Study of quark distribution amplitudes of 1S and 2S heavy quarkonium states

TL;DR

This paper investigates the quark distribution amplitudes of 1S and 2S heavy quarkonium states using Gaussian wave functions, analytically computes decay constants, and compares results with other theories.

Contribution

It introduces a method to derive quark distribution amplitudes for heavy quarkonium states with Gaussian wave functions and provides numerical comparisons.

Findings

Derived explicit forms of quark distribution amplitudes.

Calculated $\xi$-moments for heavy quarkonium states.

Compared results with existing theoretical models.

Abstract

In this paper, the quark distribution amplitudes of 1S and 2S heavy quarkonium states are studied in terms of Gaussian-type wave functions. The transverse momenta $p_\perp$ integrals of the formulae for the decay constant are performed analytically. Then the quark distribution amplitudes are obtained. In addition, the $\xi$-moments are also calculated. After fixing the relevant parameters appearing in the quark distribution amplitude, the curves of the quark distribution amplitude for 1S and 2S heavy quarkonium states are plotted. Finally, the numerical results of this approach are compared with the other theoretical predictions.