The analytic continuation of the high-energy quark-quark scattering amplitude

TL;DR

This paper proves that high-energy quark-quark scattering amplitudes, represented by Wilson line expectation values, are connected through analytic continuation between Minkowski and Euclidean space, enabling lattice computations.

Contribution

It provides a general proof linking Minkowski and Euclidean Wilson line expectation values via analytic continuation, facilitating lattice evaluations of scattering amplitudes.

Findings

Established the analytic continuation relationship between Minkowski and Euclidean Wilson lines.

Provided a theoretical foundation for computing scattering amplitudes on the lattice.

Extended previous results to more general configurations of Wilson lines.

Abstract

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.