Pion electromagnetic form factor at high precision with implications to $a_\mu^{\pi\pi}$ and the onset of perturbative QCD

Understand

We extend recently developed methods used for determining the electromagnetic charge radius and $a_\mu^{\pi\pi}$ to obtain a determination of the electromagnetic form factor of the pion, $F_\pi^V(t)$, in several significant kinematical regions, using a parametrization-free formalism based on analyticity and unitarity, and with the inclusion of precise inputs from both timelike and spacelike regions.

• On the unitarity cut, below the first inelastic threshold we use the precisely known phase of the form factor, known from $\pi\pi$ elastic scattering via the Fermi-Watson theorem, and above the inelastic threshold a conservative integral condition on the modulus.
• We also use as input the experimental values of the modulus at several energies in the elastic region, where the data from $e^+e^-\to \pi^+\pi^-$ and $\tau$ hadronic decays are mutually consistent, as well as the most recent measurements at spacelike momenta.
• The experimental uncertainties are implemented by Monte Carlo simulations.