  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 $\lambda=3/2$ evolution equation to leading logarithmic accuracy.
A physical interpretation is that one can identify a new `hidden' quantum
number which distinguishes components in the $\lambda=3/2$ 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 $\lambda=1/2$ distribution amplitudes (e.g. for the nucleon)
are studied as well. We find that the two lowest anomalous dimensions for the
$\lambda=1/2$ 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.
