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 linear combination of the flavor eigenstates, which is characterized by the mixing angle $θ$. In the present work, the possible mixing angles between the $T_{cc}$ states are calculated. Moreover, the analysis are extended for all the possible tetraquarks scenarios with two heavy and two light quarks within the molecular picture although those states have not been observed yet. Our prediction on mixing angle between doubly charmed tetraquark states shows that $SU(3)$ symmetry breaking is around $7\%$ maximally.
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…
Recently, a QCD sum-rule analysis of tetraquark molecular states has been published, having the objective of demonstrating that our previously formulated tetraquark-adequate QCD sum rules are not correct. This comment brings to the attention of the reader inconsistencies in that article and explains some subtle details of QCD sum rules for exotic states.
In "Landau equation and QCD sum rules for the tetraquark molecular states", I list out six reasons to refute the assertion of Lucha, Melikhov and Sazdjian. In "Comment on "Landau equation and QCD sum rules for the tetraquark molecular states"", they refute my viewpoint. If they want to the refute my viewpoint robustly, they should refute the six reasons one by one, and provide at least one example to illustrate that they have obtained reliable QCD sum rules for the tetraquark states and free two-meson states, respectively.
In this article, we perform a systematic study of the mass spectrum of the scalar doubly charmed and doubly bottom tetraquark states using the QCD sum rules.
In this article, we investigate the mass spectrum of the ground state hidden-charm tetraquark molecular states without strange, with strange and with hidden-strange via the QCD sum rules in a comprehensive way and revisit the assignments of the $X$, $Y$, $Z$ states in the scenario of tetraquark molecular states consistently based on the QCD sum rules.
In this article, we construct the axialvector-diquark-scalar-antidiquark type currents to interpolate the axialvector doubly heavy tetraquark states, and study them with the QCD sum rules in details by carrying out the operator product expansion up to the vacuum condensates of dimension 10.
We revisit the role of color mixing in the quark-model calculation of tetraquark states, and compare simple pairwise potentials to more elaborate string models with three- and four-body forces. We attempt to disentangle the improved dynamics of confinement from the approximations made in the treatment of the internal color degrees of freedom.
Tetraquark properties are examined in the limit of large $N_c$ of color in QCD. The qualitative differences between molecular and compact tetraquarks are outlined. Consequences of the possible existence of compact tetraquarks are analyzed and shown to lead to upper bounds in the $N_c$-behavior of their decay widths. Open questions on theoretical grounds, related to the dynamics of systems composed of two quarks and two antiquarks, are addressed.
In this article, we introduce a P-wave between the diquark and antidiquark explicitly to construct the vector tetraquark currents, and study the vector tetraquark states with the QCD sum rules systematically, and obtain the lowest vector tetraquark masses up to now. The present predictions support assigning the $Y(4220/4260)$, $Y(4320/4360)$, $Y(4390)$ and $Z(4250)$ to be the vector tetraquark states with a relative P-wave between the diquark and antidiquark pair.
We examine the interpretation of the light scalar meson nonet as tetraquark states using QCD sum rules. With the interpolating current for the tetraquark states composed of scalar diquark and scalar antidiquark, first, we construct the QCD sum rules by means of the operator product expansion up to the operators of dimension 8 and show that there is no evidence of the coupling of the tetraquark states to the light scalar meson nonet. In order to have a stable sum rule, we propose a "good" interpolating current for the tetraquarks based on chirality arguments which includes scalar and pseudoscal…
In the framework of two-flavor extended linear sigma model with mixing between scalar quarkonium and tetraquark, we investigate the role of the tetraquark in the chiral phase transition. We explore various scenarios depending on the value of various parameters in our model. The physical mass spectrum of mesons put a tight constraint on the parameter set of our model. We find a sufficiently strong cubic self interaction of the tetraquark field can drive the chiral phase transition to first order even at zero quark chemical potential. Weak or absence of the cubic self interaction term of the tet…
The QCD quark cyclobutadiene (ring-like), a new color structure of tetraquark system, is proposed and studied in the flux tube model with multi-body confinement potential. The QCD quark cyclobutadiene and other flux tube structures of tetraquark states have similar energies and they can be regarded as QCD isomeric compounds. The light tetraquark spectra ($u, d, s$ only) with ring-like and diquark-antidiquark structures are calculated in the flux tube model. The results show that many experimental states have the masses close to the calculated values if they are taken as tetraquark states. The …
We study the lowest-lying scalar mesons in the QCD sum rule by considering them as tetraquark states. We find that there are five independent currents for each state with a certain flavor structure. By forming linear combinations, we find that some mixed currents give reliable QCD sum rules. Among various tetraquark currents, we consider those which are constructed by the diquarks having anti-symmetric and symmetric flavor structures. That the results of the QCD sum rule derived from the two types of currents are similar suggests that the tetraquark states can have a large mixing between diffe…
Multiquark correlations inside hadrons can have a significant and in some cases even striking impact on the hadron spectrum. We show how such correlations in general, and mesons with a dominant tetraquark content in particular, emerge holographically in the AdS/QCD framework. On this basis, we arrive at a holographic realization of an exceptionally strong four-quark binding and a correspondingly large tetraquark component in the lightest scalar mesons. Higher-lying tetraquark excitations, on the other hand, become too broad to form supernumeral scalar states.
