A Simple Parametrisation of the Pion Form Factor

TL;DR

This paper introduces a new, simple parametrisation of the pion form factor using conformal mapping, which connects spacelike and timelike regions, respects analyticity, and fits experimental data with only five parameters.

Contribution

The authors propose a novel parametrisation that does not rely on pion-pion phase shifts and explicitly incorporates known physical constraints, improving simplicity and transparency.

Findings

Good fit to experimental data with five parameters

Explicitly accounts for the $ ho(770)$-meson pole

Respects analyticity and normalization conditions

Abstract

We discuss a novel and simple parametrisation of the pion vector form factor that transparently connects spacelike and timelike regions of the momentum transfer $q^2$. Our parametrisation employs the framework of conformal mapping and respects the known analyticity properties of the form factor, accounting explicitly for the $\rho(770)$-meson pole. The parametrisation manifestly fulfils the normalisation condition at $q^2 = 0$ as well as further restrictions at the pion production threshold and in the limit $|q^2| \to \infty$. In contrast to the widely used Omn\`es parametrisation, our approach does not use the pion-pion scattering phase shift as input. We confront the parametrisation with experimental data from $\pi H$ scattering and $\tau^- \to \pi^-\pi^0\nu$ decay. We already find a good description of the data with only five free parameters, which include the pole mass and decay width of the $\rho(770)$.