The analytic continuation of the high-energy quark-quark scattering amplitude
1 Dipartimento di Fisica, Università di Pisa, I-56100 Pisa, Italy
2 INFN, Sezione di Pisa, I-56100 Pisa, Italy
Received: 18 April 1997 / Revised version: 27 August 1997/ Published online: 20 February 1998
It is known that the high-energy quark-quark scattering amplitude can be described by the expectation value of two lightlike Wilson lines, running along the classical trajectories of the two colliding particles. Generalizing the results of a previous paper, we give here the general proof that the expectation value of two infinite Wilson lines, forming a certain hyperbolic angle in Minkowski space-time, and the expectation value of two infinite Euclidean Wilson lines, forming a certain angle in Euclidean four-space, are connected by an analytic continuation in the angular variables. This result could be used to evaluate the high-energy scattering amplitude directly on the lattice.