The Higgs-boson decay H → gg up to αs5-order under the minimal momentum space subtraction scheme

We study the Higgs-boson decay width Gamma(H -> gg) up to alpha(5)(s) order under the minimal momentum space subtraction (mMOM) scheme. A major uncertainty of a finite-order perturbative quantum chromodymaics (pQCD) prediction is the perceived ambiguity in setting the renormalization scale. In the present paper, to achieve a precise pQCD prediction without renormalization scale uncertainty, we adopt the principle of maximum conformality (PMC) to set the renormalization scale of the process. The PMC has a solid theoretical foundation, which is based on renormalization group invariance and utilizes the renormalization group equation to fix the renormalization scale of the process. The key point of the application of the PMC is how to correctly set the {beta(i)} terms of the process to achieve the correct alpha(s)-running behavior at each perturbative order. It is found that the ambiguities in dealing with the {beta(i)} terms of the decay width Gamma(H -> gg) under the (MS) over bar scheme can be avoided by using the physical mMOM scheme. For this purpose, for the first time we provide the PMC scale-setting formulas within the mMOM scheme up to a four-loop level. By using the PMC, it is found that a more reliable pQCD prediction on Gamma(H -> gg) can indeed be achieved under the mMOM scheme. As a byproduct, the convergence of the resultant pQCD series has been greatly improved due to the elimination of renormalon terms. By taking the newly measured Higgs mass, M-H = 125.09 +/- 0.21 +/- 0.11 GeV, our PMC prediction of the decay width is, Gamma(H -> gg)vertical bar(mMOM, PMC) = 339.3 +/- 1.7(-2.4)(+3.7) keV, in which the first error is from the Higgs mass uncertainty and the second error is the residual renormalization scale dependence by varying the initial renormalization scale mu(r) is an element of [M-H/2, 4M(H)].