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

TL;DR

This review assesses the experimental and theoretical status of the $J/\psi \phi$ system in $B$ decays, focusing on the emergence of a triplet of $J^{PC}=1^{++}$ states ($X(4140)$, $X(4274)$, $X(4685)$) whose $m^{2}$ values align with a possible radial trajectory, and the broader, more complex landscape revealed by LHCb amplitude analyses. It discusses wide-ranging interpretations (charmonium, tetraquark, molecular, hybrid, and threshold effects) and highlights significant discrepancies in resonance widths, particularly for $X(4140)$, as well as the role of detector-efficiency and cross-experiment differences. The review emphasizes the need for higher-statistics data with flatter efficiency profiles and continued cross-experiment validation, including searches in related vector–vector systems like $J/\psi \Upsilon$ and $\Upsilon \Upsilon$, to clarify the nature of these states and to test the radial-excitation hypothesis for heavy-quark tetraquarks. The findings bear on the understanding of exotic hadron spectroscopy and guide future experimental and theoretical efforts to discriminate among competing interpretations.

Abstract

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 $B \rightarrow J/ψφK$ 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.

Figures (12)

• Figure 1: The number of $B^{+} \rightarrow J/\psi \phi K^{+}$ candidates as a function of the mass difference between $\mu^{+}\mu^{-}K^{+}K^{-}$ and $\mu^{+}\mu^{-}$ from CDF in 2009 CDF:2009jgo (left), 2011 CDF:2011pep (middle), and the results from CMS in 2013 CMS:2013jru (right).
• Figure 2: Left: The $J/\psi \phi$ invariant-mass distribution from Belle, with the data represented by the open histogram. The solid line corresponds to the fit model, while the dashed line describes the background. The expected position of $X(4140)$ is indicated by the blue arrow Belle:2009rkh. Right: The mass distribution of $J/\psi \phi$ from BESIII, with a red dashed line representing signal Monte Carlo (MC) events of $e^{+}e^{-}\rightarrow \gamma X(4140)$, $X(4140) \rightarrow J/\psi \phi$BESIII:2014fob.
• Figure 3: Invariant-mass distribution of $J/\psi \phi$ candidates through the $B^{+} \rightarrow J/\psi \phi K^{+}$ decay channel D0:2013jvp (left) and through inclusive production D0:2015nxw (right) from $\mathrm{D\textsl{\O}}$. In the left panel, the width of the second Breit-Wigner resonance is fixed to 30 MeV (consistent with CDF data CDF:2009jgo).
• Figure 4: The $J/\psi \phi$ invariant-mass distributions for $B^{+}\rightarrow J/\psi \phi K^{+}$ (left) and $B^{0} \rightarrow J/\psi \phi K_{S}^{0}$ (right) from BABAR. The projections from the Dalitz plot fit, including $X(4140)$ and $X(4272)$ (solid red lines) are shown ($X(4140)$ is not clearly visible for $B^{0}$ data sample). A fit without resonances (dashed blue line) is also shown in the left panel. The shaded yellow histograms represent the estimated background, determined from the $\Delta E$ sideband regions BaBar:2014wwp.
• Figure 5: Invariant-mass distributions of $\phi K^{+}$ (left), $J/\psi \phi$ (middle), and $J/\psi K^{+}$ (right) for the $B^{+} \rightarrow J/\psi \phi K^{+}$ candidates in LHCb's Run 1 and Run 2 data, shown together with the LHCb 2021 model (top) and the LHCb 2016 model (bottom) LHCb:2021uow. Compared to the LHCb 2016 model, the main change in the LHCb 2021 model is to introduce additional states, such that no further state with statistical significance above 5$\sigma$ needs to be added to improve the fit to the combined Run 1 and Run 2 data. For the LHCb 2021 model, nine $\phi K^{+}$ (states with same spin parity are merged for display and labeled as $K$ in the legend), seven $J/\psi \phi$ (labeled as $X$), two $J/\psi K^{+}$ (labeled as $Z_{cs}$) and one $J/\psi \phi$ nonresonant (labeled as $X$ NR) components are considered.