Three loop estimate of the inclusive semileptonic b>c decay rate
Abstract
The renormalizationscale (μ) dependence of the twoloop inclusive semileptonic b>cl^{}νbar_{l} decay rate is shown to be significant in the pole mass scheme, and the decay rate is shown to be poorly convergent in the MSbar scheme. Threeloop contributions to the decay rate are estimated by developing Padé approximant techniques particularly suited to perturbative calculations in the pole mass scheme. An optimized Padé estimate of the threeloop contributions is obtained by comparison of the Padé estimates with the threeloop terms determined by renormalizationgroup invariance. The resulting threeloop estimate in the polemass scheme exhibits minimal sensitivity to the renormalization scale near μ=1.0 GeV, leading to an estimated decay rate of 192π^{3}Γ(b>cl^{}νbar_{l})/(G^{2}_{F}\V_{cb}\^{2})=992+/217 GeV^{5} inclusive of theoretical uncertainties and nonperturbative effects.
 Publication:

Physical Review D
 Pub Date:
 March 2002
 DOI:
 10.1103/PhysRevD.65.054021
 arXiv:
 arXiv:hepph/0109061
 Bibcode:
 2002PhRvD..65e4021A
 Keywords:

 13.20.He;
 Decays of bottom mesons;
 High Energy Physics  Phenomenology
 EPrint:
 latex2e using amsmath. 17 pages with 5 eps figures embedded in mansucript. Corrections made to eqns (47), (57) and Reference [1]