Doubly heavy tetraquarks have emerged as new probes to study the heavy hadron spectrum. With the experimental observation of the $J^P=1^+$ $T_{cc}^+$, they pose a unique opportunity to bring together efforts in experiment, phenomenology, and lattice QCD. In lattice calculations they are accessible as ground states, unlike hidden flavor tetraquarks, and this enables accurate determinations of the scattering parameters alongside the binding energies of these tetraquarks. Today, lattice calculations firmly predict $J^P=1^+$ $T_{bb}^{ud}$ and $T_{bb}^{us}$ as QCD bound states, while recent studies approaching the $J^P=1^+$ $T_{cc}^{ud}$ find it to be a virtual bound state at slightly non-physical input quark masses. Studies of the $J^P=1^+$ $T_{bc}^{ud}$ are ongoing and a new focus area. In light of these developments the evolution of this field until this point is reviewed. Emphasis is put on the methods in lattice spectroscopy that enable a robust evaluation of the lattice studies gathered. They are further reviewed towards their limitations and achievements. Current challenges and opportunities are discussed, including possibilities to approach the left-hand cut in the scattering analysis of the charm candidates and towards understanding the structure of those including two bottom quarks.
The phenomenology of the so-called X, Y and Z hadronic resonances is hard to reconcile with standard charmonium or bottomonium interpretations. It has been suggested that some of these new hadrons can possibly be described as tightly bound tetraquark states and/or as loosely bound two-meson molecules. In the present paper we focus on the hypothetical existence of flavored, doubly charmed, tetraquarks. Such states might also carry double electric charge, and in this case, if discovered, they could univocally be interpreted in terms of compact tetraquarks. Flavored tetraquarks are also amenable …
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 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…
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…
The doubly charm tetraquark with flavor $cc\bar u\bar d$ and isospin $I\!=\!0$ is investigated by calculating the $DD^*$ scattering amplitude with lattice QCD. The simulation is done on CLS ensembles with dynamical $u/d,s$ quarks and $m_π\simeq 280~$MeV for two charm quark masses, one slightly larger and one slightly lower than the physical value. The scattering amplitudes for partial waves $l=0,1$ are extracted near-threshold via the Lüscher's method by considering systems with total momenta $PL/(2π)=0,1,\sqrt{2},2$ on two spatial volumes. A virtual bound state pole in the $DD^*$ scattering a…
We use lattice QCD to investigate the spectrum of the $\bar{b} \bar{b} u d$ four-quark system with quantum numbers $I(J^P) = 0(1^+)$. We use five different gauge-link ensembles with $2+1$ flavors of domain-wall fermions, including one at the physical pion mass, and treat the heavy $\bar{b}$ quark within the framework of lattice nonrelativistic QCD. Our work improves upon previous similar computations by considering in addition to local four-quark interpolators also nonlocal two-meson interpolators and by performing a Lüscher analysis to extrapolate our results to infinite volume. We obtain a b…
We explore properties of the doubly charged vector tetraquark $Z_{\mathrm{V} }^{++}=[cu][\overline{s}\overline{d}]$ built of four quarks of different flavors using the QCD sum rule methods. The mass and current coupling of $Z_{ \mathrm{V}}^{++}$ are computed in the framework of the QCD two-point sum rule approach by taking into account quark, gluon and mixed vacuum condensates up to dimension $10$. The full width of this tetraquark is saturated by $S$-wave $Z_{\mathrm{V}}^{++} \to π^{+}D_{s1}(2460)^{+},\ ρ^{+}D_{s0}^{\ast }(2317)^{+}$, and $P$-wave $Z_{\mathrm{V}}^{++} \to π^{+}D_{s}^{+},\ K^{…
We search for possibly existent bound states in the heavy-light tetraquark channels with quark content $ \bar{b}\bar{b}ud $, $ \bar{b}\bar{b}us $ and $ \bar{b}\bar{c}ud $ using lattice QCD. We carry out calculations on several gauge link ensembles with $ N_f=2+1 $ flavours of domain-wall fermions and consider a basis of local and non-local interpolators. Besides extracting the energy spectrum from the correlation matrices, we also perform a Lüscher analysis to extrapolate our results to infinite volume.
