Renormalization of twist-three operators and integrable lattice models

We address the problem of solution of the QCD three-particle evolution equations which govern the Q²-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 g₂ x_Bj ·. 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 s y 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. q 2000 Elsevier Science B.V. All rights reserved.