Fermion scattering in the chain approximation to the $V$-$A$ theory of weak interactions

The fermion scattering cross section is calculated by means of the Bethe–Salpeter equation in the chain approximation for the four-fermion interaction. As the energy increases, the cross section increases only up to a certain value and then decreases rapidly, in contrast to the cross section calculated in the first order of perturbation theory.