We study the scaling behavior of the quark propagator on two lattices with similar physical volume in Landau gauge with $2+1$ flavors of dynamical quarks in order to test whether we are close to the continuum limit for these lattices. We use configurations generated with an improved staggered (“Asqtad”) action by the MILC collaboration. The calculations are performed on ${28}^3\times 96$ lattices with lattice spacing $a=0.09\mathrm{fm}$ and on ${20}^3\times 64$ lattices with lattice spacing $a=0.12\mathrm{fm}$. We calculate the quark mass function, $M(q^2)$, and the wave-function renormalization function, $Z(q^2)$, for a variety of bare quark masses. Comparing the behavior of these functions on the two sets of lattices we find that both $Z(q^2)$ and $M(q^2)$ show little sensitivity to the ultraviolet cutoff.

• Received 8 November 2005

DOI:https://doi.org/10.1103/PhysRevD.73.054504