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 the $\rho$ meson and the 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.

• Received 29 July 2009

DOI:https://doi.org/10.1103/PhysRevD.80.114012