Conventional Charmonium Research Articles

Searching for the open flavor tetraquark Tcs¯0(2900)++\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{c\\bar{s}0}(2900)^{++}$$\\end{document} in the process B+→K+D+D-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^+\\rightarrow K^+ D^+ D^-$$\\end{document}

Inspired by recent observations of Tcs¯0(2900)0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{c\\bar{s}0}(2900)^0$$\\end{document} in the Ds+π-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_s^+ \\pi ^-$$\\end{document} invariant mass distribution of B0→D¯0Ds+π-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^0 \\rightarrow \\bar{D}^0 D_s^+ \\pi ^-$$\\end{document} decay and Tcs¯0(2900)++\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{c\\bar{s}0}(2900)^{++}$$\\end{document} in the Ds+π+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_s^+ \\pi ^+$$\\end{document} invariant mass distribution of B+→D-Ds+π+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^+ \\rightarrow D^- D_s^+ \\pi ^+$$\\end{document} decay, we investigate the Tcs¯0(2900)++\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{c\\bar{s}0}(2900)^{++}$$\\end{document} contribution to the B+→K+D+D-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^+ \\rightarrow K^+ D^+ D^-$$\\end{document} decay in a molecular scenario, where we consider Tcs¯0(2900)++\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{c\\bar{s}0}(2900)^{++}$$\\end{document} as a D∗+K∗+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D^{*+} K^{*+}$$\\end{document} molecular state. Our estimations indicate that the fit fraction of Tcs¯0(2900)++\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{c\\bar{s}0}(2900)^{++}$$\\end{document} in the B+→K+D+D-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^+ \\rightarrow K^+ D^+ D^-$$\\end{document} is about 13%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$13\\%$$\\end{document}, and its signal is visible in the D+K+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D^+ K^+$$\\end{document} invariant mass distribution. With the involvement of Tcs¯0(2900)++\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{c\\bar{s}0}(2900)^{++}$$\\end{document}, the fit fractions of χc0(3915)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{c0}(3915)$$\\end{document} and χc2(3930)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{c2}(3930)$$\\end{document} may be much different with the ones obtained by the amplitude analysis in Ref. [Aaij et al. Phys. Rev. D 102:112003, 2020], which may shed light on the long standing puzzle of χc0(3915)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{c0}(3915)$$\\end{document} as the conventional charmonium.

Connection between near the Ds+Ds− threshold enhancement in B+→Ds+Ds−K+ and conventional charmonium χc0(2P)

Focusing on recent measurement of $B^+ \to D_s^+D_s^-K^+$ process given by the LHCb Collaboration, we propose that this newly observed near the $D_s^+D_s^-$ threshold enhancement can be due to the contribution of the $\chi_{c0}(2P)$, which is a $P$-wave charmonium below the $D_s^+D_s^-$ threshold. By performing a combined fit to the measured $D_s^+D_s^-$, $D_s^+K^+$, and $D_s^-K^+$ invariant mass spectra, introducing the $\chi_{c0}(2P)$ can well reproduce the near threshold enhancement in the $D_s^+D_s^-$ invariant mass spectrum. When depicting the whole $D_s^+D_s^-$ invariant mass spectrum, the contributions from higher charmonium $\psi(4230)$ and charmoniumlike state $X_0(4140)$ are obvious. In addition, a charmed meson $D^*(3^3S_1)$ with mass around 3015 MeV is found to be important to depict the $D_s^-K^+$ invariant mass spectrum well. Especially, the importance of node effect of the spatial wave function of the $\chi_{c0}(2P)$ is revealed, by which the anomaly of the ratio $\Gamma(X\to D^+D^-)/\Gamma(X\to D_s^+D_s^-)$ indicated by LHCb can be explained well. Finally, our scenario of the newly observed enhancement structure resulted from the $\chi_{c0}(2P)$ is enforced.

