Hidden-charm Pentaquark Research Articles

Hidden-charm and bottom tetra- and pentaquarks with strangeness in the hadro-quarkonium and compact tetraquark models

In two recent papers, we used the hadro-quarkonium model to study the properties of hidden-charm and bottom tetraquarks and pentaquarks. Here, we extend the previous results and calculate the masses of heavy-quarkonium-kaon/hyperon systems. We also compute the spectrum of hidden-charm and bottom tetraquarks with strangeness in the compact tetraquark (diquark-antidiquark) model. If heavy-light exotic systems with non-null strangeness content were to be observed experimentally, it might be possible to distinguish among the large variety of available theoretical pictures for tetra- and pentaquark states and, possibly, rule out those which are not compatible with the data.

Interpretation of the LHCb P_{c} States as Hadronic Molecules and Hints of a Narrow P_{c}(4380).

Three hidden-charm pentaquark P_{c} states, P_{c}(4312), P_{c}(4440), and P_{c}(4457) were revealed in the Λ_{b}^{0}→J/ψpK^{-} process measured by LHCb using both run I and run II data. Their nature is under lively discussion, and their quantum numbers have not been determined. We analyze the J/ψp invariant mass distributions under the assumption that the crossed-channel effects provide a smooth background. For the first time, such an analysis is performed employing a coupled-channel formalism with the scattering potential involving both one-pion exchange as well as short-range operators constrained by heavy quark spin symmetry. We find that the data can be well described in the hadronic molecular picture, which predicts seven Σ_{c}^{(*)}D[over ¯]^{(*)} molecular states in two spin multiplets, such that the P_{c}(4312) is mainly a Σ_{c}D[over ¯] bound state with J^{P}=1/2^{-}, while P_{c}(4440) and P_{c}(4457) are Σ_{c}D[over ¯]^{*} bound states with quantum numbers 3/2^{-} and 1/2^{-}, respectively. We also show that there is evidence for a narrow Σ_{c}^{*}D[over ¯] bound state in the data which we call P_{c}(4380), different from the broad one reported by LHCb in 2015. With this state included, all predicted Σ_{c}D[over ¯], Σ_{c}^{*}D[over ¯], and Σ_{c}D[over ¯]^{*} hadronic molecules are seen in the data, while the missing three Σ_{c}^{*}D[over ¯]^{*} states are expected to be found in future runs of the LHC or in photoproduction experiments.

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.

Understanding the structures of hidden-charm pentaquarks in a simple model

We discuss the possible interpretations and JP assignments for the LHCb Pc(4312), Pc(4440), and Pc(4457) pentaquark states in a simple chromomagnetic model, Hsplitting=−∑i<jCijλi⋅λjσi⋅σj and Hdecay=const. We find that both the spectrum and decay properties can be understood by assuming that they are (uud)8c(cc‾)8c states. The JP=3/2− assignment for the Pc(4312) is different from the JP=1/2− assignment in the naive ΣcD‾ molecule picture. If the former assignment is confirmed, the possible implication of the (uud)8c(cc‾)8c structure is discussed. The search for the predicted pentquark states is also called for.

Hidden-charm and hidden-bottom molecular pentaquarks in chiral effective field theory

