Scalar Tetraquark Research Articles

Scalar exotic mesons bbc¯c¯

Properties of doubly charged scalar tetraquarks bbc¯c¯ are investigated in the framework of the Quantum Chromodynamic (QCD) sum rule method. We model them as diquark–antidiquark states X 1 and X 2 built of axial-vector and pseudoscalar diquarks, respectively. The masses and current couplings of these particles are computed using the QCD two-point sum rule method. Results m 1 = (12715 ± 80) MeV and m 2 = (13370 ± 95) MeV obtained for the masses of these particles are used to determine their kinematically allowed decay modes. The full width Γ1 of the state X 1 is evaluated by taking into account its strong decays to mesons 2Bc− , and 2Bc*− . The processes X2→2Bc− , 2Bc*− and Bc−Bc−(2S) are employed to estimate Γ2. Predictions obtained for the full widths Γ1 = (63 ± 12) MeV and Γ2 = (79 ± 14) MeV of these structures and their masses may be utilized in experimental studies of fully heavy resonances.

Study of the isoscalar scalar bcu¯d¯ tetraquark Tbc with lattice QCD

We present a lattice QCD study of the elastic S-wave DB¯ scattering in search of tetraquark candidates with explicitly exotic flavor content bcu¯d¯ in the isospin I=0 and JP=0+ channel. We use four lattice QCD ensembles with dynamical u/d, s, and c quark fields generated by the MILC collaboration. A nonrelativistic QCD Hamiltonian, including improvement coefficients up to O(αsv4), is utilized for the bottom quarks. For the rest of the valence quarks we employ a relativistic overlap action. Five different valence quark masses are utilized to study the light quark mass dependence of the DB¯ scattering amplitude. The finite volume energy spectra are extracted following a variational approach. The elastic DB¯ scattering amplitudes are extracted employing Lüscher’s prescription. The light quark mass dependence of the continuum extrapolated amplitudes suggests an attractive interaction between the B¯ and D mesons. At the physical pseudoscalar meson mass (Mps=Mπ) the DB¯ scattering amplitude has a subthreshold pole corresponding to a binding energy of −39(−6+4)(−18+8) MeV with respect to the DB¯ threshold. The critical Mps at which the DB¯ scattering length diverges and the system becomes unbound corresponds to Mps*=2.94(15)(5) GeV. This result can hold significant experimental relevance in the search for a bound scalar Tbc tetraquark, which could well be the next “doubly heavy” bound tetraquark to be discovered with only weak decay modes. Published by the American Physical Society 2024

Fully charmed resonance X(6900) and its beauty counterpart

The fully heavy scalar tetraquarks T4Q=QQQ‾Q‾, (Q=c,b) are explored in the context of QCD sum rule method. We model T4Q as diquark-antidiquark systems composed of pseudoscalar constituents, and calculate their masses m(′) and couplings f(′) within the two-point sum rule approach. Our results m=(6928±50)MeV and m′=(18858±50)MeV for masses of the tetraquarks T4c and T4b prove that they can decay to hidden-flavor heavy mesons. The full width Γ4c of the T4c is evaluated by taking into account the decay channels T4c→J/ψJ/ψ, J/ψψ′, ηcηc, ηcηc(2S), ηcχc1(1P), and χc0χc0. The partial widths of these processes depend on strong couplings gi at vertices T4cJ/ψJ/ψ, T4cJ/ψψ′ etc., which are computed using the QCD three-point sum rule method. The decay T4b→ηbηb is used to find the width Γ4b of the T4b. The predictions for m and Γ4c=(128±22)MeV are compared with parameters of the fully charmed resonances reported by the LHCb, ATLAS, and CMS Collaborations. Based on this analysis, we interpret the tetraquark T4c as a candidate to the resonance X(6900). The mass m′ and width Γ4b=(94±28)MeV of the exotic meson T4b can be used in future experimental investigations of these states.

