Renormalization of twist-three operators and integrable lattice models

TL;DR

This paper investigates the renormalization of twist-three operators in QCD, revealing integrable structures in certain sectors and providing a quasiclassical approximation for their energy spectra, relevant for understanding parton correlators.

Contribution

It demonstrates the complete integrability of the quark-gluon-quark evolution equations in the multicolour limit and develops a quasiclassical expansion for the energy spectra of these systems.

Findings

Quark-gluon-quark sector is integrable in the multicolour limit.

Pure gluonic sector contains a non-integrable addendum treated perturbatively.

Quasiclassical expansion describes the energy spectra well.

Abstract

We address the problem of solution of the QCD three-particle evolution equations which govern the Q-dependence of the chiral-even quark-gluon-quark and three-gluon correlators contributing to a number of asymmetries at leading order and the transversely polarized structure function g_2(x). The quark-gluon-quark case is completely integrable in multicolour limit and corresponds to a spin chain with non-periodic boundary conditions, while the pure gluonic sector contains, apart from a piece in the Hamiltonian equivalent to XXX Heisenberg magnet of spin s = - 3/2, a non-integrable addendum which can be treated perturbatively for a bulk of the spectrum except for a few lowest energy levels. We construct a quasiclassical expansion with respect to the total conformal spin of the system and describe fairly well the energy spectra of quark-gluon-quark and three-gluon systems.