Analysis of hidden-charm pentaquark molecular states with and without strangeness via the QCD sum rules

In this study, we investigate the \begin{document}$\bar{D}\Sigma_c$\end{document}, \begin{document}$\bar{D}\Xi^\prime_c$\end{document}, \begin{document}$\bar{D}\Sigma_c^*$\end{document}, \begin{document}$\bar{D}\Xi_c^*$\end{document}, \begin{document}$\bar{D}^{*}\Sigma_c$\end{document}, \begin{document}$\bar{D}^{*}\Xi^\prime_c$\end{document}, \begin{document}$\bar{D}^{*}\Sigma_c^*$\end{document}, and \begin{document}$\bar{D}^{*}\Xi_c^*$\end{document} pentaquark molecular states with and without strangeness via the QCD sum rules in detail, focusing on the light flavor, \begin{document}$SU(3)$\end{document} , breaking effects, and make predictions for new pentaquark molecular states besides assigning \begin{document}$P_c(4312)$\end{document}, \begin{document}$P_c(4380)$\end{document}, \begin{document}$P_c(4440)$\end{document}, \begin{document}$P_c(4457)$\end{document} , and \begin{document}$P_{cs}(4459)$\end{document} self-consistently. In the future, we can search for these pentaquark molecular states in the decay of \begin{document}$\Lambda_b^0$\end{document}, \begin{document}$\Xi_b^0$\end{document} , and \begin{document}$\Xi_b^-$\end{document} . Furthermore, we discuss high-dimensional vacuum condensates in detail.     

Analysis of Pcs(4338) and related pentaquark molecular states via QCD sum rules

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

Mixing of X and Y states from QCD sum rules analysis

We study \begin{document}$ \bar{Q}Q\bar{q}q $\end{document} and \begin{document}$ \bar{Q}qQ\bar{q} $\end{document} states as mixed states in QCD sum rules. By calculating the two-point correlation functions of pure states of their corresponding currents, we review the mass and coupling constant predictions of \begin{document}$ J^{PC} = 1^{++} $\end{document}, \begin{document}$1^{--}$\end{document}, and \begin{document}$ 1^{-+} $\end{document} states. By calculating the two-point mixed correlation functions of \begin{document}$ \bar{Q}Q\bar{q}q $\end{document} and \begin{document}$ \bar{Q}qQ\bar{q} $\end{document} currents, we estimate the mass and coupling constants of the corresponding "physical state" that couples to both \begin{document}$ \bar{Q}Q\bar{q}q $\end{document} and \begin{document}$ \bar{Q}qQ\bar{q} $\end{document} currents. Our results suggest that for \begin{document}$ 1^{++} $\end{document} states, the \begin{document}$ \bar{Q}Q\bar{q}q $\end{document} and \begin{document}$ \bar{Q}qQ\bar{q} $\end{document} components are more likely to mix, while for \begin{document}$ 1^{--} $\end{document} and \begin{document}$ 1^{-+} $\end{document} states, there is less mixing between \begin{document}$ \bar{Q}Q\bar{q}q $\end{document} and \begin{document}$ \bar{Q}qQ\bar{q} $\end{document}. Our results suggest the Y series of states have more complicated components.     

Analysis of the strong decays of Pc(4312) as a pentaquark molecular state with QCD sum rules

In this article, we tentatively assign \begin{document}$P_c(4312)$\end{document} to be the \begin{document}$\bar{D}\Sigma_c$\end{document} pentaquark molecular state with the spin-parity \begin{document}$J^P={\frac{1}{2}}^-$\end{document} , and discuss the factorizable and non-factorizable contributions in the two-point QCD sum rules for the \begin{document}$\bar{D}\Sigma_c$\end{document} molecular state in detail to prove the reliability of the single pole approximation in the hadronic spectral density. We study its two-body strong decays with the QCD sum rules, and special attention is paid to match the hadron side with the QCD side of the correlation functions to obtain solid duality. We obtain the partial decay widths \begin{document}$\Gamma\left(P_c(4312)\to \eta_c p\right)=0.255\,\,{\rm{MeV}}$\end{document} and \begin{document}$\Gamma\left(P_c(4312)\to J/\psi p\right)=9.296^{+19.542}_{-9.296}\,\,{\rm{MeV}}$\end{document} , which are compatible with the experimental value of the total width, and support assigning \begin{document}$P_c(4312)$\end{document} to be the \begin{document}$\bar{D}\Sigma_c$\end{document} pentaquark molecular state.     

