Search for tetraquark states $X_{cc\bar{s}\bar{s}}$ in $D_{s}^{+}D_{s}^{+}~(D_{s}^{*+}D_{s}^{*+})$ final states at Belle
Belle Collaboration, X. Y. Gao, Y. Li, C. P. Shen, I. Adachi, H. Aihara, D. M. Asner, H. Atmacan, T. Aushev, R. Ayad, P. Behera, K. Belous, M. Bessner, V. Bhard… 展开作者
Belle Collaboration, X. Y. Gao, Y. Li, C. P. Shen, I. Adachi, H. Aihara, D. M. Asner, H. Atmacan, T. Aushev, R. Ayad, P. Behera, K. Belous, M. Bessner, V. Bhardwaj, B. Bhuyan, T. Bilka, A. Bobrov, D. Bodrov, G. Bonvicini, J. Borah, A. Bozek, M. Bračko, T. E. Browder, A. Budano, M. Campajola, D. Červenkov, M. -C. Chang, P. Chang, A. Chen, B. G. Cheon, K. Chilikin, H. E. Cho, K. Cho, S. -J. Cho, S. -K. Choi, Y. Choi, S. Choudhury, D. Cinabro, S. Cunliffe, S. Das, G. De Pietro, R. Dhamija, F. Di Capua, J. Dingfelder, Z. Doležal, T. V. Dong, D. Dossett, T. Ferber, A. Frey, B. G. Fulsom, R. Garg, V. Gaur, N. Gabyshev, A. Giri, P. Goldenzweig, T. Gu, Y. Guan, K. Gudkova, C. Hadjivasiliou, S. Halder, O. Hartbrich, K. Hayasaka, H. Hayashii, M. T. Hedges, W. -S. Hou, C. -L. Hsu, T. Iijima, K. Inami, G. Inguglia, A. Ishikawa, R. Itoh, M. Iwasaki, Y. Iwasaki, W. W. Jacobs, E. -J. Jang, S. Jia, Y. Jin, K. K. Joo, J. Kahn, A. B. Kaliyar, K. H. Kang, G. Karyan, T. Kawasaki, H. Kichimi, C. Kiesling, C. H. Kim, D. Y. Kim, K. -H. Kim, Y. -K. Kim, P. Kodyš, T. Konno, A. Korobov, S. Korpar, E. Kovalenko, P. Križan, R. Kroeger, P. Krokovny, T. Kuhr, R. Kumar, K. Kumara, A. Kuzmin, Y. -J. Kwon, Y. -T. Lai, T. Lam, J. S. Lange, M. Laurenza, S. C. Lee, C. H. Li, J. Li, L. K. Li, Y. B. Li, L. Li Gioi, J. Libby, K. Lieret, D. Liventsev, A. Martini, M. Masuda, T. Matsuda, D. Matvienko, S. K. Maurya, F. Meier, M. Merola, F. Metzner, K. Miyabayashi, R. Mizuk, G. B. Mohanty, R. Mussa, M. Nakao, Z. Natkaniec, A. Natochii, L. Nayak, M. Niiyama, N. K. Nisar, S. Nishida, K. Ogawa, S. Ogawa, H. Ono, P. Oskin, P. Pakhlov, G. Pakhlova, T. Pang, S. Pardi, H. Park, S. -H. Park, S. Patra, S. Paul, T. K. Pedlar, R. Pestotnik, L. E. Piilonen, T. Podobnik, V. Popov, E. Prencipe, M. T. Prim, M. Röhrken, A. Rostomyan, N. Rout, G. Russo, D. Sahoo, S. Sandilya, A. Sangal, L. Santelj, T. Sanuki, V. Savinov, G. Schnell, Y. Seino, K. Senyo, M. E. Sevior, M. Shapkin, C. Sharma, J. -G. Shiu, F. Simon, J. B. Singh, A. Sokolov, E. Solovieva, S. Stanič, M. Starič, Z. S. Stottler, M. Sumihama, T. Sumiyoshi, M. Takizawa, U. Tamponi, K. Tanida, F. Tenchini, M. Uchida, K. Uno, S. Uno, P. Urquijo, Y. Usov, R. Van Tonder, G. Varner, A. Vinokurova, E. Waheed, E. Wang, M. -Z. Wang, X. L. Wang, M. Watanabe, S. Watanuki, E. Won, X. Xu, B. D. Yabsley, W. Yan, S. B. Yang, H. Ye, J. H. Yin, C. Z. Yuan, Y. Zhai, Z. P. Zhang, V. Zhilich, V. Zhukova
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12 pages, 7 figures; accepted for publication as a Regular Article in Physical Review D
A search for double-heavy tetraquark state candidates $X_{cc\bar{s}\bar{s}}$ decaying to $D_{s}^{+}D_{s}^{+}$ and $D_{s}^{*+} D_{s}^{*+}$ is presented for the first time using the data samples of 102 million $Υ(1S)$ and 158 million $Υ(2S)$ events, and the data samples at $\sqrt{s}$ = 10.52~GeV, 10.58~GeV, and 10.867~GeV corresponding to integrated luminosities of 89.5~fb$^{-1}$, 711.0~fb$^{-1}$, and 121.4~fb$^{-1}$, respectively, accumulated with the Belle detector at the KEKB asymmetric energy electron-positron collider. The invariant-mass spectra of the $D_{s}^{+}D_{s}^{+}$ and $D_{s}^{*+} D_{s}^{*+}$ are studied to search for