Hidden-charm Tetraquark States Research Articles

The ground states of hidden-charm tetraquarks and their radial excitations

Inspired by the great progress in the observations of charmonium-like states in recent years, we perform a systematic analysis about the ground states and the first radially excited states of qcq¯c¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$qc\\bar{q}\\bar{c}$$\\end{document} (q = u/d and s) tetraquark systems. Their mass spectra, root mean square (r.m.s.) radii and radial density distributions are predicted within the framework of relativized quark model. By comparing with experimental data, some potential candidates for hidden-charm tetraquark states are suggested. For qcq¯c¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$qc\\bar{q}\\bar{c}$$\\end{document} (q = u/d) system, if Zc(3900)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_{c}(3900)$$\\end{document} is supposed to be a compact tetraquark state with JPC=1+-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J^{PC}=1^{+-}$$\\end{document}, Z(4430) can be interpreted as the first radially excited states of Zc(3900)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_{c}(3900)$$\\end{document}. Another broad structure Zc(4200)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_{c}(4200)$$\\end{document} can also be explained as a partner of Zc(3900)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_{c}(3900)$$\\end{document}, and it arise from a higher state with JPC=1+-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J^{PC}=1^{+-}$$\\end{document}. In addition, theoretical predictions indicate that the possible assignments for X(3930), X(4050) and X(4250) are low lying 0++\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0^{++}$$\\end{document} tetraquark states. As for the scs¯c¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$sc\\bar{s}\\bar{c}$$\\end{document} system, X(4140) and X(4274) structures can be interpreted as this type of tetraquark states with JPC=1++\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J^{PC}=1^{++}$$\\end{document}, and X(4350) can be described as a scs¯c¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$sc\\bar{s}\\bar{c}$$\\end{document} tetraquark with JPC=0++\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J^{PC}=0^{++}$$\\end{document}. With regard to qcs¯c¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$qc\\bar{s}\\bar{c}$$\\end{document} (q = u/d) system, we find two potential candidates for this type of tetraquark, which are Zcs(4000)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_{cs}(4000)$$\\end{document} and Zcs(4220)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_{cs}(4220)$$\\end{document} structures. The measured masses of these two structures are in agreement with theoretical predictions for the 1+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1^{+}$$\\end{document} state.

Ground states and first radial excitations of vector tetraquark states with explicit P-waves via QCD sum rules* *Supported by the National Natural Science Foundation of China (12175068)

In this study, we chose the diquark-antidiquark type four-quark currents with an explicit P-wave between the diquark and antidiquark pairs to study the ground states and first radial excitations of the hidden-charm tetraquark states with quantum numbers . We also obtained the lowest vector tetraquark masses and made possible assignments of the existing states. There indeed exists a hidden-charm tetraquark state with at an energy of approximately 4.75 GeV as the first radial excitation that accounts for the BESIII data.

Strong decays of the vector tetraquark states with the masses about 4.5 GeV via the QCD sum rules

We suppose that there exist three vector hidden-charm tetraquark states with the JPC=1−− at the energy about 4.5GeV, and investigate the two-body strong decays systematically. We obtain thirty QCD sum rules for the hadronic coupling constants based on rigorous quark-hadron duality, then obtain the partial decay widths, therefore the total widths approximately, which are compatible with the experimental data of the Y(4500) from the BESIII collaboration. The Y(4500) may be one vector tetraquark state having three main Fock components, or consists of three different vector tetraquark states. We can search for the typical decays Y→D¯10D0−D¯0D102, D¯1−D+−D¯−D1+2, D¯00D⁎0−D¯⁎0D002, D¯0−D⁎+−D¯⁎−D0+2, ηcω, J/ψω to diagnose the nature of the Y(4500).

