Toward the QCD $β$ Function with Dynamical Wilson Fermions

Abstract

We present data for the scaling behavior of lattice QCD with two flavors of light Wilson fermions. This is done by matching $π$ n and $ρ$ masses at the two lattice sizes of $16^3\times32 $ and $8^3\times16$. We find that at $β=6/g^2\equiv5.3$ the matching does not occur over a range extending down to $β=3.5$. For $β=5.5$ matching may be achieved at $β=4.8-4.9$, leading to a $Δβ=0.6-0.7$ which is higher than the perturbative 2-loop value of 0.45. In both cases we conclude that the simulations are very far from the perturbative scaling region.