possible resonances. No significant signals are observed, and the 90\% confidence level upper limits on the product branching fractions [${\cal B}(Υ(1S,2S) \to X_{cc\bar{s}\bar{s}} + anything) \times {\cal B}(X_{cc\bar{s}\bar{s}} \to D_{s}^{+}D_{s}^{+}(D_{s}^{*+} D_{s}^{*+}))$] in $Υ(1S,2S)$ inclusive decays and the product values of Born cross section and branching fraction [$σ(e^+e^- \to X_{cc\bar{s}\bar{s}} + anything ) \times {\cal B}(X_{cc\bar{s}\bar{s}} \to D_{s}^{+}D_{s}^{+}(D_{s}^{*+} D_{s}^{*+}))$] in $e^+e^-$ collisions at $\sqrt{s}$ = 10.52~GeV, 10.58~GeV, and 10.867~GeV under different assumptions of $X_{cc\bar{s}\bar{s}}$ masses and widths are obtained.
We analyze the Belle data [K. F. Chen {\it et al.} (Belle Collaboration), Phys.\ Rev.\ Lett.\ {\bf 100}, 112001 (2008); I. Adachi {\it et al.} (Belle Collaboration), arXiv:0808.2445] on the processes $e^+ e^- \to Υ(1S)\; π^+π^-, Υ(2S)\; π^+π^-$ near the peak of the $Υ(5S)$ resonance, which are found to be anomalously large in rates compared to similar dipion transitions between the lower $Υ$ resonances. Assuming these final states arise from the production and decays of the $J^{PC}=1^{--}$ state $Y_b(10890)$, which we interpret as a bound (diquark-antidiquark) tetraquark state $[bq][\bar{b}\ba…
Recently, the Belle Collaboration has updated the analysis of the cross sections for the processes $e^+ e^- \to Υ(nS)\, π^+ π^-$ ($n = 1,\, 2,\, 3$) in the $e^+ e^-$ center-of-mass energy range from 10.52 to 11.02~GeV. A new structure, called $Y_b (10750)$, with the mass $M (Y_b) = (10752.7 \pm 5.9^{+0.7}_{-1.1})$~MeV and the Breit-Wigner width $Γ(Y_b) = (35.5^{+17.6 +3.9}_{-11.3 -3.3})$~MeV was observed. We interpret $Y_b (10750)$ as a compact $J^{PC} = 1^{--}$ state with a dominant tetraquark component. The mass eigenstate $Y_b (10750)$ is treated as a linear combination of the diquark-antid…
Recent data from Belle show unusually large partial widths Upsilon(5S) --> Upsilon(1S) pi^+pi^- and Υ(5S) --> Υ(2S) pi^+ pi^-. The Z(4430) narrow resonance also reported by Belle in psi' pi^+ spectrum has the properties expected of a (cbar c u dbar) charged isovector tetraquark T^{+-}_cc The analogous state T^{+-} in the bottom sector might mediate anomalously large cascade decays in the Upsilon system, Upsilon(mS) --> T^{+-}_bb pi^{-+} --> Upsilon(nS) pi^+ π^-, with a tetraquark-pion intermediate state. We suggest looking for the (bbar b u dbar) tetraquark in these decays as peaks in the inva…
We calculate the cross sections and final state distributions for the processes e^+ e^- --> Upsilon(1S) (pi^+ pi^-, K^+ K^-, eta pi^0) near the Upsilon(5S) resonance based on the tetraquark hypothesis. This framework is used to analyse the data on the Upsilon(1S) pi^+ pi^- and Upsilon(1S) K^+ K^- final states [K.F. Chen et al. (Belle Collaboration), Phys. Rev. Lett. 100, 112001 (2008); I. Adachi et al. (Belle Collaboration), arXiv:0808.2445], yielding good fits. Dimeson invariant mass spectra in these processes are shown to be dominated by the corresponding light scalar and tensor states. The …
We propose a search for the newly discovered tetraquark candidate Z(4430) in photoproduction. Based on the Belle results we show that if Z(4430) is a genuine resonance, its significantly large coupling to $ψ^\primeπ$ will cause it to stand out above the background in $γp\to Z^+(4430) n\to ψ^\prime π^+ n$. We consider the dependence of the cross section for the quantum numbers ($J^{P}=1^{-}$, $1^{+}$ or $0^{-}$).
