Chiral symmetry andπ-πscattering in the covariant spectator theory

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.

Baryons as relativistic three-quark bound states

“…[697,698] the rainbow-ladder expression for the ππ scattering amplitude in the forward limit t = 0 was calculated and the scattering lengths at threshold (s = 4m 2 π ) were extracted. (A similar calculation has been recently performed in the covariant spectator approach [699].) Fig.…”

Charming quasi-exotic open-flavor mesons

“…The DSBSE approach to hadrons uses the BSE to describe mesons as quark-antiquark systems [58], a covariant Faddeev equation for a three-quark setup to study baryons [59][60][61], and more complicated equations to go beyond these configurations [62][63][64][65]. The covariant amplitudes are then used for the subsequent calculation of form factors or other transiton amplitudes [66][67][68][69][70][71][72][73][74][75][76][77].…”

Quarkonia and heavy-light mesons in a covariant quark model

“…The mixing parameter y allows to dial continuously between a scalar-plus-pseudoscalar structure, suggested recently in [1] due to chiral-symmetry constraints, and a vector structure, while preserving the same nonrelativistic limit. The precise Lorentz structure of the confining interaction is not known, and by fitting the y parameter from the mesonic spectra some further information can be gained.…”

“…Preliminary calculations using the Covariant Spectator Theory (CST) employed a scalar linear confining interaction and an additional constant vector potential to compute the mesonic mass spectra. In this work we generalize the confining interaction to include more general structures, in particular a vector and also a pseudoscalar part, as suggested by a recent study [1]. A one-gluon-exchange kernel is also implemented to describe the short-range part of the interaction.…”