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

Abstract

Renormalization Group (RG) and optimized Pad é-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 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 192π 3 Γ (b → u v ll −)/(G F 2|V ub| 2) = 2065 ± 290GeV 5 and 192π 3Γ(b → cl − v l)/G F 2|V cb| 2) = 992 ± 198 GeV 5 respectively. The errors are inclusive of theoretical uncertainties and non-perturbative effects. Ultimately, these perturbative contributions reduce the theoretical uncertainty in the extraction of teh CKM matrix elements | V vb | and | V cb | from their respective measured inclusive semileptonic branching ratio(s).