Chiral symmetry and pi-pi scattering in the Covariant Spectator Theory

TL;DR

This paper demonstrates that the Covariant Spectator Theory (CST) accurately models pi-pi scattering, satisfying chiral symmetry constraints and the Adler zero, by establishing the formalism in Minkowski space and ensuring the axial-vector Ward-Takahashi identity is upheld.

Contribution

The paper introduces a CST-based framework for pi-pi scattering that preserves chiral symmetry and satisfies the Adler zero, extending the formalism in Minkowski space.

Findings

CST pi-pi scattering amplitude satisfies the Adler zero constraint.

The axial-vector Ward-Takahashi identity is satisfied within the model.

Application of the identity allows summing quark interactions to all orders.

Abstract

The pi-pi scattering amplitude calculated with a model for the quark-antiquark interaction in the framework of the Covariant Spectator Theory (CST) is shown to satisfy the Adler zero constraint imposed by chiral symmetry. The CST formalism is established in Minkowski space and our calculations are performed in momentum space. We prove that the axial-vector Ward-Takahashi identity is satisfied by our model. Then we show that, similar to what happens within the Bethe-Salpeter formalism, application of the axial-vector Ward-Takahashi identity to the CST pi-pi scattering amplitude allows us to sum the intermediate quark-quark interactions to all orders. The Adler self-consistency zero for pi-pi scattering in the chiral limit emerges as the result for this sum.