Hidden-charm Pentaquark States Research Articles

Fine structure of pentaquark multiplets in the dynamical diquark model

We apply the dynamical diquark model to predict the spectrum of hidden-charm pentaquark states in both unflavored and open-strange sectors. Using only Hamiltonian parameters introduced in the tetraquark $S$- and $P$-wave multiplets, the model naturally produces the level spacing supported by the most recent LHCb results for ${P}_{c}$ structures. Furthermore, using model inputs obtained from data of hidden-charm, open-strange tetraquarks (${Z}_{cs}$), we predict the spectrum of ${P}_{cs}$ states, including the recently observed ${P}_{cs}(4459)$. We find all pentaquark candidates observed to date to belong to the $1P$ multiplet and hence have positive parity.

Searching for strange hidden-charm pentaquark state Pcs(4459) in γp→K+Pcs(4459) reaction

We investigate the possibility of studying the strange hidden-charm pentaquark state $P_{cs}(4459)$ by photon-induced reactions on a proton target in an effective Lagrangian approach. The production process is described by the $t$-channel $K^{-}$ exchange, the $u$-channel $\Lambda$ exchange, the contract term, and the $s$- channel nucleon pole. Our theoretical approach is based on the assumption that $P_{cs}(4459)$ with $J^{P}=1/2^{-}$ or $J^{P}=3/2^{-}$ can be interpreted as a molecule composed of $\bar{D}^{*}\Xi_c$. Using the coupling constants of the $P^{J^P}_{cs}$ to $\gamma{}\Lambda$ and $K^{-}p$ channels obtained from molecule picture of the $P^{J^{P}}_{cs}(4459)$, the total cross-sections of the process $\gamma{}p\to{}P^{J^P}_{cs}K^{+}$ is evaluated. Our calculation indicates that the cross-section for $\gamma{}p\to{}P^{1/2^{-}}_{cs}K^{+}$ and $\gamma{}p\to{}P^{3/2^{-}}_{cs}K^{+}$ are of the order of 10.0 pb and 5.0 pb, respectively. In addition, we compute the cross-section by assuming $P_{cs}(4459)$ as a compact pentaquark and find it is quite different from the results of $\bar{D}^{*}\Xi_c$ molecule. Those results can be measured in future experiments, such as the Electron-Ion Collider in China and the United States. And can be used to test the nature of the $P_{cs}$.

Hidden charm hadronic molecule with strangeness Pcs*(4739) as a ΣcD¯K¯ bound state

Motivated by the recent discovery of the first hidden charm pentaquark state with strangeness ${P}_{cs}(4459)$ by the LHCb Collaboration, we study the likely existence of a three-body ${\mathrm{\ensuremath{\Sigma}}}_{c}\overline{D}\overline{K}$ bound state, which shares the same minimal quark content as ${P}_{cs}(4459)$. The ${\mathrm{\ensuremath{\Sigma}}}_{c}\overline{D}$ and $DK$ interactions are determined by reproducing ${P}_{c}(4312)$ and ${D}_{s0}^{*}(2317)$ as ${\mathrm{\ensuremath{\Sigma}}}_{c}\overline{D}$ and $\overline{D}\overline{K}$ molecules, respectively, while the ${\mathrm{\ensuremath{\Sigma}}}_{c}\overline{K}$ interaction is constrained by chiral effective theory. We indeed find a three-body bound state by solving the Schr\"odinger equation using the Gaussian expansion method, which can be viewed as an excited hidden charm exotic state with strangeness, ${P}_{cs}^{*}(4739)$, with $I({J}^{P})=1(1/{2}^{+})$ and a binding energy of ${77.8}_{\ensuremath{-}10.3}^{+25}\text{ }\text{ }\mathrm{MeV}$. We further study its strong decays via triangle diagrams and show that its partial decay widths into $D{\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}}$ and ${D}_{s}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ are of a few tens of MeV, with the former being dominant.

