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 $\Gamma^{\rm tot}_t=1.3112^{+0.0190}_{-0.0189}$ GeV, where the error is the squared averages of the top-quark mass $\Delta m_t=\pm0.7$ GeV, the coupling constant $\Delta \alpha_s(M_Z)=\pm0.0009$ 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.