Evolution equations for quark-gluon distributions in multi-color QCD and open spin chains

TL;DR

This paper links the scale evolution of twist-3 quark-gluon distributions in multi-color QCD to integrable open Heisenberg spin chains, developing a Bethe Ansatz approach to analyze their spectrum and properties.

Contribution

It introduces a novel integrable spin chain model for QCD evolution equations and develops a Bethe Ansatz method to analyze the spectrum of anomalous dimensions.

Findings

Identification of a new quantum number separating distribution components

Development of a Bethe Ansatz technique for the spectrum analysis

Discovery of a finite mass gap in the anomalous dimension spectrum

Abstract

We study the scale dependence of the twist-3 quark-gluon parton distributions using the observation that in the multi-color limit the corresponding QCD evolution equations possess an additional integral of motion and turn out to be effectively equivalent to the Schrodinger equation for integrable open Heisenberg spin chain model. We identify the integral of motion of the spin chain as a new quantum number that separates different components of the twist-3 parton distributions. Each component evolves independently and its scale dependence is governed by anomalous dimension given by the energy of the spin magnet. To find the spectrum of the QCD induced open Heisenberg spin magnet we develop the Bethe Ansatz technique based on the Baxter equation. The solutions to the Baxter equation are constructed using different asymptotic methods and their properties are studied in detail. We demonstrate that the obtained solutions provide a good qualitative description of the spectrum of the anomalous dimensions and reveal a number of interesting properties. We show that the few lowest anomalous dimensions are separated from the rest of the spectrum by a finite mass gap and estimate its value.