The Higgs boson inclusive decay channels H → b(b)over-bar and H → gg up to four-loop level

The principle of maximum conformality (PMC) has been suggested to eliminate the renormalization scheme and renormalization scale uncertainties, which are unavoidable for the conventional scale setting and are usually important errors for theoretical estimations. In this paper, by applying PMC scale setting, we analyze two important inclusive Standard Model Higgs decay channels, H -> b (b) over bar and H -> gg, up to four-loop and three-loop levels, respectively. After PMC scale setting, it is found that the conventional scale uncertainty for these two channels can be eliminated to a high degree. There is small residual initial scale dependence for the Higgs decay widths due to unknown higher-order {beta(i)} terms. Up to four-loop level, we obtain Gamma(H -> b (b) over bar) = 2.389 +/- 0.073 +/- 0.041 MeV and up to three-loop level, we obtain Gamma(H -> gg) = 0.373 +/- 0.030 MeV, where the first error is caused by varying M-H = 126 +/- 4 GeV and the second error for H -> b (b) over bar is caused by varying the (MS) over bar -running mass m(b)(m(b)) = 4.18 +/- 0.03 GeV. Taking H -> b (b) over bar as an example, we present a comparison of three BLM-based scale-setting approaches, e.g. the PMC-I approach based on the PMC-BLM correspondence, the R-delta-scheme and the seBLM approach, all of which are designed to provide effectiveways to identify non-conformal {beta(i)}-series at each perturbative order. At four-loop level, all those approaches lead to good pQCD convergence, they have almost the same pQCD series, and their predictions are almost independent on the initial renormalization scale. In this sense, those approaches are equivalent to each other.