We find that the evolution equation for the three-particle quark-gluon
B-meson light-cone distribution amplitude (DA) of subleading twist is
completely integrable in the large Ncβ limit and can be solved exactly. The
lowest anomalous dimension is separated from the remaining, continuous,
spectrum by a finite gap. The corresponding eigenfunction coincides with the
contribution of quark-gluon states to the two-particle DA Οββ(Ο) so
that the evolution equation for the latter is the same as for the leading-twist
DA Ο+β(Ο) up to a constant shift in the anomalous dimension. Thus,
``genuine'' three-particle states that belong to the continuous spectrum
effectively decouple from Οββ(Ο) to the leading-order accuracy. In
turn, the scale dependence of the full three-particle DA turns out to be
nontrivial so that the contribution with the lowest anomalous dimension does
not become leading at any scale. The results are illustrated on a simple model
that can be used in studies of 1/mbβ corrections to heavy-meson decays in the
framework of QCD factorization or light-cone sum rules.Comment: Extended version, includes new results on the large momentum limit
and a detailed study of the evolution effects in a simple mode