Constraint on the Universal Function in Electroproduction

Abstract

We show that analyticity and asymptotic behavior impose a severe contraint on the scale-invariant function widely suggested for the behavior of$\ensuremath{\nu}{W}_{2}({q}^{2}\ensuremath{\nu})$ as ${q}^{2}\ensuremath{\rightarrow}\ensuremath{\infty}$. If the asymptotic behavior of the off-mass-shell Compton scattering amplitude is dominated by the usual (nonfixed) Regge trajectories, then our constraint is violated by the experimental candidates for the $\ensuremath{\nu}{W}_{2}$ curve. On the other hand, the introduction of a fixed pole corresponding to the one used by Damashek and Gilman alters the constraint, which is then consistant with the 18\ifmmode^\circ\else\textdegree\fi{} data.