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

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 ${\overline{m}}_b(\hat{I}¼)/{\overline{m}}_c(\hat{I}¼)=4.586(12)$ at renormalization scale $\hat{I}¼=3$\,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.

8 pages, 4 figures