Improved analysis of the decay width of $t\to Wb$ up to N$^{3}$LO QCD corrections

Abstract

In this paper, we analyze the top-quark decay $t\to Wb$ up to next-to-next-to-next-to-leading order (N$^{3}$LO) QCD corrections. For the purpose, we first adopt the principle of maximum conformality (PMC) to deal with the initial pQCD series. Then we adopt the Bayesian analysis approach, which quantifies the unknown higher-order terms' contributions in terms of a probability distribution, to estimate the possible magnitude of the uncalculated N$^{4}$LO-terms. In our calculation, an effective strong coupling constant $\alpha_{s}(Q_{*})$ is determined by using all non-conformal $\{\beta_{i}\}$ terms associated with the renormalization group equation. This leads to a next-to-leading-log PMC scale $Q_{*}^{(\rm NLL)}=10.3048$ GeV, which can be regarded as the correct momentum flow of the process. Consequently, we obtain an improved scale-invariant pQCD prediction for the top-quark decay width, e.g. $\Gamma_{t}^{\rm tot} = 1.3120 \pm 0.0038$ GeV, whose error is the squared average of the uncertainties from the decay width of $W$-boson $\Delta \Gamma_{W} = \pm 0.042$ GeV, the coupling constant $\Delta \alpha_{s}(m_{Z}) = \pm 0.0009$, and the predicted N$^{4}$LO-terms. The magnitude of the top-quark pole mass greatly affects the total decay width. By further taking the PDG top-quark pole mass error from cross-section measurements into consideration, e.g. $\Delta m_{t} = \pm 0.7$ GeV, we obtain $\Gamma_{t}^{\rm tot} = 1.3120 ^{+0.0194}_{-0.0192}$ GeV.