Analytic and unitary representation for the pion form factor at allQ2

We propose an analytic parametrization of all data for the pion form factor which can explicitly accommodate, consistent with inelastic unitarity, both higher vector-meson states and a smooth inelastic continuum, in a rather economical way. This parametrization automatically gives the asymptotic behavior expected for a quark-antiquark bound state and is free of complex zeros. We find that the best fit to the data contains no ${\rho }^{\prime }\mathrm{}\left(1250\right)\mathrm{}$ signal and a possible, broad, ${\rho }^{\prime \prime }\mathrm{}\left(1600\right)\mathrm{}$, but with rather small coupling to the photon and to the $I=J=1\mathrm{}$ $\pi -\pi$ system.