The Higgs-Boson Decay $H\to gg$ to Order ${\alpha }_s^5$ under the mMOM-Scheme

We study the decay width of the Higgs-boson $H\to gg$ up to order ${\alpha }_s^5$ under the minimal momentum space subtraction scheme (mMOM-scheme). To improve the accuracy of perturbative QCD prediction, we adopt the principle of maximum conformality (PMC) to set its renormalization scales. A detailed comparison of the total decay width and the separate decay widths at each perturbative order before and after the PMC scale setting is presented. The PMC adopts the renormalization group equation to fix the optimal scales of the process. After the PMC scale setting, the scale-dependence for both the total and the separate decay widths are greatly suppressed, and the convergence of perturbative QCD series is improved. By taking the Higgs mass $M_H=125.09\pm 0.21\pm 0.11$ GeV, as recently given by the ATLAS and CMS collaborations, we predict $\mathrm{\Gamma }(H\to gg){\mathrm{\mid }}_{\mathrm{m}\mathrm{M}\mathrm{O}\mathrm{M},\mathrm{P}\mathrm{M}\mathrm{C}}=339.1\pm 1.7_{-2.4}^{+4.0}$ keV, where the first error is for Higgs mass and the second error is the residual scale dependence by varying the initial scale ${\mu }_r\in [M_H\mathrm{/}2,4M_H]$.