The spectroscopic parameters and decay channels of the axial-vector tetraquark $T_{bb;\overline{u}\overline{s}}^{-}$ (in what follows, $T_{b: \overline{s}}^{\mathrm{AV}}$) 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 $m=(10215\pm 250)~ \mathrm{MeV}$ 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 $T_{b:\overline{s} }^{\mathrm{AV}} \to \mathcal{Z}_{b:\overline{s}}^{0}l\overlineν_l$ and nonleptonic $T_{b:\overline{s}}^{\mathrm{AV}} \to \mathcal{Z}_{b:\overline{s} }^{0}M$ decays of $T_{b:\overline{s}}^{\mathrm{AV}}$. In these processes, $ \mathcal{Z}_{b:\overline{s}}^{0}$ is a scalar tetraquark $[bc][\overline{u} \overline{s}]$ built of a color-triplet diquark and an antidiquark, whereas $M$ is one of the vector mesons $ρ^{-}$, $K^{\ast}(892)$, $D^{\ast }(2010)^{-}$, and $D_{s}^{\ast -}$. To calculate the partial widths of these decays, we use the QCD three-point sum rule approach and evaluate the weak transition form factors $G_{i}$ $(i=0,1,2,3)$, which govern these processes. The full width $Γ_{\mathrm{full}} =(12.9\pm 2.1)\times 10^{-8}~\mathrm{MeV}$ and the mean lifetime $ τ=5.1_{-0.71}^{+0.99}~\mathrm{fs}$ of the tetraquark $T_{b:\overline{s}}^{ \mathrm{AV}}$ are computed using the aforementioned weak decays. The obtained information about the parameters of $T_{b:\overline{s}}^{\mathrm{AV}}$ and $ \mathcal{Z}_{b:\overline{s}}^{0}$ is useful for experimental investigations of these double-heavy exotic mesons.
We briefly review the stability of the $QQ\bar q\bar q$-type of tetraquarks with two heavy quarks and two light antiquarks. We present the first comprehensive estimate of the lifetime and leading decay modes of the exotic meson $bb\bar u\bar d$ with double beauty.
Motivated by multiple phenomenological considerations, we perform the first search for the existence of a $\bar{b}\bar{b}bb$ tetraquark bound state with a mass below the lowest non-interacting bottomonium-pair threshold using the first-principles lattice non-relativistic QCD methodology. We use a full $S$-wave colour/spin basis for the $\bar{b}\bar{b}bb$ operators in the three $0^{++}$, $1^{+-}$ and $2^{++}$ channels. We employ four gluon field ensembles at multiple lattice spacing values ranging from $a = 0.06 - 0.12$ fm, all of which include $u$, $d$, $s$ and $c$ quarks in the sea, and one e…
In this article we present a calculation of the $bb\bar{b}\bar{b}$ tetraquark ground-state energy using a diffusion Monte Carlo method to solve the non-relativistic many-body system. The static potential for the four quark system is chosen to align with the flux-tube picture of QCD. Using this approach, we find that the $0^{++}$ state has a mass of $18.69\pm 0.03~\mbox{GeV}$, which is around 100 MeV below twice the $η_b$ mass. This bound state can behave as a four-lepton resonance via its decay to $Υ(1S) Υ(1S)^* \rightarrow \ell^+ \ell^- \ell^+ \ell^-$.
For very heavy quarks, relations derived from heavy-quark symmetry imply novel narrow doubly heavy tetraquark states containing two heavy quarks and two light antiquarks. We predict that double-beauty states will be stable against strong decays, whereas the double-charm states and mixed beauty+charm states will dissociate into pairs of heavy-light mesons. Observing a new double-beauty state through its weak decays would establish the existence of tetraquarks and illuminate the role of heavy color-antitriplet diquarks as hadron constituents.
