Integrability of Three-Particle Evolution Equations in QCD

We show that Brodsky-Lepage evolution equation for the spin-3/2 baryon distribution amplitude is completely integrable and reduces to the three-particle ${\mathrm{XXX}}_{s=-1\mathrm{}}$ Heisenberg spin chain. Trajectories of the anomalous dimensions are identified and calculated using the $1/N$ expansion. Extending this result, we prove integrability of the evolution equations for twist-3 quark-gluon operators in the large $N_c$ limit.