The role of anomalous singularity in hadronic form factors

By assuming chiral-symmetry breaking as the dominant dynamics in the light-hadron structure, we study the low-energy electromagnetic form factor of light hadrons in the Nambu-Jona-Lasinio type of models in the large-N limit from a dispersion relation point of view. In addition to the expected vector-meson pole dominance picture for tightly bound states such as the pion, it is found that the anomalous singularity, occurring only to loosely bound states of the constituent quarks, could severely alter the form factors at low momentum-transfers from the vector-meson dominance behavior. This mechanism is explicitly demonstrated in a two-dimensional version of the NJL type models, the Gross-Neveu model, in which all the interested quantities are calculated analytically and a detailed comparison with two-dimensional QCD is made. The two-dimensional analysis is then argued to be qualitatively similar to the realistic four-dimensional case. The relevance of the anomalous singularity to the phenomenology of the rho and the nucleons is indicated by quantitative estimates of the anomalous thresholds in their form factors. (orig.)