The high--energy quark--quark scattering: from Minkowskian to Euclidean theory

TL;DR

This paper explores the analytic connection between Minkowskian and Euclidean high-energy quark-quark scattering amplitudes via Wilson lines, enabling potential lattice QCD calculations of scattering processes.

Contribution

It proves the analytic continuation between Minkowski and Euclidean Wilson line expectation values, facilitating non-perturbative evaluations of scattering amplitudes.

Findings

Established the analytic relation between Minkowskian and Euclidean Wilson lines.

Suggested the possibility of computing scattering amplitudes on the lattice.

Discussed the Abelian case (QED) for comparison.

Abstract

In this paper we consider some analytic properties of the high--energy quark--quark scattering amplitude, which, as is well known, can be described by the expectation value of two lightlike Wilson lines, running along the classical trajectories of the two colliding particles. We shall prove 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 could open the possibility of evaluating the high--energy scattering amplitude directly on the lattice or using the stochastic vacuum model. The Abelian case (QED) is also discussed.