Hunting for states in the recent LHCb di-$J/\psi$ invariant mass spectrum

TL;DR

This study uses partial wave analysis with effective potentials and coupled-channel effects to interpret LHCb di-$J/$ data, identifying potential new states including the $X(6900)$ and other resonances.

Contribution

It introduces a dynamical analysis incorporating coupled-channel effects to identify multiple potential exotic states in the di-$J/$ spectrum.

Findings

Identification of a pole structure as the $X(6900)$ state.

Hints for additional states: $X(6200)$, $X(6680)$, and $X(7200)$.

Quantum number assignments for the identified states.

Abstract

Partial wave analysis is performed, with effective potentials as dynamical inputs, to scrutinize the recent LHCb data on the di-$J/\psi$ invariant mass spectrum. Coupled-channel effects are incorporated in the production amplitude via final state interactions. The LHCb data can be well described. A dynamical generated pole structure, which can be identified as the $X(6900)$ state, is found. Our analysis also provides hints for the existence of three other possible states: a bound state $X(6200)$, a broad resonant state $X(6680)$ and a narrow resonant state $X(7200)$. The $J^{PC}$ quantum numbers of the $X(6680)$ and $X(6900)$ states should be $2^{++}$, while the $X(6200)$ and $X(7200)$ states prefer $0^{++}$. To determine the above states more precisely, more experimental data for the channels, such as $J/\psi\psi(2S)$, $J/\psi\psi(3770)$, di-$\psi(2S)$, are required.