Dispersive and chiral symmetry constraints on the light meson form factors

TL;DR

This paper develops a dispersive formalism incorporating unitarity, analyticity, and OPE to analyze light meson form factors, integrating experimental and Chiral Perturbation Theory data to test QCD consistency.

Contribution

It generalizes dispersive techniques to include low energy data, enabling simultaneous analysis of pion and kaon form factors for QCD validation.

Findings

Derived strong constraints on pion electromagnetic form factor coefficients.

Tested the consistency of Chiral Perturbation Theory with QCD.

Provided a framework for including experimental data in dispersive analyses.

Abstract

The form factors of the light pseudoscalar mesons are investigated in a dispersive formalism based on hadronic unitarity, analyticity and the OPE expansion of the QCD Green functions. We propose generalizations of the original mathematical techniques, suitable for including additional low energy information provided by experiment or Chiral Perturbation Theory (CHPT). The simultaneous treatment of the electroweak form factors of the $\pi$ and $K$ mesons allows us to test the consistency with QCD of a low energy CHPT theorem. By applying the formalism to the pion electromagnetic form factor, we derive quite strong constraints on the higher Taylor coefficients at zero momentum, using information about the phase and the modulus of the form factor along a part of the unitarity cut.