THE ANALYTIC CONTINUATION OF THE HIGH-ENERGY QUARK-QUARK SCATTERING-AMPLITUDE

It is known that the high-energy quark-quark scattering amplitude can be described by the expectation value of two lightlike Wilson lines, r unning along the classical trajectories of the two colliding particles . Generalizing the results of a previous paper, we give here the gener al proof that the expectation value of two infinite Wilson lines, form ing a certain hyperbolic angle in Minkowski space-time, and the expect ation value of two infinite Euclidean Wilson lines, forming a certain angle in Euclidean four-space, are connected by an analytic continuati on in the angular variables. This result could be used to evaluate the high-energy scattering amplitude directly on the lattice.