Tetraquark States Research Articles

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.

Production of in heavy ion collisions* *Supported by Guangdong Major Project of Basic and Applied Basic Research (2020B0301030008), the National Natural Science Foundation of China (12105107) and Science and Technology Program of Guangzhou (2019050001)

The yields of with its two possible configurations, i.e., the hadronic molecular state and tetraquark state, for Pb-Pb collisions at is studied. A volume effect is found from the centrality distribution of , which could help to distinguish the inner structure of . We also show the rapidity and the transverse momentum distributions of production as well as its elliptic flow coefficient as a function of the transverse momentum.

Possible triply heavy tetraquark states in a chiral quark model

In the present work, the triply heavy tetraquarks states $QQ\overline{Q}\overline{q}$ with $Q=(c,b)$ and $q=(u,d,s)$ with all possible quantum numbers are systematically investigated in the framework of the chiral quark model with the resonating ground method. Two kinds of structures, including the meson-meson configuration (the color-singlet channels and the hidden-color channels) and the diquark-antidiquark configuration (the color sextet-antisextet and the color triplet-antitriplet), are considered. In the considered system, several bound states are obtained for the $cc\overline{c}\overline{{q}^{\ensuremath{'}}}$, $bb\overline{c}\overline{{q}^{\ensuremath{'}}}$, and $bc\overline{c}\overline{q}$ tetraquarks. From the present estimations, we find that the coupled-channel effect is of great significance for forming below-threshold tetraquark states, which are stable for strong decays.

Regge trajectories of tetraquarks and pentaquarks with massive quarks in the flux tube model

In recent years, many tetraquarks and pentaquarks have been discovered by various experimental groups and [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are some of the interesting observed tetraquark and pentaquark states. The Regge trajectories of some such states are studied in view of the flux tube model of hadrons with finite quark masses. The effect of flux tube (or string) length variation on the Regge trajectories of these states is analyzed in detail. It is observed that for a fixed angular momentum, the string length has a constant value. Some other states are also proposed and the results obtained are then compared with the studies by others. Our findings correspond rather well with those of other researchers and with those of the experiment.

Exotic states with configuration

In the framework of a non-relativistic quark model, we have calculated the masses of the (Q = c, b, s and ) tetraquark states. Using the linear and quadratic confinement potentials inside a Cornell-type potential along with all possible spin and color configurations, the Schrödinger equation masses of these tetraquark states have been calculated. Based on our numerical analysis, linear confinement and quadratic confinement produce acceptable results. Models that use linear confinement estimate charmonium-like tetraquark mass close to experimental data, as well as bottomonium-like tetraquark mass below the threshold of their meson–meson channels.

D-wave excited tetraquark states with and * *Supported by the National Natural Science Foundation of China (12175318), the National Key R & D Program of China (2020YFA0406400), the Natural Science Foundation of Guangdong Province of China (2022A1515011922), and the Fundamental Research Funds for the Central Universities

We study the mass spectra of D-wave excited tetraquark states with and in both symmetric and antisymmetric color configurations using the QCD sum rule method. We construct the D-wave diquark-antidiquark type of tetraquark interpolating currents in various excitation structures with . Our results support the interpretation of the recently observed resonance as a D-wave tetraquark state with in the or excitation mode, although some other possible excitation structures cannot be excluded exhaustively within theoretical errors. Moreover, our results provide the mass relations and for the positive and negative -parity D-wave tetraquarks, respectively. We suggest searching for these possible D-wave tetraquarks in both the hidden-charm channels and , as well as open-charm channels such as and .

1+ XTZ States within QCD Sum Rules

We present improved estimates of the couplings, masses and mass ratios of the XQ, ZQ and TQQq¯q¯′ states (Q≡c,b; q,q′≡u,d,s) using (inverse) QCD Laplace sum rules (LSR), their ratios R and double ratios (DRSR), within stability criteria. We conclude that the observed Xc(3872) and Zc(3900) are tetramoles states (superposition of quasi-degenerated molecule and tetraquark states having similar couplings to the currents) with the predicted masses: MTXc=3876(44)MeV and MTZc=3900(42)MeV. We also do an extensive analysis of the four-quark nature of different TQQq¯q¯′ axial-vector states. Then, combining R and DRSR, we reanalyze the observed state Xc(3872) and we obtain a precise prediction of MTcc1+=3886(6)MeV. Extending to the beauty sector, we find the results: MTZb=10579(99)MeV and MXb=10545(131)MeV. Finally, we confront our combined LSR ⊕ DRSR results with the ones from some other approaches (lattices and quark models).

