Determination of $\overline{m}_b/\overline{m}_c$ and $\overline{m}_b$ from $n_f=4$ lattice QCD$+$QED

TL;DR

This paper provides a nonperturbative determination of the ratio of bottom to charm quark masses using advanced lattice QCD+QED simulations, leading to precise values for the $b$-quark mass.

Contribution

It extends previous lattice QCD analyses by including finer lattices and QED effects, resulting in the first nonperturbative $n_f=4$ lattice QCD+QED determination of the mass ratio.

Findings

Mass ratio $ar{m}_b/ar{m}_c=4.586(12)$ at 3 GeV

New $b$-quark mass $ar{m}_b(3 ext{GeV})=4.513(26)$ GeV

Corresponding $b$-mass $ar{m}_b(ar{m}_b)=4.202(21)$ GeV

Abstract

We extend HPQCD's earlier $n_f=4$ lattice-QCD analysis of the ratio of $\overline{\mathrm{MSB}}$ masses of the $b$ and $c$ quark to include results from finer lattices (down to 0.03fm) and a new calculation of QED contributions to the mass ratio. We find that $\overline{m}_b(\mu)/\overline{m}_c(\mu)=4.586(12)$ at renormalization scale $\mu=3$\,GeV. This result is nonperturbative. Combining it with HPQCD's recent lattice QCD$+$QED determination of $\overline{m}_c(3\mathrm{GeV})$ gives a new value for the $b$-quark mass: $\overline{m}_b(3\mathrm{GeV}) = 4.513(26)$GeV. The $b$-mass corresponds to $\overline{m}_b(\overline{m}_b, n_f=5) = 4.202(21)$GeV. These results are the first based on simulations that include QED.