Bounds on the spacelike pion electromagnetic form factor from analyticity and unitarity

TL;DR

This paper derives bounds on the spacelike pion electromagnetic form factor using recent experimental data, phase shifts, and theoretical inputs, providing constraints that are compared with experimental results and QCD predictions.

Contribution

It introduces a formalism combining experimental data and theoretical inputs to bound the pion form factor in the spacelike region, improving understanding of its non-perturbative behavior.

Findings

Derived bounds on $F_(t)$ in the spacelike region.

Compared bounds with experimental data and QCD models.

Provided insights into non-perturbative contributions to the form factor.

Abstract

We use the recently measured accurate BaBaR data on the modulus of the pion electromagnetic form factor, $F_\pi(t)$, up to an energy of 3 GeV, the I=1 $P$-wave phase of the $\pi\pi$ scattering amplitude up to the $\omega-\pi$ threshold, the pion charge radius known from Chiral Perturbation Theory, and the recently measured JLAB value of $F_\pi$ in the spacelike region at $t=-2.45 {\rm GeV}^2$ as inputs in a formalism that leads to bounds on $F_\pi$ in the intermediate spacelike region. We compare our constraints with experimental data and with perturbative QCD along with the results of several theoretical models for the non-perturbative contributions proposed in the literature.