Heavy Meson Distribution Amplitudes of Definite Geometric Twist with Contribution of 3-Particle Distribution Amplitudes

TL;DR

This paper reformulates equations of heavy meson distribution amplitudes of definite geometric twist within HQET, deriving relations between two- and three-particle distribution amplitudes using Mellin moments and confirming previous representations.

Contribution

It introduces a set of algebraic equations linking two- and three-particle distribution amplitudes of definite geometric twist in HQET, including off-cone structure considerations.

Findings

Derived relations between two- and three-particle distribution amplitudes.

Confirmed the representation of $ abla_{ ext{twist}}$ by Kawamura et al.

Presented relations using Mellin moments and non-local distribution amplitudes.

Abstract

Under the constraints of HQET the equations of motion of heavy meson distribution amplitudes of definite geometric twist, using the knowledge of their off-cone structure, are reformulated as a set of algebraic equations. Together with equations due to various Dirac structures various relations between the (sets of) independent two- and three particle distribution amplitudes of definite geometric twist are derived and presented using both the notion of (double) Mellin moments and re-summed non-local distribution amplitudes. Resolving these relations for the independent two-particle moments in terms of three-particle double moments we confirmed the representation of $\Phi_{\pm|n}$ by Kawamura et al. (Phys. Lett. B \bf{523} (2001) 111).