Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2001-09-07
Phys.Rev.D65:054021,2002
Physics
High Energy Physics
High Energy Physics - Phenomenology
latex2e using amsmath. 17 pages with 5 eps figures embedded in mansucript. Corrections made to eqns (47), (57) and Reference [
Scientific paper
10.1103/PhysRevD.65.054021
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.
Ahmady Mohammad R.
Chishtie Farrukh A.
Elias Victor
Fariborz Amir H.
McKeon Dennis G. C.
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