On Scale Determination in Lattice QCD with Dynamical Quarks
Abstract
Dependence of a/rc (inverse Sommer parameter in units of lattice spacing a) on amq (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 163 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 amq from about 0.07 to below 0.015. Though scaling violations may indeed be present for relatively large amq, a consistent scenario at sufficiently small amq seems to emerge in the mass-independent scheme where for a fixed beta, 1/r0 and sqrtsigma have linear dependence on mq 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.