  The QCD description of exclusive decays of the $\Lambda_b$ baryon involves
hadronic matrix elements of non-local light ray operators, the light-cone
distribution amplitudes. We introduce the complete set of three--quark
distribution amplitudes and calculate the renormalization scale dependence for
the leading twist. At leading order in the strong coupling the evolution is
driven by pairwise two--quark interactions: heavy--light involving Sudakov
logarithms as in the B-meson case, and light--light as in light mesons. We
solve the evolution equation and show that its main effect is to generate a
radiative tail extending to high energies. Finally, we present simple models
for the distribution amplitudes based on QCD sum rules, and study the effect of
the evolution on these models.
