πNN,πNΔ, andππρform factors from quasi-two-body hadronic reactions

Differential cross sections for $\mathrm{pp}\to n{\Delta }^{++}$, $\mathrm{pp}\to p{\Delta }^{+}$, and ${\pi }^{+}p\to {\rho }^0{\Delta }^{++}$ at high energies, $p_L\approx 3-16$ GeV/c, and small momentum transfers, $0<\mathrm{}\left|t\right|\mathrm{}\lesssim 0.3$ ${\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c}}^2$, have been analyzed using a Reggeized one pion exchange mechanism with form factors of the monopole and the dual model type. Results strongly confirm the dual model prediction that $F_{\pi \mathrm{NN}}\mathrm{}\left(t\right)=F_{\pi N\Delta }\mathrm{}\left(t\right)=F_{\pi \pi \rho }\mathrm{}\left(t\right)\mathrm{}$ when the pion is the only virtual (off the mass shell) particle in each vertex and the form factors are all normalized to unity at $t={{\mu }_{\pi }}^2$. No evidence has been found for non-one-pion exchange contributions in the kinematic region under consideration thus leading to a model independent determination of the range and asymptotic rate parameters of the three-point functions. The results are ${\Lambda }_{\pi }\approx 800-1000$ MeV and ${\beta }_{\pi }\approx 2.5-3$, in good agreement with earlier determinations from $\mathrm{NN}$ charge exchange scattering and pion photoproduction.