Scattering from an external field in quantum chromodynamics at high energies: from foundations to interdisciplinary connections

TL;DR

This paper reviews the factorization of scattering amplitudes in high-energy QCD with external fields, introducing the color dipole model and connecting quantum chromodynamics with branching random walks to derive exact cross section formulas.

Contribution

It introduces a novel approach linking QCD scattering amplitudes to branching random walks, enabling analytical derivation of high-energy cross sections.

Findings

Derived exact large-rapidity expressions for onium-nucleus cross sections.

Connected quantum chromodynamics with classical stochastic processes.

Provided analytical formulas for asymptotics of scattering observables.

Abstract

We review the factorization of the $S$-matrix elements in the context of particle scattering off an external field, which can serve as a model for the field of a large nucleus. The factorization takes the form of a convolution of light cone wave functions describing the physical incoming and outgoing states in terms of bare partons, and products of Wilson lines. The latter represent the interaction between the bare partons and the external field. Specializing to elastic scattering amplitudes of onia at very high energies, we introduce the color dipole model, which formulates the calculation of the modulus-squared of the wave functions in quantum chromodynamics with the help of a branching random walk, and the scattering amplitudes as observables on this classical stochastic process. Methods developed for general branching processes produce analytical formulas for the asymptotics of such observables, and thus enable one to derive exact large-rapidity expressions for onium-nucleus cross sections, from which electron-nucleus cross sections may be inferred.