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

We study the scale dependence of the twist-3 quark-gluon parton distributio ns using the observation that in the multi-color limit the corresponding QC D evolution equations possess an additional integral of motion and turn out to be effectively equivalent to the Schrodinger equation for integrable op en Heisenberg spin chain model. We identify the integral of motion of the s pin chain as a new quantum number that separates different components of th e twist-3 parton distributions. Each component evolves independently and it s scale dependence is governed by anomalous dimension given by the energy o f 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 equat ion. The solutions to the Baxter equation are constructed using different a symptotic methods and their properties are studied in detail. We demonstrat e that the obtained solutions provide a good qualitative description of the spectrum of the anomalous dimensions and reveal a number of interesting pr operties. We show that the few lowest anomalous dimensions are separated fr om the rest of the spectrum by a finite mass gap and estimate its value. (C ) 2000 Elsevier Science B.V. All rights reserved.