The mass and coupling of the doubly charmed $J^P=0^{-}$ diquark-antidiquark states $T_{cc;\bar{s} \bar{s}}^{++}$ and $T_{cc;\bar{d} \bar{s}}^{++}$ that bear two units of the electric charge are calculated by means of QCD two-point sum rule method. Computations are carried out by taking into account vacuum condensates up to and including terms of tenth dimension. The dominant $S$-wave decays of these tetraquarks to a pair of conventional $ D_{s}^{+}D_{s0}^{\ast +}(2317)$ and $D^{+}D_{s0}^{\ast +}(2317)$ mesons are explored using QCD three-point sum rule approach, and their widths are found. The…
The spectroscopic parameters and decay channels of the doubly charged scalar, pseudoscalar and axial-vector charm-strange tetraquarks $Z_{ \overline{c}s}=[sd][\overline u \overline c]$ are explored within framework of the QCD sum rule. The masses and current couplings of these diquark-antidiquark states are calculated by means of two-point correlation functions and taking into account the vacuum condensates up to eight dimensions. To compute the strong couplings of $Z_{\overline{c}s}$ states with $D,\ D_{s},\ D^{\ast},\ D_{s}^{\ast},\ D_{s1}(2460),\ D_{s0}^{\ast}(2317),\ π$ and $K$ mesons we u…
In this work we investigate the existence of bound states for doubly heavy tetraquark systems $ \bar{Q}\bar{Q}'qq' $ in a full lattice-QCD computation, where heavy bottom quarks are treated in the framework of non-relativistic QCD. We focus on three systems with quark content $ \bar{b}\bar{b}ud $, $ \bar{b}\bar{b}us $ and $ \bar{b}\bar{c}ud $. We show evidence for the existence of $ \bar{b}\bar{b}ud $ and $ \bar{b}\bar{b}us $ bound states, while no binding appears to be present for $ \bar{b}\bar{c}ud $. For the bound four-quark states we also discuss the importance of various creation operator…
We present results of a lattice calculation of tetraquark states with quark contents $q_1q_2\bar{Q}\bar{Q}, \, q_1,q_2 \subset u,d,s,c$ and $Q \equiv b,c$ in both spin zero ($J=0$) and spin one ($J=1$) sectors. These calculations are performed on three dynamical $N_f = 2 + 1 + 1$ highly improved staggered quark ensembles at lattice spacings of about 0.12, 0.09 and 0.06 fm. We use the overlap action for light to charm quarks while a non-relativistic action with non-perturbatively improved coefficients with terms up to $\mathcal{O}(α_s v^4)$ is employed for the bottom quark. While considering tw…
In this work, we treat the newly observed doubly charmed four-quark state $ T_{cc}^{+}$ as an axial-vector tetraquark with content $cc\overline{u} \overline{d}$, and calculate its spectroscopic parameters and width. The mass and current coupling of the tetraquark $T_{cc}^{+}$ 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 $T_{cc}^{+}$ is evaluated using partial widths of decay processes $T_{cc}^{+} \to \widetilde{ T}π^{0}$ and $T_{cc}^{+} \to T_{cc;\overline{u}\overline{u}}^{0}π^{+}$ , whe…
We suggest to use the state $Y(4630)$, which decays predominantly to $Λ_c\barΛ_c$, as a window to the landscape of tetraquarks. We propose a simple criterion to decide whether a state is a genuine stringy exotic hadron - a tetraquark - or a "molecule". If it is the former it should be on a (modified) Regge trajectory. We present the predictions of the mass and width of the higher excited states on the $Y(4630)$ trajectory. We argue that there should exist an analogous "$Y_b$" state that decays to $Λ_b\barΛ_b$ and describe its trajectory. We conjecture also a similar trajectory for tetraquarks …
