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 $\sqrt{s}$. We sum the perturbation series to all orders in the coupling constant and all powers of $\ln s$, but ignore terms which are suppressed by a power of $s$ order by order in perturbation theory. In the $s\to \infty$ limit the amplitude vanishes as $\exp (-\alpha \ln s\ln \ln s)$, where $\alpha$ 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.