In this article, we extend our previous work to study the mass spectrum of the ground state hidden-bottom tetraquark states with the QCD sum rules in a systematic way. The predicted hidden-bottom tetraquark masses can be confronted to the experimental data in the future to diagnose the nature of the $Z_b$ states. In calculations, we observe that the scalar diquark states, the axialvector diquark states and the axialvector components of the tensor diquark state are all good diquarks in building the lowest tetraquark states.
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 st…
The properties of possibly existing tetraquarks are studied in the large-$N_{\mathrm{c}}^{}$ limit of QCD by means of four-point correlation functions of meson currents.The necessity of a detailed analysis of the singularities of Feynman diagrams, by means of the Landau equations, to recognize those diagrams that might contribute to the formation of tetraquark states, is emphasized. It is found, in general, that tetraquarks, if they exist, should have narrow widths of the order of $N_{\mathrm{c}}^{-2}$.
In this article, we take the scalar diquarks as point particles and describe them as basic quantum fields, then introduce the SU(3) color gauge interaction and new vacuum condensates to study the nonet scalar mesons as tetraquark states with the QCD sum rules. Comparing with the conventional quark currents, the diquark currents have the outstanding advantage to satisfy the two criteria of the QCD sum rules more easily.
In this article, we study the axialvector-diquark-axialvector-antidiquark ($AA$) type and scalar-diquark-scalar-antidiquark ($SS$) type fully open flavor $cs\bar{u}\bar{d}$ tetraquark states with the spin-parity $J^P={0}^+$ via the QCD sum rules. The predicted masses $M_{AA}=2.91\pm0.12\,\rm{GeV}$ and $M_{SS}=3.05\pm0.10\,\rm{GeV}$ support assigning the $X_0(2900)$ to be the $AA$-type scalar $cs\bar{u}\bar{d}$ tetraquark state.
We consider quark-hadron duality relations and QCD sum rules for correlators involving exotic tetraquark currents, here specializing to the case of quark-exchange processes. We point out the differences they exhibit with respect to the cases involving ordinary bilinear quark currents. Based on the observation that only diagrams possessing at least four-quark singularities can contribute to the formation of tetraquark states, we show that the quark-hadron duality relations and the corresponding sum rules split into two non-overlapping relations. The ultimate tetraquark-adequate QCD sum rule is …
In this letter, we take the point of view that the X(1576) be tetraquark state which consists of a scalar-diquark and an anti-scalar-diquark in relative $P$-wave, and calculate its mass in the framework of the QCD sum rules approach. The numerical value of the mass $m_X=(1.66\pm 0.14) GeV$ is consistent with the experimental data, there may be some tetraquark component in the vector meson X(1576).
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…
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.
In this article, we construct the diquark-antidiquark type current operators to study the axialvector $B_c$-like tetraquark states with the QCD sum rules. In calculations, we take the energy scale formula as a powerful constraint to choose the ideal energy scales of the QCD spectral densities and add detailed discussions to illustrate why we take the energy scale formula to improve the QCD sum rules for the doubly heavy tetraquark states. The predicted masses $M_{Z_{\bar{b}c}(1^{+-})}=7.30\pm0.08\,\rm{GeV}$ and $M_{Z_{\bar{b}c}(1^{++})}=7.31\pm0.08\,\rm{GeV}$ lie between the conventional $2\rm…
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…
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 $1^{+-}$.
