Hidden-charm Pentaquark Research Articles

Hidden-charm pentaquark states in a mass splitting model

Hidden-charm pentaquark states in a mass splitting model

Study of Hidden-Charm and Hidden-Bottom Pentaquark Resonances in the Quark Model

Inspired by the LHCb observation of hidden-charm pentaquarks, i.e., Pc(4312), Pc(4440), and Pc(4457) in the J/ψp invariant mass spectrum, a calculation of the J/ψp scattering cross-section was performed using the quark-delocalization color screening model. The results show that Pc(4312) can be identified as a hidden-charm molecular state ΣcD with JP=12−. The two-peak structure can be reproduced around 4450 MeV, which corresponds to Pc(4440) and Pc(4457). They are the resonances molecular states ΣcD* of JP=12− and JP=32−. Moreover, the Σc*D* of both JP=12− and JP=32− are possible molecular pentaquarks. Moreover, in the same theoretical frame, the calculation is extended to the Pc-like molecular pentaquarks, denoted as Pb. Several hidden-bottom pentaquarks with masses above 11 GeV and narrow widths were obtained. All of these heavy pentaquarks are worth exploring in future experiments.

On the possibility of testing the two-peak structure of the LHCb hidden-charm strange pentaquark Pcs(4459)0 in near-threshold antikaon-induced charmonium production on protons and nuclei

Accounting for the LHCb observation that the reported hidden-charm strange pentaquark Pcs(4459)0 can split into two substructures, Pcs(4455)0 and Pcs(4468)0, with a mass difference of 13 MeV as well as the newly observed hidden-charm pentaquark resonance Pcs(4338)0 with strangeness, we study within the double-peak scenario for the Pcs(4459)0 state the near-threshold J/ψ meson production from protons and nuclei by considering incoherent direct non-resonant (K−p→J/ψΛ) and two-step resonant (K−p→Pcsi0→J/ψΛ, i=1, 2, 3; Pcs10=Pcs(4338)0, Pcs20=Pcs(4455)0, Pcs30=Pcs(4468)0) charmonium production processes with the main goal of clarifying the possibility to observe within this scenario both above two substructures contributing to the Pcs(4459)0 state and the Pcs(4338)0 resonance in this production. We calculate the absolute excitation functions, energy and momentum distributions for the non-resonant, resonant and for the combined (non-resonant plus resonant) production of J/ψ mesons on protons as well as on carbon and tungsten target nuclei at near-threshold incident antikaon beam momenta by assuming the spin-parity assignments of the hidden-charm resonances Pcs(4338)0, Pcs(4455)0 and Pcs(4468)0 as JP=(1/2)−, JP=(1/2)− and JP=(3/2)− within four different realistic choices for the branching ratios of their decays to the J/ψΛ mode (0.125, 0.25, 0.5 and 1%) as well as for two options for the branching fraction of their decays to the K−p channel (0.01 and 0.001%). We show that these combined observables reveal clear sensitivity to these scenarios. Hence, they may be an important tool to provide further evidence for the existence of the above strange hidden-charm pentaquark resonances.

The pentaquark spectrum from Fermi statistics

We study compact hidden charm pentaquarks in the Born–Oppenheimer approximation, previously introduced for tetraquarks, assuming the heavy pair to be in a color octet. We show that Fermi statistics applied to the complex of the three light quarks, also in color octet, requires S-wave pentaquark ground states to consist of three octets of flavour-SU(3)_f, two with spin 1/2 and one with spin 3/2, in line with the observed, strangeness S=0,-1, spectrum. Additional lines corresponding to decays into J/psi +Sigma and J/psi +Xi are predicted. In the language of non-relativistic SU(6), ground state pentaquarks form either a {varvec{56}} or a {varvec{20}} representation, distinguished by presence or absence of pentaquarks decaying in the spin 3/2 decuplet, e.g. in J/psi +Delta ^{++}. Observation of a strangeness S=-2 or isospin I=3/2 pentaquarks would be a clear signature of compact, QCD bound pentaquarks.

Revealing the nature of hidden charm pentaquarks with machine learning

We study the nature of the hidden charm pentaquarks, i.e., the Pc4312,Pc4440 and Pc(4457), with a neural network approach in pionless effective field theory. In this framework, the normal χ2 fitting approach cannot distinguish the quantum numbers of the Pc(4440) and Pc(4457). In contrast to that, the neural network-based approach can discriminate them, which still cannot be seen as a proof of the spin of the states since pion exchange is not considered in the approach. In addition, we also illustrate the role of each experimental data bin of the invariant J/ψp mass distribution on the underlying physics in both neural network and fitting methods. Their similarities and differences demonstrate that neural network methods can use data information more effectively and directly. This study provides more insights about how the neural network-based approach predicts the nature of exotic states from the mass spectrum.

