Asymptotic behavior of the fixed-angle on-shell quark scattering amplitudes in non-Abelian gauge theories

In this paper we find the asymptotic behavior of the fixed-angle on-shell quark-quark scattering amplitude in non-Abelian gauge theories in the limit of very large center-of-mass energy √s. We sum the perturbation series to all orders in the coupling constant and all powers of lns, but ignore terms which are suppressed by a power of s order by order in perturbation theory. In the s→∞ limit the amplitude vanishes as exp(-αlnslnlns), where α is a constant. The phase of the amplitude is shown to be free from infrared divergences. Hence the phase is a perturbatively calculable function and may provide important tests of QCD.