Abstract
.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 -4m_{pi}^{2} to -infty develops. This calculation represents an essential step towards the calculation of timelike form factors in the Bethe-Salpeter approach.
Highlights
The quark-photon vertex describes the interaction of quarks with photons in quantum field theory
For timelike photon momentum, the quark-photon vertex must reflect the full excitation spectrum of quantum chromodynamics (QCD) in the vector-meson channel, a fact which is at the heart of the phenomenological success of vector-meson dominance models [13, 14]
In the Dyson-Schwinger a e-mail: angel.miramontes-lopez@uni-graz.at (DSE)/BSE formalism, the quark-photon vertex Γ μ can be described by an integral equation which is linear in Γ μ, usually called inhomogeneous BSE
Summary
The quark-photon vertex describes the interaction of quarks with photons in quantum field theory. For timelike photon momentum, the quark-photon vertex must reflect the full excitation spectrum of quantum chromodynamics (QCD) in the vector-meson channel, a fact which is at the heart of the phenomenological success of vector-meson dominance models [13, 14] (see [15]) The details of such a rich structure of the vertex are, not precisely known since they are generated by non-perturbative QCD effects. To the best of our knowledge, the rainbow-ladder (RL) truncation of the BSE interaction kernel described below is the most sophisticated truncation used so far in the calculation of hadron form factors. In this work we study an extension of the RL truncation which encodes, to some extent, the above-mentioned non-valence quark effects on the BSE interaction kernel. Note that we work in Landau gauge and in Euclidean spacetime (using the conventions in [17])
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