Tetraquark States Research Articles

Improved XTZ masses and mass ratios from Laplace sum rules at NLO

We present improved estimates of the couplings, masses and mass ratios of the ZQ,XQ 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, where the NLO factorized PT QCD corrections are included which is important for giving a meaning on the running MS‾ heavy quark mass used in the analysis. We show that combined R and DRSR can provide more precise results. In the 1st part of the paper, we conclude that the observed Xc(3872) and Zc(3900) are tetramoles states (superposition of quasi-degenerated molecule and a tetraquark states having (almost) the same coupling to the currents) with the predicted masses: MTXc=3876(44)MeV and MTZc=3900(42)MeV. In the 2nd part, we focus on the analysis of the four-quark nature of different TQQq¯q¯′1+ and 0+ states within the 3¯c3c interpolating currents. The final results from R and R⊕ DRSR are summarized in Table 7. Combined R and DRSR calibrated to the observed Xc(3872) lead to a precise prediction of e.g. MTcc1+=3886(6)MeV. In a similar way, the DRSR for the MTcc0+/MTcc1+ calibrated to MTcc1+ gives MTcc0+=3883(3)MeV. The SU3 breaking ratios MTccs¯s¯0+/MTcc0+ lead to the improved mass predictions: MTccs¯s¯0+=3988(12)MeV. In the 3rd part, the analysis is extended to the beauty mesons, where we find the tetramole masses: MTZb=10579(99)MeV and MXb=10545(131)MeV. We also observe that the Tbbq¯q¯′1+,0+ (q,q′≡u,d,s) states are (almost) stable (within the errors) against strong interactions. In the 4th part, we (critically) review and correct some recent LSR estimates of the TQQq¯q¯′1+,0+ masses. Our combined LSR ⊕ DRSR results are confronted with the ones from some other approaches (lattices and quark models) in Fig. 26.

Doubly-heavy tetraquark states and * *Partly supported by the National Natural Science Foundation of China (11847145, 11865019)

Inspired by the recent observation of a very narrow state, called , by the LHCb collaboration, the possible bound states and low-lying resonance states of the doubly-heavy tetraquark states ( ) and ( ) are searched in the framework of a chiral quark model with an accurate few-body method, the Gaussian expansion method. The real scaling method is also applied to identify the genuine resonance states. In the calculation, the meson–meson structure, diquark–antidiquark structure, and their coupling are all considered. The numerical results show: (i) For and , only states are bound in different quark structures. The binding energy varies from a few MeV for the meson–meson structure to over 100 MeV for the diquark–antidiquark structure. For example, for , in the meson–meson structure, there exists a weakly bound molecule state around 3841.4 MeV, 1.8 MeV below the , which may be a good candidate for the observed state by LHCb; however in the diquark–antidiquark structure, a deeper bound state with mass 3700.9 MeV is obtained. When considering the structure mixing, the energy of system decreases to 3660.7 MeV and the shallow bound state disappears. (ii) Besides bound states, several resonance states for with are proposed.

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

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

Mass spectra and decays of open-heavy tetraquark states

The observation of the exotic states ${X}_{0,1}(2900)$ with four open flavors by the LHCb Collaboration has promoted great interest in searching for the open-charm and open-bottom tetraquark states. In this work, we perform a systematic study of the open-heavy tetraquark systems $qq\overline{q}\overline{Q}$ ($q=u$, $d$, $s$ and $Q=c$, $b$) within the improved chromomagnetic interaction model. The mass spectra and color-spin wave functions of $S$-wave open-heavy tetraquark states with quantum numbers ${J}^{P}={0}^{+}$, ${1}^{+}$, and ${2}^{+}$ are calculated. A number of compact tetraquark states are predicted in both open-charm and open-bottom systems. The two-body decay properties of these tetraquark states are phenomenologically analyzed. Our results suggest that the exotic open-charm state ${X}_{0}(2900)$ observed by the LHCb Collaboration is likely a compact tetraquark state with quantum number $I{J}^{P}=0{0}^{+}$ (isospin singlet). For the open-bottom systems, our results also suggest a candidate for the exotic state ${X}^{\ifmmode\pm\else\textpm\fi{}}(5568)$ reported by the D0 Collaboration. The other tetraquark states predicted in this work may also be examined in future experiments.

