We have improved our previous variational method based constituent quark model by introducing a complete set of 3-dimensional harmonic oscillator bases as the spatial part of the total wave function. To assess the validity of our approach, we compared the binding energy, thus calculated with the exact value for the hydrogen model. After fitting to the masses of the ground state hadrons, we apply our new method to analyze the doubly-heavy tetraquark states $qq'\bar{Q}\bar{Q'}$ and compared the result for the binding energies with that from other works. We also calculated the ground state masses of $T_{sc} (ud\bar{s}\bar{c})$ and $T_{sb} (ud\bar{s}\bar{b})$ with $(I,S) = (0,1), (0,2)$. We found that $T_{bb} (ud\bar{b}\bar{b})$ and $us\bar{b}\bar{b}$, both with $(I,S) = (0,1)$, are stable against the two lowest threshold meson states with binding energies $-145$ MeV and $-42$ MeV, respectively. We further found that $T_{cb} (ud\bar{c}\bar{b})$ is near the lowest threshold. The spatial sizes for the tetraquarks are also discussed.
We review the predictions of the quark model for the doubly-heavy tetraquarks $QQ\bar q\bar q$. The possibility of resonances near the $BB^*$ threshold in addition to a deeply bound state is discussed.
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 compar…
We outline the most important results regarding the stability of doubly heavy tetraquarks $QQ\bar q\bar q$ with an adequate treatment of the four-body dynamics. We consider both color-mixing and spin-dependent effects. Our results are straightforwardly applied to the case of all-heavy tetraquarks $QQ\bar Q\bar Q$. We conclude that the stability is favored in the limit $M_Q/m_q \gg 1$ pointing to the stability of the $bb\bar u\bar d$ state and the instability of all-heavy tetraquarks.
We discuss the adequate treatment of the 3- and 4-body dynamics for the quark model picture of double-charm baryons and tetraquarks. We stress that the variational and Born-Oppenheimer approximations give energies very close to the exact ones, while the diquark approximation might be rather misleading. The Hall-Post inequalities also provide very useful lower bounds that exclude the possibility of stable tetraquarks for some mass ratios and some color wave functions.
We perform a constituent quark model analysis for the masses of the doubly heavy tetraquark states $T_{QQ}$ after we fix the parameters to fit the masses of the newly observed $Ξ_{cc}^{++}$ and hadrons involving heavy quarks relevant to the stability of these states. We investigate in detail how the relative distances between quark pairs vary as we change the quark content and how they affect the various contributions to the total tetraquark masses. We also find that our full calculations give in general less binding compared to simplified quark model calculations that treat quark dynamics ins…
Spectrum of the doubly heavy tetraquarks, $bb\bar q\bar q$, is studied in a constituent quark model. Four-body problem is solved in a variational method where the real scaling technique is used to identify resonant states above the fall-apart decay thresholds. In addition to the two bound states that were reported in the previous study we have found several narrow resonant states above the $BB^*$ and $B^*B^*$ thresholds. Their structures are studied and are interpreted by the quark dynamics. A narrow resonance with spin-parity $J^P=1^+$ is found to be a mixed state of a compact tetraquark and …
Energy spectrum of doubly heavy tetraquarks, $T_{QQ}$ ($QQ \bar{q} \bar{q}$ with $Q = c, b$ and $q = u, d, s$), is studied in the potential chiral-diquark model. Using the chiral effective theory of diquarks and the quark-diquark-based potential model, the $T_{bb}$, $T_{cc}$, and $T_{cb}$ tetraquarks are described as a three-body system composed of two heavy quarks and an antidiquark. We find several $T_{bb}$ bound states, while no $T_{cc}$ and $T_{cb}$ (deep) bound state is seen. We also study the change of the $T_{QQ}$ tetraquark masses under restoration of chiral symmetry.
We review the physics of doubly-heavy baryons $QQq$ and tetraquarks $QQ\bar q\bar q$. For the latter, the stability is reached for large enough mass ratio $M/m$, even when spin forces and color mixing are neglected. It is thus customarily claimed that $bb\bar q\bar q$ in its ground state cannot decay into $b\bar q+b\bar q$. In some model, $cc\bar u\bar d$ is shown to be stable if color mixing and spin effects are properly taken into account. It is conjectured that some $bc\bar q\bar q'$ benefits from favorable adjustments of the gluon tubes in the confinement regime. Some recent studies of pen…
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.
