Information on the structure of the rho meson from the pion form-factor

TL;DR

This paper investigates the structure of the rho meson using a Bethe-Salpeter approach to the pion form-factor, showing that the rho cannot be described as a pion-pion rescattering process and requires an elementary vector meson component.

Contribution

It demonstrates that the rho meson cannot be modeled solely as a pion-pion rescattering process, emphasizing the necessity of an elementary vector meson in the description.

Findings

The pion form-factor cannot be explained by pion-pion contact interaction alone.

Including an elementary vector meson yields an excellent fit to experimental data.

The rho meson appears to have a different nature than the a_1 meson, despite both being chiral partners.

Abstract

The electromagnetic pion form-factor is calculated in a Bethe-Salpeter approach which accounts for pion rescattering. In the scattering kernel the pion-pion contact interaction from lowest-order chiral perturbation theory is considered together with an optional vector meson in the s-channel. Correspondingly the virtual photon couples to a two-pion state and optionally to the vector meson. It is shown that for reasonable ranges of input parameters the experimentally observed pion form-factor cannot be described by the iterated pion-pion contact interaction alone, i.e. without an elementary vector meson. The inclusion of an elementary vector meson allows for an excellent description. This completes a recent study (``Information on the structure of the a_1 from tau decay'') where it has been shown that the a_1 meson can be well understood as a rescattering process of rho meson and pion. Here it is demonstrated that within the same formalism the rho meson cannot be understood as a pion-pion rescattering process. This suggests that the chiral partners a_1 and rho are not only different in mass, but also different in nature.