Spacelike pion form factor from analytic continuation and the onset
of perturbative QCD.
The factorization theorem for exclusive processes in perturbative QCD
predicts the behaviour 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 < 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.