Motivated by the Belle Collaboration's new observation of $Y(4626)$, we investigate the possibility of its configuration as a $P$-wave $[cs][\bar{c}\bar{s}]$ tetraquark state from QCD sum rules. Eventually, the extracted mass $4.60^{+0.13}_{-0.19}~\mbox{GeV}$ for the $P$-wave $cs$-scalar-diquark $\bar{c}\bar{s}$-scalar-antidiquark state agrees well with the experimental data of $Y(4626)$, which could support its interpretation as a $P$-wave scalar-scalar $[cs][\bar{c}\bar{s}]$ tetraquark state.
We present a tetraquark interpretation of the charged bottomonium-like states Z+-_b(10610) and Z+-_b(10650), observed by the Belle collaboration in the pi+- Upsilon(nS) (n=1,2,3) and pi+- h_b(mP) (m=1,2) invariant mass spectra from the data taken near the peak of the Upsilon(5S). In this framework, the underlying processes involve the production and decays of a vector tetraquark Y_b(10890), e+e- --> Y_b(10890) --> [Z+-_b(10610)pi-+, Z+-_b(10650)pi-+] followed by the decays [Z+-_b (10610), Z+-_b (10650)] --> pi+- Upsilon(nS), pi+- h_b(mP). Combining the contributions from the meson loops and an…
In this work, we estimate the masses of tetraquark states with four different flavors by virtue of QCD sum rules, in both $b$ and $c$ sectors. We construct four $[8_c]_{\bar{b} s} \otimes [8_c]_{\bar{d} u}$ tetraquark currents with $J^P = 0^+$, and then perform analytic calculation up to dimension eight in the Operator Product Expansion (OPE). We keep terms which are linear in the strange quark mass $m_s$, and in the end find two possible tetraquark states with masses $(5.57 \pm 0.15)$ and $(5.58 \pm 0.15)$ GeV. We find that their charmed-partner masses lie in $(2.54 \pm 0.13)$ and $(2.55 \pm …
A theoretical overview of the exotic spectroscopy in the charm and beauty quark sector is presented. These states are unexpected harvest from the $e^+e^-$ and hadron colliders and a permanent abode for the majority of them has yet to be found. We argue that some of these states, in particular the $Y_b(10890)$ and the recently discovered states $Z_b(10610)$ and $Z_b(10650)$, discovered by the Belle collaboration are excellent candidates for tetraquark states $[bq][\bar{b}\bar{q}]$, with $q=u,d$ light quarks. Theoretical analyes of the Belle data carried out in the tetraquark context is reviewed…
We have studied the mass spectra of the hidden-charm/bottom $qc\bar q\bar c$, $sc\bar s\bar c$ and $qb\bar q\bar b$, $sb\bar s\bar b$ tetraquark states with $J^{PC}=0^{++}$ and $2^{++}$ in the framework of QCD sum rules. We construct ten scalar and four tensor interpolating currents in a systematic way and calculate the mass spectra for these tetraquark states. The $X^\ast(3860)$ may be either an isoscalar tetraquark state or $χ_{c0}(2P)$. If the $X^\ast(3860)$ is a tetraquark candidate, our results prefer the $0^{++}$ option over the $2^{++}$ one. The $X(4160)$ may be classified as either the…
The X(3872) and Z(4430) are candidates of tetraquark state with a ccbar pair. We present results from Belle recently updated for the mass, branching fractions etc. in different production/decay processes of the X(3872). Results from a Dalitz analysis for B --> Z(4430) K --> psi' pi^+- K are also presented.
