In this article, we assume that there exist hidden charmed tetraquark states with the spin-parity $J^P=1^-$, and calculate their masses with the QCD sum rules. The numerical result indicates that the masses of the vector hidden charmed tetraquark states are about $M_{Z}=(5.12\pm0.15) \rm{GeV}$ or $M_{Z}=(5.16\pm0.16) \rm{GeV}$, which are inconsistent with the experimental data on the $π^+ χ_{c1}$ invariant mass distribution.
The hidden charmed mesons $Z_1$, $Z_2$ or $Z$ may be scalar hidden charmed tetraquark states, hadro-charmonium resonances or molecular states.
In this article, we assume that there exists a scalar hidden charm tetraquark state in the $π^+ χ_{c1}$ invariant mass distribution, and study its mass using the QCD sum rules. The numerical result $M_{Z}=(4.36\pm0.18) \rm{GeV}$ is consistent with the mass of the Z(4250). The Z(4250) may be a tetraquark state, other possibilities, such as a hadro-charmonium resonance and a $D_1^+\bar{D}^0+ D^+\bar{D}_1^0$ molecular state are not excluded.
Assuming X(3872) is a $qc \bar q \bar c$ tetraquark and using its mass as input, we perform a schematic study of the masses of possible heavy tetraquarks using the color-magnetic interaction with the flavor symmetry breaking corrections.
Our hadro-charmonium and compact tetraquark model predictions, published before the BESIII and LHCb experimental data for the $Z_{\rm cs}(3985)$ and $Z_{\rm cs}(4003)$ tetraquarks were released, match surprisingly well with them. Here, we extend our results for the $P_{\rm cs}$ states to $Λ$ + charmonium configurations and also our hadro-charmonium predictions for $Z_{\rm c}$ and $X_{\rm c}$ tetraquarks to charmonium + pion/eta. We use them, in combination with our previous findings, to discuss the possible emergence of SU(3)$_{\rm f}$ pentaquark octets and tetraquark nonets in the hidden-char…
We investigate the role of a scalar tetraquark state for the description of nuclear matter within the parity doublet model in the mirror assignment. In the dilatation-invariant version of the model a nucleon-nucleon interaction term mediated by the lightest scalar tetraquark field naturally emerges. At nonzero density one has, beyond the usual chiral condensate, also a tetraquark condensate. The behavior of both condensates and the restoration of chiral symmetry at high density are studied. It is shown that this additional scalar degree of freedom affects non negligibly the properties of the m…
In the present work, the triply heavy tetraquarks states $QQ\bar{Q}\bar{q}$ 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 resonance 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 $cc\bar{c}\bar{q^{'}}$, $bb\bar{…
A new method is proposed to search for the double beauty tetraquark $bb\bar{u}\bar{d}$ with a mass below the $BB$ threshold. The $b\bar{d}-\bar{b}d$ mixing can result in evolution of the tetraquark content to $b\bar{b}\bar{u}d$ with the following strong decay into the $Υ$(1S)$π^-$ and $Υ$(2S)$π^-$ final states in a secondary vertex displaced from the primary $pp$ collision vertex. This experimental signature is clean, has a high selection efficiency and can be well separated from backgrounds. Experimental signatures for searches for other double heavy tetraquarks are also discussed, suggesting…
Using the chromomagnetic interaction Hamiltonian with proper account for the SU(3) flavor symmetry breaking, we have performed a schematic study on the masses of $S-$wave heavy tetraquarks as $bq\bar{b}\bar{q}$ ($q$ denotes $u$, $d$, $s$ quark). It is found that the numeral results for $bu\bar{b}\bar{d}$ or $bd\bar{b}\bar{u}$ with $1^{+}$ quantum number are 10612 MeV and 10683 MeV respectively, which are well compatible with the recent detected charged bottomonium-like $Z_b(10610)$ and $Z_b(10650)$. Theoretically, we also investigate the possible tetraquark states of $1^{++}$ and $2^{+}$ due t…
We discuss the Operator Product Expansion (OPE) and quark-hadron duality for two-point Green functions of tetraquark currents. We emphasize that the factorizable part of the OPE series for such Green functions, including nonperturbative contributions described by QCD condensates, is saturated by the full system of ordinary hadrons and therefore cannot have any relationship to the possible tetraquark bound states. Possible tetraquark bound states may be contained in nonfactorizable parts of these Green functions. In the framework of the $1/N_c$ expansion in QCD$(N_c)$, nonfactorizable parts of …
