Pion and kaon vector form factors

Abstract

We develop a unitarity approach to consider the final state interaction corrections to the tree level graphs calculated from chiral perturbation theory $(\ensuremath{\chi}\mathrm{PT})$ 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 $\ensuremath{\chi}\mathrm{PT}$ results. A very good description of experimental data is accomplished for the vector form factors up to $\sqrt{s}<~1.2 \mathrm{GeV}$ beyond which multiparticle states play a non-negligible role. For the P-wave $\ensuremath{\pi}\ensuremath{\pi}$ phase shifts the agreement with data stands even higher up to $\sqrt{s}<~1.5 \mathrm{GeV}.$ We also consider the isospin breaking effects due to the $\ensuremath{\omega}\ensuremath{-}\ensuremath{\rho}$ mixing as a perturbation to the previous results. In addition the low and resonance energy regions are discussed in detail and for the former a comparison with one and two loop $\ensuremath{\chi}\mathrm{PT}$ is made showing a remarkable coincidence with the two loop $\ensuremath{\chi}\mathrm{PT}$ results.