Integrability of Three-Particle Evolution Equations in QCD

Abstract

We show that Brodsky-Lepage evolution equation for the spin-3/2 baryon distribution amplitude is completely integrable and reduces to the three-particle ${\mathrm{XXX}}_{s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1}$ 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.