm masses, and a series appoximation is obtained for the general mass case. $\eta_A$ is crucial for the determination of the absolute value of the Cabibbo-Kobayashi-Maskawa matrix element $V_{cb}$. The two-loop effects enhance the one-loop corrections by 21\%, removing a major theoretical uncertainty in the value of $|V_{cb}|$. Including two-loop QCD effects and previously neglected electroweak and Coulomb corrections we find $|V_{cb}| = 0.0379 \pm 0.0020({\rm stat}) \pm 0.0025({\rm syst}) \pm 0.0011({\rm theory})$. |**Andrzej Czarnecki** | |** Phys. Rev. Lett. 76 4124 1996 ** | | {{preprints:1996:ttp96-05.pdf|PDF}} {{preprints:1996:ttp96-05.ps|PostScript}} [[http://arxiv.org/abs/hep-ph/9603261|arXiv]] | | |