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

Abstract

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 (

), whereas the exact

$$\mathrm {N^5LO}$$ N 5 LO

correction remains unavailable owing to its formidable computational complexity. In this work, we estimate the

$$\mathrm {N^5LO}$$ 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

$$\alpha _s(Q_*)$$ α s ( Q ∗ )

, with the PMC scale fixed as

$$Q_*\!=\!100.102~\textrm{GeV}$$ 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

$$\Delta \delta _\textrm{QCD}|_{\textrm{PMC, BA}}^{\mathrm {N^5LO}} = \pm 1.0\times 10^{-5}$$ Δ δ QCD | PMC, BA N 5 LO = ± 1.0 × 10 - 5

. The resulting hadronic branching ratio is

$$\mathcal {B}(W\rightarrow \text {hadrons})|_\textrm{PMC} = (65.84\pm 1.54)\%$$ B ( W → hadrons ) | PMC = ( 65.84 ± 1.54 ) %

, which is consistent with experimental data within reasonable errors.