  We study the scale dependence of the twist-3 quark-gluon parton distributions
using the observation that in the multi-color limit the corresponding QCD
evolution equations possess an additional integral of motion and turn out to be
effectively equivalent to the Schrodinger equation for integrable open
Heisenberg spin chain model. We identify the integral of motion of the spin
chain as a new quantum number that separates different components of the
twist-3 parton distributions. Each component evolves independently and its
scale dependence is governed by anomalous dimension given by the energy of 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 equation. The
solutions to the Baxter equation are constructed using different asymptotic
methods and their properties are studied in detail. We demonstrate that the
obtained solutions provide a good qualitative description of the spectrum of
the anomalous dimensions and reveal a number of interesting properties. We show
that the few lowest anomalous dimensions are separated from the rest of the
spectrum by a finite mass gap and estimate its value.