Exploring fully heavy scalar tetraquarks [formula omitted

The masses, current couplings and widths of the fully heavy scalar tetraquarks X4Q=QQQ‾Q‾, Q=c,b are calculated by modeling them as four-quark systems composed of axial-vector diquark and antidiquark. The masses m(′) and couplings f(′) of these tetraquarks are computed in the context of the QCD sum rule method by taking into account a nonperturbative term proportional to the gluon condensate 〈αsG2/π〉. Results m=(6570±55)MeV and m′=(18540±50)MeV are used to fix kinematically allowed hidden-flavor decay channels of these states. It turns out that, the processes X4c→J/ψJ/ψ, X4c→ηcηc, and X4c→ηcχc1(1P) are possible decay modes of X4c. The partial widths of these channels are evaluated by means of the couplings gi,i=1,2,3 which describe strong interactions of tetraquark X4c and mesons at relevant vertices. The couplings gi are extracted from the QCD three-point sum rules by extrapolating corresponding form factors gi(Q2) to the mass-shell of a final meson. The mass of the scalar tetraquark X4b is below the ηbηb and ϒ(1S)ϒ(1S) thresholds, therefore it does not fall apart to these bottomonia, but transforms to conventional particles through other mechanisms. Comparing m=(6570±55)MeV and Γ4c=(110±21)MeV with parameters of structures observed by the LHCb, ATLAS and CMS collaborations, we interpret X4c as the resonance X(6600) reported by CMS. Comparisons are made with other theoretical predictions.

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.

Next-to-leading order (NLO) perturbative effects in QCD sum-rule analyses of light tetraquark systems: A case study in the scalar-isoscalar channel

QCD sum-rule mass predictions for tetraquark states provide insights on the interpretations and internal structure of experimentally-observed exotic mesons. However, the overwhelming majority of tetraquark QCD sum-rule analyses have been performed at leading order (LO), which raises questions about the underlying theoretical uncertainties from higher-loop corrections. The impact of next-to-leading order (NLO) perturbative effects are systematically examined in scalar (JPC=0++) isoscalar light-quark tetraquark systems where comprehensive LO sum-rule analyses have been performed and NLO perturbative corrections to the correlators have previously been calculated. Using the scalar-isoscalar state as a detailed case study to illustrate the differences between LO and NLO analyses, it is shown that NLO effects in individual Laplace sum-rules are numerically significant and have an important role in improving the reliability of the sum-rule analyses by widening the Borel window. However, ratios of sum-rules are found to be less sensitive to NLO effects with the additional advantage of cancelling the anomalous dimension that emerges from the NLO corrections. NLO mass predictions based on these sum-rule ratios are thus remarkably robust despite the slow perturbative convergence of the underlying correlator. The mass predictions 0.52GeV<mσ<0.77GeV for the lightest scalar-isoscalar σ state are in good agreement with the four-quark interpretation of the f0(500), and the relative coupling strengths of the f0(980) and f0(500) to the tetraquark current agree with the pattern found in chiral Lagrangian analyses. Effects of the σ resonance width are studied for different models, including resonance shapes inspired by chiral Lagrangians.

Newly observed exotic doubly charmed meson [formula omitted

In this work, we treat the newly observed doubly charmed four-quark state Tcc+ as an axial-vector tetraquark with content ccu‾d‾, and calculate its spectroscopic parameters and width. The mass and current coupling of the tetraquark Tcc+ are found by means of the QCD two-point sum rule method by taking into account quark, gluon and mixed condensates up to dimension 10. The width of the Tcc+ is evaluated using partial widths of decay processes Tcc+→T˜π0 and Tcc+→Tcc;u‾u‾0π+, where T˜=ccu‾d‾ and Tcc;u‾u‾0 are scalar tetraquarks. To compute the partial width of the first process, we apply the QCD three-point sum rule approach and exact numerical value of the strong coupling g that corresponds to the vertex Tcc+T˜π0. The width of the second decay is estimated using isospin symmetry and the prediction obtained for the first channel. Our results for the mass m=(3868±124)MeV and width Γ=(489±92)keV of the tetraquark Tcc+ are in a nice agreement with recent measurements of the LHCb collaboration.

