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

TL;DR

The paper tackles the ambiguity of the near-threshold X(6200) pole in the di-$J/\Psi$ system by predicting di-$J/\Psi$ and $J/\Psi\Psi(2S)$ femtoscopy correlation functions using a coupled-channel, $S$-wave framework and the Koonin-Pratt formalism with a Gaussian source. It demonstrates that the di-$J/\Psi$ correlation function $C(k)$ exhibits distinct patterns for resonant, bound, and virtual scenarios, and that these differences persist even with quantum statistics, coupled-channel dynamics, and modest off-shell variations. The analysis relies on three pole scenarios (two-channel resonance, three-channel bound, and three-channel virtual) fitted to existing invariant-mass data, and correlates the observed $C(k)$ shapes with the underlying phase shifts and pole nature. The work argues that upcoming high-statistics LHC measurements of di-$J/\Psi$ correlations can decisively identify the nature of X(6200) and thus illuminate fully-heavy tetraquark dynamics and nonperturbative double-vector-charmonium interactions.

Abstract

Recent re-analyses of the di-$J/Ψ$ invariant mass spectra reveal a state near the di-$J/Ψ$ 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-$J/Ψ$ interaction. To address this question, we predict the di-$J/Ψ$ and $J/ΨΨ(2S)$ femtoscopic correlation functions based on the Koonin-Pratt formula with a Gaussian source and the coupled-channel dynamics. Our results show that the di-$J/Ψ$ 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 $J/Ψ$ 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.

Figures (2)

• Figure 1: Di-$J/\Psi$ correlation function as a function of the relative momentum $k$ for different source sizes $R = 1$ and $3$ fm. The results are calculated with Eq. \ref{['Eq:CF2']} and three types of interactions. The bands reflect the variation in the sharp cutoff over the range $q_{\rm max}=800-1500$ MeV. The result obtained by considering only the quantum statistical effect (the so-called Bose-Einstein correlation) is also shown for comparison.
• Figure 2: $J/\Psi\Psi(2S)$ correlation function as a function of the relative momentum $k$ for different source sizes $R = 1$ and $3$ fm. The results are calculated with Eq. \ref{['Eq:CF1']} and three types of interactions. The bands reflect the variation in the sharp cutoff over the range $q_{\rm max}=800-1500$ MeV.