It is demonstrated that Gounaris-Sakurai model of the pion electromagnetic form factor is based on the P-wave iso-vector ππ scattering phase-shift given by a generalized effective-range formula of the Chew-Mandelstam type, valid exclusively only at the elastic region up to 1 GeV2. Therefore the Gounaris-Sakurai model is justified to be used in a determination of the ρ(770) meson parameters from existing data, however, in no case in a determination of the inelastic ρ(1450) and ρ(1700) resonance parameters.
We propose the pion electromagnetic form factor model found on the analyticity in the complex energy plane in which all three resonances ρ(770), ρ(1450), ρ(1700) are defined on equal level as poles on unphysical sheets of the corresponding Riemann surface. The ρ(770) meson parameters obtained in a such way coincide with the parameters obtained in the framework of the GKPY Roy-like equations analysis.