A chiral invariant Lagrangian describing the tetraquark-quarkonia interaction is considered at the leading and subleading order in the large-$N_{c}$ expansion. Spontaneous chiral symmetry breaking generates mixing of scalar tetraquark and quarkonia states and non-vanishing tetraquark condensates. In particular, the mixing strength is related to the decay strengths of tetraquark states into pseudoscalar mesons. The results show that scalar states below 1 GeV are mainly four-quark states and the scalars between 1 and 2 GeV quark-antiquark states, probably mixed with the scalar glueball in the is…
Without excluding the contributions of factorizable Feynman diagrams in the color space to the QCD sum rules by hand, we cannot obtain the conclusion that the factorizable parts of the operator product expansion series cannot have any relationship to the possible tetraquark bound states. The tetraquark couplings $f_T$ are of the order $\mathcal{O}(N_c)$ rather than of the order $\mathcal{O}(N^0_c)$ in the large $N_c$ limit, the conclusion "a possible exotic tetraquark state may appear only in $N_c$-subleading contributions to the QCD Green functions" is a paradox.
If a narrow Theta^+ pentaquark exists, it is likely that a ud\bar s-ud triquark-diquark configuration is a significant component of its wave function. If so, the mechanism responsible for the binding of a triquark and a diquark is also likely to bind the triquark to an \bar s antiquark. We discuss the expected properties of such a ud\bar s-\bar s tetraquark meson. In particular, we point out that for a 0^+ isoscalar ud\bar s\bar s meson the lowest allowed decay mode is a four-body K K pi pi channel with a small phase space and a distinctive experimental signature.
The article is devoted to double J/psi-meson production at LHC. Theoretical predictions for pp -> 2J/psi+X cross section at sqrt{s}=7 TeV for different kinematical restrictions are presented. Special attention is payed to possible contribution of novel particles -- tetraquarks build from four c-quarks. According to presented in our article estimates, it is quietly possible to observe at least one of these state (tensor meson) experimentally.
By means of unitarized Chiral Perturbation Theory it is possible to obtain a remarkable description of meson-meson scattering amplitudes up to 1.2 GeV, and generate poles associated to scalar and vector resonances. Since Chiral Perturbation Theory is the QCD low energy effective theory, it is possible then to study its large Nc limit where qqbar states are easily identified. The vectors thus generated follow closely a qqbar behavior, whereas the light scalar poles follow the large Nc behavior expected for a dominant tetraquark or two-meson structure.
In the current work spectroscopy and possibility of observation at the LHC of tetraquarks composed of 4 heavy quarks is discussed. Tetraquarks concerned are T_{4c}=[cc][cc]$, T_{4b}=[bb][bb] and T_{2[bc]}=[bc][bc]. By solving nonrelativistic Schroedinger equation masses of these states are found with the hyperfine splitting accounted for. It is shown that masses of tensor tetraquarks T_{4c}(2++) and T_{2[bc]}(2++) are high enough to observe these states as peaks in the invariant mass distributions of heavy quarkonia pairs in pp -> T_{4c}+X -> 2J/ψ+X, pp -> T_{2[bc]}+X -> 2B_{c}+X and pp -> T_{…
Inclusive production cross sections of the possible exotic state X(3872) in proton-proton, pionp-roton and proton-antiproton collisions are calculated using a statistical based model, which is previously used to describe inclusive charmed and bottomed hadron production cross sections in the low energy region. With the extensions made here, the model is capable to include tetraquarks as well, using the diquark picture of tetraquarks. The evaluated cross section ratio of $Ψ(2S)$ and $X(3872)$ at $\sqrt{s}=7$ TeV agrees well with the measured value.