Motivated by the LHCb observation of exotic states $X_{0,1}(2900)$ with four open quark flavors in the $D^- K^+$ invariant mass distribution in the decay channel $B^\pm \to D^+ D^- K^\pm$, we study the spectrum and decay properties of the open charm tetraquarks. Using the two-body chromomagnetic interactions, we find that the two newly observed states can be interpreted as a radial excited tetraquark with $J^P=0^+$ and an orbitally excited tetraquark with $J^P=1^-$, respectively. We then explore the mass and decays of the other flavor-open tetraquarks made of $su \bar d \bar c$ and $ d s \bar …
The dynamical diquark model assumes that exotic hadrons can be formed from colored diquarks. This model asserts a multiquark exotic state composed of a compact diquark $δ$ and antidiquark $\barδ$ for a tetraquark interacting through a gluonic field of finite extent. Using Born-Oppenheimer (BO) approximation and BO potential calculated numerically on the lattice, we study mass spectra of $S-$wave $cc\bar{b}\bar{b}$, $bc\bar{c}\bar{c}$, and $bc\bar{b}\bar{b}$ tetraquark systems in the basis of diquark spins. We assume that colour-antitriple diquark and colour-triplet antidiquark form tetraquark …
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…
In this work we study the mass spectra of the fully-heavy tetraquark systems, i.e. $cc\bar{c}\bar{c}$, $bb\bar{b}\bar{b}$, $bb\bar{c}\bar{c}/cc\bar{b}\bar{b}$, $bc\bar{c}\bar{c}/cc\bar{b}\bar{c}$, $bc\bar{b}\bar{b}/bb\bar{b}\bar{c}$, and $bc\bar{b}\bar{c}$, within a potential model by including the linear confining potential, Coulomb potential, and spin-spin interactions. It shows that the linear confining potential has important contributions to the masses and is crucial for our understanding of the mass spectra of the fully-heavy tetraquark systems. For the fully-heavy tetraquarks $Q_1Q_2\ba…
Many of the $XYZ$ resonances observed by the Belle, Babar, CLEO and BESIII collaborations in the past decade are difficult to interpret as conventional quark-antiquark mesons, motivating the consideration of scenarios such as multi-quark states, meson molecules, and hybrids. After a brief introduction to QCD sum-rule methods, we provide a brief but comprehensive review of the mass spectra of the quarkonium-like tetraquark states $qQ\bar q\bar Q$, doubly charmed/bottomed tetraquark states $QQ\bar q\bar q$ and the heavy quarkonium hybrid states $\bar QGQ$ in the QCD sum rules approach. Possible …
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…
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.
We have studied the masse spectra for the $cc\bar{b}\bar{b}$/$bb\bar{c}\bar{c}$ tetraquark states with quantum numbers $J^{P}=0^{\pm},1^{\pm}$, and $2^{+}$. We systematically construct the interpolating currents with various spin-parity quantum numbers and calculate their two-point correlation functions in the framework of QCD moment sum rule method. Our calculations show that the masses are about $12.3-12.4$ GeV for the positive parity $cc\bar{b}\bar{b}$ tetraquark ground states with $J^{P}=0^+, 1^+, 2^+$, while $12.8-13.1$ GeV for the negative parity channels with $J^{P}=0^-, 1^-$. The mass …
The goal of the present work is to obtain a reliable estimate of the masses of the ground and radially excited states of fully-heavy tetraquark systems. In order to do this, we use a nonrelativistic model of tetraquarks which are assumed to be compact and consist of diquark-antidiquark pairs. This nonrelativistic model is composed of Hulthen potential, a linear confining potential and spin-spin interaction. We computed ground, first, and second radially excited $cc\bar{c}\bar{c}$ and $bb\bar{b}\bar{b}$ tetraquark masses. It was found that predicted masses of ground states of $cc\bar{c}\bar{c}$…
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.
