QCD $β$ Function with Two Flavors of Dynamical Wilson Fermions

Abstract

We test the asymptotic scaling behavior of state-of-the-art simulations of QCD with two flavors of light Wilson fermions. This is done by matching $π$ and $ρ$ masses on lattices of size $16^3\times32$ and $8^3\times16$. We find that at $β=6/g^2=5.3$ matching is not possible over a range extending down to $β=3.5$. The large lattice data at $β=5.5$ matches the small lattice values at $β=4.9(1)$ leading to a shift $Δβ=0.6(1)$, considerably larger than the perturbative prediction of $0.45$. In both cases we conclude that the simulations are very far from the asymptotic scaling region.