Properties of the decay $Htogammagamma$ using the approximate $alpha_s^4$-corrections and the principle of maximum conformality

The Higgs boson decay channel, $Htogammagamma$, is one of the most important channels for probing the properties of the Higgs boson. In the paper, we reanalyze its decay width by using the QCD corrections up to $alpha_s^4$-order level. The principle of maximum conformality has been adopted to achieve a precise pQCD prediction without conventional renormalization scheme-and-scale ambiguities. By taking the Higgs mass as the one given by the ATLAS and CMS collaborations, i.e. $M_{H}=125.09pm0.21pm0.11$ GeV, we obtain $Gamma(Hto gammagamma)|_{rm LHC}=9.364^{+0.076}_{-0.075}$ KeV.