Hadronic form factors in QCD and the incompleteness problem in the time-like region

Abstract

Hadronic form factors fulfill dispersion relations and superconvergence sum rules for their spectral density as genuine imprints of QCD. We show several instances where these conditions are flagrantly violated due to the lack of information in the region above the largest known resonance mass and below the onset of perturbative QCD. We propose to use radial Regge trajectories to fill this gap and examine the consequences of such a minimal spectral hadronic ansatz. We illustrate the results with the pion charge form factor.