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Light and strange quark masses with $N_f = 2 + 1$ Wilson fermions

Gregorio Herdoíza, Fernando P. Panadero, Carlos Pena, Alejandro Sáez

Abstract

We report on the status of an update of our collaboration's previous computation of light and strange quark masses in QCD with $N_{f}=2+1$ dynamical flavours. Bare quark masses are extracted from CLS ensembles, using $O(a)$-improved Wilson fermions, and the mass renormalization is performed non-perturbatively in the Schrödinger functional scheme over a wide range of scales to make safe contact with perturbation theory. Results for five lattice spacings, down to $a\sim 0.038 \textrm{ fm}$, and pion masses reaching the physical value are included in the analysis. This allows for the exploration of different models for cutoff and chiral effects, and a controlled extrapolation to the physical point.

Light and strange quark masses with $N_f = 2 + 1$ Wilson fermions

Abstract

We report on the status of an update of our collaboration's previous computation of light and strange quark masses in QCD with dynamical flavours. Bare quark masses are extracted from CLS ensembles, using -improved Wilson fermions, and the mass renormalization is performed non-perturbatively in the Schrödinger functional scheme over a wide range of scales to make safe contact with perturbation theory. Results for five lattice spacings, down to , and pion masses reaching the physical value are included in the analysis. This allows for the exploration of different models for cutoff and chiral effects, and a controlled extrapolation to the physical point.

Paper Structure

This paper contains 8 sections, 11 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Lattice setup and ensembles
  3. Theoretical framework
  4. Simulation Setup
  5. Chiral continuum extrapolation
  6. Chiral dependence
  7. Cutoff effects and data cuts
  8. Conclusions

Figures (4)

  • Figure 1: Left: values of the lattice spacing and pion mass for the ensembles used in this work. The new ensembles with respect to Bruno:2019vup are highlighted. Right: Values of the light-light ($\overline{m}_{12}$) and light-strange ($\overline{m}_{13}$) renormalized quark masses at $\mu_{had}$ as a function of the pion mass for the same ensembles.
  • Figure 2: Results for the fit [$\chi$ptr][A][$a^{2}\phi$][$m_{\pi} < 420 \textrm{ MeV}$], with p-value $\approx$ 0.77. Top row: result for the fit form in eq.(\ref{['eq:ratio_1']}) plus cutoff effects. The right panel shows the difference with respect to the central value of the continuum curve, without projecting to zero lattice spacing. Bottom row: fit result for eq.(\ref{['eq:ratio2']}). The left plot show the result for various lattice spacings as a function of the dimensionless pion mass, as well as the continuum extrapolation (gray band). In the right plot we show the continuum-limit scaling, where the data has been projected to physical pion mass using the result of the fit.
  • Figure 3: Results for the model average for the considered set of models. The first two plots illustrate the results for the different fits, while the other two plots are the assigned weight and the p-value of the fit (vertical line indicates p-value = 0.1). The opacity of the points is proportional to the weight. The central band is the final result of the model average. The inner darker band corresponds to the statistical error and the lighter outer band to the systematic error from the model averaging procedure.
  • Figure 4: Comparison of light (left) and strange (right) quark masses renormalized in $\overline{MS}$ scheme at 2 GeV in four flavour QCD. The central band corresponds to the FLAG average FLAGCLQCD:2023sdbBruno:2019vupRBC:2014ntlBMW:2010ucxBazavov:2010yqMcNeile:2010ji.