Revisiting hidden-charm pentaquarks from QCD sum rules

We revisit hidden-charm pentaquark states P_c(4380) and P_c(4450) using the method of QCD sum rules by requiring the pole contribution to be greater than or equal to 30% in order to better that the one-pole parametrization is valid. We find two mixing currents, and our results suggest that P_c(4380) and P_c(4450) can be identified as hiddencharm pentaquark states having J~P= 3/2~-and 5/2~+, respectively. However, there still exist other possible spin-parity assignments, such as J~P = 3/2~+ and J~P = 5/2~-, which must be clarified in further theoretical and experimental studies.     

Analysis of X(5568) as Scalar Tetraquark State in Diquark-Antidiquark Model with QCD Sum Rules

In this article, we take the X(5568) as the diquark-antidiquark type tetraquark state with the spin-parity J^P=0⁺, construct the scalar-diquark-scalar-antidiquark type current, carry out the operator product expansion up to the vacuum condensates of dimension-10, and study the mass and pole residue in details with the QCD sum rules. We obtain the value M_X=(5.57±0.12) GeV, which is consistent with the experimental data. The present prediction favors assigning the X(5568) to be the scalar tetraquark state.     

Vector hidden-bottom tetraquark candidate: Y(10750)

In this article,we take the scalar diquark and antidiquark operators as the basic constituents,and construct the Cγ_5■γ_5C type tetraquark current to study Y(10750) with the QCD sum rules.The predicted mass M_Y=10.75±0.10 GeV and width Γ_Y=33.60_(-9.45)~(+16.64) MeV support the assignment of Y(10750) as the diquark-antidiquark type vector hidden-bottom tetraquark state,with a relative P-wave between the diquark and antidiquark constituents.     

Analysis of the excited Ωc states as the $\tfrac{1}{2}$± pentaquark states with QCD sum rules

We construct both the scalar-diquark-scalar-diquark-antiquark type and axialvector-diquark-axialvector-diquark-antiquark type interpolating currents to study the charmed pentaquark states ${susc}\bar{u}$ with ${J}^{P}={\tfrac{1}{2}}^{\pm }$. We employ the QCD sum rules to investigate the masses and pole residues of the charmed pentaquark states by taking into account the vacuum condensates up to dimension 13 in the operator product expansion. Our calculation results indicate that the scalar-diquark-scalar-diquark-antiquark type and axialvector-diquark-axialvector-diquark-antiquark type charmed pentaquark states ${susc}\bar{u}$ with ${J}^{P}={\tfrac{1}{2}}^{-}$ can be possible candidates of the excited Ω_c states observed in the LHCb collaboration.     

Analysis of Scalar Doubly Heavy Tetraquark States with QCD Sum Rules

In this article, we perform a detailed study of the mass spectrum of the scalar doubly charmed and doubly bottom tetraquark states using the QCD sum rules.     

QCD sum rule study for hidden-strange pentaquarks

Inspired by the LHCb observations of hidden-charm \begin{document}$ P_{c(s)} $\end{document} states, we study their hidden-strange analog\begin{document}$ P_s $\end{document} states in both the \begin{document}$ [udu][\bar ss] $\end{document} and \begin{document}$ [uds][\bar su] $\end{document} configurations. We investigate \begin{document}$ P_s $\end{document} pentaquark states in the \begin{document}$ p\eta^\prime $\end{document}, \begin{document}$ p\phi $\end{document}, \begin{document}$ \Lambda K $\end{document}, \begin{document}$ \Sigma K $\end{document}, and \begin{document}$ \Sigma^\ast K^\ast $\end{document} structures with \begin{document}$J^P ={1}/{2}^-$\end{document} and \begin{document}$ \Sigma ^\ast K $\end{document} and \begin{document}$ \Sigma K^\ast $\end{document} with \begin{document}$J^P = {3}/{2}^-$\end{document} and calculate their masses in the framework of QCD sum rules. Our numerical results show that the extracted hadron masses for all the \begin{document}$ p\eta^\prime $\end{document}, \begin{document}$ p\phi $\end{document}, \begin{document}$ \Lambda K $\end{document}, \begin{document}$ \Sigma K $\end{document}, and \begin{document}$ \Sigma^\ast K^\ast $\end{document} structures are significantly higher than the \begin{document}$ \Sigma K $\end{document} mass threshold, and the masses for \begin{document}$ \Sigma ^\ast K $\end{document} and \begin{document}$ \Sigma K^\ast $\end{document}are also higher than the threshold of the corresponding hadron; hence, no bound state exists in such channels, which is consistent with the current experimental status.     

