Gauge dependence of the perturbative QCD predictions under the momentum-space subtraction scheme * * Supported by Graduate Research and Innovation Foundation of Chongqing, China (CYB19065, ydstd1912), the National Natural Science Foundation of China (11625520, 11947406, 11905056), the China Postdoctoral Science Foundation (2019M663432) and the Chongqing Special Postdoctoral Science Foundation (XmT2019055)

Abstract

The momentum-space subtraction (MOM) scheme is one of the most frequently used renormalization schemes in perturbative QCD (pQCD) theory. In this paper, we discuss in detail the gauge dependence of the pQCD predictions obtained under the MOM scheme. Conventionally, a renormalization scale ambiguity exists for the fixed-order pQCD predictions; this assigns an arbitrary range and error for the fixed-order pQCD prediction and makes the discussions on the issue of the gauge dependence much more involved. The principle of maximum conformality (PMC) adopts the renormalization group equation to determine the magnitude of the coupling constant; hence, it determines the effective momentum flow of the process, which is independent of the choice of renormalization scale. Thus, no renormalization scale ambiguity exists in PMC predictions. To focus our attention on the MOM scheme's gauge dependence, we first apply the PMC to deal with the pQCD series. As an explicit example, we adopt the Higgs boson decay width up to its five-loop QCD contribution, to demonstrate the behavior of the gauge dependence before and after applying the PMC. Interaction vertices are chosen to define five different MOM schemes: mMOM, MOMh, MOMq, MOMg, and MOMgg. Under these MOM schemes, we obtain , , , , and ; here, the central values correspond to the Landau gauge with the gauge parameter , the first errors correspond to , and the second ones arise through taking . The uncertainty of the Higgs mass causes an extra error of (or ) keV for all the aforementioned MOM schemes. It is found that the Higgs decay width depends very weakly on the choice of MOM scheme, which is consistent with renormalization group invariance. It is found that the gauge dependence of under the scheme is less than ±1%, which is the smallest gauge dependence among all the aforementioned MOM schemes.