Using an extended chromomagnetic model, we perform a systematic study of the masses of the doubly heavy tetraquarks. We find that the ground states of the doubly heavy tetraquarks are dominated by color-triplet $\ket{(qq)^{\bar{3}_{c}}(\bar{Q}\bar{Q})^{3_{c}}}$ configuration, which is opposite to that of the fully heavy tetraquarks. The combined results suggest that the color-triplet configuration becomes more important when the mass difference between the quarks and antiquarks increases. We find three stable states which lie below the thresholds of two pseudoscalar mesons. They are the $IJ^{P…
In the paper we discuss contribution of the doubly intrinsic heavy mechanism into the production of $B_c$ meson, the doubly heavy baryons and the all-charm tetraquark at a future fixed-target experiment at the LHC (AFTER@LHC). The production cross sections and the mean values of Feynman-x for the finale states are presented.
We study the spectra of the doubly charmed tetraquark states in a diquark-antidiquark model. The doubly charmed tetraquark states form an antitriplet and a sextet configurations according to flavor SU(3) symmetry. For the tetraquark state $[qq'][\bar c\bar c]$, we show the mass for both bound and excited states. The two-body decays of tetraquark states $T^{cc}[0^+]$ and $T^{cc}[1^{--}]$ to charmed mesons have also been studied. In the end,the doubly charmed tetraquarks decays to a charmed baryon and a light baryon have been studied in the SU(3) flavor symmetry.
In the present work, the mass spectra of doubly heavy tetraquarks $T_{QQ^\prime}$ are systematically investigated in a relativized quark model. The four-body systems including the Coulomb potential, confining potential, spin-spin interactions, and relativistic corrections are solved within the variational method. Our results suggest that the $IJ^P=01^+$ $bb \bar u \bar d$ state is 54 MeV below the relevant $\bar B \bar B$ and $\bar B \bar B^*$ thresholds, which indicates that both strong and electromagnetic decays are forbidden, and thus this state can be a stable one. Its large hidden color c…
The LHCb experiment at CERN has discovered a doubly charmed isoscalar tetraquark $T_{cc}$ with the quantum numbers of $c c \bar u \bar d$ and mass of about 3875 MeV/$c^2$, decaying to $D^0 D^0 π^+$ through the intermediate channel $D^{*+} D^0$. We present a study of its strange companions with the quantum numbers of $c c \bar q \bar s$, where $q = u, d$ and isospin violation is neglected.
In the framework of the chiral quark model along with complex scaling range, we perform a dynamical study on the low-lying $S$-wave doubly-heavy tetraquark states ($QQ\bar{q}\bar{q}$, $Q=c, b$ and $q=u, d$) with an accurate computing approach, Gaussian expansion method. The meson-meson and diquark-antidiquark configurations within all possible color structures for spin-parity quantum numbers $J^P=0^+$, $1^+$ and $2^+$, and in the $0$ and $1$ isospin sectors are considered. Possible tightly bound and narrow resonance states are obtained for doubly-charm and doubly-bottom tetraquarks with $IJ^P=…
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.
