Leading-twist light cone distribution amplitudes for p-wave heavy quarkonium states

TL;DR

This paper investigates the leading-twist light-cone distribution amplitudes of p-wave heavy quarkonium states using the light-front framework, deriving relations, simplifying under non-relativistic limits, and calculating decay constants and moments for charmonium and bottomonium.

Contribution

It provides a detailed analysis of LCDAs for p-wave heavy quarkonia, including analytical simplifications and numerical results, which were not previously available.

Findings

Derived simple relations for LCDAs and decay constants.

Analytically completed ppa_12 integrations with Gaussian wave functions.

Calculated decay constants and ppa-moments consistent with other approaches.

Abstract

In this paper, a study of light-cone distribution amplitudes for p-wave heavy quarkonium states are presented. Within the light-front framework, the leading twist light-cone distribution amplitudes, and their relevant decay constants, have some simple relations. These relations can be further simplified when the non-relativistic limit and the wave function as a function of relative momentum |\vec\kappa| are taken into consideration. In addition, the \kappa_\perp integrations in the equations of LCDAs and \xi-moments can be completed analytically when the Gaussian-type wave function is considered. After fixing the parameters that appear in the wave function, the curves and the corresponding decay constants of the LCDAs are plotted and calculated for the charmonium and bottomonium states. The first three \xi-moments of the LCDAs are estimated and are consistent with those of other theoretical approaches.