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 rest, 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 typical observables to the leading-order accuracy. Our results suggest that the study of $1/m_b$ corrections to heavy-meson decays in the framework of QCD factorization or light-cone sum rules requires a much simpler nonperturbative input than it is usually assumed