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-1/2 fermions 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 ln2s multiplied by a function of t, while the amplitude for isoscalar exchange behaves as s lns 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 lns in sixth order