Effect ofπ−KInteraction on Nucleon Form Factors; Processesππ→KKandππ→ππ

$\pi -K$ coupled solutions are applied to evaluate the relative contributions of $2K$ and $2\pi$ intermediate states to the isovector part of the nucleon's electromagnetic form factor. Spin and unphysical branch cuts on the left are neglected. It is assumed that the $K$ and nucleon $N$ are coupled indirectly through the $K-\pi$ and $\pi -N$ couplings only. Approximate integrations are carried out for different limiting cases. Except in the case when $\pi -\pi$ self-coupling and $\pi -K$ coupling are both weak and the results do not show a definite trend, all other cases show that the $2K$-state contribution to the nucleon vector form factor is small. Maximum cross sections and resonance energies for the processes $\pi \pi \to \pi \pi$ and $\pi \pi \to K\overline{K}$ are also evaluated.