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

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 alpha(s) are determined by absorbing the non-conformal beta terms that govern the behavior of the running coupling by using the Renormalization Group Equation (RGE). We obtain the PMC scale Q(star) = 15.5 GeV for the top-quark decay, which is an order of magnitude smaller than the conventional choice mu(r) = m(t), reflecting the small virtuality of the QCD dynamics of the top-quark decay process. Moreover, due to the non-conformal beta terms disappear in the pQCD series, there is no renormalon divergence and the NLO QCD correction term is greatly increased while the NNLO QCD correction term is suppressed compared to the conventional results obtained at mu(r) = m(t). 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 Gamma(tot)(t) = 1.3112(-0.0189)(+0.0190) GeV, where the error is the squared averages of the top-quark mass Delta m(t) = +/- 0.7 GeV, the coupling constant Delta alpha(s) (M-Z) = +/- 0.0009 and the estimation of unknown higher-order terms using the PAA method with [N/M] = [1/1]. 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.

Automated summary

This study applies the Principle of Maximum Conformality (PMC) to analyze the top-quark decay at NNLO in QCD, eliminating renormalization scheme and scale ambiguities. The PMC scale Q(star) is determined to be 15.5 GeV, an order of magnitude smaller than the conventional choice mu(r) = m(t), indicating the small virtuality of the QCD dynamics in top-quark decay. Removal of non-conformal beta terms in the pQCD series avoids renormalon divergence, resulting in a significant increase in NLO QCD correction and suppression of NNLO QCD correction compared to conventional results obtained at mu(r) = m(t). Including NLO electroweak corrections, finite W boson width, and finite bottom quark mass, the top-quark total decay width Gamma(tot)(t) is obtained as 1.3112(-0.0189)(+0.0190) GeV.