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We use the recently measured accurate BaBaR data on the modulus of the pionelectromagnetic 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, andthe 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 theintermediate spacelike region. We compare our constraints with experimentaldata and with perturbative QCD along with the results of several theoreticalmodels for the non-perturbative contributions proposed in the literature.

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