0– – hidden-heavy tetraquark states via QCD sum rules* *Supported in part by the National Natural Science Foundation of China(12247113), the Project funded by China Postdoctoral Science Foundation (2022M723117), and the Specific Fund of Fundamental Scientific Research Operating Expenses for Undergraduate Universities in Liaoning Province, China (2024)

In this study, we evaluated the mass spectra of the prospective hidden-charm and hidden-bottom tetraquark states in molecular configuration via QCD sum rules. In our calculation, the nonperturbative condensate contributions are considered up to dimension eight in operator product expansion. It is found that there could exist 4 possible hidden-charm tetraquark states with masses , , , and GeV. Their corresponding hidden-bottom partners are found lying at , , , and GeV, respectively. The possible tetraquark decay modes were analyzed, which are expected to be measured in BESIII, BELLEII, and LHCb experiments.

An analysis of Gursey-Radicati mass formula for tetraquark systems

In this work, the extended Gursey-Radicati mass formula is used to analyze the masses of the tetraquark system with configurations /, /, / and (Q = c, b). The discovery of two singly heavy tetraquark structures and at LHCb acts as a motivation for this work. They were observed in the and invariant mass spectra in two B-decay processes and , respectively. By using the SU(3) f flavor representation, we classified the recently observed singly heavy tetraquarks having quark content and in octet representation with J P value 0+ and forming the isospin triplet(I = 1). Our thorough comparison of mass spectra with both experimental and theoretical data demonstrates reasonable agreement. Further, decay channels and widths for the hidden-charm tetraquark states are computed in the framework of the diquark-antidiquark model. Our results may provide useful enlightenment for future experimental studies.

Investigation of the tetraquark states in the improved chromomagnetic interaction model* *T. Guo is supported by the Scientific Research Foundation of Chengdu University of Technology (10912-KYQD2022-09557); J. Li and L. He are supported by the National Natural Science Foundation of China (11890712); J. Zhao is supported by the European Union's Horizon 2020 research and innovation program (824093 (STRONG-2020))

In the framework of the improved chromomagnetic interaction model, we complete a systematic study of the S-wave tetraquark states (, and ) with different quantum numbers: , , and . The mass spectra of tetraquark states are predicted, and the possible decay channels are analyzed by considering both the angular momentum and -parity conservation. The recently observed hidden-charm tetraquark states with strangeness, such as , , and , can be well explained in our model. Additionally, according to the wave function of each tetraquark state, we find that the low-lying states of each configuration have a large overlap to the and meson basis, instead of the and meson basis. This indicates that one can search these tetraquark states in future experiments via the channel of and mesons.

Magnetic moments of the vector hidden-charm tetraquark states

The magnetic moments of the vector hidden-charmed tetraquark states that have been observed and can be expected to be observed experimentally have been determined using the light-cone sum rules taking into account the diquark-antidiquark structure with the quantum numbers $ J^{PC} = 1^{--}$ and $ J^{PC} = 1^{-+}$. Since these states are considered to have different flavors of light quarks, they have nonzero magnetic moments. The results obtained in this study can be checked for consistency by various methods. The magnetic moments of hadrons encompass useful knowledge about the distribution of charge and magnetization inside hadrons, which helps us to understand their geometrical shapes.

Analysis of the pseudoscalar hidden-charm tetraquark states with the QCD sum rules

In this work, we take all the color-antitriplet diquarks, such as the scalar, pseudoscalar, vector, axialvector and tensor diquarks, as the basic constituents to construct the local pseudoscalar four-quark currents without importing the explicit P-waves to implement the negative-parity, and investigate the mass spectroscopy of the pseudoscalar hidden-charm tetraquark states without strange, with strange and with hidden-strange in the framework of the QCD sum rules in a consistent and comprehensive way. We obtain the lowest mass 4.56±0.08GeV for the pseudoscalar tetraquark state with the symbolic quark constituents cc¯ud¯, which is much larger than the experimental value 4239±18−10+45MeV extracted by the LHCb collaboration.

