Integrability and WKB solution of twist-three evolution equations

We identify an integrable one-dimensional inhomogeneous three-site open spi n chain which arises in the problem of diagonalization of twist-three quark -gluon evolution equations in QCD in the chiral-odd sector, Making use of t he existence of a non-trivial 'hidden' integral of motion the problem of di agonalization of the evolution kernels is reduced to the study of a second- order finite-difference equation which is solved in WKB approximation for l arge conformal spins of the three-particle system. The energies (alias anom alous dimensions) of eigenstates with different scale dependence are found in limiting cases and compared with numerical calculations. (C) 1999 Elsevi er Science B.V. All rights reserved.