Parametrization-free determination of the shape parameters for the pion electromagnetic form factor

Abstract

Recent data from high statistics experiments that have measured the modulus of the pion electromagnetic form factor from threshold to relatively high energies are used as input in a suitable mathematical framework of analytic continuation to find stringent constraints on the shape parameters of the form factor at $t=0$. The method uses also as input a precise description of the phase of the form factor in the elastic region based on Fermi-Watson theorem and the analysis of the $\pi \pi$ scattering amplitude with dispersive Roy equations, and some information on the spacelike region coming from recent high precision experiments. Our analysis confirms the inconsistencies of several data on the modulus, especially from low energies, with analyticity and the input phase, noted in our earlier work. Using the data on the modulus from energies above $0.65\mathrm{GeV}$, we obtain, with no specific parametrization, the prediction $<r_π^2 \r angle \in\, (0.42,\,0.44)\,\fmsq $ for the charge radius. The same formalism leads also to very narrow allowed ranges for the higher-order shape parameters at $t=0$, with a strong correlation among them.

v2 is 11 pages long using EPJ style files, and has 8 figures; Compared to v1, number of figures has been reduced, discussion has been improved significantly, minor errors have been corrected, references have added, and the manuscript has been significantly revised; this version has been accepted for publication in EPJC

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• The branching ratio $\omega \to {\pi }^{+}{\pi }^{-}$ revisited
• A dispersive analysis of the pion vector form factor and ${\tau }^{-}\to K^{-}{K}_S{\nu }_{\tau }$ decay
• Electromagnetic charge radius of the pion at high precision
• Pion electromagnetic form factor in the Covariant Spectator Theory
• Precise determination of the low-energy hadronic contribution to the muon $g-2$ from analyticity and unitarity: An improved analysis
• Two-pion low-energy contribution to the muon $g-2$ with improved precision from analyticity and unitarity
• Vector form factor of the pion in chiral effective field theory
• The electromagnetic form factor of the pion: Results from the lattice
• Hadronic vacuum polarization to three loops in chiral perturbation theory