# On the effect of resonances in the quark-photon vertex

## TL;DR

This paper investigates the analytic structure of the quark-photon vertex in a covariant Bethe-Salpeter framework, incorporating resonances like the rho meson and pion effects to improve understanding of timelike form factors.

## Contribution

It introduces explicit pion degrees of freedom into the Bethe-Salpeter interaction kernel, revealing resonance poles and branch cuts in the quark-photon vertex for timelike momenta.

## Key findings

- Rho resonance appears as a pole in the complex momentum plane.
- A multiparticle branch cut develops from -4m_π^2 to -∞.
- The approach advances the calculation of timelike form factors.

## Abstract

A calculation of hadronic timelike form factors in the Poincar\'e-covariant Bethe-Salpeter formalism necessitates knowing the analytic structure of the non-perturbative quark-photon vertex in the context of the Poincar\'e-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 $-4m_\pi^2$ to $-\infty$ develops. This calculation represents an essential step towards the calculation of timelike form factors in the Bethe-Salpeter approach.