The newly observed Pc(4312), Pc(4440) and Pc(4457) at the LHCb experiment are very close to the {varSigma}_coverline{D} and {varSigma}_c{overline{D}}^{ast } thresholds. In this work, we perform a systematic study and give a complete picture on the interactions between the {varSigma}_c^{left(ast right)} and {overline{D}}^{left(ast right)} systems in the framework of heavy hadron chiral effective field theory, where the short-range contact interaction, long-range one-pion-exchange contribution, and intermediate-range two-pion-exchange loop diagrams are all considered. We first investigate the three Pc states without and with considering the Λc contribution in the loop diagrams. It is difficult to simultaneously reproduce the three Pcs unless the Λc is included. The coupling between the {varSigma}_c^{left(ast right)}{overline{D}}^{left(ast right)} and {Lambda}_c{overline{D}}^{left(ast right)} channels is crucial for the formation of these Pcs. Our calculation supports the Pc(4312), Pc(4440) and Pc(4457) to be the S-wave hidden-charm {left[{varSigma}_coverline{D}right]}_{J=1/2}^{I=1/2},{left[{varSigma}_c{overline{D}}^{ast}right]}_{J=1/2}^{I=1/2} and {left[{varSigma}_c{overline{D}}^{ast}right]}_{J=3/2}^{I=1/2} molecular pentaquarks, respectively. Our calculation disfavors the spin assignment {J}^P=frac{1^{-}}{2} for Pc(4457) and {J}^P=frac{3^{-}}{2} for Pc(4440), because the excessively enhanced spin-spin interaction is unreasonable in the present case. We obtain the complete mass spectra of the {left[{varSigma}_c^{left(ast right)}{overline{D}}^{left(ast right)}right]}_J systems with the fixed low energy constants. Our result indicates the existence of the {left[{varSigma}_c^{ast }{overline{D}}^{ast}right]}_Jleft(J=frac{1}{2},frac{3}{2},frac{5}{2}right) hadronic molecules. The previously reported Pc(4380) might be a deeper bound one. Additionally, we also study the hidden-bottom {varSigma}_b^{left(ast right)}{B}^{left(ast right)} systems, and predict seven bound molecular states, which could serve as a guidance for future experiments. Furthermore, we also examine the heavy quark symmetry breaking effect in the hidden-charm and hidden-bottom systems by taking into account the mass splittings in the propagators of the intermediate states. As expected, the heavy quark symmetry in the bottom cases is better than that in the charmed sectors. We notice that the heavy quark symmetry in the {varSigma}_coverline{D} and {varSigma}_c^{ast}overline{D} systems is much worse for some fortuitous reasons. The heavy quark symmetry breaking effect is nonnegligible in predicting the effective potentials between the charmed hadrons.

Molecular states from varSigma ^{(*)}_c{bar{D}}^{(*)}-varLambda _c{bar{D}}^{(*)} interaction

In this work, we systemically investigate the molecular states from the varSigma ^{(*)}_c{bar{D}}^{(*)}-varLambda _c{bar{D}}^{(*)} interaction with the help of the Lagrangians with heavy quark and chiral symmetries in a quasipotential Bethe–Salpeter equation (qBSE) approach. The molecular states are produced from isodoublet (I=1/2) varSigma _c{bar{D}} interaction with spin parity J^P=1/2^- and varSigma _c{bar{D}}^* interaction with 1/2^- and 3/2^-. Their masses and widths are consistent with the P_c(4312), P_c(4440) and P_c(4457) observed at LHCb. The states, varSigma _c^*{bar{D}}^*(1/2^-), varSigma _c^*{bar{D}}^*(3/2^-) and varSigma ^*_c{bar{D}}(3/2^-), are also produced with the same parameters. The isodoublet varSigma _c^*{bar{D}}^* interaction with 5/2^-, as well as the isoquartet (I=3/2) varSigma _c{bar{D}}^* interactions with 1/2^- and 3/2^-, varSigma _c^*{bar{D}}^* interaction with 3/2^- and 5/2^-, are also attractive while very large cutoff is required to produce a molecular state. We also investigate the origin of the widths of these molecular states in the same qBSE frame. The varLambda {bar{D}}^* channel is dominant in the decays of the states, varSigma _c{bar{D}}^*(1/2^-), varSigma _c{bar{D}}^*(3/2^-), varSigma _c^*{bar{D}}(3/2^-), and varSigma _c{bar{D}}(1/2^-). The varSigma ^*_c{bar{D}}^*(1/2^-) state has large coupling to varSigma _c{bar{D}} channel while the varSigma _c{bar{D}}^*, varSigma ^*_c{bar{D}} and varLambda _c{bar{D}}^* channels provide similar contributions to the width of the varSigma ^*_c{bar{D}}^*(3/2^-) state. These results will be helpful to understand the current LHCb experimental results, and the three predicted states and the decay pattern of these hidden-charmed molecular pentaquarks can be checked in future experiments.

