Precise Charm to Strange Mass Ratio and Light Quark Masses from Full Lattice QCD

Abstract

By using a single formalism to handle charm, strange, and light valence quarks in full lattice QCD for the first time, we are able to determine ratios of quark masses to 1%. For ${m}_{c}/{m}_{s}$ we obtain 11.85(16), an order of magnitude more precise than the current PDG average. Combined with 1% determinations of the charm quark mass now possible this gives ${\overline{m}}_{s}(2\text{ }\text{ }\mathrm{GeV})=92.4(1.5)\text{ }\text{ }\mathrm{MeV}$. The MILC result for ${m}_{s}/{m}_{l}=27.2(3)$ yields ${\overline{m}}_{l}(2\text{ }\text{ }\mathrm{GeV})=3.40(7)\text{ }\text{ }\mathrm{MeV}$ for the average of $u$ and $d$ quark masses.