The two-channel exotic charmonium-like resonances in the mass region (3900–4700) MeV

Numerous resonances in the c{{bar{c}}} and 4q systems, containing c{{bar{c}}} plus s{{bar{s}}} quarks (or light q{{bar{q}}}) were observed during last decades and recently the LHCb has found a remarkable narrow peak T_{cc}(3875) in the D D^* system. Besides there are several highly excited charmonium-like resonances, which can be treated as the shifted standard charmonium states. We analyze all these groups of the resonances in the mass region (3900–4700) MeV, using relativistic strong coupling theory with possible channel coupling phenomena. For the shifted charmonium states conventional charmonium spectrum is presented, being calculated with the relativistic string Hamiltonian, which does not contain fitting parameters, while for high excitations the universal flattened confining potential is used. It is shown that X(4274), X(4500), X(4700) can be identified as 3,^3P_1, 4,^3P_0, 5,^3P_0 states. The group of exotic states are considered using the Extended Recoupling Model, where two mesons m_1,m_2 transfer into another pair of mesons m_3, m_4 and back (infinite number of times), creating the four-quark resonance. Within this approach the resonances – T_{cc}(3875), Z_c(3900), X(3915), Z_{cs}(3985), X(4014), and X(4140) – can be explained as the exotic four-quark states in the S-wave decay channels.

The Overshadowed χc1(2p) Charmoniumlike Resonance

A systematic analysis of JPC = 1++ charmoniumlike mesons with energies up to 4.0 GeV is carried out within the diabatic approach to QCD. The resulting spectrum contains only two bound states: the conventional 1p charmonium state and a D0 D̄∗0 loosely bound state which may be naturally identified with X(3872). The rest of the spectrum consists in a continuum of D0 D̄∗0 and D+D∗− scattering states, whose analysis indicates the presence of a resonance near 3.96 GeV that may be assigned to a mostly conventional 2p charmonium state. It is shown that this χc1(2p) resonance is likely overshadowed in its expected main decay channels, D0 D̄∗0 and D+D∗−, by the threshold enhancements due to the loosely bound X(3872), which may justify its lack of detection to date. Alternative discovery channels are discussed.

Measurement of e+e−→γχc0,c1,c2 cross sections at center-of-mass energies between 3.77 and 4.60 GeV

The e+e−→γχcJ (J=0, 1, 2) processes are studied at center-of-mass energies ranging from 3.773 to 4.600 GeV, using a total integrated luminosity of 19.3 fb−1 e+e− annihilation data accumulated with the BESIII detector at BEPCII. We observe for the first time e+e−→γχc1,c2 signals at s=4.180 GeV with statistical significances of 7.6σ and 6.0σ, respectively. The production cross section of e+e−→γχc1,c2 at each center-of-mass energy is also measured. We find that the line shape of the e+e−→γχc1 cross section can be described with conventional charmonium states ψ(3686), ψ(3770), ψ(4040), ψ(4160). Compared with this, for the e+e−→γχc2 channel, one more additional resonance is added to describe the cross section line shape. Its mass and width are measured to be M=4371.7±7.5±1.8 MeV/c2 and Γtot=51.1±17.6±1.9 MeV, where the first uncertainties are statistical and the second systematic. The significance of this resonance is estimated to be 5.8σ, and its parameters agree with the Y(4360) resonance previously reported in e+e−→π+π−ψ(3686), and the Y(4390) in e+e−→π+π−hc within uncertainties. No significant signal for the e+e−→γχc0 process is observed, and the upper limits of Born cross sections σB(e+e−→γχc0) at 90% confidence level are reported.Received 6 July 2021Accepted 13 September 2021DOI:https://doi.org/10.1103/PhysRevD.104.092001Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBranching fractionHadron-hadron interactionsQuark modelParticles & Fields

Study of the Y(4660) from a light-quark perspective

In this paper, we try to reveal the structure of the $Y(4660)$ from the light-quark perspective. We study the dipion invariant mass spectrum and the helicity angular distributions of the $e^+ e^- \to Y(4660) \to \psi(2S) \pi^+\pi^-$ process. In particular, we consider the effects of different light-quark SU(3) eigenstates inside the $Y(4660)$. The strong pion-pion final-state interactions as well as the $K\bar{K}$ coupled channel in the $S$-wave are taken into account model independently by using dispersion theory. We find that the light-quark SU(3) octet state plays a significant role in this transition, implying that the $Y(4660)$ contains a large light-quark component and thus might not be a pure conventional charmonium state. In the fit scheme considering both the SU(3) singlet and SU(3) octet states, two solutions are found, and both solutions reproduce the $\pi\pi$ invariant mass spectra well. New measurement data with higher statistics in the future will be helpful to better distinguish these two solutions.