Assuming $Y_{b}(10890)$ as a P-wave $bq$-scalar-diquark $\bar{b}\bar{q}$-scalar-antidiquark tetraquark state, the mass of $Y_{b}(10890)$ is computed in the framework of QCD sum rule method. Technically, contributions of operators up to dimension six are included in the operator product expansion (OPE). The numerical result $10.88\pm0.13 GeV$ for $Y_{b}(10890)$ agrees well with the experimental value, which favors the P-wave $[bq][\bar{b}\bar{q}]$ tetraquark configuration for $Y_{b}(10890)$. In the same picture, the mass of $Y(4360)$ is calculated and the result $4.32\pm0.20 GeV$ is compatible …
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-$J/ψ$ structures. …
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…
Masses of the ground-state teraquarks composed from heavy $c$ and $b$ quarks and antiquarks are calculated in the diquark-antidiquark picture in the framework of the relativistic quark model based on the quasipotential approach. The quasipotentials of the quark-quark and diquark-antidiquark interactions are constructed similarly to the previous consideration of mesons and baryons. It is assumed that the diquark and antidiquark interact in the tetraquark as a whole and the internal structure of the diquarks is taken into account. All such tetraquarks are found above the thresholds of decays to …
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…
In this talk, we briefly report the investigations of the mass spectra for the $cc\bar c\bar c, bb\bar b\bar b$, $bc\bar b\bar c$ and $cc\bar b\bar b$ tetraquark states by using the QCD moment sum rule method. The calculations for the fully-charm $cc\bar c\bar c$ tetraquarks have been successfully predicted the existence of di-$J/ψ$ resonances including $X(6900)$ in LHCb's observation. The quantum numbers for these resonance structures are also suggested. More efforts are still needed in both theoretical and experimental aspects to study the properties of these fully-heavy tetraquark states. T…
The LHCb Collaboration has reported resonant activity in the channel $D^+ K^-$, identifying two components: $X_0(2900)$ with $J^P = 0^+$ at $2866 {\pm} 7$ MeV, $Γ_0=57{\pm} 13$ MeV and $X_1(2900)$ with $J^P = 1^-$ at $2904 {\pm} 7$ MeV, $Γ_1=110{\pm} 12$ MeV. We interpret the $X_0(2900)$ component as a $cs \bar u\bar d$ isosinglet compact tetraquark, calculating its mass to be $2863 {\pm} 12$ MeV. This is the first exotic hadron with open heavy flavor. The analogous $bs\bar u\bar d$ tetraquark is predicted at $6213 {\pm} 12$ MeV. We discuss possible interpretations of the heavier and wider $X_…
We apply the QCD sum rule method to systematically study the $S$- and $P$-wave fully-strange tetraquark states within the diquark-antidiquark picture. We systematically construct their interpolating currents by explicitly adding the covariant derivative operator. Our results suggest that the $f_0(2100)$, $X(2063)$, and $f_2(2010)$ may be explained as the $S$-wave $s s \bar s \bar s$ tetraquark states with the quantum numbers $J^{PC} = 0^{++}$, $1^{+-}$, and $2^{++}$, respectively. Our results also suggest that both the $X(2370)$ and $X(2500)$ may be explained as the $P$-wave $s s \bar s \bar s…
Motivated by the LHCb's new observation of structures in the $J/ψ$-pair invariant mass spectrum, for which could be classified as possible $cc\bar{c}\bar{c}$ tetraquark candidates, we systematically study $0^{+}$ fully-charmed tetraquark states through QCD sum rules. Making the development of calculation techniques to fourfold heavy hadronic systems, four different configuration currents with $0^{+}$ are considered and vacuum condensates up to dimension $6$ are included in the operator product expansion (OPE). Finally, mass values acquired for $0^{+}$ $cc\bar{c}\bar{c}$ tetraquark states agree…
