A short review of the vector charmonium-like state $ψ(4230)$

TL;DR

The paper assesses the vector charmonium-like state $\psi(4230)$ (formerly $Y(4260)$) as an early QCD-exotic candidate, synthesizing experimental evidence and four main theoretical frameworks: compact tetraquarks, hybrids, hadro-quarkonium, and hadronic molecules. It highlights the channel-dependent, threshold-sensitive lineshapes and the suppressed di-leptonic width as key experimental constraints, and reviews how each scenario explains or challenges these features. The hadronic-molecule interpretation, especially as a near-threshold $D_1(2420)\bar{D}$ bound state, is presented as an economical explanation for several observed patterns, while the tetraquark and hybrid pictures offer richer spectra with distinctive partner states. The work stresses that future high-precision $e^+e^-$ data and searches for predicted partners in various production channels are essential to discriminate among models and to illuminate the non-perturbative dynamics at play in the charmonium mass region.

Abstract

We present a concise review of the vector charmonium state $ψ(4230)$, which was originally labelled as $Y(4260)$ in the literature. As one of the earliest candidates for a QCD exotic states, its interpretation has initiated various ideas about possible manifestations of non-perturbative mechanisms in the charmonium mass regime. In this short article we briefly review the experimental status of $ψ(4230)$ and discuss possible theoretical interpretations. We will focus on four broadly investigated scenarios, i.e. tetraquark, hybrid, hadro-quarkonium, and hadronic molecule, and highlight the key issues based on these approaches. Crucial experimental observables, e.g. mass position, lineshapes, di-lepton decay width $Γ_{ee}$, production rates in $B$ meson decays, dominant hadronic decay patterns, and the potential $1^{-+}$ and $0^{--}$ exotic partners, are assessed, which can provide crucial structure information for understanding this mysterious state.

Figures (6)

• Figure 2: The updated $P$-wave tetraquark spectroscopy (i.e. Fig.2) in Ref. Cleven:2015era. Green dashed and blue solid lines are for inputs and predictions, respectively. Figure (a) is the spectroscopy with $\psi(4008)$ and $\psi(4230)$ as inputs. Figure (b) is the spectroscopy with $\psi(4230)$ and $\psi(4360)$ as inputs.
• Figure 3: The $P$-wave diquark-antidiquark tetraquark supermultiplet with tensor force. The figure is plotted based on Tab. VI of Ref. Ali:2017wsf. The green dashed and blue solid curves are the inputs and predictions, respectively. The two $1^{-+}$ states are almost degenerate to each other, with one of them illustrated by the red dashed line.
• Figure 4: The figure is from Ref. Anwar:2018sol, which present the $cq\bar{c}\bar{q}$ tetraquark spectrum (black solid lines in comparison with the existing experimental candidates (red box)). The linear confinement potential and one-gluon-exchange potential are considered in this calculation.
• Figure 5: The figure is a combination of Fig.4, Fig.5 and Fig.7 of Ref. Berwein:2015vca. The red box, blue triangle, green circle and purple inverted triangle are the Lattice calculations HadronSpectrum:2012gic for the $H_1$, $H_2$, $H_3$, $H_4$ hybrids, respectively. The naming scheme $H_i$ follows that in Refs. Juge:1999ieBraaten:2014qkaBraaten:2014itaBraaten:2013boa, where $H_1$ ($H_2\cup H_3\cup H_4$) is the hybrid with a combination of the $J^{PC}=1^{+-}$ glue-lump and a pair of $S$-wave ($P$-wave) heavy quark and antiquark. The black hollow box, pink hollow triangle, orange hollow circle and Magenta inverted triangle are the QCD sum rule results Chen:2013zia. The black dashed lines are the charmonium hybrid multiplets from Refs. Braaten:2014qkaBraaten:2014itaBraaten:2013boa without the hyperfine splitting among the states within a given multiplet. The light blue, gray, darker green and brown bands are the results from nonrelativistic effective field theory based on the BO approximation Berwein:2015vca, where the static heavy quark pair serves as a color source and the gluon adjusts its configurations to fit a given quantum number.
• Figure 6: The updated hadro-quarkonium spectroscopy, i.e. Fig.2 in Ref. Cleven:2015era. The green dashed lines are the experimental inputs. The two blue dotted lines with quantum number $1^{--}$ (or $0^{-+}$) represent the masses of the unmixed states. The blue solid lines are the predicted partners.