Molecular tetraquarks and pentaquarks in chiral effective field theory

We studied the DD¯⁎/D¯D⁎, D⁎D¯⁎, D¯sD⁎/D¯s⁎D, BB¯⁎/B¯B⁎ and B⁎B¯⁎ di-hadron interactions in chiral effective field theory (χEFT) up to the next-to-leading (NLO) order. The above-threshold tetraquark states Zc(3900), Zc(4020), Zcs(3985), Zb(10610), Zb(10650) can be explained as the corresponding di-hadron resonances, respectively. We also studied the Σc(⁎)D¯(⁎) interactions to investigate the three hidden-charm pentaquarks Pc(4312), Pc(4440) and Pc(4457). We further used the parameters fixed from the Pc states to predict the possible molecular states in ΞcD¯(⁎), Ξc′D¯(⁎) and Ξc⁎D¯(⁎) systems. Our predictions of the ΞcD¯(⁎) bound states are very consistent with two new near-threshold structures recently observed by the LHCb Collaboration.

P_{cc}^N states in a unitarized coupled-channel approach

Starting from an effective Lagrangian with heavy quark spin symmetry embedded, the coupled-channel dynamics of the doubly charmed systems D^{(*)} Sigma _c^{(*)} is investigated. The potential underlying our investigation includes t-channel pseudoscalar and vector meson exchanges. A series of S-wave bound states with isospin I=1/2 is found by applying the first iterated solution of the N/D method: one state with binding energy 23 MeV in the 5/2^-D^*Sigma _c^* channel, three states with binding energy 26, 30 and 7 MeV (relative to the thresholds from low to high, respectively) in the 3/2^-DSigma _c^*-D^*Sigma _c-D^*Sigma _c^* system and three states with binding energy 32, 8 and 16 MeV in the 1/2^-DSigma _c-D^*Sigma _c-D^*Sigma _c^* system. Those P_{cc}^N states serve as the open-charm partners of the hidden charm pentaquarks P_{psi }^N observed by the LHCb Collaboration.

Double thresholds distort the line shapes of the PψsΛ(4338)0 resonance

Very recently, the LHCb Collaboration reported the first observation of the hidden-charm pentaquark with strangeness, ${P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}(4338{)}^{0}$. Considering this state is very close to the ${\mathrm{\ensuremath{\Xi}}}_{c}^{0}{\overline{D}}^{0}$ and ${\mathrm{\ensuremath{\Xi}}}_{c}^{+}{D}^{\ensuremath{-}}$ thresholds, we explore the possible bias of the Breit-Wigner parametrization, with emphasis on the effect of its coupling to the double thresholds ${\mathrm{\ensuremath{\Xi}}}_{c}^{0}{\overline{D}}^{0}$ and ${\mathrm{\ensuremath{\Xi}}}_{c}^{+}{D}^{\ensuremath{-}}$. We first use a qualitative picture based on the ``uniformization'' of the Riemann surface of the two-channel system to understand the positions of the enhancement. Then we use the Lippmann-Schwinger equation formalism (equivalent to the $K$-matrix parametrization) with two models, the zero-range model and the Flatt\'e model to investigate the $J/\ensuremath{\psi}\mathrm{\ensuremath{\Lambda}}$ line shapes. Our results show that the nominal peak of the ${P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}(4338{)}^{0}$ could arise either from the pole well above the ${\mathrm{\ensuremath{\Xi}}}_{c}^{+}{D}^{\ensuremath{-}}$ threshold on the $(\ensuremath{-},+)$ sheet or from the pole well below the ${\mathrm{\ensuremath{\Xi}}}_{c}^{0}{\overline{D}}^{0}$ threshold on the $(\ensuremath{-},\ensuremath{-})$ sheet in the two-channel system. Using the Breit-Wigner distribution to depict the above two line shapes could be misleading. We also find a novel type of line shapes with the enhancement constrained by the threshold difference. We urge the LHCb Collaboration to perform the refined experimental analysis considering the unitarity and analyticity, e.g., using the $K$-matrix parametrization. As a by-product, we obtain that the ratio of the isospin violating decay ${\mathrm{\ensuremath{\Gamma}}}_{{P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}\ensuremath{\rightarrow}J/\ensuremath{\psi}\mathrm{\ensuremath{\Sigma}}}/{\mathrm{\ensuremath{\Gamma}}}_{{P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}\ensuremath{\rightarrow}J/\ensuremath{\psi}\mathrm{\ensuremath{\Lambda}}}$ could be up to 10%.

