Electromagnetic Charge Radius of the Pion at High Precision.

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 ππ 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 τ 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±0.003)  fm, which amounts to an increase in precision by a factor of about 2.7 compared to the Particle Data Group average.