Nonleading Regge Behavior inνW2and the Possibility of Fixed Poles with Polynomial Residues

Abstract

We discuss some of the theoretical arguments for the existence in Compton scattering of right-signatured fixed poles with polynomial residues. We show that if one could "switch off" the strong interactions, then a fixed pole with residue linear in $q^2$ (the photon mass squared) would be necessary for the consistency of the fixed-$q^2$ dispersion relation for $\nu T_2$ (whose absorptive part $\nu W_2$ is measured in inelastic electroproduction). We show that if the above conjecture is correct, then there must be some energy dependence in $\nu W_2$ over and above the conventional leading Regge form (Pomeranchukon plus $f-A_2$). Evidence is presented for the presence of such "nonleading behavior" in a similar process. In addition we show why the on-shell ${\sigma }_{\mathrm{tot}}\left(\gamma p\right)$ could be compatible with the neglect of such a nonleading term. We find that a fixed pole with polynomial residue and the correct $q^2\to 0$ Thomson limit can be accommodated by the present data on $\nu W_2$ at large $q^2$. With the above assumptions on the fixed-pole behavior, we predict the high-energy behavior of $\nu W_2$ and find that asymptotically it must fall to a value substantially less than its present maximum magnitude.