Charmonium and charmoniumlike states at the BESIII experiment.

Charmonium is a bound state of a charmed quark and a charmed antiquark, and a charmoniumlike state is a resonant structure that contains a charmed quark and antiquark pair but has properties that are incompatible with a conventional charmonium state. While operating at center-of-mass energies from 2 to 5 GeV, the BESIII experiment can access a wide mass range of charmonium and charmoniumlike states, and has contributed significantly in this field. We review BESIII results involving conventional charmonium states, including the first observation of the M1 transition ψ(2S) → γηc(2S) and the discovery of the ψ2(3823) state; and report on studies of charmoniumlike states, including the discoveries of the Zc(3900) and Zc(4020) tetraquark candidates, the resolution of the fine structure of the Y(4260) state, the discovery of the new production process e+e− → γX(3872) and the uncovering of strong evidence for the commonality among the X(3872), Y(4260) and Zc(3900) states. The prospects for further research at BESIII and proposed future facilities are also presented.

Decay Properties of Conventional and Hybrid Charmonium Mesons

In this paper, Schrodinger equation is numerically applied through non-relativistic potential model for deriving Spectrum, radial wave functions at origin, decay constants, lepton and photon decay widths for radial and orbital excited conventional as well as hybrid charmonium mesons. These calculated results are found in agreement with others theoretical results and with the experimental observations.

Nature of the Y(4260) : A light-quark perspective

The $Y(4260)$ has been one of the most puzzling pieces among the so-called $XYZ$ states. In this paper, we try to gain insights into the structure of the $Y(4260)$ from the light-quark perspective. We study the dipion invariant mass spectrum of the $e^+ e^- \to Y(4260) \to J/\psi \pi^+\pi^-$ process and the ratio of the cross sections ${\sigma(e^+e^- \to J/\psi K^+ K^-)}/{\sigma(e^+e^- \to J/\psi \pi^+\pi^-)}$. In particular, we consider the effects of different light-quark SU(3) eigenstates inside the $Y(4260)$. The strong pion-pion final-state interactions as well as the $K\bar{K}$ coupled channel in the $S$-wave are taken into account in a model-independent way using dispersion theory. We find that the SU(3) octet state plays a significant role in these transitions, implying that the $Y(4260)$ contains a large light-quark component. Our findings suggest that the $Y(4260)$ is neither a hybrid nor a conventional charmonium state, and they are consistent with the $Y(4260)$ having a sizeable $\bar D D_1$ component which, however, is not completely dominant.

Experimental Status of Conventional Charmonium Spectroscopy

Based on data samples taken by the BESIII, Belle, KEDR and LHCb experiments, many measurements on conventional charmonium spectroscopy were finished in the past years. Some of recent results, such as precise measurements of J/ψ and ψ(2S ) masses, the J/ψ decay width, the J/ψ and ψ(2S ) electronic widths, two-photon width of χc0,2 meson, the χc1,2 resonance parameters with the decays χc0,2 → J/ψµ+µ−, the ηc resonance parameters and observations of X(3823) and X*(3860), were reported.

Charmonium at BESIII

With large J/ψ and ψ(2S ) data samples, the BESIII Collaboration has performed many studies toward conventional charmonium states below energy 3.686 GeV, which provide information on the internal structure and the interactions of the mesons. In this proceeding, just a few of them, related to (1) OZI suppressed decay search or measurement, (2) “12% rule” test, and (3) theoretical different predictions test, is focused on.

