Experimental road of the $J/\psi\phi$ mass spectrum, current status, and implications

Inspired by the $X(4140)$ structure reported in the $J/\psi \phi$ system by the CDF experiment in 2009, a series of searches have been carried out in the $J/\psi \phi$ and $J/\psi K$ channels, leading to the claim of ten structures in the $B \rightarrow J/\psi \phi K$ system. This article provides a comprehensive review of experimental developments, from the initial evidence of $X(4140)$ at CDF to the amplitude analyses and diffractive process investigations by the LHCb experiment, as well as theoretical interpretations of these states. A triplet of $J^{PC} = 1^{++}$ states with relatively large mass splittings [about 200~MeV (natural units are adopted)] has been identified in the $J/\psi \phi$ system by LHCb. Their mass-squared values align approximately linearly with a possible radial quantum number, suggesting that the triplet may represent a radially excited family. For $X(4140)$, the first state in the triplet, its width reported by LHCb is inconsistent with that measured by other experiments, and possible reasons for this discrepancy are discussed. A potential connection between an excess at 4.35~GeV in the $J/\psi \phi$ mass spectrum reported by the Belle experiment through a two-photon process and a potential spin-2 excess in the LHCb data is also investigated. In addition, potential parallels between the $J/\psi \phi$ and $J/\psi J/\psi$ systems, both composed of two vector mesons, are discussed. The continued interest in, and complexity of, these systems underscore the necessity of further experimental exploration with increased statistical precision across a variety of experiments, particularly those with relatively flat efficiency across the Dalitz plot. The $J/\psi \omega$, $\phi \phi$, $\rho \omega$, and $\rho \phi$ systems are mentioned, and the prospects for the $J/\psi \Upsilon$ and $\Upsilon \Upsilon$ systems, are also highlighted.