Decays of Pc into J/ψN and ηcN with heavy quark spin symmetry

We investigate the consequences of heavy quark spin symmetry (HQSS) on hidden-charm pentaquark $P_c$ states. As has been proposed before, assuming the $P_c(4440)$ and the $P_c(4457)$ as $S$-wave $\bar{D}^*\Sigma_c$ molecules, seven hadronic molecular states composed of $\bar{D}\Sigma_c$, $\bar{D}\Sigma_c^*$, $\bar{D}^*\Sigma_c$, and $\bar{D}^*\Sigma_c^*$ can be obtained, with the $\bar{D}\Sigma_c$ molecule corresponding to the $P_c(4312)$. These seven states can decay into $J/\psi N$ and $\eta_c N$, and we use HQSS to predict ratios of partial widths of the $S$-wave decays. For the decays into $J/\psi N$, it is found that among all six $P_c$ molecules with spin $1/2$ or $3/2$, at least four states decay much more easily into the $J/\psi N$ than the $P_c(4312)$, and two of them couple dominantly to the $\bar D^*\Sigma_c^*$. While no significant peak around the $\bar{D}^*\Sigma_c^*$ threshold is found in the $J/\psi p$ distribution, these higher $P_c$ states either are produced with lower rates or some special production mechanism for the observed $P_c$ states might play an important role, such as an intricate interplay between the production of pentaquarks and triangle singularities.

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.

Some decay properties of hidden-charm pentaquarks as baryon-meson molecules

It is pointed out that the previously suggested interpretation of the hidden-charm pentaquarks $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ as molecular bound states of $\Sigma_c \bar D$ and $\Sigma_c \bar D^*$ baryon-meson pairs gives rise to specific relations for their decays. In particular, the heavy quark spin symmetry predicts ratios of rates of decays of each of the molecules to $J/\psi p$ and to $\eta_c p$ as well as of the decays to $\Lambda_c \bar D$ and to $\Lambda_c \bar D^*$. Experimental studies of these relations would thus provide an indicative probe of the molecular structure.

Analyzing doubly heavy tetra- and penta-quark states by variational method

Motivated by the very recent observations of hidden charm pentaquarks Pc(4312)+, Pc(4440)+ and Pc(4457)+ of the LHCb Collaboration, we systematically study the spectra of the doubly-heavy (with or without charm/bottom numbers) pentaquarks and tetraquarks in non-relativistic constituent quark model. The model independent variational method is employed to solve the Schrödinger equation, where the test radial functions adopted are symmetric for the light quarks. In our study, the Pc(4312)+ may be assigned as the ground state with spin-parity 12− or 32−, while the Pc(4440)+ and Pc(4457)+ may be assigned as the excited states with 12−, which might all belong to the sextet with scc¯=1 and sℓ=32. It is notable that our working framework is quite similar to that of Hydrogen molecule, but with different potential structure. We also classify these pentaquarks and tetraquarks in light of the heavy quark symmetry and their decay properties are analyzed. Several promising channels for the observation of doubly-heavy pentaquarks and doubly-heavy tetraquarks in experiment are proposed.

Pion-induced production of hidden-charm pentaquarks Pc(4312),Pc(4440), and Pc(4457)

The production of the hidden-charm pentaquarks via a pion-induced reaction on a proton target is investigated within an effective Lagrangian approach. Three experimentally observed states, Pc(4312), Pc(4440), and Pc(4457), are considered in calculation, and the Reggeized t-channel meson exchange is considered as main background for the reaction π−p→J/ψn. The numerical results show that the experimental data of the total cross section at W≃5 GeV can be well explained by the contribution from the Reggeized t channel with reasonable cutoff. If the branching ratios Br[Pc→J/ψN]≃3% and Br[Pc→πN]≃0.05% are taken, the average value of the cross section from the Pc(4312) is about 1.2 nb/100 MeV, which is consistent with existing rude data at near-threshold energies. The results indicate that the branching ratios of the Pc state decays into J/ψN and πN should be small. The differential cross section shows a sharp increase at extreme forward angles due to the Reggeized t-channel contribution while the contributions from the Pc states are relatively flat. High-precision experimental measurement on the reaction π−p→J/ψn at near-threshold energies is suggested to confirm the LHCb hidden-charm pentaquarks as genuine states, and such measurement is also helpful to understand the origins of these resonance structures.

Electromagnetic couplings of pentaquarks

In this contribution, we discuss the electromagnetic couplings of pentaquark states with hidden charm. This work is motivated by recent experiments at CERN by the LHCb Collaboraton and current experiments at JLab to confirm the existence of hidden-charm pentaquarks in photoproduction experiments.

