Axial Correlation Functions in the epsilon-Regime: a Numerical Study with Overlap Fermions

TL;DR

This study uses overlap fermions to numerically analyze axial correlation functions in the epsilon-regime of chiral perturbation theory, highlighting finite size effects, topological influences, and challenges at low quark masses.

Contribution

It provides the first detailed numerical comparison of quenched QCD results with chiral perturbation theory predictions in the epsilon-regime using overlap fermions.

Findings

Lattices with L > 1.1 fm are needed for reliable interpretation.

Smaller lattices are insufficient compared to standard chiral perturbation theory.

Severe difficulties arise at very low quark masses, especially in trivial topological sectors.

Abstract

We present simulation results employing overlap fermions for the axial correlation functions in the epsilon-regime of chiral perturbation theory. In this regime, finite size effects and topology play a dominant role. Their description by quenched chiral perturbation theory is compared to our numerical results in quenched QCD. We show that lattices with a linear extent L > 1.1 fm are necessary to interpret the numerical data obtained in distinct topological sectors in terms of the epsilon-expansion. Such lattices are, however, still substantially smaller than the ones needed in standard chiral perturbation theory. However, we also observe severe difficulties at very low values of the quark mass, in particular in the topologically trivial sector.