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

TL;DR

This paper proposes using femtoscopic correlation functions to determine whether the $X(6200)$ state near the di-$J/ar{J}$ threshold is resonant, bound, or virtual, aiding understanding of heavy tetraquark interactions.

Contribution

It introduces a method to distinguish the nature of $X(6200)$ using di-$J/ar{J}$ femtoscopic correlation functions based on coupled-channel dynamics and the Koonin-Pratt formula.

Findings

Correlation functions differ significantly for each scenario at small source sizes.

Features are robust against quantum statistical effects and off-shell ambiguities.

Method is feasible with high $J/ar{J}$ production rates at the LHC.

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.