Weak decays of the double-beauty tetraquark

The spectroscopic parameters and decay channels of the axial-vector tetraquark 213 built of heavy diquark bb and light antidiquark us are explored using QCD sum rule method. Because this state is stable against strong and electromagnetic decays, we consider its semileptonic and nonleptonic decay modes. Partial widths of weak processes TAVb:s¯ → Z0b:s¯ lv¯l and Tb:s¯AV → Z0b:s¯ M are calculated using weak form factors Gi(q2) computed by QCD three-point sum rules: Z0b:s¯ is the scalar tetraquark with quark content bcus¯ and M is a vector meson. The full width and mean lifetime of the tetraquark TAVb:s¯ obtained in this work shed light on features of double-beauty tetraquarks and are useful for their experimental investigations.

Revisit the tetraquark candidates in the J/ψJ/ψ mass spectrum

In this paper, we introduce a relative [Formula: see text]-wave to construct the doubly-charm axialvector diquark operator, then take the doubly-charm axialvector (anti-)diquark operator as the basic constituent to construct the scalar and tensor tetraquark currents to study the scalar, axialvector and tensor fully-charm tetraquark states with the QCD sum rules. We observe that the ground state [Formula: see text]-type tetraquark states and the first radial excited states of the [Formula: see text]-type tetraquark states have almost degenerated masses, where the [Formula: see text] and [Formula: see text] stand for the diquark operators with and without the relative [Formula: see text]-wave, respectively, the broad structure above the [Formula: see text] threshold maybe consist of several diquark–antidiquark-type fully-charm tetraquark states.

Doubly-hidden scalar heavy molecules and tetraquarks states from QCD at NLO

Alerted by the recent LHCb discovery of exotic hadrons in the range (6.2 -- 6.9) GeV, we present new results for the doubly-hidden scalar heavy $(\bar QQ) (Q\bar Q)$ charm and beauty molecules using the inverse Laplace transform sum rule (LSR) within stability criteria and including the Next-to-Leading Order (NLO) factorized perturbative and $\langle G^3\rangle$ gluon condensate corrections. We also critically revisit and improve existing Lowest Order (LO) QCD spectral sum rules (QSSR) estimates of the $({ \bar Q \bar Q})(QQ)$ tetraquarks analogous states. In the example of the anti-scalar-scalar molecule, we separate explicitly the contributions of the factorized and non-factorized contributions to LO of perturbative QCD and to the $\langle\alpha_sG^2\rangle$ gluon condensate contributions in order to disprove some criticisms on the (mis)uses of the sum rules for four-quark currents. We also re-emphasize the importance to include PT radiative corrections for heavy quark sum rules in order to justify the (ad hoc) definition and value of the heavy quark mass used frequently at LO in the literature. Our LSR results for tetraquark masses summarized in Table II are compared with the ones from ratio of moments (MOM) at NLO and results from LSR and ratios of MOM at LO (Table IV). The LHCb broad structure around (6.2 --6.7) GeV can be described by the $\overline{\eta}_{c}{\eta}_{c}$, $\overline{J/\psi}{J/\psi}$ and $\overline{\chi}_{c1}{\chi}_{c1}$ molecules or/and their analogue tetraquark scalar-scalar, axial-axial and vector-vector lowest mass ground states. The peak at (6.8--6.9) GeV can be likely due to a $\overline{\chi}_{c0}{\chi}_{c0}$ molecule or/and a pseudoscalar-pseudoscalar tetraquark state. Similar analysis is done for the scalar beauty states whose masses are found to be above the $\overline\eta_b\eta_b$ and $\overline\Upsilon(1S)\Upsilon(1S)$ thresholds.