In the framework of a nonrelativistic chiral quark model, we continue to study the mass spectra of the fully-heavy $bb\bar{c}\bar{c}$ and $bc\bar{b}\bar{c}$ tetraquarks. In the present calculations, two structures, meson-meson [$\bar{Q}Q$][$\bar{Q}Q$] and diquark-antidiquark [$QQ$][$\bar{Q}\bar{Q}$] ($Q$ = $c$ or $b$), and their mixing, along with all possible color, spin configurations are considered. The calculations suggest that no bound state can be formed for $bb\bar{c}\bar{c}$ and $bc\bar{b}\bar{c}$ systems. However, resonances are possible because of the color structure. Several resonan…
In two recent papers, we used the hadro-quarkonium model to study the properties of hidden-charm and bottom tetraquarks and pentaquarks. Here, we extend the previous results and calculate the masses of heavy-quarkonium-kaon/hyperon systems. We also compute the spectrum of hidden-charm and bottom tetraquarks with strangeness in the compact tetraquark (diquark-antidiquark) model. If heavy-light exotic systems with non-null strangeness content were to be observed experimentally, it might be possible to distinguish among the large variety of available theoretical pictures for tetra- and pentaquark…
Tetraquarks QQq*q* are found to be described remarkably well with the Quantum Chromodynamics version of the Hydrogen bond, as treated with the Born-Oppenheimer approximation. We show the robustness of the method by computing the mass of the observed Tcc tetraquark following two different paths. Relying on this, we provide a prediction for the mass of the expected Tbb particle. The average sizes of tetraquarks are estimated to be approximately 3 - 5 GeV**-1. As a consequence hyperfine separations are not expected to be sizeable. We discussed possible reasons why LHCb has observed only one state…
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 $cu\bar{c}\bar{d}$ ($cu\bar{c}\bar{s}$) 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.
Based on the diquark configuration, we construct the diquark-antidiquark interpolating tetraquark currents with $J^{PC}=1^{-\pm}$ and $1^{+\pm}$, 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 $J^{PC}=0^{+\pm}$ and $0^{-\pm}$ through the QCD sum rule approach. The predicted masses can be confronted with the experimental data…
We discuss the production mechanism of fully charm tetraquark, observed recently by the LHCb at M = 6.9 GeV in the $J/ψJ/ψ$ channel. Both single parton scattering (SPS) and double parton scattering (DPS) mechanisms are considered. We calculate the distribution in the invariant mass of the four-quark system $M_{4c}$ for SPS and DPS production of $c c \bar c \bar c$ in the $k_t$-factorization approach. We present transverse momentum distribution in $p_{t,4c}$ for $c \bar c c \bar c$ system in a mass window around tetraquark mass. The calculation of the SPS $g^* g^* \to T_{4c}(6900)$ fusion mecha…
LHCb Collaboration has recently announced the observation of a doubly charmed tetraquark $T_{cc \bar{u} \bar{d}}^+$ state with spin parity $J^P = 1^+$. This exotic state can be explained as a molecular state with small binding energy. According to conventional quark model, both $D^+ D^{0\ast}$ and $(D^0 D^{+\ast})$ multiquark states are expected to have the same mass and flavor in the exact $SU(3)$ symmetry. However, since the quark masses are different, $SU(3) (SU(2))$ symmetry is violated, hence, the mass and flavor eigenstates do not coincide. The mass eigenstates can be represented as a li…
In this work, we re-investigate the mass spectrum of the ground state, first, second and third radial excited states of the diquark-antidiquark type fully-charm tetraquark states with the QCD sum rules plus Regge trajectories. We take account of the CMS and ATLAS experimental data and preform a self-consistent analysis, then try to make possible assignments of the $X(6600)$, $X(6900)$ and $X(7300)$ in the picture of tetraquark states with the $J^{PC}=0^{++}$ or $1^{+-}$.