We give heavy quark-diquark symmetry predictions for doubly heavy baryons and tetraquarks in light of the recent discovery of the $Ξ_{cc}^{++}$ by LHCb. For five excited doubly charm baryons that are predicted to lie below the $Λ_c D$ threshold, we give predictions for their electromagnetic and strong decays using a previously developed chiral Lagrangian with heavy quark-diquark symmetry. Based on the mass of the $Ξ_{cc}^{++}$, the existence of a doubly heavy bottom $I=0$ tetraquark that is stable to the strong and electromagnetic decays has been predicted. If the mass of this state is below 1…
In the light of the recent discovery of the $Ξ^{++}_{cc}$ by LHCb collaboration, we study the stable doubly heavy tetraquarks. These states are compact exotic hadrons which can be approximated as the diquark-anti-diquark correlations. In the flavor SU(3) symmetry, they form an SU(3) triplet or anti-sextet. The spectra of the stable doubly heavy tetraquark states are predicted by Sakharov-Zeldovich formula. We find that the $T^+_{cc\bar{u}\bar{d}}({\bf 3})$ is about 16MeV below the $DD^*$ threshold, while $T^{-}_{bb\bar{u}\bar{d}}({\bf 3})$ is about 73MeV below the $BB^*$ threshold. We then stu…
In the heavy-quark limit, the two heavy quarks in a doubly heavy baryon or a doubly heavy tetraquark are bound by their color-Coulomb potential into a compact diquark. The doubly heavy hadrons are related by the approximate heavy-quark--diquark symmetry of QCD to the heavy hadrons obtained by replacing the heavy diquark by a heavy antiquark. Effective field theories can be used to expand the masses of singly heavy hadrons and doubly heavy hadrons in inverse powers of the heavy quark masses. The coefficients in the expansions for doubly heavy tetraquarks can be determined from those for heavy m…
With the discovery of a doubly charmed $Ξ_{cc}$ baryon a somewhat forgotten issue of tetraquarks containing two heavy and two light (anti) quarks, ${\cal T}_{QQ}$, triggered theorist's interest. We discuss quark model estimates of ${\cal T}_{QQ}$ masses and such objects including a model where the light sector is treated as a soliton. We show that this model has different large $N_c$ limit than other approaches.
Chiral Quark Soliton Model has been successfully applied to describe heavy baryon spectrum, both for charm and bottom, leading to the conclusion that the heavy quark has no effect on the soliton. This suggests that replacing a heavy quark by a heavy anti-diquark $\bar{Q}\bar{Q}$ in color triplet should give a viable description of heavy tetraquarks. We follow this strategy to compute tetraquark masses. To estimate heavy diquark masses we use Cornell potential with appropriately rescaled parameters. The lightest charm tetraquark is 70 MeV above the $DD^*$ threshold. On the contrary, both non-st…
In the present work, we investigate the scalar, axialvector and tensor doubly-charmed tetraquark molecular states without strange, with strange and with doubly-strange via the QCD sum rules, and try to make assignment of the $T^+_{cc}$ from the LHCb collaboration in the scenario of molecular states. The predictions favor assigning the $T^+_{cc}$ to be the lighter $DD^{*}$ molecular state with the spin-parity $J^P=1^+$ and isospin $I=0$, while the heavier $DD^{*}$ molecular state with the spin-parity $J^P=1^+$ and isospin $I=1$ still escapes experimental detections, the observation of the heavi…
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.
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…
We systematically investigate the stability of the doubly heavy tetraquark states $[QQ][\bar{q}\bar{q}]$ ($Q=c$ and $b$, $q=u$, $d$ and $s$) within the framework of the color flux-tube model involving a multibody confinement potential, $σ$-exchange, one-gluon-exchange and one-Goldstone-boson-exchange interactions. Our numerical analysis indicates that the states $[bb][\bar{u}\bar{d}]$ with $01^+$ and $[bb][\bar{u}\bar{s}]$ with $\frac{1}{2}1^+$ are the most promising stable states against strong interactions. The states $[cc][\bar{u}\bar{d}]$ with $01^+$, $[bc][\bar{u}\bar{d}]$ with $00^+$, $0…
We develop a moment QCD sum rule method augmented by fundamental inequalities to study the existence of exotic doubly hidden-charm/bottom tetraquark states made of four heavy quarks. Using the compact diquark-antidiquark configuration, we calculate the mass spectra of these tetraquark states. There are 18 hidden-charm $cc\bar c\bar c$ tetraquark currents with $J^{PC} = 0^{++}$, $0^{-+}$, $0^{--}$, $1^{++}$, $1^{+-}$, $1^{-+}$, $1^{--}$, and $2^{++}$. We use them to perform QCD sum rule analyses, and the obtained masses are all higher than the spontaneous dissociation thresholds of two charmoni…
We study the mass spectra for the $cc\bar c\bar c$ and $bb\bar b\bar b$ tetraquark states by developing a moment sum rule method. Our results show that the $bb\bar b\bar b$ tetraquarks lie below the threshold of $η_b(1S)η_b(1S)$. They are probably stable and very narrow. The masses for the doubly hidden-charm states $cc\bar c\bar c$ are higher than the spontaneous dissociation thresholds of two charmonium mesons. We suggest to search for such states in the $J/ψJ/ψ$ and $η_c(1S)η_c(1S)$ channels.