Beauty tetraquark states $X(\bar b q'q'' \bar q )$ composed of $ \bar b s u \bar d$, $\bar b d s \bar u$, and $\bar b u d \bar s$, are unique that all the four valence quarks are different. Although the claim of existence of the first two states by D0 was not confirmed by data from LHCb, the possibility of such states still generated a lot of interests and should be pursued further. Non-observation of $X(\bar b q'q'' \bar q )$ states by LHCb may be just due to a still lower production rate than the limit of LHCb or at some different mass ranges. In this work we use light quark $SU(3)$ flavor s…
A new method is proposed to search for the double beauty tetraquark $bb\bar{u}\bar{d}$ with a mass below the $BB$ threshold. The $b\bar{d}-\bar{b}d$ mixing can result in evolution of the tetraquark content to $b\bar{b}\bar{u}d$ with the following strong decay into the $Υ$(1S)$π^-$ and $Υ$(2S)$π^-$ final states in a secondary vertex displaced from the primary $pp$ collision vertex. This experimental signature is clean, has a high selection efficiency and can be well separated from backgrounds. Experimental signatures for searches for other double heavy tetraquarks are also discussed, suggesting…
Institute for Physical Problems, Baku State University（巴库国立大学物理问题研究所）；University of Tehran（德黑兰大学）；Dogus University（多乌斯大学）；Istanbul Medeniyet University（伊斯坦布尔文明大学）
For very heavy quarks $Q$, relations derived from heavy-quark symmetry predict the existence of novel narrow doubly heavy tetraquark states of the form $Q_iQ_j \bar q_k \bar q_l$ (subscripts label flavors), where $q$ designates a light quark. By evaluating finite-mass corrections, we predict that double-beauty states composed of $bb\bar u \bar d$, $bb\bar u \bar s$, and $bb\bar d \bar s$ will be stable against strong decays, whereas the double-charm states $cc \bar q_k \bar q_l$, mixed beauty+charm states $bc \bar q_k \bar q_l$, and heavier $bb \bar q_k \bar q_l$ states will dissociate into pa…
Origins of contemporary $B$-physics. Mesons with beauty and charm. Stable tetraquarks? Flavor and the problem of identity. Top matters. Electroweak symmetry breaking and the Higgs sector. Future instruments.
Assuming the dominance of the spin-spin interaction in a diquark, we point out that the mass difference in the beauty sector M(Z_b^prime) - M(Z_b) scales with quark masses as expected in QCD, with respect to the corresponding mass difference M(Z_c^prime) - M(Z_c). Notably, we show that the decays Upsilon(10890) --> Upsilon(nS) pi pi and Upsilon(10890) --> (h_b(1P), h_b(2P)) pi pi are compatible with heavy-quark spin conservation if the contributions of Z_b,Z_b^prime intermediate states are taken into account, Upsilon(10890) being either a Upsilon(5S) or the beauty analog of Y_c(4260). Belle re…
The semileptonic decays of the open charm-bottom axial-vector tetraquark $ Z_{s}=[cs][\overline{b}\overline{s}]$ to $X(4274)\overline{l} ν_l$, $l=e, μ, τ$ are explored by means of the QCD three-point sum rule method. Both $Z_{s}$ and $X(4274)=[cs][\overline{c}\overline{s}]$ are treated as color sextet diquark-antidiquark states. The full width of the decays $Z_s \to X(4274)\overline{l} ν_l$ is found. Obtained predictions for $ Γ(Z_s \to X(4274)\overline{l} ν_l)$ demonstrate that, as in the case of the conventional hadrons, the semileptonic transitions form a very small part of its full width.
The semileptonic and nonleptonic decays of the double-beauty axial-vector tetraquark $T_{bb;\overline{u} \overline{d}}^{-}$ to a state $\widetilde{T}_{bc; \overline{u}\overline{d}}^{0}$ (hereafter $T_{bb}^{-}$ and $\widetilde{T} _{bc}^{0}$, respectively) are investigated in the context of the QCD sum rule method. The final-state tetraquark $\widetilde{T}_{bc}^{0}$ is treated as an axial-vector particle built of a heavy axial-vector diquark $ b^{T}γ_{μ}Cc$ and light scalar antidiquark $\overline{u}Cγ_{5} \overline{d}^{T}$. Its spectroscopic parameters are calculated using the two-points sum rul…
In this article, we study the axial-vector tetraquark state and two-quark-tetraquark mixed state consist of light quarks using the QCD sum rules. The present predictions disfavor assigning the $a_1(1420)$ as the axial-vector tetraquark state with $J^{PC}=1^{++}$, while support assigning the $a_1(1420)$ as the axial-vector two-quark-tetraquark mixed state.
Experimentally several charged axial-vector hidden-charm states were reported. Within the framework of the color-magnetic interaction, we have systematically considered the mass spectrum of the hidden-charm and hidden-bottom tetraquark states. It is impossible to accommodate all the three charged states $Z_c(3900)$, $Z_c(4025)$ and $Z_c(4200)$ within the axial vector tetraquark spectrum simultaneously. Not all these three states are tetraquark candidates. Moreover, the eigenvector of the chromomagnetic interaction contains valuable information of the decay pattern of the tetraquark states. The…
In this article, we perform a systematic study of the mass spectrum of the axial-vector hidden charmed and hidden bottom tetraquark states using the QCD sum rules, and identify the $Z^+(4430)$ as an axial-vector tetraquark state tentatively.
