M. R. Ahmady, F. A. Chishtie, V. Elias, A. H. Fariborz, D. G. C. McKeon, T. N. Sherry, T. G. Steele
Published 2001-09-07, updated 2002-08-30Version 3
The renormalization-scale ($\mu$) dependence of the two-loop inclusive semileptonic $b\to c\ell^-\bar\nu_\ell$ decay rate is shown to be significant in the pole mass scheme, and the decay rate is shown to be poorly convergent in the MS-bar scheme. Three-loop contributions to the decay rate are estimated by developing Pade approximant techniques particularly suited to perturbative calculations in the pole mass scheme. An optimized Pade estimate of the three-loop contributions is obtained by comparison of the Pade estimates with the three-loop terms determined by renormalization-group invariance. The resulting three-loop estimate in the pole-mass scheme exhibits minimal sensitivity to the renormalization scale near $\mu=1.0 GeV$, leading to an estimated decay rate of $192\pi^3\Gamma(b\to c\ell^-\bar\nu_\ell)/(G_F^2|V_{cb}|^2)=992\pm 217 GeV^5$ inclusive of theoretical uncertainties and non-perturbative effects.
Comments: latex2e using amsmath. 17 pages with 5 eps figures embedded in mansucript. Corrections made to eqns (47), (57) and Reference [1]
Journal: Phys.Rev.D65:054021,2002
Power Corrections in the Decay Rate and Distributions in $B \to X_s \ell^+ \ell^- $ in the Standard Model
Reducing the Theoretical Uncertainty in Extracting |V_{ub}| from the Inclusive Semileptonic b to u Decay Rate
Two-Loop $ O(α_sG_Fm_t^2)$ Correction to the $H\to b\bar b$ Decay Rate