Hadronic coupling constants of the lowest hidden-charm pentaquark state,using QCD sum rules with rigorous quark-hadron duality

In this article,we illustrate how to calculate the hadronic coupling constants of the pentaquark states with QCD sum rules based on rigorous quark-hadron quality.We then study the hadronic coupling constants of the lowest diquark-diquark-antiquark type hidden-charm pentaquark state with spin-parity J~P=1/2~-in detail,and calculate the partial decay widths.The total width Г(P_c)=14.32±3.31 MeV is compatible with the experimental value T_(P_c(4312))=9.8±2.7_(-4.5)~(+3.7) MeV from the LHCb collaboration and favors assigning the P_c(4312) to be the [ud][uc]c pentaquark state with J~P=1/2~-.The hadronic coupling constants have the relation ■,and favor the hadronic dressing mechanism.The P_c(4312) may have a diquark-diquark-antiquark type pentaquark core with the typical size of the qqq-type baryon states.The strong couplings to the meson-baryon pairs DE_c lead to some pentaquark molecule components,and the P_c(4312) may spend a rather large time as the DE_c molecular state.     

Scalar Hidden-Charm Tetraquark States with QCD Sum Rules

In this article, we study the masses and pole residues of the pseudoscalar-diquark-pseudoscalar-antidiquark type and vector-diquark-vector-antidiquark type scalar hidden-charm cud(cus) tetraquark states with QCD sum rules by taking into account the contributions of the vacuum condensates up to dimension-10 in the operator product expansion.The predicted masses can be confronted with the experimental data in the future. Possible decays of those tetraquark states are also discussed.     

Nonlocal condensate model for QCD sum rules

We include effects of nonlocal quark condensates into QCD sum rules (QSR) via the Källén–Lehmann representation for a dressed fermion propagator, in which a negative spectral density function manifests their nonperturbative nature. Applying our formalism to the pion form factor as an example, QSR results are in good agreement with data for momentum transfer squared up to Q²≈10 GeV²$Q^2\approx 10{\text{GeV}}^2$. It is observed that the nonlocal quark condensate contribution descends like 1/Q²$1/Q^2$, different from the exponential decrease in Q²$Q^2$ obtained in the literature, and contrary to the linear rise in the local-condensate approximation.     

Role of four-quark condensates in QCD sum rules

The QCD sum rule approach to the in-medium behavior of hadrons is discussed for the ω meson, nucleon and D meson. Emphasis is placed on the impact of four-quark condensates and on order parameters of spontaneous symmetry breaking.     

Analysis of the Light-Flavor Scalar and Axial-Vector Diquark States with QCD Sum Rules

In this article, we study the light-flavor scalar and axial-vector diquark states in the vacuum and in the nuclear matter using the QCD sum rules in a systematic way, and make reasonable predictions for their masses in the vacuum and in the nuclear matter.     

Reanalysis of the Z_c(4020), Z_c(4025), Z(4050) and Z(4250) as Tetraquark States with QCD Sum Rules

In this article, we calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and study the C γμ- Cγνtype scalar, axial-vector and tensor tetraquark states in details with the QCD sum rules. In calculations, we use the formula μ = (M 2X/ Y /Z-(2Mc)2)~(1/2) to determine the energy scales of the QCD spectral densities. The predictions MJ =2=(4.02+0.09-0.09) GeV, MJ =1=(4.02+0.07-0.08) GeV favor assigning the Zc(4020) and Zc(4025) as the JP C= 1+-or 2++diquark-antidiquark type tetraquark states, while the prediction M++J =0=(3.85+0.15-0.09) GeV disfavors assigning the Z(4050) and Z(4250) as the JP C= 0diquark-antidiquark type tetraquark states. Furthermore, we discuss the strong decays of the 0++, 1+-, 2++diquark-antidiquark type tetraquark states in details.     

QCD sum rule study of the masses of light tetraquark scalar mesons

We study the low-lying scalar mesons of light u, d, s flavors in the QCD sum rule. Having all possible combinations of tetraquark currents in the local form, QCD sum rule analysis has been carefully performed. We found that using the appropriate tetraquark currents, the masses of σ, κ, f₀ and a₀ mesons appear in the region of 0.6–1 GeV with the expected ordering. The results are compared with that of the conventional currents, where the masses are considerably larger.     

Analysis of the Triply Heavy Baryon States with QCD Sum Rules

In this article, we study the (1/2) ± and (3/2)± triply heavy baryon states in a systematic way by subtracting the contributions from the corresponding (1/2)■ and (3/2)■ triply heavy baryon states with the QCD sum rules, and make reasonable predictions for their masses.     

Heavy flavor baryon spectra via QCD sum rules

In this talk, we give a short review of our recent works on studying the singly heavy baryon, doubly heavy baryon, and triply heavy baryon spectra from QCD sum rules.