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 (N4LO), whereas the exact N5LO correction remains unavailable owing to its formidable computational complexity. In this work, we estimate the N5LO 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 αs(Q*), with the PMC scale fixed as Q* = 100.102 GeV at next-to-next-to-leading logarithmic accuracy. Based on the improved and more precise series, the 95.5% BA credible interval yields an uncertainty of ΔδQCD|PMC, BAN5LO = ± 1.0× 10−5. The resulting hadronic branching ratio is ℬ(W→ hadrons)|PMC = (65.84± 1.54)%, which is consistent with experimental data within reasonable errors.
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BibTeX
@misc{yang2026probabilitybased,
title = {{Probability-based Estimates of the Uncalculated N$^5$LO QCD Contribution to the Hadronic $W$-Boson Decay Width}},
author = {Shu-Heng Yang and Jiang Yan and Xing-Gang Wu and Zhi-Fei Wu},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29666},
eprint = {2608.29666},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29666},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Probability-based Estimates of the Uncalculated N^5LO QCD Contribution to the Hadronic W-Boson Decay Width
AU - Shu-Heng Yang
AU - Jiang Yan
AU - Xing-Gang Wu
AU - Zhi-Fei Wu
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29666
UR - https://arxiv.org/abs/2608.29666
AB - 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 (N^4LO), whereas the exact N^5LO correction remains unavailable owing to its formidable computational complexity. In this work, we estimate the N^5LO 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_*), with the PMC scale fixed as Q_* = 100.102 GeV at next-to-next-to-leading logarithmic accuracy. Based on the improved and more precise series, the 95.5% BA credible interval yields an uncertainty of Δδ_QCD|_PMC, BA^N^5LO = ± 1.0× 10^−5. The resulting hadronic branching ratio is ℬ(W→ hadrons)|_PMC = (65.84± 1.54)%, which is consistent with experimental data within reasonable errors.
ER -