QCD improved top-quark decay at next-to-next-to-leading order

Abstract

We analyse the top-quark decay at the next-to-next-to-leading order (NNLO) in QCD by using the Principle of Maximum Conformality (PMC) which provides a systematic way to eliminate renormalization scheme and scale ambiguities in perturbative QCD predictions. The PMC renormalization scales of the coupling constant αs are determined by absorbing the non-conformal β terms that govern the behavior of the running coupling by using the Renormalization Group Equation (RGE). We obtain the PMC scale Q⋆ = 15.7 GeV for the top-quark decay, which is an order of magnitude smaller than the conventional choice µr = mt. Our analyses reveal that the effective momentum flow for the top-quark decay is not the conventionally suggested µr = mt, it should be µr ≪ mt. Moreover, due to the non-conformal β terms disappear in the pQCD series, there is no renormalon divergence and the convergence of the pQCD series for the top-quark decay is greatly improved. By further including the next-to-leading (NLO) electroweak corrections, the finite W boson width and the finite bottom quark mass, we obtain the top-quark total decay width Γ tot t |PMC = 1.3383 +0.0276GeV, where the error is the squared averages of the top-quark mass ∆mt = ±1 GeV, the coupling constant ∆αs(MZ ) = ±0.0009 and the estimation of unknown higher-order terms. The PMC improved predictions for the top-quark decay are complementary to the previous PMC calculations for top-quark pair production and helpful for detailed studies of properties of the top-quark.