Strong decays of higher charmonium states into open-charm meson pairs

The open-charm strong decays of higher charmonium states up to the mass of the $6P$ multiplet are systematically studied in the $^3P_0$ model. The wave functions of the initial charmonium states are calculated in the linear potential (LP) and screened potential (SP) quark model. The decay widths for most of the well-established charmonium states above the open-charm thresholds can be reasonably described. By comparing our quark model calculations with the experimental observations we also discuss the nature of some of the newly observed charmonium-like states. It is found that (i) the $\psi(4415)$ may favor the $\psi(4S)$ or $\psi_1(3D)$ assignment. There may exist two highly overlapping vector charmonium states around 4.4 GeV; (ii) In the LP model the $J^{PC}=1^{--}$ $Y(4660)$ resonance and the $J^{PC}=0^{++}$ $X(4500)$ resonance may be assigned as the $\psi(5S)$ and $\chi_{c0}(4P)$, respectively; (iii) The newly observed state $X^*(3860)$ can be assigned as the $\chi_{c0}(2P)$ state with a narrow width of about $30$ MeV; (iv) It seems to be difficult to accommodate the $X(4140)$ and $X(4274)$ states in the same potential model as excited $\chi_{c1}$ states. (v) The $X(3940)$ resonance can be assigned as the $\eta_c(3S)$ state; (vi) The vector charmonium-like states $Y(4230/4260,4360)$ and scalar $X(4700)$ cannot be described by any conventional charmonium states self-consistently in our model.

Bethe-Salpeter wave functions of ηc(1S, 2S) and ψ(1S, 2S) states: local-potential description of the charmonium system revisited

The quark potential models with an energy-independent central potential have been successful for understanding the conventional charmonium states especially below the open charm threshold. As one might consider, however, the interquark potential is in general energy-dependent, and its tendency gets stronger in higher lying states. Confirmation of whether the interquark potential is energy-independent is also important to verify the validity of the quark potential models. In this talk, we examine the energy dependence of the charmonium potential, which can be determined from the Bethe-Salpeter (BS) amplitudes of cc̅ mesons in lattice QCD.We first calculate the BS amplitudes of radially excited charmonium states, the ηc(2S) and ψ(2S) states, using the variational method and then determine both the quark kinetic mass and the charmonium potential within the HAL QCD method. Through a direct comparison of charmonium potentials determined from both the 1S and 2S states, we confirm that neither the central nor spin-spin potential shows visible energy dependence at least up to 2S state.

Can X(3915) be the tensor partner of the X(3872)?

It has been proposed recently (Phys. Rev. Lett.115 (2015) 022001) that the charmoniumlike state named X(3915) and suggested to be a 0++ scalar, is just the helicity-0 realisation of the 2++ tensor state χc2(3930). This scenario would call for a helicity-0 dominance, which were at odds with the properties of a conventional tensor charmonium, but might be compatible with some exotic structure of the χc2(3930). In this paper, we investigate, if such a scenario is compatible with the assumption that the χc2(3930) is a {D}^{ast }{overline{D}}^{ast } molecular state — a spin partner of the X(3872) treated as a shallow bound state. We demonstrate that for a tensor molecule the helicity-0 component vanishes for vanishing binding energy and accordingly for a shallow bound state a helicity-2 dominance would be natural. However, for the χc2(3930), residing about 100 MeV below the {D}^{ast }{overline{D}}^{ast } threshold, there is no a priori reason for a helicity-2 dominance and thus the proposal formulated in the above mentioned reference might indeed point at a molecular structure of the tensor state. Nevertheless, we find that the experimental data currently available favour a dominant contribution of the helicity-2 amplitude also in this scenario, if spin symmetry arguments are employed to relate properties of the molecular state to those of the X(3872). We also discuss what research is necessary to further constrain the analysis.

Analysis of the mass and width of Y(4274) as axialvector molecule-like state

In this article, we assign Y(4274) to the color octet–octet type axialvector molecule-like state with J^{PC}=1^{++} tentatively, and construct the color octet–octet type axialvector current to study its mass and width with the QCD sum rules in details. The predicted mass favors assigning the Y(4274) to a color octet–octet type molecule-like state, but the predicted width strongly disfavors assigning the Y(4274) to the color octet–octet type molecule-like state. The Y(4274) may be the conventional charmonium state chi _{c1}(mathrm 3P), and it is important to observe the decay Y(4274)rightarrow J/psi omega to diagnose the nature of Y(4274).