Hidden charm pentaquark states in a diquark model

The mass spectrum of hidden charm pentaquark states composed of two diquarks and an antiquark are calculated by use of an effective Hamiltonian which includes explicitly the spin, color, and flavor dependent interactions. The results show that the $P_c(4312)^+$ and $P_c(4440)^+$ states could be explained as hidden charm pentaquark states with isospin and spin-parity $IJ^P=1/2\left(3/2^-\right)$, the $P_c(4457)^+$ state could be explained as a hidden charm pentaquark state with $IJ^P=1/2\left(5/2^-\right)$, and the $P_{cs}(4459)^+$ state could be explained as a hidden charm pentaquark state with $IJ^P=0\left(1/2^-\right)$ or $0\left(3/2^-\right)$. Predications for the masses of other possible pentaquark states are also given, and the possible decay channels of these hidden charm pentaquark states are discussed.

Hadronic coupling constants of the lowest hidden-charm pentaquark state, using QCD sum rules with rigorous quark-hadron duality * *Supported by National Natural Science Foundation of China (11775079)

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 in detail, and calculate the partial decay widths. The total width is compatible with the experimental value from the LHCb collaboration, and favors assigning the to be the pentaquark state with . The hadronic coupling constants have the relation , and favor the hadronic dressing mechanism. The may have a diquark-diquark-antiquark type pentaquark core with the typical size of the -type baryon states. The strong couplings to the meson-baryon pairs lead to some pentaquark molecule components, and the may spend a rather large time as the molecular state.

Analysis of the Pcs(4459) as the hidden-charm pentaquark state with QCD sum rules

In this paper, we study the scalar-diquark–scalar-diquark–antiquark-type [Formula: see text] pentaquark state with the QCD sum rules, the predicted mass [Formula: see text] is in excellent agreement with the experimental data [Formula: see text] from the LHCb collaboration, and supports assigning the [Formula: see text] to be the hidden-charm pentaquark state with the spin-parity [Formula: see text]. We take into account the flavor [Formula: see text] mass-breaking effect, and estimate the mass spectrum of the diquark–diquark–antiquark-type [Formula: see text] pentaquark states with the strangeness [Formula: see text].

Magnetic dipole moments of the hidden-charm pentaquark states: P_c(4440), P_c(4457) and P_{cs}(4459)

In this work, we employ the light-cone QCD sum rule to calculate the magnetic dipole moments of the P_c(4440), P_c(4457) and P_{cs}(4459) pentaquark states by considering them as the diquark–diquark–antiquark and molecular pictures with quantum numbers J^P = frac{3}{2}^-, J^P = frac{1}{2}^- and J^P = frac{1}{2}^-, respectively. In the analyses, we use the diquark–diquark–antiquark and molecular form of interpolating currents, and photon distribution amplitudes to obtain the magnetic dipole moment of pentaquark states. Theoretical examinations on magnetic dipole moments of the hidden-charm pentaquark states, are essential as their results can help us better figure out their substructure and the dynamics of the QCD as the theory of the strong interaction. As a by product, we extract the electric quadrupole and magnetic octupole moments of the P_c(4440) pentaquark. These values show a non-spherical charge distribution.

Hidden-charm pentaquarks with triple strangeness due to the Ωc(*)D¯s(*) interactions

Motivated by the successful interpretation of these observed $P_c$ and $P_{cs}$ states under the meson-baryon molecular picture, we systematically investigate the possible hidden-charm molecular pentaquark states with triple strangeness which is due to the $\Omega_{c}^{(*)}\bar{D}_s^{(*)}$ interactions. We perform a dynamical calculation of the possible hidden-charm molecular pentaquarks with triple strangeness by the one-boson-exchange model, where the $S$-$D$ wave mixing effect and the coupled channel effect are taken into account in our calculation. Our results suggest that the $\Omega_{c}\bar D_s^*$ state with $J^P={3}/{2}^{-}$ and the $\Omega_{c}^{*}\bar D_s^*$ state with $J^P={5}/{2}^{-}$ can be recommended as the candidates of the hidden-charm molecular pentaquark with triple strangeness. Furthermore, we discuss the two-body hidden-charm strong decay behaviors of these possible hidden-charm molecular pentaquarks with triple strangeness by adopting the quark-interchange model. These predictions are expected to be tested at the LHCb, which can be as a potential research issue with more accumulated experimental data in near future.

