Precise charm to strange mass ratio and light quark masses from full lattice QCD

TL;DR

By using a single formalism to handle charm, strange, and light valence quarks in full lattice QCD for the first time, this work is able to determine ratios of quark masses to 1%.

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 $\bar{m}_s(2{\rm GeV}) =$ 92.4(1.5) MeV. The MILC result for $m_s/m_l = 27.2(3) $ yields $\bar{m}_l(2{\rm GeV})$ = 3.40(7) MeV for the average of $u$ and $d$ quark masses.

Figures (2)

• Figure 1: Grey points show the raw data for every ratio of $m_c/m_s$ on each ensemble (Table \ref{['tab:charmmass']}); these ratios are fit to eq. \ref{['eq:fit']}. The dashed line and associated grey error band (and red point at $a=0$) show our extrapolation of the resulting tuned $m_c/m_s$ to the continuum limit. Blue points with error bars are from a simple interpolation, separately for each ensemble, to the correct $m_c/m_s$, and are shown for illustration.
• Figure 2: Our results for the 4 lightest quark masses compared to the current PDG evaluations (shaded bands) pdg09. Each mass is quoted in the $\overline{MS}$ scheme at its conventional scale: 2 GeV for $u$, $d$, $s$ ($n_f=3$); $m_c$ for $c$ ($n_f=4$).