Molecular tetraquarks and pentaquarks in chiral effective field theory

We studied the DD¯⁎/D¯D⁎, D⁎D¯⁎, D¯sD⁎/D¯s⁎D, BB¯⁎/B¯B⁎ and B⁎B¯⁎ di-hadron interactions in chiral effective field theory (χEFT) up to the next-to-leading (NLO) order. The above-threshold tetraquark states Zc(3900), Zc(4020), Zcs(3985), Zb(10610), Zb(10650) can be explained as the corresponding di-hadron resonances, respectively. We also studied the Σc(⁎)D¯(⁎) interactions to investigate the three hidden-charm pentaquarks Pc(4312), Pc(4440) and Pc(4457). We further used the parameters fixed from the Pc states to predict the possible molecular states in ΞcD¯(⁎), Ξc′D¯(⁎) and Ξc⁎D¯(⁎) systems. Our predictions of the ΞcD¯(⁎) bound states are very consistent with two new near-threshold structures recently observed by the LHCb Collaboration.

Electromagnetic form factors of the Bc-like tetraquarks: Molecular and diquark-antidiquark pictures

In this study, we use the molecular and diquark-antidiquark tetraquark pictures to investigate magnetic and quadrupole moments of the Bc-like ground state tetraquarks with the QCD light-cone sum rules with quantum numbers JP=1+. In the numerical analysis, to obtain the magnetic and quadrupole moments of Bc-like tetraquark states molecular and diquark-antidiquark forms of interpolating currents, and photon distribution amplitudes have been used. The magnetic moments are acquired as μZucu¯b¯Mol=1.18−0.40+0.52μN, μZucu¯b¯Di=3.05−0.95+1.19μN, μZdcd¯b¯Mol=0.32−0.10+0.18μN, and μZdcd¯b¯Di=2.38−0.75+0.95μN. The hadrons' magnetic and quadrupole moments are another fundamental observable as their mass, which provides information on the underlying quark structure and dynamics. The results obtained in both pictures are quite different from each other. Any experimental measurement of the magnetic moments can provide an understanding of the internal structure of these states. We get nonzero but small values for the quadrupole moments of Bc-like tetraquark states showing non-spherical charge distributions. Hopefully, the examinations given in this study will be helpful to an experimental search of them, which will be an interesting research subject.

The strong coupling gXJ/ψϕ of X(4700)→J/ψϕ in the light-cone sum rules

We assign the scalar tetraquark and the D-wave tetraquark state for X(4700) and calculate the width of the decay X(4700)→J/ψϕ within the framework of light-cone sum rules. The strong coupling gXJ/ψϕ is obtained by considering the technique of soft-meson approximation. We also investigate the mass and the decay constant of X(4700) in the framework of SVZ sum rules. Our prediction for the mass is in agreement with the experimental measurement. For the decay width of X(4700)→J/ψϕ, if we assigns X(4700) as a scalar csc¯s¯ tetraquark state, we obtain Γ=(109−24+35) MeV. On the contrary, if X(4700) is assigned as a D-wave tetraquark state, we obtain Γ=(17.1−4.0+6.2) MeV which is much smaller than the scalar one.

X(3872) and Tcc : Structures and productions in heavy ion collisions

We argue why the recently observed ${T}_{cc}$ could either be a compact multiquark configuration or a loosely bound molecular configuration composed of charmed mesons, whereas the $X(3872)$ is most likely a molecular configuration. The argument is based on different short range interactions for these tetraquark states coming from the color-color and color-spin interaction in a quark model, and the presence of a common strong $D$-wave mixing at larger distance similar to the deuteron case, which for the molecular configurations leads to large sizes. Such an analogy at large distance allows us to calculate the transverse momentum dependence of the loosely bound molecular configuration of tetraquarks produced in heavy ion collisions using the coalescence model that successfully reproduces the deuteron data using the proton spectra. The ratio of the integrated $X(3872)$ yield obtained from our method to the $\ensuremath{\psi}(2S)$ yield obtained from the statistical hadronization model method is calculated to be $0.806\ifmmode\pm\else\textpm\fi{}0.234$, which is a factor of 2.47 larger than that obtained by using statistical model predictions for both particles and in line with the data from the CMS experiment. As the previously calculated transverse momentum distribution of the ${T}_{cc}$ assuming the structure to be a compact multiquark configuration is markedly different, experimental measurements of the transverse distribution of the tetraquark states will discriminate between their two possible structures.

