Bottom and Charm Mass determinations from global fits to $Q\bar{Q}$ bound states at N$^3$LO

TL;DR

This paper uses high-order QCD calculations to determine bottom and charm quark masses from quarkonium spectra, accounting for finite charm mass effects and scheme variations, achieving precise mass and coupling constant estimates.

Contribution

It provides a detailed N$^3$LO analysis of bottomonium states including charm mass effects, and extracts quark masses and alpha_s with improved precision.

Findings

Bottom quark mass: 4.216 ± 0.039 GeV

Charm quark mass: 1.273 ± 0.054 GeV

Alpha_s at m_Z: 0.1178 ± 0.0051

Abstract

The bottomonium spectrum up to $n = 3$ is studied within Non-Relativistic Quantum Chromodynamics up to N$^3$LO. We consider finite charm quark mass effects both in the QCD potential and the $\overline{\mathrm{MS}}$-pole mass relation up to third order in the $\Upsilon$-scheme counting. The $u = 1/2$ renormalon of the static potential is canceled by expressing the bottom quark pole mass in terms of the MSR mass. A careful investigation of scale variation reveals that, while $n = 1, 2$ states are well behaved within perturbation theory, $n = 3$ bound states are no longer reliable. We carry out our analysis in the $n_\ell = 3$ and $n_\ell = 4$ schemes and conclude that, as long as finite $m_c$ effects are smoothly incorporated in the MSR mass definition, the difference between the two schemes is rather small. Performing a fit to $b\bar{b}$ bound states we find $\overline{m}_b(\overline{m}_b) = 4.216\pm 0.039$ GeV. We extend our analysis to the lowest lying charmonium states finding $\overline{m}_c(\overline{m}_c)=1.273 \pm 0.054$ GeV. Finally, we perform simultaneous fits for $\overline{m}_b$ and $\alpha_s$ finding $\alpha_s^{(n_f=5)}(m_Z)=0.1178\pm 0.0051$. Additionally, using a modified version of the MSR mass with lighter massive quarks we are able to predict the uncalculated $\mathcal{O}(\alpha_s^4)$ virtual massive quark corrections to the relation between the $\overline{\mathrm{MS}}$ and pole masses.