Isotropic and Anisotropic Lattice Spacing Corrections for I=2 pi-pi Scattering from Effective Field Theory

TL;DR

This paper calculates finite lattice spacing corrections for I=2 pi-pi scattering using effective field theory, improving the accuracy of lattice QCD results for scattering parameters.

Contribution

It provides the first detailed analysis of isotropic and anisotropic lattice spacing effects on I=2 pi-pi scattering within effective field theory, including pion properties.

Findings

Lattice spacing effects appear at next-to-leading order in lattice-physical parameters.

Results correct phase shift calculations from lattice data.

Determined pion masses and decay constants in the lattice context.

Abstract

The calculation of the finite lattice spacing corrections for I=2 pi-pi scattering is carried out for isotropic and anisotropic Wilson lattice actions. Pion masses and decay constants are also determined in this context. These results correct the phase shift calculated from the lattice, which is connected to the scattering length and effective range in this low energy scattering process. When in terms of the lattice-physical parameters for either Wilson action, these lattice spacing effects first appear at the next-to-leading order counter-terms.