Analysis of the vector hidden-charm tetraquark states without explicit P-waves via the QCD sum rules

In the present work, we adopt the scalar, pseudoscalar, vector, axialvector and tensor (anti)diquark operators as the elementary building blocks to construct vector and tensor local four-quark currents without introducing explicit P-waves, and explore the mass spectrum of the vector hidden-charm tetraquark states via the QCD sum rules comprehensively, and revisit the interpretations of the existing Y states in the scenario of vector tetraquark states. We resort to the energy scale formula to enhance the pole contributions and improve the convergent behaviors of the operator product expansion, and we should bear in mind that the predictions are rather sensitive to the particular energy scales which obey the uniform/same constraint. The predicted vector hidden-charm tetraquark states can be confronted to the experimental data in the future.

Magnetic dipole moments of the Zc(4020)+ , Zc(4200)+ , Zcs(4000)+ and Zcs(4220)+ states in light-cone QCD

The magnetic dipole moments of the $Z_{c}(4020)^+$, $Z_{c}(4200)^+$, $Z_{cs}(4000)^{+}$ and $Z_{cs}(4220)^{+}$ states are extracted in the framework of the light-cone QCD sum rules. In the calculations, we use the hadronic molecular form of interpolating currents, and photon distribution amplitudes to get the magnetic dipole moment of $Z_{c}(4020)^+$, $Z_{c}(4200)^+$, $Z_{cs}(4000)^{+}$ and $Z_{cs}(4220)^{+}$ tetraquark states. The magnetic dipole moments are obtained as $\mu_{Z_{c}} = 0.66^{+0.27}_{-0.25}$, $\mu_{Z^{1}_{c}}=1.03^{+0.32}_{-0.29}$, $\mu_{Z_{cs}}=0.73^{+0.28}_{-0.26}$, $\mu_{Z^1_{cs}}=0.77^{+0.27}_{-0.25}$ for the $Z_{c}(4020)^+$, $Z_{c}(4200)^+$, $Z_{cs}(4000)^{+}$ and $Z_{cs}(4220)^{+}$ states, respectively. We observe that the results obtained for the $Z_{c}(4020)^+$, $Z_{c}(4200)^+$, $Z_{cs}(4000)^{+}$ and $Z_{cs}(4220)^{+}$ states are large enough to be measured experimentally. As a by product, we predict the magnetic dipole moments of the neutral $Z_{cs}(4000)$ and $Z_{cs}(4220)$ states. The results presented here can serve to be helpful knowledge in experimental as well as theoretical studies of the properties of hidden-charm tetraquark states with and without strangeness.

Implications of the [formula omitted] and [formula omitted] as two different states

Recently, the hidden charm tetraquark states Zcs(3985) and Zcs(4000) with strangeness were observed by the BESIII and LHCb collaborations, respectively, which are great breakthroughs for exploring exotic quantum chromodynamics (QCD) structures. The first and foremost question is whether they are the same state. In this work, we explore the implications of the narrower state Zcs(3985) in BESIII and the wider one Zcs(4000) in LHCb as two different states. Within a solvable nonrelativistic effective field theory, we include the possible violations of heavy quark spin symmetry and SU(3) flavor symmetry in a comprehensive approach. If Zcs(3985) and Zcs(4000) are two different states, our results show that Zcs(4000)/Zcs(3985) is the pure (|D‾s∗D〉+/-|D‾sD∗〉)/2 state, and the SU(3) flavor partner of Zc(3900) is Zcs(4000) rather than the Zcs(3985). Another two important consequences are the existence of a tensor D‾s∗D∗ resonance with mass about 4126 MeV and width 13 MeV, and the suppression of the decay mode Zcs(3985)→J/ψK. The two consequences can be tested in experiments and distinguish the two-state interpretation from the one-state scheme.

Analysis of Zcs (3985) as the axialvector tetraquark state * *Supported by National Natural Science Foundation of China (11775079)

In this study, we choose the scalar and axialvector diquark operators in the color antitriplet as the fundamental building blocks to construct four-quark currents and investigate the diquark-antidiquark type axialvector tetraquark states in the framework of the QCD sum rules. The predicted tetraquark mass is in excellent agreement with the experimental value from the BESIII collaboration, which supports identifying as the cousin of with quantum numbers . We take into account the light flavor mass-breaking effect to estimate the mass spectrum of the diquark-antidiquark type hidden-charm tetraquark states with strangeness according to previous studies.

