QCD $\beta$ 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 $\pi$ and $\rho$ masses on lattices of size $16^3\times 32$ and $8^3\times 16$. We find that at $\beta =6/g^2=5.3$ matching is not possible over a range extending down to $\beta =3.5$. The large lattice data at $\beta =5.5$ matches the small lattice values at $\beta =4.9(1)$ leading to a shift $\Delta \beta =0.6(1)$, 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.

11 pages latex with 6 postscript figures included by epsf. Text includes extensions and minor revisions. To be published in Phys. Rev. D1