Reggeization of elementary fermions in arbitrary renormalizable gauge theories

An arbitrary, renormalizable non-Abelian gauge theory with gauge group $\mathcal{G}$ and arbitrary scalar and fermion structure is considered. Necessary conditions for all the fermions of the theory to lie on Regge trajectories are derived. If no fermion transforms as a singlet under $\mathcal{G}$, then all fermions Reggeize. If some fermions transform as singlets under $\mathcal{G}$, then certain group-theoretic constraints on the fermion mass matrix must be satisfied if all fermions are to Reggeize. These methods are applied to the Weinberg-Salam and grand unified theories. As a by-product of this study, kinematical-singularity-free, signatured helicity amplitudes are constructed which allow for $P$ and $\mathrm{CP}$ violation. Such amplitudes may be useful for applications outside the context of the Regge program.