Pion scattering in Wilson ChPT

TL;DR

This paper calculates pion scattering amplitudes within Wilson chiral perturbation theory, revealing how lattice artifacts modify scattering lengths and introduce new chiral logarithms, especially in the chiral limit.

Contribution

It provides analytic expressions for pion scattering lengths in Wilson ChPT across different regimes, highlighting the impact of lattice spacing effects on low-energy pion interactions.

Findings

I=0 and I=2 scattering lengths do not vanish in the chiral limit due to O(a^2) terms.

Additional chiral logarithms proportional to a^2 ln M_π^2 appear in one-loop results.

Lattice artifacts significantly alter continuum chiral perturbation theory predictions.

Abstract

We compute the scattering amplitude for pion scattering in Wilson chiral perturbation theory for two degenerate quark flavors. We consider two different regimes where the quark mass m is of order (i) a\Lambda_QCD^2 and (ii) a^2\Lambda_QCD^3. Analytic expressions for the scattering lengths in all three isospin channels are given. As a result of the O(a^2) terms the I=0 and I=2 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 for regime (ii). These contributions significantly modify the familiar results from continuum chiral perturbation theory.