Approximate N$^5$LO Higgs boson decay width $\Gamma(H\to\gamma\gamma)$

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 Principal of Maximum Conformality (PMC), which applies the renormalization group equation recursively to set the effective magnitude of $\alpha_s$ of the process, the remaining conformal coefficients will be well matched with the corresponding $\alpha_s$ 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 $\Gamma(H\to\gamma\gamma)$ which has been calculated up to N$^4$LO QCD corrections, we derive its PMC series by using the PMC single-scale setting approach and estimate its unknown N$^5$LO 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 $M_t$=172.69 GeV and the Higgs mass $M_H$=125.25 GeV as inputs, we obtain $\Gamma(H\to\gamma\gamma) =9.56504~{\rm keV}$ and the estimated N$^5$LO contribution to the total decay width is $\Delta\Gamma_H=\pm1.65\times10^{-4}~{\rm keV}$ for the smallest credible interval of $95.5\%$ degree-of-belief.