We develop a unitarity approach to consider the final state interaction
corrections to the tree level graphs calculated from Chiral Perturbation Theory
(χPT) allowing the inclusion of explicit resonance fields. The method is
discussed considering the coupled channel pion and kaon vector form factors.
These form factors are then matched with the one loop χPT results. A very
good description of experimental data is accomplished for the vector form
factors and for the ππ P-wave phase shifts up to s​≲1.2
GeV, beyond which multiparticle states play a non negligible role. In
particular the low and resonance energy regions are discussed in detail and for
the former a comparison with one and two loop χPT is made showing a
remarkable coincidence with the two loop χPT results.Comment: 20 pages, 7 figs, to appear in Phys. Rev.