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.

Comments: 8 pages, 1 figure, uses revtex and amstex. Presentation improved in several places, Eqs. (11b) and (27) corrected, a few misprints fixed, acknowledgement enlarged