Using a relativized diquark model Hamiltonian, we calculate the masses of $J^{PC}=0^{++}$ ground-state tetraquarks in the following systems: $b s \bar b \bar s$, $bb \bar n \bar n$ ($n=u, d$), $bb \bar s \bar s$, $cc\bar c \bar c$, $b b \bar b \bar b$, $b c\bar b \bar c$ and $b b \bar c \bar c$. We also compute extensive spectra for the fully-heavy quark flavour combinations. Finally, as a test of the diquark model approach, we compute the masses of fully-heavy baryons in the diquark model. Our results may be compared soon to the forthcoming experimental data for fully-heavy three-quark system…
We present a general class of operators resembling compact tetraquarks which have a range of colour-flavour-spin structures, transform irreducibly under the symmetries of the lattice and respect other relevant symmetries. These constructions are demonstrated in lattice QCD calculations with light quarks corresponding to $m_π=$ 391 MeV. Using the distillation framework, correlation functions involving large bases of meson-meson and tetraquark operators are computed in the isospin-1 hidden-charm and doubly-charmed sectors, and finite-volume spectra are extracted with the variational method. We f…
Motivated by the latest discovery of doubly-charmed tetraquark $T^+_{cc}$ by LHCb collaboration, we have studied the magnetic moments of the possible doubly-heavy pentaquark states with quantum numbers $J^P = 1/2^-$ and $J^P = 3/2^-$ within the light-cone sum rules method. In the analysis, these possible pentaquark states are considered in diquark-diquark-antiquark structure. The magnetic moments of hadrons encode helpful details about the distributions of the charge and magnetization inside the hadrons, which help us to figure out their geometric configurations. As a by product, the electric …
The weak decays of the axial-vector tetraquark $T_{bb;\bar{u} \bar{d}}^{-}$ to the scalar state $Z_{bc;\bar{u} \bar{d}}^{0}$ are investigated using the QCD three-point sum rule approach. In order to explore the process $T_{bb; \bar{u} \bar{d}}^{-} \to Z_{bc;\bar{u} \bar{d}}^{0}l \bar{ν_l}$, we recalculate the spectroscopic parameters of the tetraquark $T_{bb;\bar{u} \bar{d}}^{-}$ and find the mass and coupling of the scalar four-quark system $Z_{bc;\bar{u} \bar{d}}^{0}$, which are important ingredients of calculations. The spectroscopic parameters of these tetraquarks are computed in the frame…
The past seventeen years have witnessed tremendous progress on the experimental and theoretical explorations of the multiquark states. The hidden-charm and hidden-bottom multiquark systems were reviewed extensively in [Phys. Rept. 639 (2016) 1-121]. In this article, we shall update the experimental and theoretical efforts on the hidden heavy flavor multiquark systems in the past three years. Especially the LHCb collaboration not only confirmed the existence of the hidden-charm pentaquarks but also provided strong evidence of the molecular picture. Besides the well-known $XYZ$ and $P_c$ states,…
We investigate a doubly-bottomed tetraquark state $T_{bb}$ $(bb \bar{u}\bar{d})$ with quantum number $I(J^P)=0(1^+)$ in $(2+1)$-flavor lattice QCD. Using the Non-Relativistic QCD (NRQCD) quark action for $b$ quarks, we have extracted the coupled channel potential between $\bar{B}\bar{B}^*$ and $\bar{B}^* \bar{B}^*$ in the HAL QCD method at $a \approx 0.09$ {fm} on $32^3\times 64$ lattices. The potential predicts an existence of a bound $T_{bb}$ below the $\bar{B}\bar{B}^*$ threshold. At the physical pion mass $m_π\approx140$ {MeV} extrapolated from $m_π\approx 410,\, 570,\, 700$ {MeV}, a bindi…
DeepQuark: A Deep-Neural-Network Approach to Multiquark Bound States
School of Physics, Peking University, Beijing 100871, China（北京大学物理系）；School of Physics, Southeast University, Nanjing 211189, China（东南大学物理系）；School of Physics（物理系）；Center of High Energy Physics, Peking University, Beijing 100871, China（北京大学高能物理中心）
