Chiral interpolation in a finite volume

TL;DR

This paper introduces a new computational scheme within chiral perturbation theory to interpolate between epsilon and p regimes, enabling precise analysis of finite volume effects in lattice QCD near the physical pion mass.

Contribution

The paper develops a novel interpolation method in chiral perturbation theory that combines features of epsilon and p regimes for better finite volume analysis in lattice QCD.

Findings

Successfully applied to lattice QCD data near physical quark masses

Extracted a pion mass of 99(4) MeV from the data

Demonstrated improved understanding of finite volume effects

Abstract

A simulation of lattice QCD at (or even below) the physical pion mass is feasible on a small lattice size of \sim 2 fm. The results are, however, subject to large finite volume effects. In order to precisely understand the chiral behavior in a finite volume, we develop a new computational scheme to interpolate the conventional epsilon and p regimes within chiral perturbation theory. In this new scheme, we calculate the two-point function in the pseudoscalar channel, which is described by a set of Bessel functions in an infra-red finite way as in the epsilon regime, while chiral logarithmic effects are kept manifest as in the p regime. The new ChPT formula is compared to our 2+1- flavor lattice QCD data near the physical up and down quark mass, mud \sim 3 MeV on an L \sim 1.8 fm lattice. We extract the pion mass = 99(4) MeV, from which we attempt a chiral "interpolation" of the observables to the physical point.