  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 $N_c$ 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 $\phi_-(\omega)$ so
that the evolution equation for the latter is the same as for the leading-twist
DA $\phi_+(\omega)$ up to a constant shift in the anomalous dimension. Thus,
``genuine'' three-particle states that belong to the continuous spectrum
effectively decouple from $\phi_-(\omega)$ 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 $1/m_b$ corrections to heavy-meson decays in the
framework of QCD factorization or light-cone sum rules.
