Theoretical Update of Pseudoscalar Meson Distribution Amplitudes of Higher Twist: The Nonsinglet Case

TL;DR

The paper develops a complete, model-independent framework for the twist-3 and twist-4 two- and three-particle light-cone distribution amplitudes of pseudoscalar nonsinglet mesons, incorporating meson-mass corrections. By combining nonlocal operator identities with conformal partial wave expansion and QCD equations of motion, it expresses the DAs for $\pi$, $K$, and $\eta$ in terms of a small set of nonperturbative parameters (e.g., $a_2$, $\eta_3$, $\omega_3$, $\eta_4$, $\omega_4$) with scale dependence governed by perturbative renormalization. The analysis shows meson-mass corrections are negligible for the pion but can dominate for kaons and eta octet states, significantly affecting the normalization and shape of certain DAs (notably $\mathbb{A}$). The resulting parametrizations are intended to improve predictions for hard exclusive processes, including $B$-meson decays to light mesons and meson transition form factors, via QCD sum rules on the light-cone.

Abstract

We discuss the two and three particle light-cone distribution amplitudes (DAs) of pseudoscalar nonsinglet mesons of twist 3 and 4. Using nonlocal operator identities and conformal expansion, we derive closed expressions for several DAs. We also include meson-mass corrections which prove to be dominant in the twist 4 DAs of K and eta mesons. Explicit parametrizations for the DAs of pi, K and eta mesons are given, with the numerical input parameters determined from QCD sum rules.