Chiral symmetry and π-π scattering in the covariant spectator theory

Elmar P. Biernat, M. T. Peña, J. E. Ribeiro, Alfred Stadler, and Franz Gross
Phys. Rev. D 90, 096008 – Published 14 November 2014

Abstract

The π-π 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 π-π scattering amplitude allows us to sum the intermediate quark-quark interactions to all orders. The Adler self-consistency zero for π-π scattering in the chiral limit emerges as the result for this sum.

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  • Received 5 August 2014

DOI:https://doi.org/10.1103/PhysRevD.90.096008

© 2014 American Physical Society

Authors & Affiliations

Elmar P. Biernat1,*, M. T. Peña1,2,†, J. E. Ribeiro3,‡, Alfred Stadler4,1,§, and Franz Gross5,∥

  • 1Centro de Física Teórica de Partículas (CFTP), Instituto Superior Técnico (IST), Universidade de Lisboa, 1049-001 Lisboa, Portugal
  • 2Departamento de Física, Instituto Superior Técnico (IST), Universidade de Lisboa, 1049-001 Lisboa, Portugal
  • 3Centro de Física das Interações Fundamentais (CFIF), Instituto Superior Técnico (IST), Universidade de Lisboa, 1049-001 Lisboa, Portugal
  • 4Departamento de Física, Universidade de Évora, 7000-671 Évora, Portugal
  • 5Thomas Jefferson National Accelerator Facility (JLab), Newport News, Virginia 23606, USA

  • *elmar.biernat@tecnico.ulisboa.pt
  • teresa.pena@tecnico.ulisboa.pt
  • emilioribeiro@tecnico.ulisboa.pt
  • §stadler@uevora.pt
  • gross@jlab.org

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Issue

Vol. 90, Iss. 9 — 1 November 2014

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