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

TL;DR

This paper introduces a parametrization-free method to determine the shape parameters of the pion electromagnetic form factor at zero momentum transfer, using high-statistics experimental data and analytic continuation techniques.

Contribution

It develops a novel approach combining analytic continuation and phase input to constrain pion form factor shape parameters without relying on specific parametrizations.

Findings

Charge radius predicted as (0.42, 0.44) fm².

Confirmed inconsistencies in low-energy modulus data.

Derived narrow ranges for higher-order shape parameters.

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 $0.65 \,{\rm GeV}$, we obtain, with no specific parametrization, the prediction $<r_\pi^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.