We study the tetraquark state with I^G J^{PC} = 0^+ 1^{-+} in the QCD sum rule. We exhaust all possible flavor structures by using a diquark-antidiquark construction and find that the flavor structure 3*6+6*3 is preferred. There are altogether four independent currents which have the quark contents q s \bar q \bar s. By using both the Shifman-Vainshtein-Zakharov (SVZ) sum rule and the finite energy sum rule, these currents lead to mass estimates around 1.8 - 2.1 GeV, where the uncertainty is due to the mixing of two single currents. Its possible decay modes are S-wave b_1(1235) ηand b_1(1235) …
Using a soft-wall AdS/QCD approach we derive the Schrödinger-type equation of motion for the tetraquark wave function, which is dual to the dimension-4 AdS bulk profile. The latter coincides with the number of constituents in the leading Fock state of the tetraquark. The obtained equation of motion is solved analytically, providing predictions for both the tetraquark wave function and its mass. A low mass limit for possible tetraquark states is given by $M \ge 2 κ= 1$ GeV, where $κ= 0.5$ GeV is the typical value of the scale parameter in soft-wall AdS/QCD. We confirm results of the COMPASS Col…
We summarize the main features of the spectroscopy, production and decays of the $J^{PC}=1^{--}$ tetraquarks in the $b\bar{b}$ sector, concentrating on the lowest state called $Y_b(10890)$. The tetraquark framework is used to analyze the BaBar data on the $e^+ e^- \to b\bar{b}$ cross section ($R_b$ energy scan) between $\sqrt{s}= 10.54$ and 11.20 GeV and the Belle data on the processes $e^+e^- \to Υ(1S) π^+π^-,Υ(2S) π^+π^-$ near the peak of the $Υ(5S)$ resonance. The BaBar $R_b$ energy scan is consistent with an additional state at a mass of 10.90 GeV and a width of about 28 MeV, in broad agre…
We study the possible exotic states with $J^{PC} = 0^{+-}$ using the tetraquark interpolating currents with the QCD sum rule approach. The extracted masses are around 4.85 GeV for the charmonium-like states and 11.25 GeV for the bottomomium-like states. There is no working region for the light tetraquark currents, which implies the light $0^{+-}$ state may not exist below 2 GeV.
Possibility of an axial vector isoscalar tetraquark with $ud\bar{s}\bar{s}$ is discussed. If the pentaquark $Θ^+(1540)$ has the $(qq)_{\bar{3}}(qq)_{\bar{3}}\bar{q}$ configuration, the isoscalar $ud\bar{s}\bar{s}$($\vartheta^+$-meson) state with $J^P=1^+$ is expected to exist in the mass region lower than or close to the mass of $Θ^+(1540)$. Within a flux-tube quark model, a possible resonant state of $ud\bar{s}\bar{s}(J^{P}=1^{+})$ is suggested to appear around 1.4 GeV with the width ${\cal{O}}(20\sim 50)$ MeV. We propose that the $\vartheta^+$-meson is a good candidate for the tetraquark sea…
Motivated by the LHCb's new observation of structures in the $J/ψ$-pair invariant mass spectrum, for which could be classified as possible $cc\bar{c}\bar{c}$ tetraquark candidates, we systematically study $0^{+}$ fully-charmed tetraquark states through QCD sum rules. Making the development of calculation techniques to fourfold heavy hadronic systems, four different configuration currents with $0^{+}$ are considered and vacuum condensates up to dimension $6$ are included in the operator product expansion (OPE). Finally, mass values acquired for $0^{+}$ $cc\bar{c}\bar{c}$ tetraquark states agree…
Possible experimental searches of doubly charmed baryons and tetraquarks at fixed target experiments with high energy hadron beams and a high intensity spectrometer are considered here. The baryons considered are: $Ξ_{cc}^{+}$ (ccd), $Ξ_{cc}^{++}$ (ccu), and $Ω_{cc}^{+}$ (ccs); and the tetraquark is T ($cc\bar{u}\bar{d}$). Estimates are given of masses, lifetimes, internal structure, production cross sections, decay modes, branching ratios, and yields. Experimental requirements are given for optimizing the signal and minimizing the backgrounds. This paper is designed as an experimental and the…
