Electromagnetic charge radius of the pion at high precision

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_π=(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.

6 pages, 2 figures, typos corrected, citations added, version accepted for publication in Physical Review Letters

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• Chiral extrapolation of hadronic vacuum polarization
• The scalar, vector and tensor form factors for the pion and kaon from lattice QCD
• Radiative corrections to semileptonic beta decays: Progress and challenges
• Dispersion relations for the hadronic VVA correlator
• Universality of minimal length
• Two-Meson Form Factors in Unitarized Chiral Perturbation Theory
• A Simple Parametrisation of the Pion Form Factor
• Thermal effects on sound velocity peak and conformality in isospin QCD
• Investigating saturation effects and the virtual pion in leading neutron events at HERA with the dipole model
• Improved $K_{e3}$ radiative corrections sharpen the $K_{\mu 2}$--$K_{l3}$ discrepancy