High-energy behavior of fermion-fermion scattering in a supersymmetric field theory

Abstract

The high-energy behavior of the fermion-fermion and fermion-antifermion scattering amplitudes of a class of field theories, containing a spin-\textonehalf{} fermion field, a scalar field, and a pseudoscalar field, are investigated. These theories consist of a supersymmetric model, the Yukawa model, and the linear $\ensuremath{\sigma}$ model. In the leading-logarithm approximation, ladders with fermions running along the sides in the $t$ channel and mesons as rungs dominate in each order of two classes of diagrams. The sums of the dominant series give rise to fixed Regge cuts for all the three theories; the amplitude of the supersymmetric theory possesses a definite signature, while those of the other two lack it. A comparison of the result of the supersymmetric theory with the results of an asymptotically free theory and the spontaneously broken non-Abelian gauge theory is made.