Elucidating the rho-meson's role as intermediate resonance in the time-like electromagnetic pion form factor

Abstract

Motivated by the planned measurements of the time-like electromagnetic proton form factors an exploratory study of the time-like electromagnetic pion form factor is presented in a formalism which describes mesons as Poincaré-invariant bound states. In the respective quark interaction kernel, beyond the gluon-intermediated interactions for valence-type quarks, non-valence effects are included by allowing the pions to couple back in a self-consistent manner to the quarks. Consequently, the opening of the dominant $\rho$ decay channel, $\rho \to \pi \pi$, and the presence of a multi-particle branch cut, setting in when the two-pion threshold is crossed, are included consistently, first in the correspondingly calculated quark-photon vertex, and then consequently in the time-like electromagnetic pion form factor. The obtained results are in agreement with the available experimental data and provide further evidence for the efficacy of a vector-meson dominance model. Effects of going beyond the here employed isospin-symmetric limit are discussed. Last but not least, an outlook is provided on how to include in Poincaré-covariant Faddeev approaches the effects of intermediate resonances in the calculation of baryon properties.

9 pages, 6 figures; submitted to EPJ Web of Conferences

References in corpus (5)

• Baryons as relativistic three-quark bound states
• Nucleon electromagnetic form factors from the covariant Faddeev equation
• Quark Confinement: The Hard Problem of Hadron Physics
• Delta and Omega electromagnetic form factors in a Dyson-Schwinger/Bethe-Salpeter approach
• Elucidating the effect of intermediate resonances in the quark interaction kernel on the time-like electromagnetic pion form factor

Cited by in corpus (2)

• The analytic structure of three-point functions from contour deformations
• Timelike form factor for the anomalous process ${\gamma }^{\ast }\pi \to \pi \pi$