Toward the QCD $\beta$ Function with Dynamical Wilson Fermions

TL;DR

This study investigates the scaling behavior of lattice QCD with two light Wilson fermions, revealing significant deviations from perturbative predictions at certain coupling values.

Contribution

The paper provides empirical data on the non-perturbative scaling behavior of lattice QCD with Wilson fermions, highlighting discrepancies with perturbative expectations.

Findings

Matching of meson masses does not occur at certain couplings.

Observed $eta$-shift exceeds perturbative predictions.

Simulations are far from the perturbative scaling region.

Abstract

We present data for the scaling behavior of lattice QCD with two flavors of light Wilson fermions. This is done by matching $\pi$ n and $\rho$ masses at the two lattice sizes of $16^3\times32 $ and $8^3\times16$. We find that at $\beta=6/g^2\equiv5.3$ the matching does not occur over a range extending down to $\beta=3.5$. For $\beta=5.5$ matching may be achieved at $\beta=4.8-4.9$, leading to a $\Delta \beta =0.6-0.7$ 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.