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

## TL;DR

This paper investigates the scaling behavior of lattice QCD simulations with two flavors of Wilson fermions, revealing significant deviations from expected asymptotic scaling predictions.

## Contribution

It provides the first detailed comparison of large and small lattice data to test asymptotic scaling in two-flavor Wilson fermion QCD.

## Key findings

- Matching fails at certain $eta$ values, indicating non-asymptotic behavior.
- Observed shift in $eta$ is larger than perturbative predictions.
- Simulations are far from the asymptotic scaling region.

## 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 $16^3\times32$ and $8^3\times16$. 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.