Chiral symmetry andπ-πscattering in the covariant spectator theory

Abstract

The $\ensuremath{\pi}$-$\ensuremath{\pi}$ 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 $\ensuremath{\pi}$-$\ensuremath{\pi}$ scattering amplitude allows us to sum the intermediate quark-quark interactions to all orders. The Adler self-consistency zero for $\ensuremath{\pi}$-$\ensuremath{\pi}$ scattering in the chiral limit emerges as the result for this sum.