Nature of the $X(6900)$ in partial wave decomposition of $J/\psi J/\psi$ scattering

TL;DR

This study analyzes the $X(6900)$ resonance in $J/ar{J}$ scattering using partial wave decomposition, unitarization, and fits to LHCb data, suggesting it is a compact tetraquark with specific quantum numbers.

Contribution

It introduces a coupled-channel scattering analysis with partial wave decomposition and unitarization to characterize the $X(6900)$ resonance, providing its pole parameters and quantum number assignment.

Findings

The $X(6900)$ has a mass of approximately 6861 MeV and width of 129 MeV.

It is identified as a $0^{++}$ quantum state.

The resonance behaves as a normal Breit-Wigner, indicating a compact tetraquark structure.

Abstract

In this letter, we perform partial wave decomposition on coupled-channel scattering amplitudes, $J/\psi J/\psi$-$J/\psi \psi(2S)$-$J/\psi \psi(3770)$, to study the resonance appears in these processes. Effective Lagrangians are used to describe the interactions of four charmed vector mesons, and the scattering amplitudes are calculated up to the next-to-leading order. Partial wave projections are performed, and unitarization is implemented by Pad\'e approximation. Then we fit the amplitudes to the $J/\psi J/\psi$ invariant mass spectra measured by LHCb and determine the unknown couplings. The pole parameters of the $X(6900)$ are extracted as $M=6861.0^{+6.3}_{-8.8}$~MeV and $\Gamma=129.0^{+5.6}_{-3.4}$~MeV. Our analysis implies that its quantum number prefers to be $0^{++}$. The pole counting rule and phase shifts show that it is a normal Breit-Wigner resonance and, hence, should be a compact tetraquark.