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The experimental data on the electromagnetic form factor of charged pionsavailable at spacelike momenta are analyzed using the Dispersive Matrix (DM)approach, which describes the momentum dependence of hadronic form factorswithout introducing any explicit parameterization and includes properly theconstraints coming from unitarity and analyticity. The unitary bound isevaluated nonperturbatively making use of the results of lattice QCDsimulations of suitable two-point correlation functions contributing to the HVPterm of the muon. Thanks to the DM method we determine the pion charge radiusfrom existing spacelike data in a completely model-independent way andconsistently with the unitary bound, obtaining $< r_\pi >_{DM} = 0.703 \pm0.027$ fm. This finding differs by $\simeq 1.6$ standard deviations from thelatest PDG value $< r_\pi >_{PDG} = 0.659 \pm 0.004$ fm, which is dominated bythe very precise results of dispersive analyses of timelike data coming frommeasurements of the cross section of the $e^+ e^- \to \pi^+ \pi^-$ process. Wehave analyzed the spacelike data using also traditional $z$-expansions, likethe Boyd-Grinstein-Lebed (BGL) or Bourrely-Caprini-Lellouch (BCL) fittingfunctions and adopting a simple procedure that incorporates ab initio thenon-perturbative unitary bound in the fitting process. We get $< r_\pi >_{BGL}= 0.711 \pm 0.039$ fm and $< r_\pi >_{BCL} = 0.709 \pm 0.028$ fm in niceagreement with the DM result. We have addressed also the issue of the onset ofperturbative QCD by performing a sensitivity study of the pion form factor atlarge spacelike momenta, based only on experimental spacelike data andunitarity. Hence, although the leading pQCD behaviour is found to set in onlyat very large momenta, our DM bands may provide information about thepre-asymptotic effects related to the scale dependence of the pion distributionamplitude.

Dispersive analysis of the experimental data on the electromagnetic form factor of charged pions at spacelike momenta