$I=2$ pion scattering amplitude with Wilson fermions

TL;DR

This study explores the $I=2$ pion scattering amplitude at threshold using Wilson fermions, finding good agreement with chiral perturbation theory and showing the interaction is attractive, with no signs of problematic chiral behavior.

Contribution

First exploratory calculation of $I=2$ $$ pion scattering with Wilson fermions in the quenched approximation, including all contractions and deriving inequalities.

Findings

Good agreement with chiral perturbation theory predictions.

No evidence of bad chiral behavior within 10% errors.

Interaction in the antisymmetric two-pion state is attractive.

Abstract

We present an exploratory calculation of the $I=2$ $\pi-\pi$ scattering amplitude at threshold using Wilson fermions in the quenched approximation, including all the required contractions. We find good agreement with the predictions of chiral perturbation theory even for pions of mass 560-700 MeV. Within the 10\% errors, we do not see the onset of the bad chiral behavior expected for Wilson fermions. We also derive rigorous inequalities that apply to 2-particle correlators and as a consequence show that the interaction in the antisymmetric state of two pions has to be attractive.