Approximate N5LO Higgs Boson Decay Width Γ(H→γγ)

Abstract

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 principle 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 order, leading to a scheme-and-scale invariant and more convergent perturbative series. The PMC series, being satisfied with the standard renormalization group invariance, has a rigorous foundation. Thus it not only can be widely applied to virtually all high-energy hadronic processes, but also can be a 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 first derive its PMC series by using the PMC single-scale setting approach and then estimate its unknown N5LO contributions by using a Bayesian analysis. The newly suggested Bayesian-based approach estimates the magnitude of the UHO contributions based on an optimized analysis of the 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.