We have systematically calculated the mass spectra for S-wave and P-wave fully-charm $cbar{c}cbar{c}$ and fully-bottom $bbar{b}bbar{b}$ tetraquark states in the $mathbf{8}_{[Qbar{Q}]}otimes mathbf{8}_{[Qbar{Q}]}$ color configuration, by using the mom
ent QCD sum rule method. The masses for the fully-charm $cbar ccbar c$ 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 $mathbf{8}_{[cbar{c}]}otimes mathbf{8}_{[cbar{c}]}$ components in LHCbs di-$J/psi$ structures. For the fully-bottom $bbar{b}bbar{b}$ system, their masses are calculated around 18.2 GeV for S-wave tetraquark states while 18.4-18.6 GeV for P-wave ones, which are below the $eta_beta_b$ and $Upsilon(1S)Upsilon(1S)$ two-meson decay thresholds.
We have studied the masse spectra for the $ccbar{b}bar{b}$/$bbbar{c}bar{c}$ 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 $ccbar{b}bar{b}$ 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 predictions for the positive parity $ccbar{b}bar{b}$ ground states are lower than the $B_{c}B_{c}$ threshold, implying that these tetraquarks can only decay via weak interaction and thus are expected to be stable and narrow.
We study the mass spectra of the $NOmega$ dibaryons in the $^{3}S_1$ and $^{5}S_2$ channels with $J^{P}=1^{+}$ and $2^{+}$ respectively, by using the method of QCD sum rules. We construct two dibaryon interpolating currents in the molecular picture a
nd calculate their correlation functions and spectral densities up to dimension-16 condensates. Our results indicate that there may exist an $NOmega$ dibaryon bound state in the $^{5}S_2$ channel with a binding energy of about $21 mathrm{MeV}$. The masses of the $^{3}S_1$ $NOmega$ dibaryons with $J^{P}=1^{+}$ are predicted to be higher than the $NOmega$ and $LambdaXi$ thresholds, and thus can decay into these final states directly in S-wave. The $NOmega (^{5}S_2)$ dibaryon bound state can decay into the octet-octet final states $LambdaXi$ and $SigmaXi$ in D-wave via the quark rearrangement mechanism. The existence of these $NOmega$ dibaryons may be identified in the relativistic heavy-ion collision experiments in the future.
We study the existence of fully-heavy hidden-flavor $bcbar{b}bar{c}$ tetraquark states with various $J^{PC}=0^{pm+}, 0^{--},1^{pmpm}, 2^{++}$, by using the moment QCD sum rule method augmented by fundamental inequalities. Using the moment sum rule an
alyses, our calculation shows that the masses for the S-wave positive parity $bcbar{b}bar{c}$ 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, such results are below the thresholds $T_{eta_ceta_b}/T_{Upsilonpsi}$ and $T_{B_cB_c}$, implying that these S-wave positive parity $bcbar{b}bar{c}$ tetraquark states are probably stable against the strong interaction. For the P-wave negative parity $bcbar{b}bar{c}$ tetraquarks, their masses in the $[mathbf{bar{3}_c}]_{bc}otimes[mathbf{3_c}]_{bar{b}bar{c}}$ channel are around $12.9-13.2$ GeV, while a bit higher in the $[mathbf{6_c}]_{bc}otimes[mathbf{bar{6}_c}]_{bar{b}bar{c}}$ channel. They can decay into the $cbar c+bbar b$ and $cbar b+bbar c$ final states via the spontaneous dissociation mechanism, including the $J/psiUpsilon$, $eta_cUpsilon$, $J/psieta_b$, $B_c^+B_c^-$ channels.
We have calculated the mass spectra for the $bar{D}_s^{(*)}D^{(*)}$ molecular states and $scbar qbar c$ 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 two almost degenerate states, as the strange partners of the $X(3872)$ and $Z_c(3900)$. We propose to carefully examine the $Z_{cs}(3985)$ in future experiments to verify this. One may also search for more hidden-charm four-quark states with strangeness not only in the open-charm $bar{D}_s^{(*)}D^{(*)}$ channels, but also in the hidden-charm channels $eta_c K/K^ast$, $J/psi K/K^ast$.
We have studied the masses for fully open-flavor tetraquark states $bcbar{q}bar{s}$ and $scbar{q}bar{b}$ with quantum numbers $J^{P}=0^{+},1^{+}$. We systematically construct all diquark-antiquark interpolating currents and calculate the two-point co
rrelation 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 $bcbar{q}bar{s}$ tetraquark states and $7.0-7.1$ GeV for the $scbar{q}bar{b}$ tetraquarks. The masses of $bcbar{q}bar{s}$ tetraquarks are below the thresholds of $bar{B}_{s}D$ and $bar{B}_{s}^{*}D$ final states for the scalar and axial-vector channels respectively. The $scbar{q}bar{b}$ tetraquark states with $J^{P}=1^{+}$ lie below the $B_{c}^{+}K^{*}$ and $B_{s}^{*}D$ thresholds. Such low masses for these possible tetraquark states indicate that they can only decay via weak interaction and thus are very narrow and stable.
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.
We improve the Monte-Carlo based QCD sum rules by introducing the rigorous Holder-inequality-determined sum rule window and a Breit-Wigner type parametrization for the phenomenological spectral function. In this improved sum rule analysis methodology
, the sum rule analysis window can be determined without any assumptions on OPE convergence or the QCD continuum.Therefore an unbiased prediction can be obtained for the phenomenological parameters (the hadronic mass and width etc.). We test the new approach in the $rho$ meson channel with re-examination and inclusion of $alpha_s$ corrections to dimension-4 condensates in the OPE. We obtain results highly consistent with experimental values. We also discuss the possible extension of this method to some other channels.