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…
Spectroscopic parameters and widths of the fully open-flavor axial-vector and pseudoscalar tetraquarks $X_{\mathrm{AV}}$ and $X_{\mathrm{PS}}$ with content $[ud][\overline{c}\overline{s}]$ are calculated by means of the QCD sum rule methods. Masses and current couplings of $X_{\mathrm{AV}}$ and $X_{ \mathrm{PS}}$ are found using two-point sum rule computations performed by taking into account various vacuum condensates up to dimension $10$. The full width of the axial-vector state $X_{\mathrm{AV}}$ is evaluated by including into analysis $S$-wave decay modes $X_{\mathrm{AV}}\to D^{\ast }(2010)…
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.
In this article, we distinguish the charge conjunctions of the interpolating currents, calculate the contributions of the vacuum condensates up to dimension-10 in a consistent way in the operator product expansion, study the masses and pole residues of the $J^{PC}=1^{+\pm}$ hidden charmed tetraquark states with the QCD sum rules, and explore the energy scale dependence in details for the first time. The predictions $M_{X}=3.87^{+0.09}_{-0.09}\,\rm{GeV}$ and $M_{Z}=3.91^{+0.11}_{-0.09}\,\rm{GeV}$ support assigning the $X(3872)$ and $Z_c(3900)$ (or $Z_c(3885)$) as the $1^{++}$ and $1^{+-}$ diqua…
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 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…
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 article, we study the axial-vector mesons $Z_b(10610)$ and $Z_b(10650)$ with the $Cγ_μ-Cγ_5$ type and $Cγ_μ-Cγ_ν$ type interpolating currents respectively by carrying out the operator product expansion to the vacuum condensates up to dimension-10. In calculations, we explore the energy scale dependence of the QCD spectral densities of the hidden bottom tetraquark states in details for the first time, and suggest a formula $μ=\sqrt{M^2_{X/Y/Z}-(2{\mathbb{M}}_b)^2}$ with the effective mass ${\mathbb{M}}_b=5.13\,\rm{GeV}$ to determine the energy scales. The numerical results favor assigni…
Using the Woods Saxon plus Coulomb type of interaction between two hadron molecules, we have calculated the binding energies and masses of the tetraquark states such as $D\bar{D}$, $D\bar{D}^*$, $D^*\bar{D}^*$, $D^+\bar{D}^*$ in the charm sector and $B\bar{B}$, $B^*\bar{B}^*$, $B\bar{B}^*$ in the bottom sector.
Motivated by the latest discovery of a new tetraquark $T_{cc}^+$ with two charm quarks and two light antiquarks by LHCb Collaboration, we investigated the $DD^*$ hadronic molecule interpretation of $T_{cc}^+$. By calculation, the mass and the decay width of this new structure $T_{cc}^+$ can be understood in one-meson exchange potential model. The binding energies for these $DD^*$ hadronic molecules with $J^P=1^+$ are around $1MeV$. Besides, we also studied the possible beauty-partners $T_{bb}(10598)$ of hadronic molecule $T^+_{cc}$, which may be feasible in future LHCb experiments.
In this paper, we choose the scalar and axialvector diquark operators in the color antitriplet as the fundamental building blocks to construct the four-quark currents and investigate the diquark-antidiquark type axialvector tetraquark states $c\bar{c}u\bar{s}$ in the framework of the QCD sum rules. The predicted tetraquark mass $M_Z=3.99\pm0.09\,\rm{GeV}$ is in excellent agreement with the experimental value $3985.2^{+2.1}_{-2.0}\pm1.7\,\rm{MeV}$ from the BESIII collaboration, which supports identifying the $Z_{cs}(3985)$ as the cousin of the $Z_c(3900)$ with the quantum numbers $J^{PC}=1^{+-}…
The mass and coupling of the axial-vector tetraquark $T_{bc;\bar{u}\bar{d} }^{0}$ (in a short form $T_{bc}^{0}$) are calculated by means of the QCD two-point sum rule method. In computations we take into account contributions arising from various quark, gluon and mixed vacuum condensates up to dimension 10. The central value of the mass $m=(7105 \pm 155)~\mathrm{ MeV}$ lies below the thresholds for the strong and electromagnetic decays of $T_{bc}^{0}$ state, and hence it transforms to conventional mesons only through the weak decays. In the case of $m=7260~\mathrm{MeV}$ the tetraquark $T_{bc}^…
We investigate the chiral structure of local vector and axial-vector tetraquark currents, and study their chiral transformation properties. We consider the charge-conjugation parity and classify all the isovector vector and axial-vector local tetraquark currents of quantum numbers I(G)J(PC)=1(-)1(-+), I(G)J(PC)=1(+)1(--), I(G)J(PC)=1(-)1(++) and I(G)J(PC)=1(+)1(+-). We find that there is a one to one correspondence among them. Using these currents, we perform QCD sum rule analyses. Our results suggest that there is a missing b1 state having I(G)J(PC)=1(+)1(+-) and a mass around 1.47-1.66 GeV.
