Regular Article - Theoretical Physics
On the effect of resonances in the quark-photon vertex
Institute of Physics, University of Graz, NAWI Graz, 8010, Graz, Austria
* e-mail: email@example.com
Accepted: 3 August 2019
Published online: 2 October 2019
A calculation of hadronic timelike form factors in the Poincaré-covariant Bethe-Salpeter formalism necessitates knowing the analytic structure of the non-perturbative quark-photon vertex in the context of the Poincaré-covariant Bethe-Salpeter formalism. We include, in the interaction between quark and antiquark, the possibility of non-valence effects by introducing pions as explicit degrees of freedom. These encode the presence of intermediate resonances in the Bethe-Salpeter interaction kernel. We calculate the vertex for real as well as complex photon momentum. We show how the vertex reflects now the correct physical picture, with the rho resonance appearing as a pole in the complex momentum plane. A multiparticle branch cut for values of the photon momentum from to develops. This calculation represents an essential step towards the calculation of timelike form factors in the Bethe-Salpeter approach.
© The Author(s), 2019