Abstract:We show that the Brodsky-Lepage evolution equation for the 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.

We develop a new theoretical framework for the description of leading twist light-cone baryon distribution amplitudes which is based on integrability of the helicity λ = 3/2 evolution equation to leading logarithmic accuracy. A physical interpretation is that one can identify a new 'hidden' quantum number which distinguishes components in the λ = 3/2 distribution amplitudes with different scale dependence. The solution of the corresponding evolution equation is reduced to a simple three-term recurrence relation. The exact analytic solution is found for the component with the lowest anomalous dimension for all moments N, and the WKB-type expansion is constructed for other levels, which becomes asymptotically exact at large N. Evolution equations for the λ = 1/2 distribution amplitudes (e.g. for the nucleon) are studied as well. We find that the two lowest anomalous dimensions for the λ = 1/2 operators (one for each parity) are separated from the rest of the spectrum by a finite 'mass gap'. These special states can be interpreted as scalar diquarks.

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Erratum: Scale dependence of twist-three contributions to single spin asymmetries [Phys. Rev. D 80, 114002 (2009)]

We develop a general theoretical framework for the description of higher-twist baryon operators which makes maximal use of the conformal symmetry of the QCD Lagrangian. The conformal operator basis is constructed for all twists. The complete analysis of the one-loop renormalization of twist-4 operators is given. The evolution equation for three-quark operators of the same chirality turns out to be completely integrable. The spectrum of anomalous dimensions coincides in this case with the energy spectrum of the twist-4 subsector of the SU (2, 2) Heisenberg spin chain. The results are applied to give a general classification and calculate the scale dependence of subleading twist-4 nucleon distribution amplitudes that are relevant for hard exclusive reactions involving a helicity flip. In particular we find an all-order expression (in conformal spin) for the contributions of geometric twist-3 operators to the (light-cone) twist-4 nucleon distribution amplitudes, which are usually referred to as Wandzura-Wilczek terms.