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• W3121957221 abstract "We examine the perturbative calculation of the inclusive semi-leptonic decay rate Γ for the b quark, using mass-independent renormalization. To finite order of perturbation theory the series for Γ will depend on the unphysical renormalization scale parameter μ and on the particular choice of mass-independent renormalization scheme; these dependencies will only be removed after summing the series to all orders. In this paper we show that all explicit μ-dependence of Γ, through powers of ln(μ), can be summed by using the renormalization group equation. We then find that this explicit μ-dependence can be combined together with the implicit μ-dependence of Γ (through powers of both the running coupling a(μ) and the running b quark mass m(μ)) to yield a μ-independent perturbative expansion for γ in terms of a(μ) and m(μ) both evaluated at a renormalization scheme independent mass scale [Formula: see text] which is fixed in terms of either the “[Formula: see text] mass” [Formula: see text] of the b quark or its pole mass m pole . At finite order the resulting perturbative expansion retains a degree of arbitrariness associated with the particular choice of mass-independent renormalization scheme. We use the coefficients c i and g i of the perturbative expansions of the renormalization group functions β(a) and γ(a), associated with a(μ) and m(μ) respectively, to characterize the remaining renormalization scheme arbitrariness of Γ. We further show that all terms in the expansion of Γ can be written in terms of the c i and g i coefficients and a set of renormalization scheme independent parameters τ i . A second set of renormalization scheme independent parameters σ i is shown to play a very similar role in the perturbative expansion of m pole in terms of m(μ) and a(μ). We illustrate our approach by a perturbative computation of Γ using the [Formula: see text] renormalization scheme. Two other particular mass independent renormalization schemes are briefly considered." @default.
• W3121957221 created "2021-02-01" @default.
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• W3121957221 date "2021-08-01" @default.
• W3121957221 modified "2023-10-16" @default.
• W3121957221 title "Renormalization mass scale and scheme dependence in the perturbative contribution to inclusive semi-leptonic b decays" @default.
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• W3121957221 doi "https://doi.org/10.1139/cjp-2018-0739" @default.
• W3121957221 hasPublicationYear "2021" @default.
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