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In the present work, the doubly-charm and doubly-bottom pentaquark molecular states $D^{(*)}\Sigma_c^{(*)}$ and $B^{(*)}\Sigma_b^{(*)}$ are studied via the QCD sum rules. Sixteen color singlet-singlet type currents with the definite isospin-spin-parity $IJ^P$ are constructed to interpolate the corresponding hadronic states with the same quantum numbers. The masses and pole residues of those doubly-heavy pentaquark molecular states are calculated, the results show that their masses are all below the corresponding meson-baryon thresholds, which means that they are possible bound states, not resonant states, moreover, the possible decay channels for the doubly-charm molecular states are given., Comment: 12 pages, 10 figures

In the present work, the strong decays of the newly observed $P_{cs}(4338)$ as well as its high isospin cousin $P_{cs}(4460)$ are studied via the QCD sum rules. According to conservation of isospin, spin and parity, the hadronic coupling constants in four decay channels are obtained, then the partial decay widths are obtained. The total width of the $P_{cs}(4338)$ coincides with the experimental data nicely, while the predictions for the $P_{cs}(4460)$ can be testified in the future experiment, and shed light on the nature of the $P_{cs}(4338)$., Comment: 13 pages, 12 figures

In the present work, considering the conservation of isospin in the strong decays, we investigate the strong decays of the pentaquark molecule candidate $P_c(4312)$ and its possible higher isospin cousin $P_c(4330)$ in the framework of the QCD sum rules. What's more, the pole residue of the $\Delta$ baryon with isospin eigenstate $|II_3\rangle=|\frac{3}{2}\frac{1}{2}\rangle$ is obtained. If the possible pentaquark molecule candidate $P_c(4330)$ could be testified in the future experiment, it would shed light on interpretations of the $P_c$ states., Comment: 13 pages, 5 figures

In this work, we tentatively identify the $P_{cs}(4338)$ as the $\bar{D}\Xi_c$ molecular state, and distinguish the isospins of the current operators to explore the $\bar{D}\Xi_c$, $\bar{D}\Lambda_c$, $\bar{D}_s\Xi_c$, $\bar{D}_s\Lambda_c$, $\bar{D}^*\Xi_c$, $\bar{D}^*\Lambda_c$, $\bar{D}^*_s\Xi_c$ and $\bar{D}^*_s\Lambda_c$ molecular states without strange, with strange and with double strange in the framework of the QCD sum rules in details. The present explorations favor identifying the $P_{cs}(4338)$ ($P_{cs}(4459)$) as the $\bar{D}\Xi_c$ ($\bar{D}^*\Xi_c$) molecular state with the spin-parity $J^P={\frac{1}{2}}^-$ (${\frac{3}{2}}^-$) and isospin $(I,I_3)=(0,0)$, the observation of their cousins with the isospin $(I,I_3)=(1,0)$ in the $J/\psi\Sigma^0/\eta_c\Sigma^0$ invariant mass distributions would decipher their inner structures., Comment: 20 pages, 5 figures

In the paper, we construct eight color singlet-singlet type five-quark currents with distinguished isospins to study the $\bar{D}\Xi^{\prime}$, $\bar{D}\Xi_c^{*}$, $\bar{D}^{*}\Xi_c^{\prime}$ and $\bar{D}^{*}\Xi_c^{*}$ molecular states with strangeness via the QCD sum rules. Numerical results show that the central values of the pentaquark masses with higher (lower) isospin are slightly above (below) the thresholds of the corresponding meson-baryon pairs, and support assigning the $P_{cs}(4459)$ as the $\bar{D}\Xi_c^{*}$ molecular state with the quantum numbers $IJ^P=0{\frac{3}{2}}^-$. The other predictions can be confronted to the experimental data in the future.

In this article, we construct the color singlet-singlet type five-quark currents with the isospins $(I,I_3)=(\frac{1}{2},\frac{1}{2})$ and $(\frac{3}{2},\frac{1}{2})$ unambiguously to explore the $\bar{D}\Sigma_c$, $\bar{D}\Sigma_c^*$, $\bar{D}^*\Sigma_c$ and $\bar{D}^*\Sigma_c^*$ pentaquark states via the QCD sum rules for the first time, where the $\bar{D}$, $\Sigma_c$, $\cdots$ represent the color-singlet clusters having the same quantum numbers as the corresponding physical mesons or baryons. The numerical results support assigning the $P_c(4312)$, $P_c(4380)$, $P_c(4440)$ and $P_c(4457)$ as the $\bar{D}\Sigma_c$, $\bar{D}\Sigma_c^*$, $\bar{D}^*\Sigma_c$ and $\bar{D}^*\Sigma_c^*$ pentaquark states with the isospin $I=\frac{1}{2}$, respectively. The corresponding $\bar{D}\Sigma_c$, $\bar{D}\Sigma_c^*$, $\bar{D}^*\Sigma_c$ and $\bar{D}^*\Sigma_c^*$ pentaquark states with the isospin $I=\frac{3}{2}$ have slightly larger masses, the observations of the higher pentaquark candidates in the $J/\psi \Delta$ invariant mass spectrum would shed light on the nature of the $P_c$ states, and make contributions in distinguishing the scenarios of color antitriplet-antitriplet-antitriplet type and color singlet-singlet type pentaquark states.

