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First determination of the strange and light quark masses from full lattice QCD

HPQCD collaboration, MILC collaboration, UKQCD collaboration, C. Aubin, C. Bernard, C. Davies, C. DeTar, Steven Gottlieb, A. Gray, E. Gregory, J. Hein, U. Heller, J. Hetrick, G. Lepage, Q. Mason, J. Osborn, J. Shigemitsu, R. Sugar, D. Toussaint, H. Trottier, M. Wingate

TL;DR

This work determines the strange and light quark masses from full lattice QCD with 2+1 dynamical quarks using improved staggered fermions, anchored to physical $m_\pi$ and $m_K$ and analyzed with S$\chi$PT to control chiral and lattice-spacing extrapolations. Quark masses in the lattice scheme are perturbatively matched to $\overline{\text{MS}}$ at 2 GeV using a one-loop renormalization factor $Z_m$ with a $q^*$-BLM scale, yielding $m_s^{\overline{\text{MS}}}(2{\rm GeV})=76(8)$ MeV and $\hat m^{\overline{\text{MS}}}(2{\rm GeV})=2.8(3)$ MeV, with $m_s/\hat m = 27.4(1)(4)(0)(1)$. The results represent a marked reduction in systematic uncertainties compared with earlier lattice and sum-rule determinations, aided by simulations close to the physical light-quark regime and careful treatment of EM effects. The study demonstrates the viability of improved staggered quarks for precision quark-mass determinations and highlights the need for higher-order perturbative renormalization to further reduce the dominant remaining uncertainties.

Abstract

We compute the strange quark mass $m_s$ and the average of the $u$ and $d$ quark masses $\hat m$ using full lattice QCD with three dynamical quarks combined with experimental values for the pion and kaon masses. The simulations have degenerate $u$ and $d$ quarks with masses $m_u=m_d\equiv \hat m$ as low as $m_s/8$, and two different values of the lattice spacing. The bare lattice quark masses obtained are converted to the $\msbar$ scheme using perturbation theory at $O(alpha_s)$. Our results are: $m_s^\msbar$(2 GeV) = 76(0)(3)(7)(0) MeV, $\hat m^\msbar$(2 GeV) = 2.8(0)(1)(3)(0) MeV and $m_s/\hat m$ = 27.4(1)(4)(0)(1), where the errors are from statistics, simulation, perturbation theory, and electromagnetic effects, respectively.

First determination of the strange and light quark masses from full lattice QCD

TL;DR

This work determines the strange and light quark masses from full lattice QCD with 2+1 dynamical quarks using improved staggered fermions, anchored to physical and and analyzed with SPT to control chiral and lattice-spacing extrapolations. Quark masses in the lattice scheme are perturbatively matched to at 2 GeV using a one-loop renormalization factor with a -BLM scale, yielding MeV and MeV, with . The results represent a marked reduction in systematic uncertainties compared with earlier lattice and sum-rule determinations, aided by simulations close to the physical light-quark regime and careful treatment of EM effects. The study demonstrates the viability of improved staggered quarks for precision quark-mass determinations and highlights the need for higher-order perturbative renormalization to further reduce the dominant remaining uncertainties.

Abstract

We compute the strange quark mass and the average of the and quark masses using full lattice QCD with three dynamical quarks combined with experimental values for the pion and kaon masses. The simulations have degenerate and quarks with masses as low as , and two different values of the lattice spacing. The bare lattice quark masses obtained are converted to the scheme using perturbation theory at . Our results are: (2 GeV) = 76(0)(3)(7)(0) MeV, (2 GeV) = 2.8(0)(1)(3)(0) MeV and = 27.4(1)(4)(0)(1), where the errors are from statistics, simulation, perturbation theory, and electromagnetic effects, respectively.

Paper Structure

This paper contains 6 sections, 4 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Lattice data
  3. Chiral Fits and Systematic Errors
  4. Connecting $m^{\text{lattice}}$ with $m^{\text{$\overline{\text{MS}}$}}$
  5. Comparison with previous determinations
  6. Conclusions

Figures (2)

  • Figure 1: Partially quenched data for squared meson masses made out of valence quarks $x$ and $y$ as a function of $m_x/m'_s$. We show results from two lattices: a coarse lattice with sea quark masses $a\hat{m}'=0.01$, $am'_s=0.05$, and a fine lattice with $a\hat{m}'=0.0062$, $am'_s=0.031$. Three sets of "kaon" points with $m_y=m'_s, 0.8 m'_s, 0.6 m'_s$, are plotted for each lattice. "Pion" points have $m_x=m_y$. The solid lines come from a fit to all the data (not just that plotted). The statistical errors in the points, as well as the variation in the data with sea quark masses are not visible on this scale. The green dashed lines give the continuum fit described in the text, and the magenta vertical dotted line gives the physical $\hat{m}/m_s$ obtained.
  • Figure 2: Lattice results for two masses which show sensitivity to $m_s$, plotted against $\hat{m}'/m_s'$. The valence $s$ masses are taken at the $m_s$ values determined here. The bursts give the corresponding experimental result. The squares are $2m_{B_{s,av}}-m_\Upsilon$ for two of the coarse ensembles. The upper results are for the mass of the $\Omega$ ($sss$) baryon, on both coarse (diamonds) and fine (crosses) ensembles.