Some remarks on $X(6900)$

TL;DR

This paper analyzes LHCb data on the $X(6900)$ resonance using a Flatté-like parameterization, concluding that its nature—whether a confining or molecular state—cannot be definitively determined with current data.

Contribution

It applies a momentum-dependent Flatté-like model and spectral sum rules to analyze the $X(6900)$, providing insights into its possible nature and quantum numbers.

Findings

Both confining and molecular state interpretations are possible.

The lowest state in di-$J/ar{J}$ system likely shares quantum numbers with $X(6900)$.

$X(6900)$ probably is not a $J/ar{J}(2S)$ molecular state.

Abstract

The analysis of the LHCb data on $X(6900)$ found in the di-$\jpsi$ system is performed using a momentum-dependent Flatt\'{e}-like parameterization. The use of the pole counting rule and spectral density function sum rule give consistent conclusions that both confining states and molecular states are possible, or it is unable to distinguish the nature of $X(6900)$, if only the di-$\jpsi$ experimental data with current statistics are available. Nevertheless, we found that the lowest state in the di-$J/\psi$ system has very likely the same quantum numbers as $X(6900)$, and $X(6900)$ is probably not interpreted as a $J/\psi-\psi(2S)$ molecular state.