In the present work, we construct eight six-quark currents to study the $\Sigma_c\bar{\Sigma}_c$ baryonium and $\Sigma_c\Sigma_c$ dibaryon states via the QCD sum rules. For either $\Sigma_c\bar{\Sigma}_c$ baryonium or $\Sigma_c\Sigma_c$ dibaryon states, we construct four currents with the $J^P=1^-, 1^+, 0^+$ and $0^-$. Except the current $1^+$ of $\Sigma_c\Sigma_c$, we find the Borel windows for the other seven. There are two possible $\Sigma_c\bar{\Sigma}_c$ molecular states or compact six-quark states with the $J^P=1^-$ and $0^-$. The results of the current $0^+$ of $\Sigma_c\Sigma_c$ show a possible $\Sigma_c\Sigma_c$ molecular state with $20$ MeV binding energy. We find two $\Sigma_c\bar{\Sigma}_c$ baryonium resonances states with the $J^P=1^+, 0^+$ and two $\Sigma_c\Sigma_c$ dibaryon resonances states with the $J^P=0^-, 1^-$, respectively. Pole residues of the seven states are also calculated., Comment: arXiv admin note: text overlap with arXiv:2107.04751

Recently, scientists have made great progresses in experiments in searching for the excited states of $\Xi_{b}$ and $\Lambda_{b}$ baryons such as the $\Lambda_{b}(6072)$, $\Lambda_{b}(6146)$, $\Lambda_{b}(6152)$, $\Xi_{b}(6227)$, $\Xi_{b}(6100)$, $\Xi_{b}(6327)$ and $\Xi_{b}(6333)$. Stimulated by these progresses, we give a systematical analysis about the $1D$ and $2D$ states of $\Xi_{b}$ and $\Lambda_{b}$ baryons with the method of QCD sum rules. By constructing three types of interpolating currents, we calculate the masses and pole residues of these heavy baryons with different excitation modes $(L_{\rho},L_{\lambda})=(0,2)$, $(2,0)$ and $(1,1)$. As a result, we decode the inner structures of $\Lambda_{b}(6146)$, $\Lambda_{b}(6152)$, $\Xi_{b}(6327)$ and $\Xi_{b}(6333)$, and favor assigning these states as the $1D$ baryons with the quantum numbers $(L_{\rho},L_{\lambda})=(0,2)$ and $\frac{3}{2}^{+}$, $\frac{5}{2}^{+}$, $\frac{3}{2}^{+}$ and $\frac{5}{2}^{+}$, respectively. In addition, the predictions about the masses and pole residues of the other $1D$ and $2D$ states of $\Xi_{b}$ and $\Lambda_{b}$ baryons in this paper are helpful in studying the D-wave bottom baryons in experiments in the future.

In this article, we construct the six-quark currents with the $J^P=0^+$, $0^-$, $1^+$ and $1^-$ to study the $\Lambda_c$$\Lambda_c$ dibaryon and $\Lambda_c$$\bar{\Lambda}_c$ baryonium states via QCD sum rules. We consider the vacuum condensates up to dimension 16 and truncation of the order $\mathcal{O}(\alpha_s^k )$ with $k\leq3$. The predicted masses are $5.11_{-0.12}^{+0.15}$GeV, $4.66_{-0.06}^{+0.10}$GeV, $4.99_{-0.09}^{+0.10}$GeV $4.68^{+0.08}_{-0.08}$GeV for the $J^P=0^+$, $0^-$, $1^+$ and $1^-$ states, respectively, which can be confronted to the experimental data in the future considering the high integrated luminosity at the center-of-mass energy about $4.8\,\rm{GeV}$ at the BESIII. We find the terms with $\frac{3}{2}< k \leq 3$ do play a tiny role, and we can ignore these terms safely in the QCD sum rules., Comment: 49 pages,16 figures

In this article, we firstly derive two QCD sum rules QCDSR I and QCDSR II which are respectively used to extract observable quantities of the ground states and the first radially excited states of D-wave vector $\rho$ and $\phi$ mesons. In our calculations, we consider the contributions of vacuum condensates up to dimension-7 in the operator product expansion. The predicted masses for $1^{3}D_{1}$ $\rho$ meson and $2^{3}D_{1}$ $\phi$ meson are consistent well with the experimental data of $\rho$($1700$) and $\phi$($2170$). Besides, our analysis indicates that it is reliable to assign the recent reported $Y$($2040$) state as the $2^{3}D_{1}$ $\rho$ meson. Finally, we obtain the decay constants of these states with QCDSR I and QCDSR II. These predictions are helpful not only to reveal the structure of the newly observed $Y$($2040$) state but also to establish $\phi$ meson and $\rho$ meson families.