Relation between pole and running masses of heavy quarks using the principle of maximum conformality

TL;DR

This paper applies the Principle of Maximum Conformality to accurately relate pole and running masses of heavy quarks in QCD, eliminating scale ambiguities and providing precise mass values.

Contribution

It introduces a scale-setting method using PMC to determine heavy quark masses with reduced theoretical uncertainties in pQCD.

Findings

PMC determines optimal renormalization scales for heavy quark masses.

Precise PMC pole masses for bottom and top quarks are obtained.

Running mass of the top quark is accurately estimated at the PMC scale.

Abstract

The relation of the pole and running heavy quark masses of order $\mathcal{O}\left(\alpha_s^4\right)$ in perturbative quantum chromodynamics (pQCD) can be obtained using the Principle of Maximum Conformality (PMC), a formalism that provides a rigorous method for eliminating renormalization scale and scheme ambiguities for observables in pQCD. Using PMC, an optimal renormalization scale for the heavy quark mass ratio is determined, independent of the renormalization scale and scheme up to order $\alpha_s^4$. Precise values are then obtained for the PMC pole masses of the heavy quarks $M_b^{\text{PMC}}=4.86^{+0.03}_{-0.02}$ GeV, $M_t^{\text{PMC}}=172.3\pm 0.6$ GeV, and the running mass $\overline{m}_t^{\text{PMC}}=162.6\pm 0.7$ GeV at the PMC scale.