Semi-inclusive electroproduction of hidden-charm and double-charm hadronic molecules

The semi-inclusive electroproduction of exotic hadrons, including the $T_{cc}$, $P_{cs}$, and hidden-charm baryon-antibaryon states, is explored under the assumption that they are $S$-wave hadronic molecules of a pair of charmed hadrons. We employ the Monte Carlo event generator Pythia to produce the hadron pairs and then bind them together to form hadronic molecules. With the use of such a production mechanism, the semi-inclusive electroproduction rates are estimated at the order-of-magnitude level. Our results indicate that a larger number of $P_{cs}$ states and $\Lambda_c\bar{\Lambda}_c$ molecules can be produced at the proposed electron-ion colliders in China (EicC) and in the US (EIC). The results also suggest that the $T_{cc}$ states and other hidden-charm baryon-antibaryon states can be searched for at EIC. Besides, the potential 24-GeV upgrade of the Continuous Beam Accelerator Facility at the Thomas Jefferson National Accelerator Facility can play an important role in the search for the hidden-charm tetraquark and pentaquark states due to its high luminosity.

Investigation of magnetic moment of Pcs(4338) and Pcs(4459) pentaquark states

In this study, we discuss the magnetic moment of Pcs(4338) and Pcs(4459) hidden-charmed pentaquarks, which are closely related to their substructures. The magnetic moments of these states are calculated with the help of the QCD light-cone sum rules method with quantum numbers I(JP)=0(1/2−) and I(JP)=0(3/2−) for Pcs(4338) and Pcs(4459), respectively. Our predictions for the magnetic moment μPcs=0.34±0.12μN for the Pcs(4338) state, and μPcs=−1.67±0.58μN for the Pcs(4459) state. As a by-product, the magnetic moments of the isospin−1 partners of these states have also been obtained. The magnetic moments are obtained as μPcs=0.63±0.21μN and μPcs=−3.33±1.04μN for the isospin-1 partners of the Pcs(4338) and Pcs(4459) states, respectively. Our results regarding the magnetic moments of these color singlet-singlet type pentaquark states are compared with the results in the literature.

Hidden-flavor pentaquarks

We have recently studied hidden-charm pentaquarks, $c\overline{c}qqq$, using the dynamical correlations between the heavy quarks arising from the Coulomb-like nature of the short-range interaction. A pattern was obtained that compares well with the experimental data. We extend our description to other flavor sectors which can be framed within the same type of structures discussed in the original paper. A detailed comparison is made with other results in the literature and with experimental data. The predictions will be a useful tool to discriminate between different models of multiquark system dynamics.

Search for hidden-charm pentaquark states in three-body final states

The three pentaquark states, P_c(4312), P_c(4440) and P_c(4457), discovered by the LHCb Collaboration in 2019, are often interpreted as {bar{D}}^{(*)}Sigma _c molecules. Together with their four {bar{D}}^{(*)}Sigma _{c}^{*} partners dictated by heavy quark spin symmetry they represent a complete multiplet of hadronic molecules of {bar{D}}^{(*)}Sigma _{c}^{(*)}. The pentaquark states were observed in the J/psi p invariant mass distributions of the Lambda _brightarrow J/psi p K decay. It is widely recognized that to understand their nature, other discovery channels play an important role. In this work, we investigate two three-body decay modes of the {bar{D}}^{(*)}Sigma _{c}^{(*)} molecules. The tree-level modes proceed via off-shell Sigma _{c}^{(*)} baryons, {bar{D}}^{(*)}Sigma _{c}^{(*)} rightarrow {bar{D}}^{(*)}left( Sigma _{c}^{(*)}rightarrow Lambda _{c}pi right) rightarrow {bar{D}}^{(*)}Lambda _{c}pi , while the triangle-loop modes proceed through {bar{D}}^{*}Sigma _{c}^{(*)}rightarrow J/psi Npi , eta _{c}Npi via {bar{D}}Sigma _{c}^{(*)} rescattering to J/psi N and eta _{c}N. Our results indicate that the decay widths of the P_{c}(4457) and {bar{D}}^{(*)}Sigma _{c}^{*} states into {bar{D}}^{(*)}Lambda _{c}pi are several MeV, as a result can be observed in the upcoming Run 3 and Run 4 of LHC. The partial decay widths into {bar{D}}^{(*)}Lambda _{c}pi of the P_{c}(4312) and P_{c}(4440) states range from tens to hundreds of keV. In addition, the partial decay widths of {bar{D}}^{*}Sigma _{c} molecules into J/psi N pi and eta _c N pi are several keV and tens of keV, respectively, and the partial decay widths of {bar{D}}^{*}Sigma _{c}^{*} molecules into J/psi N pi vary from several keV to tens of keV. In particular, we show that the spin-5/2 {bar{D}}^{*}Sigma _{c}^{*} state can be searched for in the J/psi N pi and {bar{D}}^{*}Lambda _{c}pi invariant mass distributions, while the latter one is more favorable. These three-body decay modes of the pentaquark states are of great value to further observations of the pentaquark states and to a better understanding of their nature.