A family of double-beauty tetraquarks: Axial-vector state * *The work of K. A, B. B., and H. S was Supported in part by the TUBITAK (119F050)

The spectroscopic parameters and decay channels of the axial-vector tetraquark (in what follows, ) are explored using the quantum chromodynamics (QCD) sum rule method. The mass and coupling of this state are calculated using two-point sum rules by taking into account various vacuum condensates, up to 10 dimensions. Our prediction for the mass of this state confirms that it is stable with respect to strong and electromagnetic decays and can dissociate to conventional mesons only via weak transformations. We investigate the dominant semileptonic and nonleptonic decays of . In these processes, is a scalar tetraquark built of a color-triplet diquark and an antidiquark, whereas M is one of the vector mesons , , , and . To calculate the partial widths of these decays, we use the QCD three-point sum rule approach and evaluate the weak transition form factors ( ), which govern these processes. The full width and the mean lifetime of the tetraquark are computed using the aforementioned weak decays. The obtained information about the parameters of and is useful for experimental investigations of these double-heavy exotic mesons.

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 $\mathcal{O}(\alpha_s^2)$.

Stable scalar tetraquark $$T_{bb;\bar{u}\bar{d}}^{-}$$

The mass and coupling of the scalar tetraquark $T_{bb;\overline{u}\overline{d }}^{-}$ (hereafter $T_{b:\overline{d}}^{-} $) are calculated in the context of the QCD two-point sum rule method. In computations we take into account effects of various quark, gluon and mixed condensates up to dimension ten. The result obtained for the mass of this state $m=(10135\pm 240)~\mathrm{MeV} $ demonstrates that it is stable against the strong and electromagnetic decays. We also explore the dominant semileptonic $T_{b:\overline{d}}^{-} \to \widetilde{Z}_{bc;\bar{u}\bar{d}}^{0}l\overline{\nu }_{l}$ and nonleptonic decays $T_{b:\overline{d}}^{-} \to \widetilde{Z}_{bc;\bar{u}\bar{ d}}^{0}M$, where $\widetilde{Z}_{bc;\bar{u}\bar{d}}^{0}$ is the scalar tetraquark composed of color-sextet diquark and antidiquark, and $M$ is one of the final-state pseudoscalar mesons $\pi^{-}, K^{-}, D^{-}$ and $D_s^{-}$ , respectively. The partial widths of these processes are calculated in terms of the weak form factors $G_{1(2)}(q^2)$, which are determined from the QCD three-point sum rules. Predictions for the mass, full width $\Gamma _{\mathrm{full}} =(10.88\pm 1.88)\times 10^{-10}~\mathrm{MeV}$, and mean lifetime $\tau=0.61_{-0.09}^{+0.13}~\mathrm{ps}$ of the $T_{b:\overline{d} }^{-}$ obtained in the present work can be used in theoretical and experimental studies of this exotic state.

Decay modes of the scalar exotic meson Tbs;u¯d¯−

We investigate the semileptonic decay of the scalar tetraquark $T_{bs; \overline{u}\overline{d}}^{-}$ to final state $T_{cs;\overline{u}\overline{d} }^{0} l \overline{\nu}_l$, which proceeds due to the weak transition $b \to c l \overline{\nu}_l$. For these purposes, we calculate the spectroscopic parameters of the final-state scalar tetraquark $T_{cs;\overline{u}\overline{ d}}^{0}$. In calculations we use the QCD sum rule method by taking into account the quark, gluon, and mixed condensates up to dimension 10. The mass of the $T_{cs;\overline{u}\overline{d}}^{0}$ obtained in the present work $( 2878 \pm 128 )~\mathrm{MeV}$ indicates that it is unstable against the strong interactions, and can decay to the mesons $D^{0}\overline{K}^{0}$ and $D^{+}K^{-}$. Partial widths of these $S$-wave modes as well as the full width of the tetraquark $T_{cs;\overline{u}\overline{d}}^{0}$ are found by means of the QCD light-cone sum rule method and technical tools of the soft-meson approximation. The partial widths of the main semileptonic processes $T_{bs;\overline{u}\overline{d}}^{-} \to T_{cs;\overline{u} \overline{d}}^{0}l\overline{\nu}_l$, $l=e, \mu$, and $\tau$ are computed by employing the weak form factors $G_{1}(q^2)$ and $G_{2}(q^2)$, which are extracted from the QCD three-point sum rules. We also trace back the weak transformations of the stable tetraquark $T_{bb;\overline{u}\overline{d} }^{-} $ to conventional mesons. The obtained results for the full width $ \Gamma_{\mathrm{full}}=(3.28\pm 0.60) \times 10^{-10}~\mathrm{MeV} $ and mean lifetime $\tau=2.01_{-0.31}^{+0.44}~\mathrm{ps}$ of $T_{bs;\overline{u} \overline{d}}^{-}$, as well as predictions for decay channels of the tetraquark $T_{bb;\overline{u}\overline{d}}^{-}$ can be used in experimental studies of these exotic states. \end{abstract}