Charmonium spectrum and electromagnetic transitions with higher multipole contributions

The charmonium spectrum is calculated with two nonrelativistic quark models, the linear potential model and the screened potential model. Using the obtained wavefunctions, we evaluate the electromagnetic transitions of charmonium states up to $4S$ multiplet. The higher multipole contributions are included by a multipole expansion of the electromagnetic interactions. Our results are in reasonable agreement with the measurements. As conventional charmonium states, the radiative decay properties of the newly observed charmonium-like states, such as $X(3823)$, $X(3872)$, $X(4140/4274)$, are discussed. The $X(3823)$ as $\psi_2(1D)$, its radiative decay properties well agree with the observations. From the radiative decay properties of $X(3872)$, one can not exclude it as a $\chi_{c1}(2P)$ dominant state. We also give discussions of possibly observing the missing charmonium states in radiative transitions, which might provide some useful references to look for them in forthcoming experiments. The higher multipole contributions to the electromagnetic transitions are analyzed as well. It is found that the higher contribution from the magnetic part could give notable corrections to some E1 dominant processes by interfering with the E1 amplitudes. Our predictions for the normalized magnetic quadrupole amplitudes $M_2$ of the $\chi_{c1,2}(1P)\to J/\psi \gamma$ processes are in good agreement with the recent CLEO measurements.

Canonical description of the new LHCb resonances

The LHCb Collaboration has recently observed four $J/\psi\phi$ structures called $X(4140)$, $X(4274)$, $X(4500)$ and $X(4700)$ in the $B^{+}\to J/\psi\phi K^{+}$ decays. We study them herein using a nonrelativistic constituent quark model in which the degrees of freedom are quark-antiquark and meson-meson components. The $X(4140)$ resonance appears as a cusp in the $J/\psi\phi$ channel due to the near coincidence of the $D_{s}^{\pm}D_{s}^{\ast\pm}$ and $J/\psi\phi$ mass thresholds. The remaining three $X(4274)$, $X(4500)$ and $X(4700)$ appear as conventional charmonium states with quantum numbers $3^{3}P_{1}$, $4^{3}P_{0}$ and $5^{3}P_{0}$, respectively; and whose masses and widths are slightly modified due to their coupling with the corresponding closest meson-meson thresholds. A particular feature of our quark model is a lattice-based screened linear confining interaction that has been constrained in the light quark sector and usually produces higher excited heavy-quark states with lower masses than standard quark model predictions.

Exotic vector charmonium and its leptonic decay width**The numerical calculations were carried out on Tianhe-1A at the National Supercomputer Center (NSCC) in Tianjin and the GPU cluster at Hunan Normal University. This work is supported in part by the National Science Foundation of China (NSFC) (11575196, 11575197, 11335001, 11405053), Y.C. and Z.L. also acknowledge the support of NSFC (11261130311) (CRC

We propose a novel type of interpolating field operator, which manifests the hybrid-like configuration that the charm quark-antiquark pair recoils against gluonic degrees of freedom. A heavy vector charmonium-like state with a mass of 4.33(2),GeV is disentangled from the conventional charmonium states in the quenched approximation. This state has affinity for the hybrid-like operators but couples less to the relevant quark bilinear operator. We also try to extract its leptonic decay constant and give a tentative upper limit that it is less than one tenth of that of J/ψ, which corresponds to a leptonic decay width about dozens of eV. The connection of this state with X(4260) is also discussed.

Study of the XYZ states at the BESIII

With its unique data samples at energies of 3.8–4.6 GeV, the BESIII experiment made a significant contribution to the study of charmonium and charmonium-like states, i.e., the XYZ states.We review the results for observations of the Z c (3900) and Z c (4020) states, the X(3872) in e + e - annihilation, and charmonium ?(1 3 D 2) state, as well as measurements of the cross-sections of ?? cJ and ?J/?, and the search for e + e - ? ?? cJ and ?Y (4140). We also present data from BESIII that may further strengthen the study of the XYZ and conventional charmonium states, and discuss perspectives on future experiments.

Coulomb gauge approach for charmonium meson and hybrid radiative transitions

We consider the lowest order interaction of the Foldy-Wouthuysen QED and QCD Hamiltonian in the Coulomb gauge approach, to describe radiative transitions between conventional and hybrids charmonium mesons. The results are compared to potential quark models and lattices calculations.