Precise determination of the top-quark on-shell mass via its scale- invariant perturbative relation to the top-quark mass * * Supported in part by the National Natural Science Foundation of China (12247129, 12175025, 12347101) and the Graduate Research and Innovation Foundation of Chongqing, China (ydstd1912)

The principle of maximum conformality (PMC) provides a systematic approach to solve the conventional renormalization scheme and scale ambiguities. Scale-fixed predictions of physical observables using the PMC are independent of the choice of renormalization scheme – a key requirement for renormalization group invariance. In this paper, we derive new degeneracy relations based on the renormalization group equations that involve both the usual β-function and the quark mass anomalous dimension -function. These new degeneracy relations enable improved PMC scale-setting procedures for correct magnitudes of the strong coupling constant and -running quark mass to be determined simultaneously. By using these improved PMC scale-setting procedures, the renormalization scale dependence of the -on-shell quark mass relation can be eliminated systematically. Consequently, the top-quark on-shell (or ) mass can be determined without conventional renormalization scale ambiguity. Taking the top-quark mass GeV as the input, we obtain GeV. Here, the uncertainties arise from errors combined with those from and the approximate uncertainty resulting from the uncalculated five-loop terms predicted through the Padé approximation approach.