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

TL;DR

This paper investigates violations of dispersion relations in hadronic form factors due to incomplete spectral data and proposes using radial Regge trajectories to improve the spectral modeling, exemplified with the pion charge form factor.

Contribution

It introduces a method to address spectral density gaps in hadronic form factors using radial Regge trajectories, enhancing the understanding of QCD spectral properties.

Findings

Identifies violations of dispersion relations in spectral densities.

Proposes radial Regge trajectories to fill spectral gaps.

Demonstrates the approach with the pion charge form factor.

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.