Constraining the low energy pion electromagnetic form factor with space-like data

TL;DR

This paper develops a method to constrain the pion electromagnetic form factor using space-like data, providing bounds on its expansion coefficients relevant for calculating the muon g-2 contribution.

Contribution

It extends analyticity-based techniques to incorporate experimental space-like data, yielding bounds on form factor coefficients and analyzing their consistency with chiral perturbation theory.

Findings

Bounds on form factor expansion coefficients derived from space-like data.

The form factor coefficient in chiral perturbation theory is consistent with these bounds.

Sensitivity analysis shows robustness of the bounds with respect to input variations.

Abstract

The pionic contribution to the g-2 of the muon involves a certain integral over the the modulus squared of F_\pi(t), the pion electromagnetic form factor. We extend techniques that use cut-plane analyticity properties of F_\pi(t) in order to account for present day estimates of the pionic contribution and experimental information at a finite number of points in the space-like region. Using data from several experiments over a large kinematic range for |t|, we find bounds on the expansion coefficients of F_\pi(t), sub-leading to the charge radius. The value of one of these coefficients in chiral perturbation theory respects these bounds. Furthermore, we present a sensitivity analysis to the inputs. A brief comparison with results in the literature that use observables other than the g-2 and timelike data is presented.