Integrability of three-particle evolution equations in QCD

Abstract

We show that Brodsky-Lepage evolution equation for the leading twist spin 3/2 baryon distribution amplitude is completely integrable and reduces to the three-particle XXX_{s=-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 and derive explicit expressions for the corresponding integrals of motion.

Figures (1)

• Figure 1: The spectrum of eigenvalues for the conserved charge $Q_{3/2}$ (a) and for the spin 3/2 Hamiltonian $H_{3/2}$ (b), see text.