Testing the consistency of the $\omega\pi$ transition form factor with unitarity and analyticity

TL;DR

This paper performs a dispersive analysis of the $ce oc$ transition form factor, revealing discrepancies between theoretical constraints and some experimental data, and emphasizes the need for more precise measurements.

Contribution

It introduces a parameterization-free dispersive approach incorporating experimental data, highlighting conflicts with existing measurements and supporting renewed experimental efforts.

Findings

Discrepancies between theoretical constraints and experimental data below 0.6 GeV.

Confirmation of conflict around 0.6 GeV in the form factor region.

Support for more precise measurements of the $ce oc$ transition form factor.

Abstract

We perform a dispersive analysis of the $\omega\pi$ electromagnetic transition form factor, using as input the discontinuity provided by unitarity below the $\omega\pi$ threshold and including for the first time experimental data on the modulus measured from $e^+e^-\to\omega\pi^0$ at higher energies. The input leads to stringent parameterization-free constraints on the modulus of the form factor below the $\omega\pi$ threshold, which are in disagreement with some experimental values measured from $\omega\to \pi^0\gamma^*$ decay. We discuss the dependence on the input parameters in the unitarity relation, using for illustration an $N/D$ formalism for the P partial wave of the scattering process $\omega\pi \to \pi\pi$, improved by a simple prescription which simulates the rescattering in the crossed channels. Our results confirm the existence of a conflict between experimental data and theoretical calculations of the $\omega\pi$ form factor in the region around 0.6 GeV and bring further arguments in support of renewed experimental efforts to measure more precisely the $\omega\to\pi^0\gamma^*$ decay.