Probability-based estimates of the uncalculated N5LO QCD contribution to the hadronic W-boson decay width

The perturbative QCD corrections to the hadronic decay width of the W boson are currently known up to next-to-next-to-next-to-next-to-leading order ( N⁴LO N 4 LO ), whereas the exact N⁵LO N 5 LO correction remains unavailable owing to its formidable computational complexity. In this work, we estimate the N⁵LO N 5 LO contributions by adopting Bayesian analysis (BA). Before performing the estimation, the principle of maximum conformality (PMC) is employed to improve the precision of the initial scale-dependent perturbative series. Through recursive application of the renormalization group equation, non-conformal terms are absorbed into the strong running coupling, yielding a scheme-independent, scale-invariant perturbative series with improved convergence. The PMC procedure determines an effective coupling α ₛ(Q_*) α s ( Q ∗ ) , with the PMC scale fixed as Q_*\!=\!100.102~GeV Q ∗ = 100.102 GeV at next-to-next-to-leading logarithmic accuracy. Based on the improved and more precise series, the $$95.5%$$ 95.5 % BA credible interval yields an uncertainty of Δ δ QCD|PMC, BAN⁵LO = ± 1.0× 10⁻⁵ Δ δ QCD | PMC, BA N 5 LO = ± 1.0 × 10 - 5 . The resulting hadronic branching ratio is B(W→ hadrons)|PMC = (65.84± 1.54)% B ( W → hadrons ) | PMC = ( 65.84 ± 1.54 ) % , which is consistent with experimental data within reasonable errors.