We study the existence of fully-heavy hidden-flavor $bc\bar{b}\bar{c}$ tetraquark states with various $J^{PC}=0^{\pm+}, 0^{--},1^{\pm\pm}, 2^{++}$, by using the moment QCD sum rule method augmented by fundamental inequalities. Using the moment sum rule analyses, our calculation shows that the masses for the S-wave positive parity $bc\bar{b}\bar{c}$ tetraquark states are about $12.2-12.4$ GeV in both $[\mathbf{\bar{3}_c}]_{bc}\otimes[\mathbf{3_c}]_{\bar{b}\bar{c}}$ and $[\mathbf{6_c}]_{bc}\otimes[\mathbf{\bar{6}_c}]_{\bar{b}\bar{c}}$ color configuration channels. Except for two $0^{++}$ states,…
In this article, we distinguish the charge conjugations of the interpolating currents, calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and study the masses and pole residues of the $J^{PC}=1^{-\pm}$ hidden charmed tetraquark states with the QCD sum rules. We suggest a formula $μ=\sqrt{M^2_{X/Y/Z}-(2{\mathbb{M}}_c)^2}$ with the effective mass ${\mathbb{M}}_c=1.8\,\rm{GeV}$ to estimate the energy scales of the QCD spectral densities of the hidden charmed tetraquark states, which works very well. The numerical results disfavor assigning …
In this study, we investigate the discovery potential of double-charm tetraquarks $T^{\{cc\}}_{[\bar{q}\bar{q}']}$. We find that their production cross sections at the LHCb with $\sqrt{s} = 13$ TeV reach $\mathcal{O}(10^4)$ pb, which indicates that the LHCb has collected $\mathcal{O}(10^8)$ such particles. Through the decay channels of $T^{\{cc\}}_{[\bar{u}\bar{d}]}\to D^{+}K^{-}π^{+}$ or $D^0D^+γ$ (if stable) or $T^{\{cc\}}_{[\bar{u}\bar{d}]}\to D^0D^{*+}\to D^0D^0π^+$ (if unstable), it is highly expected that they get discovered at the LHCb in the near future. We also discuss the productions…
In the simple color-magnetic interaction model, we investigate possible ground $cs\bar{c}\bar{s}$ tetraquark states in the diquark-antidiquark basis. We use several methods to estimate the mass spectrum and discuss possible assignment for the $X$ states observed in the $J/ψϕ$ channel. We find that assigning the Belle $X(4350)$ as a $0^{++}$ tetraquark is consistent with the tetraquark interpretation for the $X(4140)$ and $X(4270)$ while the interpretation of the $X(4500)$ and $X(4700)$ needs orbital or radial excitation. There probably exist several tetraquarks around 4.3 GeV that decay into $…
In the framework of the quark delocalization color screening model (QDCSM), we systematically investigate the double-charm and double-strange tetraquark systems $cc\bar{s}\bar{s}$ with two structures: meson-meson and diquark-antidiquark. The bound-state calculation shows that there is no any bound state in present work. However, by applying a stabilization calculation and coupling all channels of both two structures, two new resonance states with $IJ^{P}=00^{+}$ are obtained. One is more possible to be a molecular resonance state with a mass and width around $4256$ MeV and $60$ MeV, respective…
Inspired by recent measurement of possible fully charmed tetraquarks in LHCb Collaboration, we investigate the mass spectra of fully heavy tetraquarks $QQ \bar Q \bar Q$ in an extended relativized quark model. Our estimations indicate that the broad structure around 6.4 GeV should contain one or more ground $cc \bar c \bar c$ tetraquark states, while the narrow structure near 6.9 GeV can be categorized as the first radial excitation of $cc \bar c \bar c$ system. Moreover, with the wave functions of the tetraquarks and mesons, the strong decays of tetraquarks into heavy quarkonium pair are qual…