In this article, we take the point of view that the charmed scalar meson $D_{s0}(2317)$ be a tetraquark state and devote to calculate its mass within the framework of the QCD sum rules approach in the heavy quark limit. The numerical values for the mass of the $D_{s0}(2317)$ are consistent with the experimental data, there must be some tetraquark component in the scalar meson $D_{s0}(2317)$. Detailed discussions about the threshold parameter and Borel parameter for the multiquark states are also presented.
In this article, we take the point of view that Y(2175) be a tetraquark state which consists of color octet constituents, and calculate its mass and decay constant within the framework of the QCD sum rule approach. We release standard criterion in the QCD sum rules approach and take more phenomenological analysis, the value of the mass of Y(2175) is consistent with experimental data; there may be some tetraquark components in the state Y(2175). If we retain standard criterion, larger mass than experimental data can be obtained, the current $J_μ(x)$ can interpolate a tetraquark state with large…
In this article, we assign the $Z_c^\pm(3900)$ to be the diquark-antidiquark type axialvector tetraquark state, study its magnetic moment with the QCD sum rules in the external weak electromagnetic field by carrying out the operator product expansion up to the vacuum condensates of dimension 8. We pay special attention to matching the hadron side with the QCD side of the correlation function to obtain solid duality, the routine can be applied to study other electromagnetic properties of the exotic particles.
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 ex…
The tetraquark assignement for light scalar states below 1 GeV is discussed on the light of strong decays. The next-to-leading order in the large-N expansion for the strong decays is considered. Mixing with quarkonia states above 1 GeV is investigated within a chiral approach and the inclusion of finite-width effects is taken into account.
In this article, we take the $X(5568)$ as the diquark-antidiquark type tetraquark state with the spin-parity $J^P=0^+$, construct the scalar-diquark-scalar-antidiquark type current, carry out the operator product expansion up to the vacuum condensates of dimension-10, and study the mass and pole residue in details with the QCD sum rules. We obtain the value $M_X=\left(5.57\pm0.12 \right) \,\rm{GeV}$, which is consistent with the experimental data. The present prediction favors assigning the $X(5568)$ to be the scalar tetraquark state.
In this article, we construct the axialvector-diquark-axialvector-antidiquark type currents to interpolate the scalar, axialvector, vector, tensor doubly charmed tetraquark states, and study them with QCD sum rules systematically by carrying out the operator product expansion up to the vacuum condensates of dimension 10 in a consistent way, the predicted masses can be confronted to the experimental data in the future. We can search for those doubly charmed tetraquark states in the Okubo-Zweig-Iizuka super-allowed strong decays to the charmed meson pairs.
In this article, we take the $X(4140)$ as the diquark-antidiquark type $cs\bar{c}\bar{s}$ tetraquark state with $J^{PC}=1^{++}$, and study the mass and pole residue with the QCD sum rules in details by constructing two types interpolating currents. The numerical results $M_{X_{L,+}}=3.95\pm0.09\,\rm{GeV}$ and $M_{X_{H,+}}=5.00\pm0.10\,\rm{GeV}$ disfavor assigning the $X(4140)$ to be the $J^{PC}=1^{++}$ diquark-antidiquark type $cs\bar{c}\bar{s}$ tetraquark state. Moreover, we obtain the masses of the $J^{PC}=1^{+-}$ diquark-antidiquark type $cs\bar{c}\bar{s}$ tetraquark states as a byproduct. …
In this article, we construct the axialvector-diquark-axialvector-antidiquark type currents to study both the vector and axialvector $QQ\bar{Q}\bar{Q}$ tetraquark states with the QCD sum rules, and obtain the masses $M_{Y(cc\bar{c}\bar{c},1^{+-})} =6.05\pm0.08\,\rm{GeV}$, $M_{Y(cc\bar{c}\bar{c},1^{--})} =6.11\pm0.08\,\rm{GeV}$, $M_{Y(bb\bar{b}\bar{b},1^{+-})} =18.84\pm0.09\,\rm{GeV}$, $M_{Y(bb\bar{b}\bar{b},1^{--})} =18.89\pm0.09\,\rm{GeV}$. The vector tetraquark states lie $40\,\rm{MeV}$ above the corresponding centroids of the $0^{++}$, $1^{+-}$ and $2^{++}$ tetraquark states, which is a typ…
We study details of QCD sum rules à la Shifman-Vainshtein-Zakharov for exotic tetraquark states. We point out that duality relations for correlators involving exotic currents have fundamental differences compared with the duality relations for the correlators of bilinear quark currents: namely, the $O(1)$ and $O(α_s)$ [$α_s$ the strong coupling constant] terms in the operator product expansion for the exotic correlators exactly cancel against the contributions of the two-meson states on the hadron side of QCD sum rules. As a result, the tetraquark properties turn out to be related to the speci…
We use the twist dimensions of the operators underlying the dynamical behavior of exclusive production processes as a tool for determining the structure of exotic heavy-quark states such as the $Z_c^+(4430)$ tetraquark. The resulting counting rules predict distinctive fall-offs of the cross sections in center-of-mass energy, thus distinguishing whether the tetraquarks are segregated into di-meson molecules, diquark-antidiquark pairs, or more democratically arranged four-quark states. In addition, we propose straightforward methods of experimentally producing additional exotic multiquark states…
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…
Frequently, theoretical discussions of multiquark hadron states prove to be contaminated or even dominated by contributions of conventional hadrons. For the approach to QCD bound states in terms of QCD sum rules, we show how to get rid of all unwanted ordinary-hadron ballast by boiling down the traditional QCD sum-rule formalism to the nonconventional aspects in the focus of interest.
