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

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.

16 pages, 12 figures; version published in Phys. Rev. D

References in corpus (2)

• Infrared Properties of QCD from Dyson-Schwinger equations
• The Flavor Structure of the Excited Baryon Spectra from Lattice QCD

Cited by in corpus (9)

• Baryons as relativistic three-quark bound states
• Comparison of two Minkowski-space approaches to heavy quarkonia
• Covariant spectator theory of quark-antiquark bound states: Mass spectra and vertex functions of heavy and heavy-light mesons
• Covariant Spectator Theory of heavy-light and heavy mesons and the predictive power of covariant interaction kernels
• Quark mass function from a one-gluon-exchange-type interaction in Minkowski space
• Pion observables calculated in Minkowski and Euclidean spaces with Ansätze for quark propagators
• Simple high-accuracy method for solving bound-state equations with the Cornell potential in momentum space
• Application of the Covariant Spectator Theory to the study of heavy and heavy-light mesons
• Removal of singularities from the covariant spectator theory