Renormalization of twist-three operators and integrable lattice models Original Research Article

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(xBj). 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=−32, 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.