Analytic pion form factor

TL;DR

This paper models the pion electromagnetic form factor using a vector dominance approach that transitions to perturbative QCD at high momentum, successfully fitting both spacelike and timelike data and revealing the need for an additional meson resonance.

Contribution

It extends a vector dominance model with dispersion relations to describe pion form factors across all momentum transfers, incorporating new data and suggesting an extra meson resonance.

Findings

Good fit to all data, especially newer timelike measurements.

High-$q^2$ data indicates the necessity of an extra $ ho$-like meson.

Model successfully connects spacelike and timelike regions analytically.

Abstract

The pion electromagnetic form factor and two-pion production in electron-positron collisions are simultaneously fitted by a vector dominance model evolving to perturbative QCD at large momentum transfer. This model was previously successful in simultaneously fitting the nucleon electromagnetic form factors (spacelike region) and the electromagnetic production of nucleon-antinucleon pairs (timelike region). For this pion case dispersion relations are used to produce the analytic connection of the spacelike and timelike regions. The fit to all the data is good, especially for the newer sets of time-like data. The description of high-$q^2$ data, in the time-like region, requires one more meson with $\rho$ quantum numbers than listed in the 2014 Particle Data Group review.