Production of hidden-charm and hidden-bottom pentaquark states in electron-proton collisions * *Supported by the National Natural Science Foundation of China (11975278, 11405222), Key Research Program of the Chinese Academy of Sciences (XDPB09)

Electro-production of several pentaquark states is investigated in this study. The eSTARlight package is adapted to study the electro-production of and via pentaquark and resonance channels in and scattering processes at the proposed electron-ion colliders (EICs). The results obtained in this study are compared to those of non-resonance t-channels, which are described in the pomeron exchange model developed in our studies. Some pseudo-rapidity and rapidity distributions of and are presented for the proposed EICs, including EicC and EIC-US. It is found that EicC is a good platform to identify states in the future.

Pentaquark components in low-lying baryon resonances

We study pentaquark states of both light $q^4\bar q$ and hidden heavy $q^3 Q\bar Q$ (q = u,d,s quark in SU(3) flavor symmetry; Q = c, b quark) systems with a general group theory approach in the constituent quark model, and the spectrum of light baryon resonances in the ansatz that the $l=1$ baryon states may consist of the $q^3$ as well as $q^4\bar q$ pentaquark component. The model is fitted to ground state baryons and light baryon resonances which are believed to be normal three-quark states. The work reveals that the $N(1535)1/2^{-}$ and $N(1520)3/2^-$ may consist of a large $q^4\bar q$ component while the $N(1895)1/2^{-}$ and $N(1875)3/2^-$ are respectively their partners, and the $N^+(1685)$ might be a $q^4\bar q$ state. By the way, a new set of color-spin-flavor-spatial wave function for $q^3 Q\bar Q$ systems in the compact pentaquark picture are constructed systematically for studying hidden charm pentaquark states.

Doubly charmed pentaquarks

The LHCb Collaboration, using its full data set from runs $1$ and $2$, announced in $2019$ a surprising update of the hidden-charm pentaquark states $P_c(4380)^+$ and $P_c(4450)^+$, observed in 2015. A new state, $P_c(4312)^+$, was clearly seen at lower energies; furthermore, the original $P_c(4450)$ resonance was resolved into two individual states, named the $P_c(4440)^+$ and the $P_c(4457)^+$. Motivated by the fact that these new hidden-charm pentaquark states were successfully predicted by our chiral quark model, we extend herein such study to the doubly charmed sector. The analyzed total spin and parity quantum numbers are $J^P=\frac12^-$, $\frac32^-$ and $\frac52^-$, in the $I=\frac12$ and $\frac32$ isospin channels. We find several possible narrow baryon-meson resonances (theoretical masses in parenthesis): $IJ^P = \frac12 \frac12^-$ $\Sigma_c D(4356)$, $\frac12 \frac32^-$ $\Sigma^*_c D(4449)$, $\frac32 \frac12^-$ $\Sigma_c D(4431)$, $\frac32 \frac12^-$ $\Sigma_c D(4446)$, $\frac32 \frac32^-$ $\Sigma_c D^*(4514)$ and $\frac32 \frac52^-$ $\Xi^*_{cc} \rho(4461)$ whose widths are $4.8$, $8.0$, $2.6$, $2.2$, $4.0$ and $3.0\,\text{MeV}$, respectively. Moreover, one shallow bound-state is found, too, with quantum numbers $IJ^P = \frac12 \frac32^-$ $\Xi^*_{cc} \pi(3757)$. These doubly charmed pentaquark states are expected to be identified in future experiments.

