QCDβfunction 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 ${16}^3$×32 and $8^3$×16. We find that at $\beta =\frac{6}{g^2}=5.3\mathrm{}$ matching is not possible over a range extending down to $\beta =3.5\mathrm{}$. The large lattice data at $\beta =5.5\mathrm{}$ matches the small lattice values at $\beta =4.9\mathrm{}\left(1\right)\mathrm{}$ leading to a shift $\Delta \beta =0.6\mathrm{}\left(1\right)\mathrm{}$, 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.