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Many charmonium-like and bottomonium-like $XYZ$ resonances have been observed by the Belle, Babar, CLEO and BESIII collaborations in the past decade. They are difficult to fit in the conventional quark model and thus are considered as candidates of exotic hadrons, such as multi-quark states, meson molecules, and hybrids. In this talk, we first briefly introduce the method of QCD sum rules and then provide a short review of the mass spectra of the quarkonium-like tetraquark states and the heavy quarkonium hybrids in the QCD sum rules approach. Possible interpretations of the $XYZ$ resonances are briefly discussed.
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We use the Laplace/Borel sum rules (LSR) and the finite energy/local duality sum rules (FESR) to investigate the non-strange $udbar ubar d$ and hidden-strange $usbar ubar s$ 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 $udbar ubar d$ systems have good behaviour of sum rule stability and expansion series convergence in both the LSR and FESR analyses, while the LSR for the $usbar ubar s$ states do not associate with convergent OPE series in the stability regions and only the FESR can provide valid results. We give the mass predictions $1.43pm0.09$ GeV and $1.54pm0.12$ GeV for the $udbar ubar d$ and $usbar ubar s$ tetraquark states, respectively. Our results indicate that the $0^{+-}$ isovector $usbar ubar s$ tetraquark may only decay via weak interaction mechanism, e.g. $X_{usbar{u}bar{s}}to Kpipi$, since its strong decays are forbidden by kinematics and the symmetry constraints on the exotic quantum numbers. It is predicted to be very narrow, if it does exist. The $0^{+-}$ isoscalar $usbar ubar s$ tetraquark is also predicted to be not very wide because its dominate decay mode $X_{usbar{u}bar{s}}tophipipi$ is in $P$-wave.
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, $Gamma_0=57{pm} 13$ MeV and $X_1(2900)$ with $J^P = 1^-$ at $2904 {pm} 7$ MeV, $Gamma_1=110{pm} 12$ MeV. We interpret the $X_0(2900)$ component as a $cs bar ubar d$ isosinglet compact tetraquark, calculating its mass to be $2863 {pm} 12$ MeV. This is the first exotic hadron with open heavy flavor. The analogous $bsbar ubar d$ tetraquark is predicted at $6213 {pm} 12$ MeV. We discuss possible interpretations of the heavier and wider $X_1(2900)$ state and examine potential implications for other systems with two heavy quarks.
We investigate the exotic $OmegaOmega$ dibaryon states with $J^P=0^+$ and $2^+$ in a molecular picture. We construct the scalar and tensor $Omega$$Omega$ molecular interpolating currents and calculate their masses within the method of QCD sum rules. Our results indicate that the mass of the scalar dibaryon state is $m_{OmegaOmega, , 0^+}=(3.33pm0.22) ,unit$, which is about $15 ,mathrm{MeV}$ below the $2m_Omega$ threshold. This result suggests the existence of a loosely bound molecular state of the $J^P=0^+$ scalar $OmegaOmega$ dibaryon with a small binding energy around 15 MeV. The mass of the tensor dibaryon is predicted to be $m_{OmegaOmega,, 2^+}=(3.24pm0.23), mbox{GeV}$, which may imply a deeper molecular state of the tensor $OmegaOmega$ dibaryon than the scalar channel. These exotic strangeness $S=-6$ and doubly-charged $OmegaOmega$ dibaryon states may be identified in the heavy-ion collision processes.
In this work, we study systematically the mass splittings of the $qqbar{Q}bar{Q}$ ($q=u$, $d$, $s$ 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 $nnbar{Q}bar{Q}$ ($n=u$, $d$) and $nsbar{Q}bar{Q}$ systems either with $J=0$ or with $J=1$. Possible decay patterns of the tetraquarks are briefly discussed.
In the present work, we investigate the production of $P_{c}$ and $Z_c(3900)/Z_{cs}(3985)$ states in the processes of $pi p rightarrow Z_{c}(3900) P_{c} $/$Kprightarrow Z_{cs}(3985) P_{c}$ with an effective Lagrangian approach. Our estimations indicates that the cross sections depends on the model parameters and beam energies, in particular, the cross sections for $pi p to Z_c(3900) P_c(4312)$ and $pi p to Z_c(3900) P_c(4440)$ are similar and can reach up to 10 nb, while those for $pi p to Z_c(3900) P_c(4457)$ can be 30 nb. As for $Kp to Z_{cs}(3985)P_c$, the cross sections are about 2.5 times smaller than those for $pi p to Z_c(3900) P_c$. The discussed processes in the present work, especially $pi p to Z_c(3900) P_c(4457)$, may be accessible by the the high-energy pion and kaon beams in the facilities of J-PARC and COMPASS.
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