Ξbb and Ωbbb molecular states * * Partly supported by the National Natural Science Foundation of China (11975083, 11947413, 11847317, 11565007, 11735003, 1191101015). Q. X Yu acknowledges the support from the National Natural Science Foundation of China (11775024, 11575023, 11805153) and China Scholarship Council. Partly supported by the Spanish Ministerio de Economia y Competitividad and European FEDER funds (FIS2017- 84038-C2-1-P

Using the vector exchange interaction in the local hidden gauge approach, which in the light quark sector generates the chiral Lagrangians and has produced realistic results for and the hidden charm pentaquark states, we study the meson-baryon interactions in the coupled channels that lead to the and excited states of the molecular type. We obtain seven states of the type with energies between and MeV, and one state at MeV.

Analysis of the Pc(4312), Pc(4440), Pc(4457) and related hidden-charm pentaquark states with QCD sum rules

In this paper, we restudy the ground state mass spectrum of the diquark–diquark–antiquark-type [Formula: see text] pentaquark states with the QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of dimension 13 in a consistent way. The predicted masses support assigning the [Formula: see text] to be the hidden-charm pentaquark state with [Formula: see text], assigning the [Formula: see text] to be the hidden-charm pentaquark state with [Formula: see text], [Formula: see text] or [Formula: see text], assigning the [Formula: see text] to be the hidden-charm pentaquark state with [Formula: see text] or [Formula: see text].

Hidden-charm pentaquarks with color-octet substructure in QCD sum rules

We study the hidden-charm pentaquark states $udsc\bar{c}$ with spins 1/2, 3/2, and 5/2 within the QCD sum-rule approach. First, we construct the currents for the particular configuration of pentaquark states that consist of the flavor singlet three-quark cluster $uds$ of spins 1/2 and 3/2 and the two-quark cluster $\bar cc$ of spin 1, where both clusters are in a color-octet state. From the QCD sum rules obtained by the operator product expansion up to dimension-10 condensates, the extracted masses for the pentaquark states $uds$-$\bar{c}c$ are about 4.6 GeV (5.6 GeV) for spin 1/2$^\pm$, about 5.1 GeV (6.0 GeV) for spin 3/2$^\pm$, about 6.1 GeV (5.9 GeV) for spin 5/2$^\pm$, where the masses of the positive parity states are given in parentheses. Additionally, based on the flavor singlet pentaquark states, it is also shown that other pentaquark states of clusters like $udc$-$\bar{c}s$ and $usc$-$\bar cd$ lead to masses similar to the $uds$-$\bar cc$ case within error bars. Furthermore, in order to see whether any of the states, observed by the LHCb Collaboration, could be understood as the pentaquark of two clusters in the color-octet state, we study the pentaquark formed by the two clusters $udc$-$\bar cu$, where the three-quark cluster is assumed to have the same flavor structure as the above $uds$ cluster. We come to the conclusion that if the observed pentaquark will be found to have spin 1/2 and negative parity, then it could be described as a state of two color-octet clusters.

Possible interpretations of the Pc(4312) , Pc(4440) , and Pc(4457)

Based on our previous QCD sum rule studies on hidden-charm pentaquark states, we discuss possible interpretations of the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$, which were recently observed by LHCb. Our results suggest that the $P_c(4312)$ can be well interpreted as the $[\Sigma_c^{++} \bar D^-]$ bound state with $J^P = 1/2^-$, while the $P_c(4440)$ and $P_c(4457)$ can be interpreted as the $[\Sigma_c^{+} \bar D^0]$ bound state with $J^P = 1/2^-$, the $[\Sigma_c^{*++} \bar D^{-}]$ and $[\Sigma_c^{+} \bar D^{*0}]$ bound states with $J^P = 3/2^-$, or the $[\Sigma_c^{*+} \bar D^{*0}]$ bound state with $J^P = 5/2^-$. We propose to measure their spin-parity quantum numbers to verify these assignments.

