On Scale Determination in Lattice QCD with Dynamical Quarks

TL;DR

This study investigates how the lattice scale in QCD simulations depends on quark mass, revealing that at small quark masses, the dependence is consistent with physical expectations and allows for accurate scale setting.

Contribution

It demonstrates that in lattice QCD with Wilson fermions, the quark mass dependence of scale-setting parameters becomes linear at small masses, clarifying the nature of scaling violations.

Findings

Linear dependence of 1/r_0 and sqrt{sigma} on quark mass at small am_q

Evidence for a consistent physical scenario at low quark masses

Lattice scale determined with chiral extrapolation to the physical point

Abstract

Dependence of a/r_c (inverse Sommer parameter in units of lattice spacing a) on am_q (quark mass in lattice unit) has been observed in all lattice QCD simulations with sea quarks including the ones with improved actions. How much of this dependence is a scaling violation has remained an intriguing question. Our approach has been to investigate the issue with an action with known lattice artifacts, i.e., the standard Wilson quark and gauge action with beta=5.6 and 2 degenerate flavors of sea quarks on 16^3 times 32 lattices. In order to study in detail the sea quark mass dependence, measurements are carried out at eight values of the PCAC quark mass values am_q from about 0.07 to below 0.015. Though scaling violations may indeed be present for relatively large am_q, a consistent scenario at sufficiently small am_q seems to emerge in the mass-independent scheme where for a fixed beta, 1/r_0 and sqrt{sigma} have linear dependence on m_q as physical effects similar to the quark mass dependence of the rho mass. We present evidence for this scenario and accordingly extract the lattice scale (a = 0.0805(7) fm, a^{-1} = 2.45(2) GeV) by chiral extrapolation to the physical point.