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 …
Flavour-exotic tetraquark mesons, by definition bound states of two quarks and two antiquarks of four mutually different quark flavours, are, for given Lorentz features, subject to two incompatible constraints: On the one hand, within quantum chromodynamics a formation of compact tetraquark states is most easily envisaged by merging two colour-antisymmetric two-quark clusters, a diquark and an antidiquark. This path, however, leads to merely a single tetraquark state of chosen Lorentz characteristics. On the other hand, in the limit of the number of colour degrees of freedom growing beyond bou…
Discussing four-point Green functions of bilinear quark currents in large-$N_c$ QCD, we formulate rigorous criteria for selecting diagrams appropriate for the analysis of potential tetraquark poles. We find that both flavor-exotic and cryptoexotic (i.e., flavor-nonexotic) tetraquarks, if such poles exist, have a width of order $O(1/N_c^2)$, so they are parametrically narrower compared to the ordinary $\bar qq$ mesons, which have a width of order $O(1/N_c)$. Moreover, for flavor-exotic states, the consistency of the large-$N_c$ behavior of "direct" and "recombination" Green functions requires t…
In this article, we study the $S\bar{S}$ type scalar tetraquark state $cq\bar{c}\bar{q}$ in details 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 $M_{Z_c}=\left(3.82^{+0.08}_{-0.08}\right)\,\rm{GeV}$, which is the lowest mass for the hidden charmed tetraquark states from the QCD sum rules. Furthermore, we calculate the hadronic coupling constants $G_{Z_cη_cπ}$ and $G_{Z_cDD}$ with the three-point QCD sum rules, then study the strong decays $ Z_c\to η_cπ\, ,\, DD$, and observe that the…
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 $4.56\pm0.08\,\rm{GeV}$ for the pseudoscalar tetraquark state with…
In this article, we study the $J^{PC}=0^{++}$ and $2^{++}$ $QQ\bar{Q}\bar{Q}$ tetraquark states with the QCD sum rules, and obtain the predictions $M_{X(cc\bar{c}\bar{c},0^{++})} =5.99\pm0.08\,\rm{GeV}$, $M_{X(cc\bar{c}\bar{c},2^{++})} =6.09\pm0.08\,\rm{GeV}$, $M_{X(bb\bar{b}\bar{b},0^{++})} =18.84\pm0.09\,\rm{GeV}$ and $M_{X(bb\bar{b}\bar{b},2^{++})}=18.85\pm0.09\,\rm{GeV}$, which can be confronted to the experimental data in the future. Furthermore, we illustrate that the diquark-antidiquark type tetraquark state can be taken as a special superposition of a series of meson-meson pairs and em…
A salient feature shared by all tetraquark candidates observed in experiment is the absence of flavor-exotic states of the type $\bar a b\bar c d$, with four different quark flavors. This phenomenon may be understood from the properties of large-$N_c$ QCD: On the one hand, consistency conditions for flavor-exotic Green functions, potentially containing these tetraquark poles, require the existence of two tetraquarks $T_A$ and $T_B$: each of them should decay dominantly via a single two-meson channel, $T_A\to M_{\bar a b}M_{\bar c d}$ and $T_B\to M_{\bar a d}M_{\bar c b}$, with suppressed rates…
By using QCD sum rules, the mass of the hidden charm tetraquark $[cu][\bar{c}\bar{d}]$ state with $I^{G} (J^{P}) = 1^+ (1^{+})$ (HCTV) is estimated, which presumably will turn out to be the newly observed charmonium-like resonance $Z_c^+(3900)$. In the calculation, contributions up to dimension eight in the operator product expansion(OPE) are taken into account. We find $m_{1^+}^c = (3912^{+306}_{-153}) \, \text{MeV}$, which is consistent, within the errors, with the experimental observation of $Z_c^+(3900)$. Extending to the b-quark sector, $m_{1^+}^b = (10561^{+395}_{-163}) \,\text{MeV}$ is …
AdS/QCD correspondence allows to compute the quark-antiquark potential in the static limit. We use this piece of information together with the Salpeter equation (Schroedinger equation with relativistic kinematics) and a short range hyperfine splitting potential to describe the bound states of quark-antiquark. Comparison with experiment permits to fit the parameters of the model, namely the quark masses and the quark potential parameters. A discussion of heavy tetraquark masses, prompted by the hypothesis of a diquark-antidiquark structure for the puzzling state X(3872), is also presented.
