Finite volume corrections to pi-pi scattering

TL;DR

This paper calculates the leading exponential finite volume corrections to pi-pi scattering in lattice QCD using one-loop chiral perturbation theory, improving the accuracy of scattering parameter extraction.

Contribution

It provides a detailed one-loop chiral perturbation theory analysis of exponential finite volume effects for I=2 pi-pi scattering near threshold.

Findings

Derived explicit formulas for exponential corrections

Quantified the size of corrections near the chiral limit

Enhanced the precision of lattice QCD scattering studies

Abstract

Lattice QCD studies of hadron-hadron interactions are performed by computing the energy levels of the system in a finite box. The shifts in energy levels proportional to inverse powers of the volume are related to scattering parameters in a model independent way. In addition, there are non-universal exponentially suppressed corrections that distort this relation. These terms are proportional to exp(-m_pi L) and become relevant as the chiral limit is approached. In this paper we report on a one-loop chiral perturbation theory calculation of the leading exponential corrections in the case of I=2 pi-pi scattering near threshold.