Asymptotic Vertex Function in a Crossing-Symmetric Bootstrap Model of the Hadrons

An asymptotic solution to an off-shell, nonlinear, crossing-symmetric bootstrap equation for the vertex function is found, thus determining the explicit dependence of the asymptotic vertex function on all three variables. The equation bootstraps the entire vertex function rather than just the coupling constant, and describes the constituents of a composite particle as composite particles. The asymptotic solution is characterized by a constant which we show to be universal, i.e., independent of the types of particles coupling to a given vertex. This allows us to predict the relative rates of decrease of all hadronic form factors. The predicted behavior for the $\mathrm{NN}\gamma$ and the $N^{*}N\gamma$ form factors is in good agreement with experiment. Several extensions and further tests of the theory are proposed and will be discussed in future papers.