Investigating the internal structure of $X(6900)$ in the $2J/ψ$ decay channel

TL;DR

This work investigates the internal structure of the fully heavy tetraquark candidate $X(6900)$ by computing the decay width $\Gamma(X(6900)\to 2J/\psi)$ within a covariant, nonlocal framework. Treating $X(6900)$ as a $[cc][\bar{c}\bar{c}]$ tetraquark with $J^{PC}=2^{++}$, it compares two spin-coupling schemes, axial-vector–axial-vector (A-A) and vector–vector (V-V), using compositeness-condition–driven couplings $g_X$ and $g_{J/\psi}$. The numerical analysis shows $\Gamma_{AA}$ is larger and consistent with experimental measurements, while $\Gamma_{VV}$ cannot fit the data except for extreme parameter choices, thus favoring an A-A internal structure. The results validate the covariant approach for fully heavy exotics and provide guidance for interpreting $X(6900)$ and related states, with implications for diquark correlations in QCD. Overall, the study advances our understanding of multiquark dynamics and informs future experimental and theoretical explorations of fully heavy tetraquarks.

Abstract

Assuming $X(6900)$ is a tetraquark state, the decay width of $X(6900)\to 2J/ψ$ is calculated in a covariant quark model, with the diquark-antidiquark $[cc][\bar{c}\bar{c}]$ picture. Two possible structures, vector-vector and axial-vector--axial-vector coupling, are investigated. The result indicates that the axial-vector--axial-vector coupling is consistent with the experiments.

Figures (3)

• Figure 1: Feynman diagrams in this paper. (a), (b) and (c) are three $X \to 2J/\psi$ Feynman diagrams. (d) and (e) are the mass operators of $X(6900)$ ($\Pi_{X}^{\mu\nu,\alpha\beta}$) and $J/\psi$ ($\Pi_{J/\psi}^{\mu \nu}$), respectively. The red and green dots denote the interactions from $\mathcal{L}_{X}$ and $\mathcal{L}_{J/\psi}$, respectively.
• Figure 2: Numerical results of $g_X$
• Figure 3: Decay width of $X(6900)\to 2J/\psi$. (a) A-A coupling. (b) V-V coupling.