Constraints on the $\omega\pi$ form factor from analyticity and unitarity

TL;DR

This paper uses analyticity and unitarity principles to derive bounds on the $$ form factor, revealing discrepancies with experimental data around 0.6 GeV and providing a theoretical consistency check.

Contribution

It introduces a unitarity bounds approach to constrain the $$ form factor using QCD inputs and pion data, highlighting discrepancies with experimental measurements.

Findings

Derived bounds on the $$ form factor in the elastic region.

Confirmed disagreement between theoretical bounds and experimental data around 0.6 GeV.

Provided a consistency check for dispersion relation results.

Abstract

Motivated by the discrepancies noted recently between the theoretical calculations of the electromagnetic $\omega\pi$ form factor and certain experimental data, we investigate this form factor using analyticity and unitarity in a framework known as the method of unitarity bounds.We use a QCD correlator computed on the spacelike axis by operator product expansion and perturbative QCD as input, and exploit unitarity and the positivity of its spectral function, including the two-pion contribution that can be reliably calculated using high-precision data on the pion form factor. From this information, we derive upper and lower bounds on the modulus of the $\omega\pi$ form factor in the elastic region. The results provide a significant check on those obtained with standard dispersion relations, confirming the existence of a disagreement with experimental data in the region around 0.6 GeV.