Fermion-fermion scattering in a Yang-Mills theory at high energy: Sixth-order perturbation theory

We study the high-energy behavior of the elastic scattering of two isospin-½ ferminos interacting through the Yang-Mills field. The Higgs mechanism is invoked so that there is no infrared divergence. In the sixth order, the amplitude for isovector exchange is found to behave as $s{\ln }^{2}s$ multiplied by a function of $t$, while the amplitude for isoscalar exchange behaves as $s\ln s$ multiplied by another function of $t$. These results are qualitatively different from the answers previously given in the literature. In particular, there is no contribution to the leading terms from large transverse momentum transfers; this is the reason why we obtain one less factor of $\ln s$ in sixth order.