Study of $X(6900)$ with unitarized coupled channel scattering amplitudes

TL;DR

This paper models the $X(6900)$ resonance using unitarized coupled channel scattering amplitudes of vector mesons, fitting experimental data to determine its properties and nature.

Contribution

It introduces a unitarized coupled channel approach with effective Lagrangians to analyze the $X(6900)$ resonance, providing new insights into its quantum numbers and structure.

Findings

The $X(6900)$ likely has quantum number $0^{++}$.

The resonance is consistent with being a compact tetra-quark.

High-quality fits to experimental data were achieved.

Abstract

In this paper, we study the resonant state $X(6900)$. The scattering amplitudes of coupled channels, $J/\psi J/\psi$-$J/\psi \psi(2S)$-$J/\psi \psi(3770)$, are constructed with the interaction of four vector mesons described by effective Lagrangians. The amplitudes are calculated up to one loop, decomposed by partial wave projection, and unitarized by Pad$\acute{e}$ approximation. These amplitudes are fitted to the latest experimental data sets of di-$J/\psi$ and $J/\psi \psi(2S)$ invariant mass spectra of LHCb, CMS, and ATLAS. High-quality solutions are obtained. With these partial wave amplitudes, we extract the pole parameters of the $X(6900)$. Its quantum number is likely to be $0^{++}$. According to the pole counting rule as well as analysis of the phase shifts of the partial waves, it supports our previous conclusion that the $X(6900)$ prefers to be a compact tetra-quark.