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

Abstract

The high-energy behavior of fermion-boson and boson-boson scattering amplitudes of a supersymmetric field theory containing a spin-1/2 fermion field, a scalar field, and a pseudoscalar field is investigated. The results can be easily modified to apply to the Yukawa model and the neutral version of the linear $\ensuremath{\sigma}$ model. The results are also compared to those of fermion-fermion scattering in the same 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 sum of the dominant series give rise to fixed Regge cuts for all amplitudes in each of the three theories. All amplitudes in the supersymmetric theory possess a definite signature factor, while the amplitudes for fermion-fermion and fermion-antifermion scattering in the $Y$ model and the $\ensuremath{\sigma}$ model lack it. The results of the supersymmetric theory are also compared to the results of the spontaneously broken non-Abelian gauge theory.