Determination of the top-quark $\overline{\mathrm{MS}}$ running mass via its perturbative relation to the on-shell mass with the help of principle of maximum conformality

Abstract

In the paper, we study the properties of the top-quark $\overline{\mathrm{MS}}$ running mass computed from its on-shell mass by using both the four-loop $\overline{\mathrm{MS}}$-on-shell relation and the principle of maximum conformality (PMC) scale-setting approach. The PMC adopts the renormalization group equation to set the correct magnitude of the strong running coupling of the perturbative series, its prediction avoids the conventional renormalization scale ambiguity, and thus a more precise pQCD prediction can be achieved. After applying the PMC to the four-loop $\overline{\mathrm{MS}}$-on-shell relation and taking the top-quark on-shell mass $M_t=172.9\pm 0.4$ GeV as an input, we obtain the renormalization scale-invariant $\overline{\mathrm{MS}}$ running mass at the scale $m_t$, e.g., $m_t(m_t)\simeq 162.6\pm 0.4$ GeV, in which the error is the squared average of those from $\Delta {\alpha }_s(M_Z)$, $\Delta M_t$, and the approximate error from the uncalculated five-loop terms predicted by using the Padé approximation approach.

arXiv comment8 pages, 2 figures

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• $Z$-boson hadronic decay width up to $\mathcal{O}({\alpha }_s^4)$-order QCD corrections using the single-scale approach of the principle of maximum conformality
• Reanalysis of the top-quark pair hadroproduction and a precise determination of the top-quark pole mass at the LHC
• 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 ${\overline{m}}_t({\overline{m}}_t)$
• A new analysis of the pQCD contributions to the electroweak parameter $\rho$ using the single-scale approach of principle of maximum conformality