Holographic tetraquarks and the newly observed Tcc+ at LHCb

We describe a heavy and exotic tetraquark state as a holographic molecule, by binding the lightest heavy-light meson $({0}^{\ensuremath{-}},{1}^{\ensuremath{-}})$ multiplet to a flavored sphaleron, in the bulk of the Witten-Sakai-Sugimoto model. Bound tetraquark states emerge as Efimov states in the heavy quark limit, with a binding energy for a charm tetraquark comparable to the ${T}_{cc}^{+}$ recently reported by the LHCb collaboration, but with a substantially smaller width, for a large but finite 't Hooft coupling. Fixing the parameters of the model at the empirical mass of ${T}_{cc}^{+}$, allows for a prediction of the bindings of the undiscovered bottom-charm and bottom tetraquarks.

Study of double J∕ψ production mechanisms at COMPASS

During the past 40 years, the production of pairs of [Formula: see text] mesons in high-energy hadron collisions has been studied by several experiments. Despite the experimental and theoretical efforts, the origin of the process and the relative weight of different production mechanisms remain unknown. Depending on the energy scale, the double [Formula: see text] production can be described by single- and/or double-parton scattering sub-processes and gluon–gluon fusion or quark–antiquark annihilation mechanisms. The process can also be related to the hypothesis of the intrinsic charm of hadrons and the existence of exotic tetraquark states which were predicted by various theoretical models and have recently been observed by the LHCb experiment. To study dimuon pair production, the COMPASS experiment at CERN uses a 190[Formula: see text]GeV/[Formula: see text] negative pion beam impinging on different nuclear targets. First preliminary COMPASS results on [Formula: see text] pair production will be presented. The search for possible signals from exotic resonances and the study of double [Formula: see text] production mechanisms will be discussed.

Study of light tetraquark spectroscopy

We calculate the masses of the $qq\overline{q}\overline{q}$ tetraquark ground state and first radial excited state in a constituent quark model where the Cornell-like potential and one-gluon exchange spin-spin coupling are employed. The three coupling parameters for the Cornell-like potential and one-gluon exchange spin-spin coupling are proposed mass-dependent in accordance with lattice QCD data, and all model parameters are predetermined by studying light, charmed, and bottom mesons. The theoretical predictions for light tetraquarks are compared with the observed exotic meson states in the light-unflavored meson sector, and tentative assignments are suggested. The work suggests that ${f}_{0}(1500)$ and ${f}_{0}(1710)$ might be ground light tetraquark states with $J=0$.

Mass spectra of doubly heavy tetraquarks in an improved chromomagnetic interaction model

Doubly heavy tetraquark states are the prime candidates for tightly bound exotic states. We present a systematic study of the mass spectra of the $S$-wave doubly heavy tetraquark states $QQ\bar{q}\bar{q}$ ($q=u, d, s$ and $Q=c, b$) with different quantum numbers $J^P=0^+$, $1^+$, and $2^+$ in the framework of the improved chromomagnetic interaction (ICMI) model. The parameters in the ICMI model are obtained by fitting the conventional hadron spectra and are used directly to predict the masses of the tetraquark states. For heavy quarks, the uncertainties of the parameters are obtained by comparing the masses of doubly and triply heavy baryons with those given by lattice QCD, QCD sum rules, and potential models. Several compact and stable bound states are found in both the doubly charmed and doubly bottomed tetraquark systems. The predicted mass of the $cc\bar u\bar d$ state is consistent with the recent measurement from the LHCb collaboration.

