Improved analysis of the decay width of t→ Wb up to N³LO QCD corrections

In this paper, we analyze the top-quark decay t→ Wb up to next-to-next-to-next-to-leading order (N³LO) 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 N⁴LO QCD corrections. In our calculation, an effective strong coupling constant αₛ(Q*) is determined by using all non-conformal \βᵢ\ 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 Γₜᵗᵒᵗ = 1.3172 ± 0.0038 GeV, where the error is the squared average of the uncertainties from the decay width of W-boson Δ ΓW = ± 0.042 GeV, the coupling constant Δ αₛ(mZ) = ± 0.0009 and the predicted N⁴LO-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 mₜ = ± 0.7 GeV into consideration, we obtain Γₜᵗᵒᵗ = 1.3172 +0.0194-0.0192 GeV.