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.

arXiv comment16 pages, 12 figures; version published in Phys. Rev. D

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• Charming quasi-exotic open-flavor mesons
• The quark spectral functions and the Hadron Vacuum Polarization from application of DSEs in Minkowski space
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• Application of the Covariant Spectator Theory to the study of heavy and heavy-light mesons
• Simple high-accuracy method for solving bound-state equations with the Cornell potential in momentum space
• Pion observables calculated in Minkowski and Euclidean spaces with Ansätze for quark propagators
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• Relativistic phenomenology of meson spectra with a covariant quark model in Minkowski space
• Removal of singularities from the covariant spectator theory
• Quarkonia and heavy-light mesons in a covariant quark model
• Quark model with chiral-symmetry breaking and confinement in the Covariant Spectator Theory
• Chiral-symmetry breaking and confinement in Minkowski space