Coupled-channel approach to Tcc+ including three-body effects

A coupled-channel approach is applied to the charged tetraquark state ${T}_{cc}^{+}$ recently discovered by the LHCb Collaboration. The parameters of the interaction are fixed by a fit to the observed line shape in the three-body ${D}^{0}{D}^{0}{\ensuremath{\pi}}^{+}$ channel. Special attention is paid to the three-body dynamics in the ${T}_{cc}^{+}$ due to the finite life time of the ${D}^{*}$. An approach to the ${T}_{cc}^{+}$ is argued to be self-consistent only if both manifestations of the three-body dynamics, the pion exchange between the $D$ and ${D}^{*}$ mesons and the finite ${D}^{*}$ width, are taken into account simultaneously to ensure that three-body unitarity is preserved. This is especially important to precisely extract the pole position in the complex energy plane whose imaginary part is very sensitive to the details of the coupled-channel scheme employed. The ${D}^{0}{D}^{0}$ and ${D}^{0}{D}^{+}$ invariant mass distributions, predicted based on this analysis, are in good agreement with the LHCb data. The low-energy expansion of the ${D}^{*}D$ scattering amplitude is performed and the low-energy constants (the scattering length and effective range) are extracted. The compositeness parameter of the ${T}_{cc}^{+}$ is found to be close to unity, which implies that the ${T}_{cc}^{+}$ is a hadronic molecule generated by the interactions in the ${D}^{*+}{D}^{0}$ and ${D}^{*0}{D}^{+}$ channels. Employing heavy-quark spin symmetry, an isoscalar ${D}^{*}{D}^{*}$ molecular partner of the ${T}_{cc}^{+}$ with ${J}^{P}={1}^{+}$ is predicted under the assumption that the $D{D}^{*}\text{\ensuremath{-}}{D}^{*}{D}^{*}$ coupled-channel effects can be neglected.

Can we understand the decay width of the [formula omitted] state?

Inspired by the recent discovery of a doubly charmed tetraquark state Tcc+ by the LHCb Collaboration, we employ the effective Lagrangian approach to investigate the decay width of Tcc+→D+D0π0/D0D0π+ and Tcc+→D0D+γ with the assumption that Tcc+ is an isoscalar DD⁎ molecule. We show that both the Tcc→DDπ and Tcc→DDγ modes contribute to the decay width of Tcc, with the former being dominant. The resulting total decay width of about Γ=63 keV is smaller than the experimental decay width obtained from the Breit-Wigner fit of the LHCb data, Γ=410±165±43−38+18 keV, while close to the number obtained from the alternative unitary analysis, Γ=48±2−14+0 keV, which supports the molecular nature of Tcc.

Masses of fully heavy tetraquark states from a four-quark static potential model

In this article, we study the ground-state mass of full-heavy tetraquarks $cc\overline{c}\overline{c}$ and $bb\overline{b}\overline{b}$ with solving the nonrelativistic four-body systems. The flux-tube configurations, the tetraquark four-body potential butterfly, and the dimeson potential flip-flop of SU(3) lattice quantum chromodynamics have been applied to describe the tetraquark interaction. Our numerical analysis indicates that the disconnected and connected static potentials can predict the mass of tetraquark very close to experimental data.

Forming molecular states with hadronic rescattering

A method for modelling the prompt production of molecular states using the hadronic rescattering framework of the general-purpose Pythia event generator is introduced. Production cross sections of possible exotic hadronic molecules via hadronic rescattering at the LHC are calculated for the chi _{c1}(3872) resonance, a possible tetraquark state, as well as three possible pentaquark states, P_c^+(4312), P_c^+(4440), and P_c^+(4457). For the P_c^+ states, the expected cross section from Lambda _b decays is compared to the hadronic-rescattering production. The chi _{c1}(3872) cross section is compared to the fiducial chi _{c1}(3872) cross-section measurement by LHCb and found to contribute at a level of {mathcal {O}({1%})}. Finally, the expected yields of mathrm {P_c^{+}} production from hadronic rescattering during Run 3 of LHCb are estimated. The prompt background is found to be significantly larger than the prompt mathrm {P_c^{+}} signal from hadronic rescattering.

Multiquark-Oriented QCD Sum Rules

We propose to increase the factual reliability of descriptions of exotic multiquark hadrons utilizing the approach to bound states of strongly interacting constituents known as QCD sum rules, by allowing exclusively all contributions that potentially bear some relevance for multiquark states to enter the correlation functions that form the main ingredient of this framework. The route to this goal is illustrated for the (presumably least involved) special case of tetraquark states.

