Higher Twist Distribution Amplitudes of Vector Mesons in QCD: Formalism and Twist Three Distributions

TL;DR

The paper develops a systematic, QCD-consistent framework for twist-3 light-cone distribution amplitudes of vector mesons, leveraging conformal expansion and exact equations of motion to relate two- and three-particle distributions. It provides complete, SU(3)-aware models for ρ, ω, K*, and φ that satisfy all constraints and includes renormalization-group evolution in the leading-log approximation, with nonperturbative inputs from QCD sum rules. The resulting DAs—both chiral-odd and chiral-even—are expressed in terms of a minimal set of parameters, enabling practical use in hard exclusive processes and B decays, and offering a foundation for extending to higher twists. The work highlights how conformal symmetry structured by SL(2,R) organizes higher-twist operators, ensuring controlled truncation and predictable scale dependence, while acknowledging limitations near end-points and in SU(3) breaking for certain observables.

Abstract

We present a systematic study of twist three light-cone distribution amplitudes of vector mesons in QCD, which is based on conformal expansion and takes into account meson and quark mass corrections. A complete set of distribution amplitudes is constructed for rho, omega, K* and phi mesons, which satisfies all (exact) equations of motion and constraints from conformal expansion. Nonperturbative input parameters are calculated from QCD sum rules, including an update of SU(3) breaking corrections in the leading twist distributions.

Figures (3)

• Figure 1: (a) Leading twist 2 distribution amplitude $\phi_\parallel(u)$ for a longitudinally polarized vector meson, (b) $\phi_\perp(u)$ for a transversely polarized one. Renormalization point is $\mu=1\,$GeV.
• Figure 2: Two-particle twist 3 distribution amplitudes for the $\rho$ meson.
• Figure 3: Two-particle twist 3 distribution amplitudes for the $\rho$, $K^*$ and $\phi$ meson.