Two-loop QCD corrections to b->c transitions at zero recoil

Complete two-loop QCD corrections to b --> 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 22%, removing a major theoretical uncertainty in the value of \V-cb\. Including two-loop QCD effects and previously neglected electroweak corrections we find \V-cb\ = 0.0383 +/- 0.0021(stat) +/- 0.0025(syst) +/- 0.0011(theory).