[en] 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