Regge behavior and daughter degeneracies in fourth - order spinor - vector scattering

Abstract

For the equal-mass scattering of spin-$\frac{1}{2}$ nucleons and neutral vector mesons, we discuss the Regge behavior of the amplitude and consider the questions posed by the existence of degenerate daughter trajectories within the framework of fourth-order perturbation theory. A formalism for the identification of daughter contributions is developed and the algebraic solution to the equations constraining the residues of the daughters is presented. By applying these ideas to the results of a previous calculation, we find that, while to fourth order sufficient information exists to resolve the degeneracy and to test for its breaking, the daughter contributions cannot be clearly identified due to the presence of new singularities having the form ${t}^{\ensuremath{-}1}{\mathrm{ln}}^{2}t$ to fourth order. The possible origin of these terms is discussed and is tentatively ascribed to the existence of fixed poles of order three at the negative half-integer values of $J$.