Wilson-loop formalism for Reggeon exchange in soft high-energy scattering

TL;DR

This paper develops a nonperturbative QCD framework using Wilson loops to describe Reggeon exchange in high-energy meson scattering, connecting Minkowski and Euclidean theories and relating to gauge/gravity duality.

Contribution

It introduces a Wilson-loop formalism for Reggeon exchange in meson scattering, incorporating nonperturbative effects and analytic continuation from Euclidean to Minkowski space.

Findings

Derived a path integral expression for Reggeon exchange amplitudes.

Connected the formalism to gauge/gravity duality approaches.

Provided a method to reconstruct Minkowski results from Euclidean calculations.

Abstract

We derive a nonperturbative expression for the non-vacuum, qqbar-Reggeon-exchange contribution to the meson-meson elastic scattering amplitude at high energy and low momentum transfer, in the framework of QCD. Describing the mesons in terms of colourless qqbar dipoles, the problem is reduced to the two-fermion-exchange contribution to the dipole-dipole scattering amplitudes, which is expressed as a path integral, over the trajectories of the exchanged fermions, of the expectation value of a certain Wilson loop. We also show how the resulting expression can be reconstructed from a corresponding quantity in the Euclidean theory, by means of analytic continuation. Finally, we make contact with previous work on Reggeon exchange in the gauge/gravity duality approach.