Emergence of molecular-type characteristic spectrum of hidden-charm pentaquark with strangeness embodied in the [formula omitted] and Pcs(4459)

Inspired by the newly observed PψsΛ(4338) and the reported Pcs(4459), we indicate the existence of the molecular-type characteristic mass spectrum for hidden-charm pentaquark with strangeness. It shows that the Pcs(4459) may contain two substructures corresponding to the ΞcD¯⁎ molecular states with JP=1/2− and 3/2−, while there exists the corresponding ΞcD¯ molecular state with JP=1/2−. As the prediction, we present another characteristic mass spectrum of the Ξc′D¯(⁎) molecular states. Experimental confirmation of these characteristic mass spectra is a crucial step of constructing hadronic molecular family.

Magnetic moments of hidden-charm strange pentaquark states* *Supported by the National Natural Science Foundation of China (11905171, 12047502) and the Natural Science Basic Research Plan in Shaanxi Province of China (2022JQ-025)

In this study, the magnetic moments of hidden-charm strange pentaquark states with quantum numbers, , , and are calculated in the molecular, diquark-diquark-antiquark, and diquark-triquark models. The numerical results demonstrate that the magnetic moments change for different spin-orbit couplings within the same model and when involving different models with the same angular momentum.

What can we learn from the electromagnetic properties of hidden-charm molecular pentaquarks with single strangeness?

Inspired by the observation of the ${P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}(4459)$ and ${P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}(4338)$, we systematically investigate the magnetic moments, the transition magnetic moments, and the radiative decay behaviors of the $S$-wave isoscalar ${\mathrm{\ensuremath{\Xi}}}_{c}^{(\ensuremath{'})}{\overline{D}}^{(*)}$ molecular pentaquark states in this work. Our quantitative investigation shows that their electromagnetic properties can provide important hints to decode the inner structure of these discussed isoscalar ${\mathrm{\ensuremath{\Xi}}}_{c}^{(\ensuremath{'})}{\overline{D}}^{*}$ molecular pentaquarks. As a potential research issue, we suggest future experiments to focus on the electromagnetic properties of these isoscalar ${\mathrm{\ensuremath{\Xi}}}_{c}^{(\ensuremath{'})}{\overline{D}}^{(*)}$ molecular pentaquarks, which are a typical hidden-charm molecular pentaquark system with single strangeness.

Five-flavor pentaquarks and other light- and heavy-flavor symmetry partners of the LHCb hidden-charm pentaquarks

The discovery of three pentaquark peaks — the Pc(4312), Pc(4440) and Pc(4457) — by the LHCb collaboration has a series of interesting consequences for hadron spectroscopy. If these hidden-charm objects are indeed hadronic molecules, as suspected, they will be constrained by heavy-flavor and SU(3)-flavor symmetries. The combination of these two symmetries will imply the existence of a series of five-flavor pentaquarks with quark content b¯csdu and bc¯sdu, that is, pentaquarks that contain each of the five quark flavors that hadronize. In addition, from SU(3)-flavor symmetry alone we expect the existence of light-flavor partners of the three Pc pentaquarks with strangeness S=−1 and S=−2. The resulting structure for the molecular pentaquarks is analogous to the light-baryon octet — we can label the pentaquarks as PQ′Q¯N, PQ′Q¯Λ, PQ′Q¯Σ, PQ′Q¯Ξ depending on their heavy- and light-quark content (with N, Λ, Σ, Ξ the member of the light-baryon octet to which the light-quark structure resembles and Q′, Q¯ the heavy quark-antiquark pair). In total we predict 45 new pentaquarks from heavy- and light-flavor symmetries alone, which extend up to 109 undiscovered states if we also consider heavy-quark spin symmetry. If an isoquartet (I=3/2) hidden-charm pentaquark is ever observed, this will in turn imply a second multiplet structure resembling the light-baryon decuplet: PQ′Q¯Δ, PQ′Q¯Σ⁎, PQ′Q¯Ξ⁎, PQ′Q¯Ω.