Scalar or Vector Tetraquark State Candidate: Zc(4100)**supported by National Natural Science Foundation under Grant No. 11775079.

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 Zc(4100) to be a scalar or vector tetraquark state. If the Zc(4100) is a scalar tetraquark state without mixing effects, it should have a mass about 3.9 GeV or 4.0 GeV rather than 4.1 GeV; on the other hand, if the Zc(4100) is a vector tetraquark state, it should have a mass about 4.2 GeV rather than 4.1 GeV. However, if we introduce mixing, a mixing scalar tetraquark state can have a mass about 4.1 GeV. As a byproduct, we obtain an axialvector tetraquark candidate for the Zc(4020).

Strong decays of double-charmed pseudoscalar and scalar ccu¯d¯ tetraquarks

The strong decays of the pseudoscalar and scalar double-charmed tetraquarks $ T_{cc;\overline{u}\overline{d}}^{+}$ and $\widetilde{T}_{cc;\overline{u} \overline{d}}^{+}$ are investigated in the framework of the QCD sum rule method. The mass and coupling of these exotic four-quark mesons are calculated in the framework of the QCD two-point sum rule approach by taking into account vacuum condensates of the quark, gluon, and mixed local operators up to dimension 10. Our results for masses $m_{T}=(4130~\pm 170)~ \mathrm{MeV} $ and $m_{\widetilde{T}}=(3845~\pm 175)~\mathrm{MeV}$ demonstrate that these tetraquarks are strong-interaction unstable resonances and decay to conventional mesons through the channels $T_{cc; \overline{u}\overline{d}}^{+} \to D^{+}D^{\ast }(2007)^{0},~D^{0}D^{\ast }(2010)^{+}$ and $\widetilde{T}_{cc;\overline{u}\overline{d}}^{+}\to D^{+}D^{0}$. Key quantities necessary to compute the partial width of these decay modes, i.e., the strong couplings of two $D$ mesons and a corresponding tetraquark $g_i,~i=1,2$, and $G$ are extracted from the QCD three-point sum rules. The full width $\Gamma _{T}=(129.9\pm 23.5)~\mathrm{ MeV}$ demonstrates that the tetraquark $T_{cc;\overline{u}\overline{d}}^{+}$ is a broad resonance, whereas the scalar exotic meson with $\Gamma _{ \widetilde{T}}=(12.4\pm 3.1)~\mathrm{MeV}$ can be classified as a relatively narrow state.

Melting temperature for scalar hadrons in AdS / QCD models

We consider an analysis to potentials related to Schrödinger like equations for scalar fields in a 5D AdS black hole background with dilaton in order to get melting temperatures for different hadrons in a thermal bath. In approach considered it is not necessary to calculate spectral functions and it is easy to get results for different kind of hadrons. Here we present results for scalar mesons, glueballs, hybrid mesons and tetraquarks.

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.

Masses of Charmed and Bottom Tetraquarks in the Non-Relativistic Quark Model

Heavy tetraquark states are studied within the diquark-antidiquark picture in the framework of a simple constituent quark model. Considering hyperfine spin and isospin interactions, we predict the masses of the scalar diquarks and of the open and hidden charmed and bottom scalar tetraquarks. Our results indicate the scalar resonances [Formula: see text] and [Formula: see text] have a sizable tetraquark amount in their wave function, while it turns out the scalar state [Formula: see text] should not be considered as being predominately diquark-antidiquark bound states.