The electromagnetic pion form factor and its phase

TL;DR

This paper introduces a dispersion relation method to determine the pion's electromagnetic form factor and phase, extending analysis above inelastic thresholds and providing new insights into QCD behavior.

Contribution

It presents a novel dispersive approach that recovers the pion form factor's phase and parts above inelastic regions, enhancing understanding of hadronic structure.

Findings

Extracted P-wave ππ phase shift

Derived bounds in the spacelike region

Provided insights into perturbative QCD onset

Abstract

In this work, we employ a dispersion relation that allows to recover the electromagnetic form factor of the pion from its modulus along the unitarity cut. Unlike the standard dispersive approach, this method extends in a straightforward manner above the inelastic region, allowing us to obtain the form factor's phase, as well as its real and imaginary parts. As applications, we extract the $P$-wave $\pi\pi$ phase shift, the octet form factor, derive bounds in the spacelike region, and offer insights into the onset of perturbative QCD.