Discussion on Scalar Meson a0(980) as a Tetraquark State with the QCD Sum Rules including the Contribution from Instanton

Discussion on Scalar Meson <i>a</i>₀(980) as a Tetraquark State with the QCD Sum Rules including the Contribution from Instanton

Semi-inclusive electroproduction of hidden-charm and double-charm hadronic molecules

The semi-inclusive electroproduction of exotic hadrons, including the $T_{cc}$, $P_{cs}$, and hidden-charm baryon-antibaryon states, is explored under the assumption that they are $S$-wave hadronic molecules of a pair of charmed hadrons. We employ the Monte Carlo event generator Pythia to produce the hadron pairs and then bind them together to form hadronic molecules. With the use of such a production mechanism, the semi-inclusive electroproduction rates are estimated at the order-of-magnitude level. Our results indicate that a larger number of $P_{cs}$ states and $\Lambda_c\bar{\Lambda}_c$ molecules can be produced at the proposed electron-ion colliders in China (EicC) and in the US (EIC). The results also suggest that the $T_{cc}$ states and other hidden-charm baryon-antibaryon states can be searched for at EIC. Besides, the potential 24-GeV upgrade of the Continuous Beam Accelerator Facility at the Thomas Jefferson National Accelerator Facility can play an important role in the search for the hidden-charm tetraquark and pentaquark states due to its high luminosity.

Fragmentation production of fully-charmed tetraquarks at the LHC

The $X(6900)$ resonance, very recently discovered in the double-$J/\psi$ channel at LHCb experiment, has spurred intensive interest in unravelling the nature of the fully charmed tetraquark state. The aim of this paper is to present a model-independent theoretical framework to study the inclusive production of this novel species of exotic hadrons, the resonances composed of four heavy quark (commonly referred to as $T_{4c}$), at large $p_T$ in hadron collision experiments. Appealing to asymptotic freedom and the fact $m_c\gg \Lambda_{\rm QCD}$, we propose that the nonpertubative yet universal gluon-to-$T_{4c}$ fragmentation function, can be decomposed into the product of the perturbatively calculable short-distance coefficient and the long-distance NRQCD matrix elements. We compute the short-distance coefficient at lowest-order in $\alpha_s$ and velocity expansion. Adopting the diquark ansatz to roughly estimate those not-yet-known NRQCD matrix elements, together with the standard QCD factorization theorem, we predict the differential production rates for the $T_{4c/4b}(0^{++})$ and $T_{4c/4b}(2^{++})$ at large $p_T$ in $pp$ collision, which eagerly awaits the confrontation with the future LHC experiments.

Discovery of Tcs¯0a(2900)0,++ implies new charmed-strange pentaquark system

Inspired by the very recently discovered tetraquark states $T_{c\bar s 0}^a(2900)^{0,++}$ from the LHCb Collaboration, we predict the existence of a new charmed-strange pentaquark system, $c\bar s nnn$, which is closely connected to $c\bar s n\bar n$ by exchanging $\bar n$ into $nn$ with $n=u,d$. Especially, it is suggested to experimentally search for the predicted new pentaquark system via the weak decays of $B$ mesons or $b$-baryons, with the support from the study of the mass spectrum and the decay properties. The predicted new pentaquark system must attract extensive attention from experimentalists and theorists when it constructs the ``particle zoo 2.0" in the near future.

