ρDominance and Electromagnetic Form Factors

A finite-width expression for the pion form factor with the correct analytic properties is equated to the nucleon isovector form factor $F_1^{}{}_{}{}^V\mathrm{}\left(t\right)\mathrm{}$, and the nucleon data are used to determine the parameters. The predicted ${\left|F_{\pi }\mathrm{}\right(t\left)\right|}^2$ is found to agree reasonably well with the colliding-beam data, and the predicted branching ratio $\frac{\Gamma (\rho \to e^{+}{e}^{-})}{\Gamma (\rho \to {\pi }^{+}{\pi }^{-})}$ and $\rho -\gamma$ coupling constant are consistent with the Orsay results. The width ${\Gamma }_{\rho }(\rho \to {\pi }^{+}{\pi }^{-})=112\mathrm{}$ MeV, and $m_{\rho }=765\mathrm{}$ MeV. The nucleon and pion mean-charge radii are found to be $〈r_N〉=0.86\mathrm{}$ F and $〈r_{\pi }〉=0.70\mathrm{}$ F.