Precise determination of the top-quark on-shell mass $M_t$ via its scale-invariant perturbative relation to the top-quark $\overline{\mathrm{MS}}$ mass ${\overline{m}}_t({\overline{m}}_t)$

Abstract

It has been shown that the principle of maximum conformality (PMC) provides a systematic way to solve conventional renormalization scheme and scale ambiguities. The scale-fixed predictions for physical observables using the PMC are independent of the choice of renormalization scheme -- a key requirement of renormalization group invariance. In the paper, we derive new degeneracy relations based on the renormalization group equations that involve both the usual $\beta$-function and the quark mass anomalous dimension ${\gamma }_m$-function, respectively. These new degeneracy relations lead to an improved PMC scale-setting procedures, such that the correct magnitudes of the strong coupling constant and the $\overline{\mathrm{MS}}$-running quark mass can be fixed simultaneously. By using the improved PMC scale-setting procedures, the renormalization scale dependence of the $\overline{\mathrm{MS}}$-on-shell quark mass relation can be eliminated systematically. Consequently, the top-quark on-shell (or $\overline{\mathrm{MS}}$) mass can be determined without conventional renormalization scale ambiguity. Taking the top-quark $\overline{\mathrm{MS}}$ mass ${\overline{m}}_t({\overline{m}}_t)=162.5_{-1.5}^{+2.1}$ GeV as the input, we obtain $M_t\simeq 172.41_{-1.57}^{+2.21}$ GeV. Here the uncertainties are combined errors with those also from $\Delta {\alpha }_s(M_Z)$ and the approximate uncertainty stemming from the uncalculated five-loop terms predicted through the Padé approximation approach.

arXiv comment15 pages, 2 figures, to be published in Chinese Physics C

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