Solitons in high-energy QCD

TL;DR

This paper investigates the asymptotic behavior of reggeon states in high-energy QCD, revealing that they form soliton-like waves described by advanced mathematical functions, enhancing understanding of quantum chromodynamics at high energies.

Contribution

It introduces a novel application of finite-gap theory to construct explicit soliton solutions for reggeon states in multi-color QCD.

Findings

Reggeon trajectories exhibit soliton wave behavior.

Explicit solutions are expressed via Riemann theta-functions.

The study advances the mathematical understanding of high-energy QCD phenomena.

Abstract

We study the asymptotic solutions of the Schr\"odinger equation for the color-singlet reggeon compound states in multi-color QCD. We show that in the leading order of asymptotic expansion, quasiclassical reggeon trajectories have a form of the soliton waves propagating on the 2-dimensional plane of transverse coordinates. Applying methods of the finite-gap theory we construct their explicit form in terms of Riemann theta-functions and examine their properties.