Analysis of the hidden-charm tetraquark mass spectrum with the QCD sum rules

In this article, we take the pseudoscalar, scalar, axialvector, vector, tensor (anti)diquark operators as the basic constituents, and construct the scalar, axialvector and tensor tetraquark currents to study the mass spectrum of the ground state hidden-charm tetraquark states with the QCD sum rules in a comprehensive way. We revisit the assignments of the $X$, $Y$, $Z$ states, such as the $X(3860)$, $X(3872)$, $X(3915)$, $X(3940)$, $X(4160)$, $Z_c(3900)$, $Z_c(4020)$, $Z_c(4050)$, $Z_c(4055)$, $Z_c(4100)$, $Z_c(4200)$, $Z_c(4250)$, $Z_c(4430)$, $Z_c(4600)$, etc in the scenario of tetraquark states in a consistent way based on the QCD sum rules. Furthermore, we discuss the feasibility of applying the QCD sum rules to study the tetraquark states and tetraquark molecular states (more precisely, the color-singlet-color-singlet type tetraquark states), which begin to receive contributions at the order $\mathcal{O}(\alpha_s^0)$, not at the order $\mathcal{O}(\alpha_s^2)$.

The scalar and pseudoscalar hidden-charm tetraquark states with QCD sum rules

Based on the diquark configuration, we construct the diquark–antidiquark interpolating tetraquark currents with [Formula: see text] and [Formula: see text], which can couple to the scalar and pseudoscalar tetraquark states, respectively, since they are not conserved currents. Then, we investigate their two-point correlation functions including the contributions of the vacuum condensates up to dimension-10 and extract the masses and pole residues of the tetraquark states with [Formula: see text] and [Formula: see text] through the QCD sum rule approach. The predicted masses can be confronted with the experimental data in the future. Moreover, we briefly discuss the possible decay patterns of the tetraquark states.

Scalar Hidden-Charm Tetraquark States with QCD Sum Rules**Supported by the National Natural Science Foundation of China under Grant No. 11375063, the Fundamental Research Funds for the Central Universities under Grant Nos. 2016MS155 and 2016MS133

In this article, we study the masses and pole residues of the pseudoscalar-diquark-pseudoscalar-antidiquark type and vector-diquark-vector-antidiquark type scalar hidden-charm () tetraquark states with QCD sum rules by taking into account the contributions of the vacuum condensates up to dimension-10 in the operator product expansion. The predicted masses can be confronted with the experimental data in the future. Possible decays of those tetraquark states are also discussed.

Analysis of the tensor–tensor type scalar tetraquark states with QCD sum rules

In this article, we study the ground states and the first radial excited states of the tensor-tensor type scalar hidden-charm tetraquark states with the QCD sum rules. We separate the ground state contributions from the first radial excited state contributions unambiguously, and obtain the QCD sum rules for the ground states and the first radial excited states, respectively. Then we search for the Borel parameters and continuum threshold parameters according to four criteria and obtain the masses of the tensor-tensor type scalar hidden-charm tetraquark states, which can be confronted to the experimental data in the future.

Searching for hidden-charm baryonium signals in QCD sum rules

We give an explicit QCD sum rule investigation to hidden-charm baryonium states with the quark content $u\bar u d\bar d c\bar c$, spin $J=0/1/2/3$, and of both positive and negative parities. We systematically construct the relevant local hidden-charm baryonium interpolating currents, which can actually couple to various structures, including hidden-charm baryonium states, charmonium states plus two pions, and hidden-charm tetraquark states plus one pion, etc. We do not know which structure these currents couple to at the beginning, but after sum rule analyses we can obtain some information. We find some of them can couple to hidden-charm baryonium states, using which we evaluate the masses of the lowest-lying hidden-charm baryonium states with quantum numbers $J^P=2^-/3^-/0^+/1^+/2^+$ to be around 5.0 GeV. We suggest to search for hidden-charm baryonium states, especially the one of $J=3^-$, in the $D$-wave $J/\psi \pi \pi$ and $P$-wave $J/\psi \rho$ and $J/\psi \omega$ channels in this energy region.

