QCD $\beta$ Function with Two Flavors of Dynamical Wilson Fermions

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 $\beta =6\mathrm{/}{g}^2=5.3$ 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 $\mathrm{\Delta }\beta =0.6(1)$, 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.