We have calculated the mass spectra for the $\bar{D}_s^{(*)}D^{(*)}$ molecular states and $sc\bar q\bar c$ tetraquark states with $J^P=0^+, 1^+, 2^+$. The masses of the axial-vector $\bar{D}_sD^{*}$, $\bar{D}_s^{*}D$ molecular states and $\mathbf{1}_{[sc]} \oplus \mathbf{0}_{[\bar q \bar{c}]}$, $\mathbf{0}_{[sc]} \oplus \mathbf{1}_{[\bar q \bar{c}]}$ tetraquark states are predicted to be around 3.98 GeV, which are in good agreement with the mass of $Z_{cs}(3985)^-$ from BESIII \cite{besiii2020Zcs}. In both the molecular and diquark-antidiquark pictures, our results suggest that there may exist…
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…
Possible experimental searches of doubly charmed baryons and tetraquarks at fixed target experiments with high energy hadron beams and a high intensity spectrometer are considered here. The baryons considered are: $Ξ_{cc}^{+}$ (ccd), $Ξ_{cc}^{++}$ (ccu), and $Ω_{cc}^{+}$ (ccs); and the tetraquark is T ($cc\bar{u}\bar{d}$). Estimates are given of masses, lifetimes, internal structure, production cross sections, decay modes, branching ratios, and yields. Experimental requirements are given for optimizing the signal and minimizing the backgrounds. The discussion is in the spirit of an experimenta…
Within the framework of QCD sum rules, we have investigated the tetraquark states with three heavy quarks. We systematically construct the interpolating currents for the possible $cc\bar{c}\bar{q}$, $cc\bar{b}\bar{q}$, $bc\bar{b}\bar{q}$, $bb\bar{b}\bar{q}$ tetraquark states with quantum numbers $J^{P}=0^{+}$ and $J^{P}=1^{+}$. Using these interpolating currents, we have calculated the two-point correlation functions and extracted the mass spectra for the above tetraquark states. We also discuss the decay patterns of these tetraquarks, and notice that the $cc\bar{c}\bar{q}$, $cc\bar{b}\bar{q}$…
We calculate the spectrum of $q\bar q c \bar c$ and $s\bar s c \bar c$ tetraquarks, where $q$, $s$ and $c$ stand for light ($u,d$), strange and charm quarks, respectively, in a relativized diquark model, characterized by one-gluon-exchange (OGE) plus confining potential. In the diquark model, a $q\bar q c \bar c$ ($s\bar s c \bar c$) tetraquark configuration is made up of a heavy-light diquark, $q c$ ($sc$), and anti-diquark, $\bar q \bar c$ ($\bar s \bar c$). According to our results, 13 charmonium-like observed states can be accommodated in the tetraquark picture, both in the hidden-charm ($…
The existence of a shallow or virtual tetraquark state, $cc\bar{u}\bar{d}$, is discussed. Using the putative masses for the doubly charmed baryons ($ccu/ccd$) from SELEX, the mass of the $cc\bar{u}\bar{d}$ state is estimated to be about $3.9 GeV$, only slightly above the $DD^*$ threshold. The experimental signatures for various $cc\bar{u}\bar{d}$ masses are also discussed.
We investigate the mass spectrum of the $ss \bar s \bar s$ tetraquark states within the relativized quark model. By solving the Schrödinger-like equation with the relativized potential, the masses of the $S-$ and $P-$wave $ss \bar s \bar s$ tetraquarks are obtained. The screening effects are also taken into account. It is found that the observed resonant structure $X(2239)$ in the $e^+e^- \to K^+K^-$ process by BESIII Collaboration can be assigned as a $P-$wave $1^{--}$ $ss \bar s \bar s$ tetraquark state. Furthermore, the radiative transition and strong decay behaviors of this structure are a…
We combine lattice QCD results for the potential of two static antiquarks in the presence of two quarks $q q$ of finite mass and quark model techniques to study possibly existing $q q \bar{b} \bar{b}$ tetraquarks. While there is strong indication for a bound four-quark state for $q q = (ud-du) / \sqrt{2}$, i.e. isospin $I=0$, we find clear evidence against the existence of corresponding tetraquarks with $q q \in \{ uu , (ud+du) / \sqrt{2} , dd \}$, i.e. isospin $I=1$, $q q = s s$ and $q q = c c$.