Hidden-charm pentaquark states through current algebra: from their production to decay * *Supported by the National Natural Science Foundation of China (11722540, 12075019), the Jiangsu Provincial Double-Innovation Program (JSSCRC2021488), and the Fundamental Research Funds for the Central Universities

There may be seven hadronic molecular states. We construct their corresponding interpolating currents and calculate their masses and decay constants using QCD sum rules. Based on these results, we calculate their relative production rates in decays using current algebra, that is, , where and are two different states. We also study their decay properties via Fierz rearrangement and further calculate these ratios in the mass spectrum, that is, . Our results suggest that the molecular states of and may be observed in future experiments.

P c resonances in the compact pentaquark picture

P c resonances are studied in the approach of quark model and group theory. It is found that there are totally 17 possible pentaquark states with the quark contents (q are u and d quarks; Q is c quark) in the compact pentaquark picture, where the hidden charm pentaquark states may take the color singlet–singlet and color octet–octet configurations. The theoretical results of partial decay widths of the pentaquark states show that open charm channels are the dominant decay modes for almost all hidden charm pentaquark states, but there are four pentaquark states which decay through the pJ/ψ channel with sizable partial decay widths.

Anticharmed strange pentaquarks from the one-boson-exchange model

Inspired by the LHCb's discovery of hidden-charm pentaquarks, the anticharmed strange pentaquarks ${P}_{\overline{c}s}$ in a favor of the hadronic molecule picture are investigated from the one-boson-exchange model. Similar to the hidden-charm pentaquarks, three molecular bound states, one with spin parity ${J}^{P}=1/{2}^{\ensuremath{-}}$ below the $\overline{D}\mathrm{\ensuremath{\Sigma}}$ threshold and another two with ${J}^{P}={1/{2}^{\ensuremath{-}},3/{2}^{\ensuremath{-}}}$ below the ${\overline{D}}^{*}\mathrm{\ensuremath{\Sigma}}$ threshold, are predicted at 3--3.2 GeV mass region. The mass ordering of the later two states can be interchanged by different reductions of the $\ensuremath{\delta}(\mathbit{r})$ term. Furthermore, resonances associated with these three bound states are examined by considering ${D}_{s}^{\ensuremath{-}}N\ensuremath{-}\overline{D}\mathrm{\ensuremath{\Lambda}}\ensuremath{-}\overline{D}\mathrm{\ensuremath{\Sigma}}\ensuremath{-}{\overline{D}}^{*}\mathrm{\ensuremath{\Lambda}}\ensuremath{-}{\overline{D}}^{*}\mathrm{\ensuremath{\Sigma}}$ coupled-channel dynamics, and decay widths of them are predicted. Our study indicates that the ${D}_{s}^{\ensuremath{-}}p$ invariant mass spectrum in the ${\overline{B}}_{s}^{0}\ensuremath{\rightarrow}\overline{n}{D}_{s}^{\ensuremath{-}}p$ decay is an appropriate place to detect the ${P}_{\overline{c}s}$ pentaquarks.

Double triangle cusps relevant to Pc(4312)+ , Pc(4380)+, and Pc(4457)+

A novel scenario is proposed for hidden charm pentaquark (Pc)-like structures in Λ 0 b → J/ψpK−. The scenario is based on kinematical singularities arising from double triangle mechanisms. Anomalous threshold cusps due to the singularities are, compared with ordinary P(∗) c D¯(∗) one-loop thresh-old cusp, significantly more singular. It is demonstrated that an interference among the double triangle mechanisms and other common mechanisms generates peaks very similar to the Pc(4312)+, Pc(4380)+, and Pc(4457)+ peak structures. While hadron molecules and compact pentaquarks have been common models to explain the Pc states, the present model is a completely different one. The present model includes only one pentaquark state Pc(4440)+. However, we find that the Pc(4440)+ width and strength are significantly smaller than those from the LHCb analysis. The P + c signals are searched for in J/ψ photoproduction but not found. A search was also made in Λ 0 b → J/ψpπ− data, finding only a possible P c(4440)+-like signal. The present model is consistent with the experimental situation