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

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.