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Three Loop Estimate of the Inclusive Semileptonic $b\to c$ Decay Rate

M. R. Ahmady·F. A. Chishtie·V. Elias·A. H. Fariborz·D. G. C. McKeon·T. N. Sherry·T. G. Steele
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Abstract

The renormalization-scale ($μ$) dependence of the two-loop inclusive semileptonic $b\to c\ell^-\barν_\ell$ 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 $μ=1.0 GeV$, leading to an estimated decay rate of $192π^3Γ(b\to c\ell^-\barν_\ell)/(G_F^2|V_{cb}|^2)=992\pm 217 GeV^5$ inclusive of theoretical uncertainties and non-perturbative effects.

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M. R. Ahmady, F. A. Chishtie, V. Elias, A. H. Fariborz, D. G. C. McKeon, T. N. Sherry, T. G. Steele. 2002-08-30. Three Loop Estimate of the Inclusive Semileptonic $b\to c$ Decay Rate. https://doi.org/10.1103/physrevd.65.054021

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