Improved analysis of the decay width of t→ Wb up to N^3LO QCD corrections

In this paper, we analyze the top-quark decay t→ Wb up to next-to-next-to-next-to-leading order (N^3LO) QCD corrections. For the purpose, we first adopt the principle of maximum conformality (PMC) to deal with the initial pQCD series, and then we adopt the Bayesian analysis approach, which quantifies the unknown higher-order (UHO) terms' contributions in terms of a probability distribution, to estimate the possible magnitude of the N^4LO QCD corrections. In our calculation, an effective strong coupling constant α_s(Q_*) is determined by using all non-conformal {β_i} terms associated with the renormalization group equation. This results in the next-to-leading-log PMC scale Q_*^( NLL)=10.3048 GeV, which could 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 Γ_t^ tot = 1.3172 ± 0.0038 GeV, where the error is the squared average of the uncertainties from the decay width of W-boson ΔΓ_W = ± 0.042 GeV, the coupling constant Δα_s(m_Z) = ± 0.0009 and the predicted N^4LO-level UHO-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 Δ m_t = ± 0.7 GeV into consideration, we obtain Γ_t^ tot = 1.3172 ^+0.0194_-0.0192 GeV.