Neural network study of hidden-charm pentaquark resonances

Recently, the LHCb experiment announced the observation of hidden-charm pentaquark states , , and near and thresholds. In this present work, we studied these pentaquarks in the framework of the nonrelativistic quark model with four types of potential. We solved five-body Schrödinger equation by using the artificial neural network method and made predictions of parities for these states, which are not yet determined by experiment. The mass of another possible pentaquark state near the with is also calculated.

Strong LHCb evidence supporting the existence of the hidden-charm molecular pentaquarks

On March 26th, 2019, at the Rencontres de Moriond QCD conference, the LHCb Collaboration reported the observation of three new pentaquarks, namely $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$, which are consistent with the loosely bound molecular hidden-charm pentaquark states composed of an S-wave charmed baryon $\Sigma_c$ and an S-wave anti-charmed meson ($\bar{D}, \bar{D}^*$). In this work, we present a direct calculation by the one-boson-exchange (OBE) model and demonstrate explicitly that the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ do correspond to the loosely bound $\Sigma_c\bar{D}$ with $(I=1/2,J^P=1/2^-)$, $\Sigma_c\bar{D}^*$ with $(I=1/2,J^P=1/2^-)$ and $\Sigma_c\bar{D}^*$ with $(I=1/2,J^P=3/2^-)$, respectively.

Isospin breaking decays as a diagnosis of the hadronic molecular structure of the Pc(4457)

The LHCb Collaboration announced the observation of three narrow structures consistent with hidden-charm pentaquark states. They are candidates of hadronic molecules formed of a pair of a charmed baryon and an anticharmed meson. Among them, the $P_c(4457)$ mass is consistent with earlier predictions of a $\Sigma_c\bar D^*$ molecule with $I=1/2$. We point out that if such a picture were true, one would have $\mathcal{B}(P_c(4457)\to J/\psi \Delta^+)/\mathcal{B}(P_c(4457)\to J/\psi p)$ at the level ranging from a few percent to about 30%. Such a large isospin breaking decay ratio is two to three orders of magnitude larger than that for normal hadron resonances. It is a unique feature of the $\Sigma_c\bar D^*$ molecular model, and can be checked by LHCb.

Tetraquarks with hidden charm and strangeness as ϕ−ψ(2S) hadrocharmonium

In the hadrocharmonium picture a $\bar cc$ state and a light hadron form a bound state. The effective interaction is described in terms of the chromoelectric polarizability of the $\bar cc$ state and energy-momentum-tensor densities of the light hadron. This picture is justified in the heavy quark limit, and may successfully account for a hidden-charm pentaquark state recently observed by LHCb. In this work we extend the formalism to the description of hidden-charm tetraquarks, and address the question of whether the resonant states observed by LHCb in the $J/\psi$-$\phi$ spectrum can be described as hadrocharmonia. This is a non-trivial question because nothing is known about the $\phi$ meson energy-momentum-tensor densities. With rather general assumptions about energy-momentum-tensor densities in the $\phi$-meson we show that a $\psi(2S)$-$\phi$ bound state can exist, and obtain a characteristic relation between its mass and width. We show that the tetraquark $X(4274)$ observed by LHCb in $J/\psi$-$\phi$ spectrum is a good candidate for a hadrocharmonium. We make predictions which will allow testing this picture. Our method can be generalized to identify other potential hadrocharmonia.

Revisiting hidden-charm pentaquarks from QCD sum rules * * Supported by National Natural Science Foundation of China (11722540, 11261130311), Fundamental Research Funds for the Central Universities, and Foundation for Young Talents in College of Anhui Province (gxyq2018103)

We revisit hidden-charm pentaquark states and 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 and can be identified as hidden-charm pentaquark states having and , respectively. However, there still exist other possible spin-parity assignments, such as and , which must be clarified in further theoretical and experimental studies.