Hidden-charm pentaquarks and Pc states

Recently, the LHCb Collaboration reported three $P_c$ states in the ${J/\psi}p$ channel. We systematically study the mass spectrum of the hidden charm pentaquark in the framework of an extended chromomagnetic model. For the $nnnc\bar{c}$ pentaquark with $I=1/2$, we find that (i) the lowest state is $P_{c}(4327.0,1/2,1/2^{-})$ [We use $P_{c}(m,I,J^{P})$ to denote the $nnnc\bar{c}$ pentaquark], which corresponds to the $P_{c}(4312)$. Its dominant decay mode is $\Lambda_{c}\bar{D}^{*}$. (ii) We find two states in the vicinity of $P_{c}(4380)$. The first one is $P_{c}(4367.4,1/2,3/2^{-})$ and decays dominantly to $N{J/\psi}$ and $\Lambda_{c}\bar{D}^{*}$. The other one is $P_{c}(4372.4,1/2,1/2^{-})$. Its dominant decay mode is $\Lambda_{c}\bar{D}$, and its partial decay width of $N\eta_{c}$ channel is comparable to that of $N{J/\psi}$. (iii) In higher mass region, we find $P_{c}(4476.3,1/2,3/2^{-})$ and $P_{c}(4480.9,1/2,1/2^{-})$, which correspond to $P_{c}(4440)$ and $P_{c}(4457)$. In the open charm channels, both of them decay dominantly to the $\Lambda_{c}\bar{D}^{*}$. (iv) We predict two states above $4.5~\text{GeV}$, namely $P_{c}(4524.5,1/2,3/2^{-})$ and $P_{c}(4546.0,1/2,5/2^{-})$. The masses of the $nnnc\bar{c}$ state with $I=3/2$ are all over $4.6~\text{GeV}$. Moreover, we use the model to explore the $nnsc\bar{c}$, $ssnc\bar{c}$ and $sssc\bar{c}$ pentaquark states.

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.

Hidden-charm pentaquark formation in antiproton-deuterium collisions

The possibility of observing formation of hidden-charm pentaquarks as $s$-channel resonances in antiproton - deuteron collisions is discussed. It is pointed out that the masses of the reported by LHCb pentaquark resonances in the $J/\psi \, p$ channel are very close to a special value of the mass at which formation of a pentaquark by antiproton incident on a deuteron at rest requires exactly the same momentum of the $\bar p$ as needed for the formation in the $s$ channel of the charmonium resonance in $\bar p p$ collisions with the proton being at rest. For this reason the former process can be rather completely described within the notion of the deuteron being a shallow bound state of two nucleons without resorting to models describing its short-distance structure. It is argued that a similar kinematical coincidence can be expected for (yet) hypothetical pentaquark resonances in the $\eta_c \, N$ channel, and that these can be sought for once antiproton - deuterium collisions become available for experimentation.

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.

Hidden charm pentaquarks: mass spectrum, magnetic moments and photocouplings

We develop an extension of the usual three-flavor quark model to four flavors (u, d, s and c), and discuss the classification of pentaquark states with hidden charm (). We fit our model to the known baryon spectrum and we predict the double and triple charm baryons, finding good agreement with the most recent lattice QCD calculations. We compute the ground state of hidden charm pentaquarks and their associated magnetic moments and electromagnetic couplings, of interest to pentaquark photoproduction experiments.

Anatomy of the newly observed hidden-charm pentaquark states: Pc(4312), Pc(4440) and Pc(4457)

We study the newly reported hidden-charm pentaquark candidates Pc(4312), Pc(4440) and Pc(4457) from the LHCb Collaboration, in the framework of the effective-range expansion and resonance compositeness relations. The scattering lengths and effective ranges from the S-wave ΣcD¯ and ΣcD¯⁎ scattering are calculated by using the experimental results of the masses and widths of the Pc(4312), Pc(4440) and Pc(4457). Then we calculate the couplings between the J/ψp,ΣcD¯ channels and the pentaquark candidate Pc(4312), with which we further estimate the probabilities of finding the J/ψp and ΣcD¯ components inside Pc(4312). The partial decay widths and compositeness coefficients are calculated for the Pc(4440) and Pc(4457) states by including the J/ψp and ΣcD¯⁎ channels. Similar studies are also carried out for the three Pc states by including the ΛcD¯⁎ and ΣcD¯(⁎) channels.