Baxter Equation for the QCD Odderon

TL;DR

This paper investigates the QCD odderon Hamiltonian using the Bethe Ansatz, reformulating the Baxter equation to derive new eigenvector and eigenvalue expressions, advancing understanding of high-energy QCD integrable models.

Contribution

It introduces a new formulation of the Baxter equation for the QCD odderon and derives explicit expressions for eigenvectors and eigenvalues using the Bethe Ansatz.

Findings

Reformulated Baxter equation as a linear triangular system

Derived new expressions for eigenvectors and eigenvalues

Discussed quantization of conserved quantities

Abstract

The Hamiltonian derived by Bartels, Kwiecinski and Praszalowicz for the study of high-energy QCD in the generalized logarithmic approximation was found to correspond to the Hamiltonian of an integrable $XXX$ spin chain. We study the odderon Hamiltonian corresponding to three sites by means of the Bethe Ansatz approach. We rewrite the Baxter equation, and consequently the Bethe Ansatz equations, as a linear triangular system. We derive a new expression for the eigenvectors and the eigenvalues, and discuss the quantization of the conserved quantities.