When studying tetraquark states using the method of QCD sum rules, we find some tetraquark currents, such as $\bar u_L γ_μd_L~\bar d_L γ^μu_L$ and $\bar u_L γ_μd_L~\bar d_R γ^μu_R$, etc. We calculate their correlation functions using the method of operator product expansion, and find that non-perturbative QCD effects do not contribute much to them. This indicates the possible existence of tetraquark states composed of bare quarks with abnormally small masses. We study the possible assignment of the $X17$ as such a state. We argue that the Atomki experiments might observe a new type of nuclear …
Based on the recent proposal for the tetraquarks with the mixing scheme, we investigate fall-apart decays of $a_0(980), a_0(1450)$ into two lowest-lying mesons. This mixing scheme suggests that $a_0(980)$ and $a_0(1450)$ are the tetraquarks with the mixtures of two spin configurations of diquark and antidiquark. Due to the relative sign differences in the mixtures, the couplings of fall-apart decays into two mesons are strongly enhanced for $a_0(980)$ but suppressed for $a_0(1450)$. We report that this expectation is supported by their experimental decays. In particular, the ratios of the asso…
Diquarks with $J^{P}=0^{\pm}$, $1^{\pm}$ containing a heavy (charm or bottom) quark and a light quark are investigated using QCD Laplace sum rules. Masses are determined using appropriately constructed gauge invariant correlation functions, including for the first time next-to-leading order perturbative contributions. The $J^P=0^+$ and $1^+$ charm-light diquark masses are respectively found to be 1.86$\pm$0.05 GeV and 1.87$\pm$0.10 GeV, while those of the $0^+$ and $1^+$ bottom-light diquarks are both determined to be 5.08$\pm$0.04 GeV. The sum rules derived for heavy-light diquarks with negat…
In this work, we continue to study the mass spectra of fully-heavy tetraquarks $cc\bar{c}\bar{c}$ with the quantum numbers of $J^{PC}=0^{++}, 1^{+-}, 2^{++}$ in the nonrelativistic chiral quark model. With the help of the Gaussian Expansion Method, we present dynamical computations for $cc\bar{c}\bar{c}$ state with considering two structures, meson-meson [$\bar{c}c$][$\bar{c}c$] and diquark-antidiquark [$cc$][$\bar{c}\bar{c}$] and their mixing. The results manifest that the energies of the low-lying states are all higher than the meson-meson thresholds [$\bar{c}c$][$\bar{c}c$]. However, resona…
In the framework of QCD Sum Rules we investigate the $q q^\prime \bar{Q} \bar{Q}$ tetraquark structure with quantum number $J^P = 1^+$, which are embedded in two types of configurations, the $[8_c]_{q \bar{Q}} \otimes [8_c]_{q^\prime \bar{Q}}$ and $[1_c]_{q \bar{Q}} \otimes [1_c]_{q^\prime \bar{Q}}$ with $Q = b, c$, $q = u$, and $q^\prime = d, s$. Our finding confirms the Lattice QCD result that the bottom tetraquark states could exist and their masses are evaluated. In the calculation, the non-perturbative condensate contributions up to dimension eight in operator product expansion are consid…
The compact tetraquark states with fully heavy quark contents $QQ\bar Q\bar Q$ are studied as the bound states of the diquark-antidiquark within the Bethe-Salpeter framework. The (anti)diquark masses and form factors used are the same as we calculated the doubly heavy baryons in a previous work. Under the instantaneous approximation, the three-dimensional (Bethe-)Salpeter equation of the tetraquarks is derived and solved numerically to obtain the corresponding mass spectra and wave functions of the tetraquarks with $J^{PC}=0^{++}$, $1^{+-}$, and $2^{++}$. Our results show that the three ground…
Recent data from Belle show unusually large partial widths Upsilon(5S) --> Upsilon(1S) pi^+pi^- and Υ(5S) --> Υ(2S) pi^+ pi^-. The Z(4430) narrow resonance also reported by Belle in psi' pi^+ spectrum has the properties expected of a (cbar c u dbar) charged isovector tetraquark T^{+-}_cc The analogous state T^{+-} in the bottom sector might mediate anomalously large cascade decays in the Upsilon system, Upsilon(mS) --> T^{+-}_bb pi^{-+} --> Upsilon(nS) pi^+ π^-, with a tetraquark-pion intermediate state. We suggest looking for the (bbar b u dbar) tetraquark in these decays as peaks in the inva…
