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The momentum space subtraction (MOM) scheme is one of the most frequentlyused renormalization schemes in perturbative QCD (pQCD) theory. In the paper,we make a detailed discussion on the gauge dependence of the pQCD predictionunder the MOM scheme. Conventionally, there is renormalization scale ambiguityfor the fixed-order pQCD predictions, which assigns an arbitrary range and anarbitrary error for the fixed-order pQCD prediction. The principle of maximumconformality (PMC) adopts the renormalization group equation to determine themagnitude of the coupling constant and hence determines an effective momentumflow of the process, which is independent to the choice of renormalizationscale. There is thus no renormalization scale ambiguity in PMC predictions. Toconcentrate our attention on the MOM gauge dependence, we first apply the PMCto deal with the pQCD series. We adopt the Higgs boson decay width,$\Gamma(H\to gg)$, up to five-loop QCD contributions as an example to show howthe gauge dependence behaves before and after applying the PMC. It is foundthat the Higgs decay width $\Gamma (H\to gg)$ depends very weakly on thechoices of the MOM schemes, being consistent with the renormalization groupinvariance. It is found that the gauge dependence of $\Gamma(H\to gg)$ underthe $\rm{MOMgg}$ scheme is less than $\pm1\%$, which is the smallest gaugedependence among all the mentioned MOM schemes.

Gauge dependence of the perturbative QCD predictions under the momentum space subtraction scheme