We apply the method of QCD sum rules to study the $s s \bar s \bar s$ tetraquark states of $J^{PC} = 0^{-+}$. We construct all the relevant $s s \bar s \bar s$ tetraquark currents, and find that there are only two independent ones. We use them to further construct two weakly-correlated mixed currents. One of them leads to reliable QCD sum rule results and the mass is extracted to be $2.51^{+0.15}_{-0.12}$ GeV, suggesting that the $X(2370)$ or the $X(2500)$ can be explained as the $ss\bar s\bar s$ tetraquark state of $J^{PC} = 0^{-+}$. To verify this interpretation, we propose to further study …
We study the mass spectra of D-wave excited $cs\bar{c}\bar{s}$ tetraquark states with $J^{PC}=1^{++}$ and $1^{+-}$ in both symmetric $\mathbf{6}_{cs}\otimes\bar{\mathbf{6}}_{\bar{c}\bar{s}}$ and antisymmetric $\bar{\mathbf{3}}_{cs}\otimes\mathbf{3}_{\bar{c}\bar{s}}$ color configurations by using the QCD sum rule method. We construct the D-wave diquark-antidiquark type of $cs\bar{c}\bar{s}$ tetraquark interpolating currents in various excitation structures with $(L_λ,L_ρ\{l_{ρ_1},l_{ρ_2}\})=(2,0\{0,0\}),(1,1\{1,0\}),(1,1\{0,1\}),(0,2\{1,1\}),(0,2\{2,0\}),(0,2\{0,2\})$. Our results support to in…
We use the Laplace/Borel sum rules (LSR) and the finite energy/local duality sum rules (FESR) to investigate the non-strange $ud\bar u\bar d$ and hidden-strange $us\bar u\bar s$ tetraquark states with exotic quantum numbers $J^{PC}=0^{+-}$ . We systematically construct all eight possible tetraquark currents in this channel without covariant derivative operator. Our analyses show that the $ud\bar u\bar d$ systems have good behaviour of sum rule stability and expansion series convergence in both the LSR and FESR analyses, while the LSR for the $us\bar u\bar s$ states do not associate with conver…
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,…
In present work, we systematically calculate the mass spectra of open charm and bottom tetraquarks $q q\bar q \bar Q$ within an extended relativized quark model. The four-body relativized Hamiltonians including the Coulomb potential, confining potential, spin-spin interactions, and relativistic corrections are solved by using the variational method. It is found that the predicted masses of four $0^+$ $ud\bar s \bar c$ states are 2765, 3065, 3152, and 3396 MeV, which disfavor the assignment of the newly observed $X_0(2900)$ as a compact tetraquark. Moreover, the whole mass spectra of the open c…
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…
We apply the method of QCD sum rules to study the structure $X$ newly observed by the BESIII Collaboration in the $ϕη^\prime$ mass spectrum in 2.0-2.1 GeV region in the $J/ψ\rightarrow ϕηη^\prime$ decay. We construct all the $s s \bar s \bar s$ tetraquark currents with $J^{PC} = 1^{+-}$, and use them to perform QCD sum rule analyses. One current leads to reliable QCD sum rule results and the mass is extracted to be $2.00^{+0.10}_{-0.09}$ GeV, suggesting that the structure $X$ can be interpreted as an $s s \bar s \bar s$ tetraquark state with $J^{PC} = 1^{+-}$. The $Y(2175)$ can be interpreted …
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…
Motivated by the observation of exotic structure around 6900MeV in the $J/ψ$-pair mass spectrum using proton-proton collision data by the LHCb collaboration, we study the spectra of fully-heavy tetraquarks within Bethe-Salpeter equation and Regge trajectory relation. The $X(6900)$ may be explained as a radially excited state with quark content $cc\bar{c}\bar{c}$ and spin-parity $0^{++}(3S)$ or $2^{++}(3S)$ or an orbitally excited $2P$ state. New $cc\bar{c}\bar{c}$ structures around 6.0GeV, 6.5GeV, and 7.1GeV are predicted together. Other $bb\bar{b}\bar{b}$ and $bc\bar{b}\bar{c}$ structures whi…
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…
In this work, we study systematically the mass splittings of the $qq\bar{Q}\bar{Q}$ ($q=u$, $d$, $s$ and $Q=c$, $b$) tetraquark states with the color-magnetic interaction by considering color mixing effects and estimate roughly their masses. We find that the color mixing effect is relatively important for the $J^P=0^+$ states and possible stable tetraquarks exist in the $nn\bar{Q}\bar{Q}$ ($n=u$, $d$) and $ns\bar{Q}\bar{Q}$ systems either with $J=0$ or with $J=1$. Possible decay patterns of the tetraquarks are briefly discussed.
The exact eigenenergies of the $T_{4c}=[cc][\bar{c}\bar{c}]$, $T_{4b}=[bb][\bar{b}\bar{b}]$, and $T_{2[bc]}=[bc][\bar{b}\bar{c}]$ tetraquarks are calculated within the extended transitional Hamiltonian approach, in which the so-called Bethe \emph{ansatz} within an infinite-dimensional Lie algebra is used. We fit the parameters appearing in the transitional region from phenomenology associated with potential candidates of tetraquarks. The rotation and vibration transitional theory seems to provide a better description of heavy tetraquarks than other attempts within the same formalism. Our resul…
