Spacelike pion form factor from analytic continuation and the onset of perturbative QCD

TL;DR

This paper uses analytic continuation to establish bounds on the pion electromagnetic form factor, indicating that the onset of perturbative QCD behavior occurs above 7 GeV^2, based on experimental data and theoretical models.

Contribution

It introduces a model-independent analytic continuation method to bound the pion form factor, refining the energy scale where perturbative QCD becomes applicable.

Findings

Bounds exclude perturbative QCD regime below 7 GeV^2

Inclusion of experimental data tightens the bounds significantly

Method provides almost model-independent constraints on the form factor

Abstract

The factorization theorem for exclusive processes in perturbative QCD predicts the behavior of the pion electromagnetic form factor $F(t)$ at asymptotic spacelike momenta $t(=-Q^2)<0$. We address the question of the onset energy using a suitable mathematical framework of analytic continuation, which uses as input the phase of the form factor below the first inelastic threshold, known with great precision through the Fermi-Watson theorem from $\pi\pi$ elastic scattering, and the modulus measured from threshold up to 3 GeV by the BaBar Collaboration. The method leads to almost model-independent upper and lower bounds on the spacelike form factor. Further inclusion of the value of the charge radius and the experimental value at $-2.45 \gev^2$ measured at JLab considerably increases the strength of the bounds in the region $ Q^2 \lesssim 10 \gev^2$, excluding the onset of the asymptotic perturbative QCD regime for $Q^2< 7\gev^2$. We also compare the bounds with available experimental data and with several theoretical models proposed for the low and intermediate spacelike region.