With the experimental observation of several credible candidates for multiquark hadrons, the latter states re-entered the focus of interest of theoretical strong-interaction physics. Proper treatment of hadronic bound states by quantum chromodynamics, QCD, the quantum field theory governing all strong interactions, necessitates a nonperturbative approach. A well-established framework of this kind is provided by QCD sum rules relating hadron features to the parameters of QCD. Conceptual reconsideration, however, reveals that, in order to really match the peculiarities of multiquarks, the long-s…
In this paper we present in greater detail previous work on the Born-Oppenheimer approximation to treat the hydrogen bond of QCD, and add a similar treatment of doubly heavy baryons. Doubly heavy exotic resonances X and Z can be described as color molecules of two-quark lumps, the analogue of the H_2 molecule, and doubly heavy baryons as the analog of the H_2^+ ion, except that the two heavy quarks attract each other. We compare our results with constituent quark model and lattice QCD calculations and find further evidence in support of this upgraded picture of compact tetraquarks and baryons.
We study a QCD sum rule analysis for an exotic tetraquark ud bar[s] bar[s] of J^P=0^+ and I = 1. We construct q q bar[q] bar[q] currents in a local product form and find that there are five independent currents for this channel. Due to high dimensional nature of the current, it is not easy to form a good sum rule when using a single current. This means that we do not find any sum rule window to extract reliable results, due to the insufficient convergence of the OPE and to the exceptional important role of QCD continuum. Then we examine sum rules by using currents of linear combinations of two…
In this article, we separate the vector and axialvector components of the tensor diquark operators explicitly, construct the axialvector-axialvector type and vector-vector type scalar tetraquark currents and scalar-tensor type tensor tetraquark current to study the scalar, vector and axialvector tetraquark states with the QCD sum rules in a consistent way. The present calculations do not favor assigning the $Z_c(4100)$ to be a scalar or vector tetraquark state. If the $Z_c(4100)$ is a scalar tetraquark state without mixing effects, it should have a mass about $3.9\,\rm{GeV}$ or $4.0\,\rm{GeV}$…
In this work, we study the $D\bar{D}$, $DD$, $D\bar{D}_s$, $DD_s$, $D_s\bar{D}_s$ and $D_sD_s$ tetraquark molecular states with the $J^{PC}=0^{++}$ via the QCD sum rules. The prediction $M_{D_s\bar {D}_s} = 3.98\pm0.10\, \rm{GeV}$ is in very good agreement with the experimental value $M_{X(3960)} = 3956 \pm 5\pm 10 \,\rm{MeV}$ 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 gr…
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…
In this paper we perform a detailed study of the masses and mixing of the single charmed scalar tetraquarks: $c q \bar{q} \bar{q}$. We also give a systematic analysis of these tetraquark states by weight diagrams, quantum numbers and flavor wave functions. Tetraquark masses are calculated using four different fits. The following SU(3)$_\mathrm{F}$ representations are discussed: $\bar{15}_\mathrm{S}$, $\bar{3}_\mathrm{S}$, $6_\mathrm{A}$ and $\bar{3}_\mathrm{A}$. We use the flavor-spin Glozman-Riska interaction Hamiltonian with SU(3) flavor symmetry breaking. There are 27 different tetraquarks …
