Evolution equation for the higher-twist B-meson distribution amplitude

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 φ_-(ω) so that the evolution equation for the latter is the same as for the leading-twist DA φ₊(ω) up to a constant shift in the anomalous dimension. Thus, ''genuine'' three-particle states that belong to the continuous spectrum effectively decouple from φ_-(ω) 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.