Higher mass spectra of the fully-charmed and fully-bottom tetraquarks

In this work, we calculate the higher mass spectra for the $2S$- and $1D$-wave fully-charmed and fully-bottom tetraquark states in a nonrelativistic potential quark model. The $2S$-wave fully-charmed/bottom tetraquark states lie in the mass range of $\ensuremath{\sim}(6.9,7.1)/(19.7,19.9)\text{ }\mathrm{GeV}$, apart from the highest ${0}^{++}$ state ${T}_{(cc\overline{c}\overline{c}){0}^{++}}(7185)/{T}_{(bb\overline{b}\overline{b}){0}^{++}}(19976)$. Most of the $2S$-wave states highly overlap with the high-lying $1P$-wave states. The masses for the $1D$-wave fully-charmed/bottom tetraquark states are predicted to be in the range of $\ensuremath{\sim}(6.7,7.2)/(19.5,20.0)\text{ }\text{ }\mathrm{GeV}$. The mass range for the $D$-wave tetraquark states cover most of the mass range of the $P$-wave states and the whole mass range of the $2S$-wave states. The narrow structure $X(6900)$ recently observed at LHCb in the di-$J/\ensuremath{\psi}$ invariant mass spectrum may be caused by the $1P$-, or $2S$-, or $1D$-wave ${T}_{(cc\overline{c}\overline{c})}$ states. The vague structure $X(7200)$ may be caused by the highest $2S$-wave state ${T}_{(cc\overline{c}\overline{c}){0}^{++}}(7185)$, two low-lying $3S$-wave states ${T}_{(cc\overline{c}\overline{c}){0}^{++}}(7240)$ and ${T}_{(cc\overline{c}\overline{c}){2}^{++}}(7248)$, and/or the high-lying $1D$-wave states with masses around 7.2 GeV and ${J}^{PC}={0}^{++},{1}^{++},{2}^{++},{3}^{++}$, or ${4}^{++}$. While it is apparent that the potential quark model calculations predict more states than the structures observed in the di-$J/\ensuremath{\psi}$ invariant mass spectrum, our calculations will help further understanding of the properties of these fully-heavy tetraquark states in their strong and magnetic interactions with open channels based on explicit quark model wave functions.

Exotic fully heavy QQ¯QQ¯ tetraquark states in 8[QQ¯]⊗8[QQ¯] color configuration

We have systematically calculated the mass spectra for S-wave and P-wave fully-charm $c\bar{c}c\bar{c}$ and fully-bottom $b\bar{b}b\bar{b}$ tetraquark states in the $\mathbf{8}_{[Q\bar{Q}]}\otimes \mathbf{8}_{[Q\bar{Q}]}$ color configuration, by using the moment QCD sum rule method. The masses for the fully-charm $c\bar cc\bar c$ tetraquark states are predicted about $6.3-6.5$ GeV for S-wave channels and $7.0-7.2$ GeV for P-wave channels. These results suggest the possibility that there are some $\mathbf{8}_{[c\bar{c}]}\otimes \mathbf{8}_{[c\bar{c}]}$ components in LHCb's di-$J/\psi$ structures. For the fully-bottom $b\bar{b}b\bar{b}$ system, their masses are calculated around 18.2 GeV for S-wave tetraquark states while 18.4-18.8 GeV for P-wave ones, which are below the $\eta_b\eta_b$ and $\Upsilon(1S)\Upsilon(1S)$ two-meson decay thresholds.

Mixing angles between the tetraquark states with two heavy quarks within QCD sum rules

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 $\theta$. 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.