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 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…
In this article, we study the axialvector-diquark-axialvector-antidiquark type scalar, axialvector, tensor and vector $ss\bar{s}\bar{s}$ tetraquark states with the QCD sum rules. The predicted mass $m_{X}=2.08\pm0.12\,\rm{GeV}$ for the axialvector tetraquark state is in excellent agreement with the experimental value $(2062.8 \pm 13.1 \pm 4.2) \,\rm{MeV}$ from the BESIII collaboration and supports assigning the new $X$ state to be a $ss\bar{s}\bar{s}$ tetraquark state with $J^{PC}=1^{+-}$. The predicted mass $m_{X}=3.08\pm0.11\,\rm{GeV}$ disfavors assigning the $ϕ(2170)$ or $Y(2175)$ to be the…
Possibility of an axial vector isoscalar tetraquark with $ud\bar{s}\bar{s}$ is discussed. If the pentaquark $Θ^+(1540)$ has the $(qq)_{\bar{3}}(qq)_{\bar{3}}\bar{q}$ configuration, the isoscalar $ud\bar{s}\bar{s}$($\vartheta^+$-meson) state with $J^P=1^+$ is expected to exist in the mass region lower than or close to the mass of $Θ^+(1540)$. Within a flux-tube quark model, a possible resonant state of $ud\bar{s}\bar{s}(J^{P}=1^{+})$ is suggested to appear around 1.4 GeV with the width ${\cal{O}}(20\sim 50)$ MeV. We propose that the $\vartheta^+$-meson is a good candidate for the tetraquark sea…
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. …
We study features of the resonances $X(2100)$ and $X(2239)$ by treating them as the axial-vector and vector tetraquarks with the quark content $ss \overline{s}\overline{s}$, respectively. The spectroscopic parameters of these exotic mesons are calculated in the framework of the QCD two-point sum rule method. Obtained prediction for the mass $m=(2067 \pm 84)~\mathrm{MeV}$ of the axial-vector state is in excellent agreement with the mass of the structure $X(2100)$ recently observed by the BESIII Collaboration in the decay $J/ψ\to ϕηη^{\prime}$ as the resonance in the $ϕη^{\prime}$ mass spectrum.…
In order to investigate the possibility of the recently observed $X(5568)$ being a $0^{+}$ tetraquark state, we make an improvement to the study of the related various configuration states in the framework of the QCD sum rules. Particularly, to ensure the quality of the analysis, condensates up to dimension $12$ are included to inspect the convergence of operator product expansion (OPE) and improve the final results of the studied states. We note that some condensate contributions could play an important role on the OPE side. By releasing the rigid OPE convergence criterion, we arrive at the n…
In this article, we study the mass spectrum of the scalar hidden charm and hidden bottom tetraquark states which consist of the axial-axial type and the vector-vector type diquark pairs with the QCD sum rules.