The observed mass pattern of scalar resonances below 1 GeV gives preference to the tetraquark assignment over the conventional $\bar qq$ assignment for these states. We present a search for tetraquarks with isospins 0, 1/2, 1 in lattice QCD, where the isospin channels 1/2 and 1 have not been studied before. We determine three energy levels in each isospin channel using the variational method. The scattering states and possible tetraquark states are distinguished by considering the volume-dependence of spectral weights and by considering the time-dependence of correlators near t~T/2. We find no…
In order to explore the possible existence of the exotic $0^{--}$ state, we have constructed the tetraquark interpolating operators systematically. As a byproduct, we notice the $0^{+-}$ tetraquark operators without derivatives do not exist. The special Lorentz structure of the $0^{--}$ currents forbids the four-quark correction to the spectral density. Now the gluon condensate is the dominant power correction. Within the framework of the finite energy sum rule, none of the seven interpolating currents supports a resonant signal. Therefore we conclude that the exotic $0^{--}$ state does not ex…
In the simple color-magnetic interaction model, we investigate possible ground $cs\bar{c}\bar{s}$ tetraquark states in the diquark-antidiquark basis. We use several methods to estimate the mass spectrum and discuss possible assignment for the $X$ states observed in the $J/ψϕ$ channel. We find that assigning the Belle $X(4350)$ as a $0^{++}$ tetraquark is consistent with the tetraquark interpretation for the $X(4140)$ and $X(4270)$ while the interpretation of the $X(4500)$ and $X(4700)$ needs orbital or radial excitation. There probably exist several tetraquarks around 4.3 GeV that decay into $…
Motivated by the LHCb observation of exotic states $X_{0,1}(2900)$ with four open quark flavors in the $D^- K^+$ invariant mass distribution in the decay channel $B^\pm \to D^+ D^- K^\pm$, we study the spectrum and decay properties of the open charm tetraquarks. Using the two-body chromomagnetic interactions, we find that the two newly observed states can be interpreted as a radial excited tetraquark with $J^P=0^+$ and an orbitally excited tetraquark with $J^P=1^-$, respectively. We then explore the mass and decays of the other flavor-open tetraquarks made of $su \bar d \bar c$ and $ d s \bar …
In this work, we study systematically the mass splittings of the $qq\bar{Q}\bar{Q}$ ($q=u$, $d$, $s$ and $Q=c$, $b$) tetraquark states with the color-magnetic interaction by considering color mixing effects and estimate roughly their masses. We find that the color mixing effect is relatively important for the $J^P=0^+$ states and possible stable tetraquarks exist in the $nn\bar{Q}\bar{Q}$ ($n=u$, $d$) and $ns\bar{Q}\bar{Q}$ systems either with $J=0$ or with $J=1$. Possible decay patterns of the tetraquarks are briefly discussed.
Assuming the dominance of the spin-spin interaction in a diquark, we point out that the mass difference in the beauty sector M(Z_b^prime) - M(Z_b) scales with quark masses as expected in QCD, with respect to the corresponding mass difference M(Z_c^prime) - M(Z_c). Notably, we show that the decays Upsilon(10890) --> Upsilon(nS) pi pi and Upsilon(10890) --> (h_b(1P), h_b(2P)) pi pi are compatible with heavy-quark spin conservation if the contributions of Z_b,Z_b^prime intermediate states are taken into account, Upsilon(10890) being either a Upsilon(5S) or the beauty analog of Y_c(4260). Belle re…
In this work, we estimate the masses of tetraquark states with four different flavors by virtue of QCD sum rules, in both $b$ and $c$ sectors. We construct four $[8_c]_{\bar{b} s} \otimes [8_c]_{\bar{d} u}$ tetraquark currents with $J^P = 0^+$, and then perform analytic calculation up to dimension eight in the Operator Product Expansion (OPE). We keep terms which are linear in the strange quark mass $m_s$, and in the end find two possible tetraquark states with masses $(5.57 \pm 0.15)$ and $(5.58 \pm 0.15)$ GeV. We find that their charmed-partner masses lie in $(2.54 \pm 0.13)$ and $(2.55 \pm …