Assignments of the X 4140 , X 4500 , X 4630 , and X 4685 Based on the QCD Sum Rules

In this article, we take into account our previous calculations based on the QCD sum rules, and tentatively assign the X 4630 as the D s ∗ D ¯ s 1 − D s 1 D ¯ s ∗ tetraquark molecular state or c s P c ¯ s ¯ A + c s A c ¯ s ¯ P tetraquark state with the J P C = 1 − + , and assign the X 3915 and X 4500 as the 1S and 2S c s A c ¯ s ¯ A tetraquark states, respectively, with the J P C = 0 + + . Then, we extend our previous works to investigate the LHCb’s new tetraquark candidate X 4685 as the first radial excited state of the X 4140 with the QCD sum rules and obtain the mass M X = 4.70 ± 0.12 GeV , which is in very good agreement with the experimental value 4684 ± 7 − 16 + 13 MeV . Furthermore, we investigate the two-meson scattering state contributions in details and observe that the two-meson scattering states alone cannot saturate the QCD sum rules, the contributions of the tetraquark states play an unsubstitutable role, and we can saturate the QCD sum rules with or without the two-meson scattering states.

Masses and strong decays of open charm hexaquark states Sigma _{c}^{(*)}{Sigma }_{c}^{(*)}

Inspired by the recent discovery of the doubly charmed tetraquark state T_{cc}^{+} by the LHCb Collaboration, we perform a systematic study of masses and strong decays of open charm hexaquark states {Sigma }_{c}^{(*)}Sigma _{c}^{(*)}. Taking into account heavy quark spin symmetry breaking, we predict several bound states of isospin I=0, I=1, and I=2 in the one boson exchange model. Moreover, we adopt the effective Lagrangian approach to estimate the decay widths of {Sigma }_{c}^{(*)}Sigma _{c}^{(*)} rightarrow Lambda _{c}Lambda _{c} and their relevant ratios via the triangle diagram mechanism, which range from a few MeV to a few tens of MeV. We strongly recommend future experimental searches for the {Sigma }_{c}^{(*)}Sigma _{c}^{(*)} hexaquark states in the Lambda _cLambda _c invariant mass distributions.

Does vacuum saturation work for the higher-dimensional vacuum condensates in the QCD sum rules?

In the QCD sum rules for the tetraquark (molecular) states, the higher-dimensional vacuum condensates play an important role in extracting the tetraquark masses. We carry out the operator product expansion up to the vacuum condensates of dimension-10 and observe that the vacuum condensates of dimensions 6, 8 and 10 have the same expressions but opposite signs for the [Formula: see text]-type and [Formula: see text]-type four-quark currents, which make their influences distinguishable, and they are excellent channels to examine the vacuum saturation approximation. We introduce a parameter [Formula: see text] to parametrize the derivation from the vacuum saturation or factorization approximation, and choose two sets of parameters to examine the influences on the predicted tetraquark masses, which can be confronted to the experimental data in the future. In all the channels, smaller value of the [Formula: see text] leads to better convergent behavior in the operator product expansion, which favors the vacuum saturation approximation.

Investigating new type of doubly charmed molecular tetraquarks composed of charmed mesons in the H and T doublets

Stimulated by the newly reported doubly-charmed tetraquark state $T_{cc}^+$ by LHCb, we carry out a systematic investigation of the $S$-wave interactions between the charmed meson ($D,\,D^{*}$) in $H$-doublet and the charmed meson ($D_{1},\,D_{2}^{*}$) in $T$-doublet by adopting the one-boson-exchange model. Both the $S$-$D$ wave mixing effect and the coupled channel effect are taken into account. By performing a quantitative calculation, we suggest that the $S$-wave $D^{*} D_{1}$ states with $I(J^{P})=0(0^{-},\,1^{-})$ and the $S$-wave $D^{*}D_{2}^{*}$ state with $I(J^{P})=0(1^{-})$ should be viewed as the most promising candidates of the doubly-charmed molecular tetraquark states, and the $S$-wave $DD_{1}$ state with $I(J^{P})=0(1^{-})$, the $S$-wave $DD_{2}^{*}$ state with $I(J^{P})=0(2^{-})$, and the $S$-wave $D^{*}D_{2}^{*}$ state with $I(J^{P})=0(2^{-})$ are the possible doubly-charmed molecular tetraquark candidates. With the accumulation of experimental data at Run III and after High-Luminosity-LHC upgrade, these predicted doubly-charmed molecular tetraquark states can be accessible at LHCb in the near future.