Geometry dependence of RMT-based methods to extract the low-energy constants Sigma and F

TL;DR

This paper investigates how lattice geometry influences RMT-based methods for extracting low-energy constants in QCD, proposing optimal configurations to minimize systematic errors and demonstrating this with lattice data.

Contribution

It introduces a systematic study of lattice geometry effects on RMT methods for low-energy constant extraction and suggests optimal geometries for accurate results.

Findings

Optimal lattice geometries reduce systematic deviations from RMT.

Determined $$ and $F$ using different geometries, showing geometry dependence.

Validated the approach with lattice configurations from JLQCD.

Abstract

The lowest-order low-energy constants $\Sigma$ and $F$ of chiral pertubation theory can be extracted from lattice data using methods based on the equivalence of random matrix theory (RMT) and QCD in the epsilon regime. We discuss how the choice of the lattice geometry affects such methods. In particular, we show how to minimize systematic deviations from RMT by an optimal choice of the lattice geometry in the case of two light quark flavors. We illustrate our findings by determining $\Sigma$ and $F$ from lattice configurations with two dynamical overlap fermions generated by JLQCD, using two different lattice geometries.