Light Quark Masses from Lattice QCD

TL;DR

This work consolidates lattice QCD determinations of light quark masses across Wilson, clover, and staggered fermions in quenched and nf=2 settings, demonstrating that continuum-limit results agree across discretizations. It provides MSbar masses at 2 GeV with clear quantification of statistical and systematic errors, finding notably lower values than many phenomenological estimates, and shows these masses coherently impact the ε'/ε prediction and the quark condensate via GMOR. The analysis emphasizes discretization and nf-extrapolation as major uncertainties, highlighting the need for more unquenched data to pin down the physical nf=3 case. Overall, the paper strengthens lattice QCD’s role in precise quark mass determinations and related chiral observables, while outlining pathways for further refinement.

Abstract

We present estimates of the masses of light quarks using lattice data. Our main results are based on a global analysis of all the published data for Wilson, Sheikholeslami-Wohlert (clover), and staggered fermions, both in the quenched approximation and with $n_f=2$ dynamical flavors. We find that the values of masses with the various formulations agree after extrapolation to the continuum limit for the $n_f=0$ theory. Our best estimates, in the MSbar scheme at $μ=2 GeV$, are $\mbar=3.4 +- 0.4 +- 0.3 MeV$ and $m_s = 100 +- 21 +- 10 MeV$ in the quenched approximation. The $n_f=2$ results, $\mbar = 2.7 +- 0.3 +- 0.3 MeV$ and $m_s = 68 +- 12 +- 7 MeV$, are preliminary. (A linear extrapolation in $n_f$ would further reduce these estimates for the physical case of three dynamical flavors.) These estimates are smaller than phenomenological estimates based on sum rules, but maintain the ratios predicted by chiral perturbation theory. The new results have a significant impact on the extraction of $ε'/ε$ from the Standard Model. Using the same lattice data we estimate the quark condensate using the Gell-Mann-Oakes-Renner relation. Again the three formulations give consistent results after extrapolation to $a=0$, and the value turns out to be correspondingly larger, roughly preserving $m_s \vev{\bar ψψ}$.

Figures (11)

• Figure 1: The behavior of $\hbox{$\overline{m}$}({\hbox{$\overline{MS}$}},2 \mathord{\rm \;GeV})$ extracted using the quenched $M_\pi$ data in the TAD1 lattice scheme defined in the text. The scale is set by $M_\rho$. We do not show the fit to the clover data for clarity.
• Figure 2: Three different fits to quenched Wilson data for $\hbox{$\overline{m}$}({\hbox{$\overline{MS}$}},2 \mathord{\rm \;GeV})$. The solid line is a linear fit to points at $\beta \ge 5.93$, while the dotted line includes a quadratic correction. The dashed line is the quadratic fit to points at $\beta \ge 6.0$.
• Figure 3: The behavior of $\hbox{$\overline{m}$}({\hbox{$\overline{MS}$}},2 \mathord{\rm \;GeV})$, extracted using $M_\pi$ data for $n_f =2$ simulations. The scale is set by $M_\rho$, and the lattice scheme is TAD1.
• Figure 4: Comparison of $m_s({\hbox{$\overline{MS}$}},2 \mathord{\rm \;GeV})$ extracted using $M_\phi$ against the lowest order chiral prediction $m_s = 25.9\hbox{$\overline{m}$}$. The data are for the quenched Wilson theory.
• Figure 5: Comparison of $m_s({\hbox{$\overline{MS}$}},2 \mathord{\rm \;GeV})$ extracted using $M_\phi$ for the quenched Wilson, and staggered theories.