Hidden charm octet tetraquarks from a diquark-antidiquark model

Four exotic charmonium-like states, i.e. $X(4140)$, $X(4274)$, $X(4500)$, and $X(4700)$, have been observed very recently by LHCb Collaboration in the decay process $B^+\to J/\psi \phi K^+$ using the 3${\rm fb}^{-1}$ data of $p\bar p$ collision at $\sqrt s= 7$ and $8$ TeV. In this paper, we investigate systematically the properties of hidden charm tetraquark states. The hidden charm tetraquarks form an octet configuration and a singlet configuration according to flavor $SU(3)$ symmetry. Based on a diquark-antidiquark model, the hidden charm tetraquarks spectra are given. The previous XYZ exotic states altogether with the newly ones $X(4140)$, $X(4274)$, $X(4500)$, and $X(4700)$, can be well classified into certain representations. The spin-parities and masses of the XYZ are predicted, most of which are in agreement with the data. We particularly find that $Z_c(4430)$ may be treated as the first radial excitation of $Z_c(3900)$, while the $Y(1^{--})$ states can be obtained by the first orbital excitation of the $X/Z$ states. Besides, we calculate the decay widths of the hidden charm tetraquarks into two charmed mesons. This work gives a general tetraquark description for the XYZ states, which is helpful to uncover their inner structures.

The lowest hidden charmed tetraquark state from QCD sum rules

In this paper, we study the [Formula: see text] type scalar tetraquark state [Formula: see text] in detail with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension 10 in the operator product expansion, and obtain the value [Formula: see text], which is the lowest mass for the hidden charmed tetraquark states from the QCD sum rules. Furthermore, we calculate the hadronic coupling constants GZcηcπand GZcDDwith the three-point QCD sum rules, then study the strong decays Zc→ηcπ, DD, and observe that the total width ΓZc≈21 MeV . The present predictions can be confronted with the experimental data in the future at the BESIII, LHCb and Belle-II.

Analysis of the $$Z_c(4020)$$ Z c ( 4020 ) , $$Z_c(4025)$$ Z c ( 4025 ) , $$Y(4360)$$ Y ( 4360 ) , and $$Y(4660)$$ Y ( 4660 ) as vector tetraquark states with QCD sum rules

In this article, we distinguish the charge conjugations of the interpolating currents, calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and study the masses and pole residues of the $J^{PC}=1^{-\pm}$ hidden charmed tetraquark states with the QCD sum rules. We suggest a formula $\mu=\sqrt{M^2_{X/Y/Z}-(2{\mathbb{M}}_c)^2}$ with the effective mass ${\mathbb{M}}_c=1.8\,\rm{GeV}$ to estimate the energy scales of the QCD spectral densities of the hidden charmed tetraquark states, which works very well. The numerical results disfavor assigning the $Z_c(4020)$, $Z_c(4025)$, $Y(4360)$ as the diquark-antidiquark (with the Dirac spinor structure $C-C\gamma_\mu$) type vector tetraquark states, and favor assigning the $Z_c(4020)$, $Z_c(4025)$ as the diquark-antidiquark type $1^{+-}$ tetraquark states. While the masses of the tetraquark states with symbolic quark structures $c\bar{c}s\bar{s}$ and $c\bar{c}(u\bar{u}+d\bar{d})/\sqrt{2}$ favor assigning the $Y(4660)$ as the $1^{--}$ diquark-antidiquark type tetraquark state, more experimental data are still needed to distinguish its quark constituents. There are no candidates for the positive charge conjugation vector tetraquark states, the predictions can be confronted with the experimental data in the future at the BESIII, LHCb and Belle-II.