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

TL;DR

This paper derives an exact, integrable evolution equation for the three-particle quark-gluon B-meson distribution amplitude, revealing how different states contribute to the scale dependence relevant for heavy-meson decay analyses.

Contribution

It presents the first exact solution for the evolution equation of the subleading twist B-meson distribution amplitude in the large N_c limit, showing decoupling of certain states and implications for decay calculations.

Findings

The evolution equation is completely integrable and solvable.

The lowest anomalous dimension is separated by a finite gap.

The scale dependence of the three-particle DA is nontrivial.

Abstract

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.