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

Abstract

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 $|V_{cb}|=0.0379\pm 0.0020(\mathrm{stat})\pm 0.0025(\mathrm{syst})\pm 0.0011(\mathrm{theory})$.

8 pages, Revtex, one figure included

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Cited by in corpus (60)

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