The precision and predictive power of perturbative QCD (pQCD) prediction depends on both a precise, convergent fixed-order series and a reliable way of estimating the contributions of unknown higher-order (UHO) terms. It has been shown that by applying the Principal of Maximum Conformality (PMC), which applies the renormalization group equation recursively to set the effective magnitude of αs of the process, the remaining conformal coefficients will be well matched with the corresponding αs at each orders, leading to a scheme-and-scale invariant and convergent perturbative series. Thus different from conventional scheme-and-scale dependent fixed-order series, the PMC series will provide a more reliable platform for estimating UHO contributions. In this paper, by using the total decay width Γ(H→γγ) which has been calculated up to N4LO QCD corrections, we derive its PMC series by using the PMC single-scale setting approach and estimate its unknown N5LO contributions by using the Bayesian analysis. The Bayesian-based approach estimates the magnitude of the UHO contributions based on an optimized analysis of probability density distribution, and the predicted UHO contribution becomes more accurate when more loop terms have been known to tame the probability density function. Using the top-quark pole mass Mt=172.69 GeV and the Higgs mass MH=125.25 GeV as inputs, we obtain Γ(H→γγ)=9.56504keV and the estimated N5LO contribution to the total decay width is ΔΓH=±1.65×10−4keV for the smallest credible interval of 95.5% degree-of-belief.
@article{arxiv.2312.01373,
title = {Approximate N$^5$LO Higgs boson decay width $\Gamma(H\to\gamma\gamma)$},
author = {Yu-Feng Luo and Jiang Yan and Zhi-Fei Wu and Xing-Gang Wu},
journal= {arXiv preprint arXiv:2312.01373},
year = {2024}
}