Experimental road of the J/ψφ mass spectrum, current status, and implications

Inspired by the X(4140) structure reported in the J/ψφ system by the CDF experiment in 2009, a series of searches have been carried out in the J/ψφ and J/ψK channels, leading to the claim of ten structures in the B → J/ψφK 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/ψφ 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/ψφ 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/ψφ and J/ψJ/ψ 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/ψω, φφ, ρω, and ρφ systems are mentioned, and the prospects for the J/ψΥ and ΥΥ systems, are also highlighted.