Padé/renormalization-group improvement of inclusive semileptonic b decay rates

Abstract

Renormalization Group (RG) and optimized Pade-approximant methods are used to estimate the three-loop perturbative contributions to the inclusive semileptonic b --> u and b --> c decay rates. It is noted that the (MS) over bar scheme works favorably in the b --> u case whereas the pole mass scheme shows better convergence in the b --> c case. Upon the inclusion of the estimated three-loop contribution, we find the full perturbative decay rate to be 192pi3 Gamma(b --> uv(l)l(-))/(G(F)(2)\V-ubc\(2)) = 2065 +/- 290GeV(5) and 192 pi(3) Gamma(b --> cl(-)v(l))/(G(F)(2) \V-cb\(2)) = 992 +/- 198GeV(5), respectively. The errors axe inclusive of theoretical uncertainties and non-perturbative effects. Ultimately, these perturbative contributions reduce the theoretical uncertainty in the extraction of the CKM matrix elements \V-ub\ and \V-cb\ from their respective measured inclusive semileptonic branching ratio(s).