Probing the di-$J/\Psi$ interaction and the nature of $X(6200)$ with femtoscopic correlation functions

Abstract

Recent re-analyses of the di-$J/\Psi$ invariant mass spectra reveal a state near the di-$J/\Psi$ threshold, referred to as the $X(6200)$. Yet the nature of this near-threshold pole--whether it is a resonant, bound, or virtual state--remains unresolved due to our limited understanding of the di-$J/\Psi$ interaction. To address this question, we predict the di-$J/\Psi$ and $J/\Psi\Psi(2S)$ femtoscopic correlation functions based on the Koonin-Pratt formula with a Gaussian source and the coupled-channel dynamics. Our results show that the di-$J/\Psi$ correlation function exhibits distinctly different behaviors in each scenario, especially for small source sizes ($R\sim1$ fm), providing a clear experimental observable to distinguish the nature of $X(6200)$. These distinguishing features persist even when quantum statistical effects and coupled-channel dynamics are included and show negligible sensitivity to off-shell ambiguities. Given the high $J/\Psi$ production rates and clean detection channels at the LHC, we hope that these discoveries will stimulate further experimental studies and help clarify the nature of double-vector-charmonium interactions and the nonperturbative dynamics of fully-heavy tetraquark systems.