THE HIGH-ENERGY QUARK-QUARK SCATTERING - FROM MINKOWSKIAN TO EUCLIDEAN THEORY

In this paper we consider some analytic properties of the high-energy quark-quark scattering amplitude, which, as is well known, can be desc ribed by the expectation value of two lightlike Wilson lines, running along the classical trajectories of the two colliding particles. We wi ll show that the expectation value of two infinite Wilson lines, formi ng a certain hyperbolic angle in Minkowski space-time, and the expecta tion value of two infinite Euclidean Wilson lines, forming a certain a ngle in Euclidean four-space, are connected by an analytic continuatio n in the angular variables: the proof is given for an Abelian gauge th eory (QED) in the so-called quenched approximation and for a non-Abeli an gauge theory (QCD) up to the fourth order in the renormalized coupl ing constant in perturbation theory. This could open the possibility o f evaluating the high-energy scattering amplitude directly on the latt ice or using the stochastic vacuum model.