Quarkonium light-cone distribution amplitudes: twist structure and mass dependence

TL;DR

This paper systematically studies the twist structure and mass dependence of quarkonium light-cone distribution amplitudes using a light-front quark model, revealing universal behaviors and convergence properties in the heavy-quark limit.

Contribution

It provides a comprehensive analysis of quarkonium LCDAs, highlighting their evolution with quark mass and the emergence of twist-independence in the heavy-quark limit, which was not previously detailed.

Findings

Charge-conjugation symmetry enforces vanishing of odd Gegenbauer and ξ-moments.

Pseudoscalar twist-2 and twist-3 LCDAs become identical.

LCDAs become narrower and peaked with increasing quark mass.

Abstract

We present a systematic study of the leading- and next-to-leading-twist light-cone distribution amplitudes (LCDAs) of ground-state pseudoscalar and vector quarkonium within the light-front quark model (LFQM). By implementing the replacement $M \to M_0$, we analyze the longitudinal and transverse structures of the LCDAs, together with their Gegenbauer moments, $\xi$-moments, and transverse momentum moments. We show that charge-conjugation symmetry enforces the exact vanishing of all odd Gegenbauer moments and odd $\xi$-moments. For pseudoscalar quarkonium, the twist-2 and twist-3 LCDAs become identical, which leads to the same Gegenbauer moments, $\xi$-moments, and transverse momentum moments. For vector quarkonium, although the twist-2 and twist-3 LCDAs differ in the case of finite quark masses, they progressively converge as the quark mass increases. In the heavy-quark limit, all quarkonium LCDAs satisfy $\phi^A_{2} = \phi^P_{3} \simeq \phi^{\parallel}_{2} \simeq \phi^{\perp}_{3}$, demonstrating an emergent twist-independence of quarkonium distribution amplitudes. We further find that the LCDAs become increasingly peaked and narrower with increasing quark mass, indicating that the meson system becomes increasingly close to a nonrelativistic bound state, with a more uniform and stable distribution of internal longitudinal momentum. For all quarkonium, the peak value exhibits a simple phenomenological scaling behavior governed by the ratio $m/\beta$. The transverse momentum moments increase with the meson mass, indicating a progressively more compact bound-state structure. These results reveal a universal and systematic evolution of quarkonium LCDAs driven by the quark mass.