In this article, we tentatively assign the $Z_c^\pm(3900)$ to be the diquark-antidiquark type axialvector tetraquark state, study the hadronic coupling constants $G_{Z_cJ/ψπ}$, $G_{Z_cη_cρ}$, $G_{Z_cD \bar{D}^{*}}$ with the QCD sum rules in details. We take into account both the connected and disconnected Feynman diagrams in carrying out the operator product expansion, as the connected Feynman diagrams alone cannot do the work. Special attentions are paid to matching the hadron side of the correlation functions with the QCD side of the correlation functions to obtain solid duality, the routine…
In this article, we tentatively assign the $X(3915)$ and $X(4500)$ to be the ground state and the first radial excited state of the axialvector-diquark-axialvector-antidiquark type scalar $cs\bar{c}\bar{s}$ tetraquark states, respectively, assign the $X(4700)$ to be the ground state vector-diquark-vector-antidiquark type scalar $cs\bar{c}\bar{s}$ tetraquark state, and study their masses and pole residues with the QCD sum rules in details by calculating the contributions of the vacuum condensates up to dimension 10. The numerical results support assigning the $X(3915)$ and $X(4500)$ to be the g…
In this article, we construct both the $[sc]_T[\bar{s}\bar{c}]_A+[sc]_A[\bar{s}\bar{c}]_T$ type and $[sc]_T[\bar{s}\bar{c}]_V-[sc]_V[\bar{s}\bar{c}]_T$ type axialvector currents with $J^{PC}=1^{++}$ to study the mass of the $X(4140)$ with the QCD sum rules. The predicted masses support assigning the $X(4140)$ to be the $[sc]_T[\bar{s}\bar{c}]_V-[sc]_V[\bar{s}\bar{c}]_T$ type axialvector tetraquark state. Then we study the hadronic coupling constant $g_{XJ/ψϕ}$ with the QCD sum rules based on solid quark-hadron duality, and obtain the decay width $Γ(X(4140)\to J/ψϕ)=86.9\pm22.6\,{\rm{MeV}}$, wh…
Multiquark states have been advocated to explain recent experimental data in the heavy-light sector, and there are already speculations about multiquarks containing only heavy quarks and antiquarks. With a rigorous treatment of the four-body problem in current quark models, full-charm $(cc\bar c\bar c)$ and full-beauty $(bb\bar b\bar b)$ tetraquarks are found to be unbound. Thus their stability should rely on more subtle effects that are not included in the simple picture of constituent quarks. The case of $(bc\bar b\bar c)$ might be more favorable if the naive color-additive model of confinem…
Stimulated by the renewed observation of $D_{s0}^{*}(2317)$ signal and its updated mass value $2318.3\pm1.2\pm1.2~\mbox{MeV}/c^{2}$ in the process $e^{+}e^{-}\rightarrow D_{s}^{*+}D_{s0}^{*}(2317)^{-}+c.c.$ by BESIII Collaboration, we devote to reinvestigate $D_{s0}^{*}(2317)$ as a $0^{+}$ tetraquark state from QCD sum rules. Technically, four different possible currents are adopted and high condensates up to dimension $12$ are included in the operator product expansion (OPE) to ensure the quality of QCD sum rule analysis. In the end, we obtain the mass value $2.37^{+0.50}_{-0.36}~\mbox{GeV}$ …
In this article, we study the first radial excited states of the scalar, axialvector, vector and tensor diquark-antidiquark type $cc\bar{c}\bar{c}$ tetraquark states with the QCD sum rules and obtain the masses and pole residues, then we use the Regge trajectory to obtain the masses of the second radial excited states. The predicted masses support assigning the broad structure from 6.2 to 6.8 GeV in the di-$J/ψ$ mass spectrum to be the first radial excited state of the scalar, axialvector, vector or tensor $cc\bar{c}\bar{c}$ tetraquark state, and assigning the narrow structure at about 6.9 GeV…
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…
Motivated by the LHCb's very recent observation of exotic $X_{0}(2900)$ in the $B^{+}\rightarrow D^{+}D^{-}K^{+}$ process, for which could be a good open charm $ud\bar{c}\bar{s}$ tetraquark candidate, we endeavor to investigate its possibility by means of QCD sum rules. In technique, four configurations of interpolating currents with $J^{P}=0^{+}$ are studied for the $ud\bar{c}\bar{s}$ tetraquark state. In the end, mass values are calculated to be $2.76^{+0.16}_{-0.23}~\mbox{GeV}$ for the axial vector diquark-axial vector antidiquark configuration and $2.75^{+0.15}_{-0.24}~\mbox{GeV}$ for the …
This talk briefly discusses the set of meson resonances discovered in the latest decade. They are frequently treated in the literature as tetraquarks or hadron molecules. Our consideration (using the energy-time uncertainty relation) suggests, however, that the most reasonable description for each of them may be a two- (or more-) component Fock column, with one line being a conventional quark-antiquark pair, and the other line(s) corresponding to a charmed (or beauty) meson-antimeson pair near its threshold. Detailed investigation of decay properties might allow to reveal presence of several F…
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.
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.
