# Electromagnetic charge radius of the pion at high precision

## TL;DR

This paper determines the pion charge radius with high precision using a novel formalism based on analyticity and unitarity, combining timelike and spacelike data without relying on specific parametrizations.

## Contribution

It introduces a new method that leverages phase information and high-precision data to accurately determine the pion charge radius, improving previous precision significantly.

## Key findings

- Charge radius of the pion is $0.657 m$ with an uncertainty of $0.003 m$
- Precision improved by a factor of about 2.7 over previous averages
- Method does not depend on the unknown phase above the inelastic threshold

## Abstract

We present a determination of the pion charge radius from high precision data on the pion vector form factor from both timelike and spacelike regions, using a novel formalism based on analyticity and unitarity. At low energies, instead of the poorly known modulus of the form factor, we use its phase, known with high accuracy from Roy equations for $\pi\pi$ elastic scattering via the Fermi-Watson theorem. We use also the values of the modulus at several higher timelike energies, where the data from $e^+e^-$-annihilation and $\tau$-decay are mutually consistent, as well as the most recent measurements at spacelike momenta. The experimental uncertainties are implemented by Monte-Carlo simulations. The results, which do not rely on a specific parametrization, are optimal for the given input information and do not depend on the unknown phase of the form factor above the first inelastic threshold. Our prediction for the charge radius of the pion is $r_\pi=(0.657 \pm 0.003) \fm $, which amounts to an increase in precision by a factor of about 2.7 compared to the PDG average.