Inverse Excitation Hierarchy in Doubly-Heavy Tetraquarks within the Diquark Model
Nagoya University（名古屋大学）；Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University（名古屋大学小林-益川粒子宇宙起源研究所）；Research Center for Nuclear Physics, Osaka University（大阪大学核物理研究中心）；Advanced Science Research Center, Japan Atomic Energy Agency（日本原子能研究开发机构先进科学研究中心）
We investigate the possibility of $qq^\prime \bar b \bar b$ tetraquark bound states using $n_f=2+1$ lattice QCD ensembles with pion masses $\simeq 164$, $299$, and $415$ MeV. Motivated by observations from heavy baryon phenomenology, we consider two lattice interpolating operators both of which are expected to couple efficiently to tetraquark states: one with diquark-antidiquark and one with a meson-meson structure. Using nonrelativistic QCD to simulate the bottom quarks, we study the $ud\bar b \bar b$, $\ell s\bar b \bar b$ channels with $\ell=u,d$, and find unambiguous signals for strong-int…
Spectrum of the low-lying hidden- and double-charm tetraquark states are investigated in a nonrelativistic quark potential model, where the Instanton-induced interaction is taken as the residual spin-dependent hyperfine interaction between quarks. The model parameters are fixed by fitting the spectrum of the ground hadron states. Our numerical results show that masses of several presently studied tetraquark states are close to those of the experimentally observed candidates of exotic meson, which indicates that the corresponding compact tetraquark components may take considerable probabilities…
We study the weak decays of exotic tetraquark states ${b\bar c}{q\bar q}$ with two heavy quarks. Under the SU(3) symmetry for light quarks, these tetraquarks can be classified into an octet plus a singlet: $3\bigotimes\bar 3=1\bigoplus8$. We will concentrate on the octet tetraquarks with $J^{P}=0^{+}$, and study their weak decays, both semileptonic and nonleptonic. Hadron-level effective Hamiltonian is constructed according to the irreducible representations of the SU(3) group. Expanding the Hamiltonian, we obtain the decay amplitudes parameterized in terms of a few irreducible quantities. Bas…
We discuss the production of the exotic doubly-charmed tetraquark mesons ${\rm T}_{{\rm c}{\rm c}}({\rm c}{\rm c}\bar{\rm u}\bar{\rm d})$ from electron-positron collisions. ${\rm T}_{{\rm c}{\rm c}}({\rm c}{\rm c}\bar{\rm u}\bar{\rm d})$ is a compact exotic hadron whose binding energy is provided by the diquark correlations. We evaluate the production cross section in the electron-positron collisions using the nonrelativistic QCD framework, and investigate the difference of the production cross section for different color configurations in two charm quarks (antitriplet and sextet), where the m…
We investigate the production of exotic tetraquarks, $QQ\bar{q}\bar{q} \equiv T_{QQ}$ ($Q=c$ or $b$ and $q=u$ or $d$), in relativistic heavy-ion collisions using the quark coalescence model. The $T_{QQ}$ yield is given by the overlap of the density matrix of the constituents in the emission source with the Wigner function of the produced tetraquark. The tetraquark wave function is obtained from exact solutions of the four-body problem using realistic constituent models. The production yields are typically one order of magnitude smaller than previous estimations based on simplified wave functio…
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…
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…
In this article, we take the scalar diquark and antidiquark operators as the basic constituents, construct the $Cγ_5\otimes\stackrel{\leftrightarrow}{\partial}_μ\otimes γ_5C$ type tetraquark current to study the $Y(10750)$ with the QCD sum rules. The predicted mass $M_{Y}=10.75\pm0.10\,\rm{GeV}$ and width $Γ_Y= 33.60^{+16.64}_{-9.45}\,{\rm{MeV}}$ support assigning the $Y(10750)$ to be the diquark-antidiquark type vector hidden-bottom tetraquark state, which has a relative P-wave between the diquark and antidiquark constituents.