We investigate the recent evidence for a charged $X(5568)$ meson as an exotic open-flavor tetraquark state $su\bar b\bar d$ with $J^P=0^+/1^+$ in the framework of QCD sum rules. We use the color antisymmetric $[\mathbf{\bar 3_c}]_{su} \otimes [\mathbf{3_c}]_{\bar{b}\bar d}$ tetraquark currents in both scalar and axial-vector channels to perform evaluations and numerical analyses. Our results imply that the $X(5568)$ can be interpreted as both the scalar $su\bar b\bar d$ tetraquark state and the axial-vector one, which are in good agreement with the experimental measurement. We also discuss the…
The charged axial-vector $J^{P}=1^{+}$ tetraquarks $Z_{q}=[cq][\bar {b} \bar q ]$ and $Z_{s}=[cs][\bar {b} \bar s]$ with the open charm-bottom contents are studied in the diquark-antidiquark model. The masses and meson-current couplings of these states are calculated by employing QCD two-point sum rule approach, where the quark, gluon and mixed condensates up to eight dimensions are taken into account. These parameters of the tetraquark states $ Z_{q}$ and $Z_{s}$ are used to analyze the vertices $Z_q B_c ρ$ and $Z_s B_c ϕ$ to determine the strong $g_{Z_qB_c ρ}$ and $g_{Z_sB_c ϕ}$ couplings. F…
In this article, we construct the $[sc]_A[\bar{s}\bar{c}]_V-[sc]_V[\bar{s}\bar{c}]_A$ type tensor current to study the mass and width of the $X(4274)$ with the QCD sum rules in details. The predicted mass $M_{X}=(4.27\pm0.09) \, \rm{GeV}$ for the $J^{PC}=1^{++}$ tetraquark state is in excellent agreement with the experimental data $4273.3 \pm 8.3 ^{+17.2}_{-3.6} \mbox MeV}$ from the LHCb collaboration. The central value of the width $Γ(X(4274)\to J/ψϕ)=47.9\,{\rm{MeV}}$ is in excellent agreement with the experimental data $56 \pm 11 ^{+8}_{-11} \mbox MeV}}$ from the LHCb collaboration. The pre…
We have studied the masses for fully open-flavor tetraquark states $bc\bar{q}\bar{s}$ and $sc\bar{q}\bar{b}$ with quantum numbers $J^{P}=0^{+},1^{+}$. We systematically construct all diquark-antiquark interpolating currents and calculate the two-point correlation functions and spectral densities in the framework of QCD sum rule method. Our calculations show that the masses are about $7.1-7.2$ GeV for the $bc\bar{q}\bar{s}$ tetraquark states and $7.0-7.1$ GeV for the $sc\bar{q}\bar{b}$ tetraquarks. The masses of $bc\bar{q}\bar{s}$ tetraquarks are below the thresholds of $\bar{B}_{s}D$ and $\bar…
We investigate properties of the ground-state and first radially excited four-quark mesons $X_0$ and $X_0^{\prime}$ with a diquark-antidiquark structure $[ud][\overline{c}\overline{s}]$ and spin-parities $J^{\mathrm{P} }=0^{+}$. Our aim is to reveal whether or not one of these states can be identified with the resonance $X_0(2900)$, recently discovered by the LHCb collaboration. We model $X_0$ and $X_0^{\prime}$ as tetraquarks composed of either axial-vector or scalar diquark and antidiquark pairs. Their spectroscopic parameters are computed by employing the QCD two-point sum rule method and i…
In this article, we study the $Z_c(3900)$ with the QCD sum rules in details by including the two-particle scattering state contributions and nonlocal effects between the diquark and antidiquark constituents. The two-particle scattering state contributions cannot saturate the QCD sum rules at the hadron side, the contribution of the $Z_c(3900)$ plays an un-substitutable role, we can saturate the QCD sum rules with or without the two-particle scattering state contributions. If there exists a barrier or spatial separation between the diquark and antidiquark constituents, the Feynman diagrams can …
We study the exotic $bc\bar{q}\bar{q}$, $bc\bar{s}\bar{s}$ and $qc\bar{q}\bar{b}$, $sc\bar{s}\bar{b}$ systems by constructing the corresponding tetraquark currents with $J^P=0^+$ and $1^+$. After investigating the two-point correlation functions and the spectral densities, we perform QCD sum rule analysis and extract the masses of these open-flavor tetraquark states. Our results indicate that the masses of both the scalar and axial vector tetraquark states are about $7.1-7.2$ GeV for the $bc\bar{q}\bar{q}$ system and $7.2-7.3$ GeV for the $bc\bar{s}\bar{s}$ system. For the $qc\bar{q}\bar{b}$ t…
