Properties of the decay $H\to \gamma \gamma$ using the approximate ${\alpha }_s^4$-corrections and the principle of maximum conformality

The Higgs boson decay channel, $H\to \gamma \gamma$, 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. $M_H=125.09\pm 0.21\pm 0.11$ GeV, we obtain $\Gamma(H\to \gamma\gamma)|{\rm LHC}=9.364^{+0.076}{-0.075}$ KeV.