Pion Scattering in Wilson Chiral Perturbation Theory

TL;DR

This paper calculates pion scattering amplitudes within Wilson Chiral Perturbation Theory, accounting for lattice spacing effects and revealing how these influence scattering lengths and chiral logarithms, impacting lattice QCD analyses.

Contribution

It provides analytic expressions for scattering lengths considering O(a^2) effects and discusses their implications for lattice QCD simulations.

Findings

Scattering lengths do not vanish in the chiral limit due to O(a^2) terms.

Presence of a^2 ln M_pi^2 chiral logs complicates low-energy constant extraction.

Lattice spacing effects significantly modify continuum chiral behavior.

Abstract

We compute the scattering amplitude in Wilson Chiral Perturbation Theory for two flavors. The lattice spacing effects due to the explicit chiral symmetry breaking are kept through O(a^2), and we consider the regime where the quark mass m is of order a^2 Lambda_^3. Analytic expressions for the scattering lengths in different isospin channels are given. As a result of the O(a^2) terms the scattering lengths do not vanish in the chiral limit. Moreover, additional chiral logarithms proportional to a^2 ln M_pi^2 are present in the one-loop results. These contributions can obscure the continuum chiral logarithms and the determination of low-energy constants from numerical lattice simulations.