Conserved Currents, Reggeization, and Mandelstam Counting in Second-Order Perturbation Theory

Abstract

We consider the spinor pole in second-order spinor-vector and spinor-axial-vector scattering for all possible couplings and show that, except for the vector ${\gamma }^{\mu }$ coupling, none of the amplitudes factor. Therefore, only in the case of ${\gamma }^{\mu }$ coupling does the spinor lie on a nondegenerate Regge trajectory for all values of the coupling constant. The degeneracy in the case of the axial-vector ${\gamma }^{\mu }\gamma 5$ coupling is less than for the remainder of the couplings. We also consider the axial-vector pole in pseudoscalar-vector scattering and show that for one particular pseudoscalar-vector-axial-vector coupling, the sense amplitudes factor. These results are reconciled with the Mandelstam counting procedure, and the effects of gauge invariance and isospin on factorization are investigated.