Spectrum of the S-wave fully-heavy tetraquark states

In present work, spectrum of the S-wave fully-heavy tetraquark states QQbar{Q}bar{Q} (Q=c,b), i.e., ccbar{c}bar{c}, bbbar{b}bar{b}, ccbar{b}bar{b}/bbbar{c}bar{c}, bcbar{c}bar{c}/ ccbar{b}bar{c}, bbbar{c}bar{b}/cbbar{b}bar{b}, and bcbar{b}bar{c} are systematically investigated within a nonrelativistic constituent quark model, in which the instanton-induced and one-gluon-exchange interactions are taken into account as the residual spin-dependent hyperfine interaction. Our results show that the states with ccbar{c}bar{c} and bbbar{b}bar{b} components could be located around 6500 MeV and 19,200 MeV, respectively. Based on our calculations, the new X(6900) state observed by LHCb may be not a ground ccbar{c}bar{c} tetraquark state, while it could be an orbitally or radially excited state of ccbar{c}bar{c} system. On the other hand, the recently reported X(6600) state by CMS and ATLAS can be explained as a ground ccbar{c}bar{c} tetraquark state with spin-parity J^{PC} =0^{++}.

Two-photon decay of X(6900) from light-by-light scattering at the LHC

The LHCb Collaboration has recently discovered a structure around 6.9 GeV in the double-$J/\ensuremath{\psi}$ mass distribution, possibly a first fully charmed tetraquark state $X(6900)$. Based on vector-meson dominance (VMD) such a state should have a significant branching ratio for decaying into two photons. We show that the recorded LHC data for the light-by-light scattering may indeed accommodate for such a state, with a $\ensuremath{\gamma}\ensuremath{\gamma}$ branching ratio of order of ${10}^{\ensuremath{-}4}$, which is larger even than the value inferred by the VMD. The spin-parity assignment ${0}^{\ensuremath{-}+}$ is in better agreement with the VMD prediction than ${0}^{++}$, albeit not significantly at the current precision. Further light-by-light scattering data in this region, clarifying the nature of this state, should be obtained in the Run 3 and probably in the high-luminosity phase of the LHC (Run 4 etc.).

Analysis of the X(3960) and related tetraquark molecular states via the QCD sum rules

In this work, we study the Dbar{D}, DD, Dbar{D}_s, DD_s, D_sbar{D}_s and D_sD_s tetraquark molecular states with the J^{PC}=0^{++} via the QCD sum rules. The prediction M_{D_sbar{D}_s} = 3.98pm 0.10, text {GeV} is in very good agreement with the experimental value M_{X(3960)} = 3956 pm 5pm 10 ,text {MeV} from the LHCb collaboration and supports assigning the X(3960) as the D_s^+D_s^- molecular state with the J^{PC}=0^{++}. We take account of our previous works on the four-quark states consisting of two color-neutral clusters and acquire the mass spectrum of the ground state hidden-charm and doubly-charm tetraquark molecular states.

Strange cousin of Z c (4020/4025) as a tetraquark state* *Supported by the National Natural Science Foundation of China (12175068)

Motivated by the analogous properties of and , we tentatively assign as the -type hidden-charm tetraquark state with , where A denotes the axialvector diquark states, and explore -type tetraquark states without strange, with strange, and with hidden-strange via QCD sum rules in a consistent manner. We then explore the hadronic coupling constants in the two-body strong decays of tetraquark states without and with strange via QCD sum rules based on rigorous quark-hadron duality and acquire partial and total decay widths. The present calculations support assigning as the -type tetraquark state with , while the predictions for its strange cousin state can be confronted with experimental data in the future.

Masses of doubly heavy tetraquarks QQq̄n̄ with JP = 1+

In this paper, we apply the method of QCD sum rules to study the doubly heavy tetraquark states [Formula: see text] with spin-parity [Formula: see text] and strangeness [Formula: see text] using careful estimates of the Borel and threshold parameters involved. Masses of the doubly bottom and charmed tetraquarks with isospin [Formula: see text] are computed precisely via taking into account multifarious condensates up to dimension 10. Compared with the two-heavy meson thresholds, we find that all nonstrange doubly-bottom tetraquarks and a doubly-charmed tetraquarks associated with [Formula: see text] with [Formula: see text] are stable against strong decay into two bottom mesons while a doubly-charmed tetraquark associated with current [Formula: see text] is unstable against strong decay. By the way, weak decay widths of the doubly bottom tetraquarks are also given.