Pentaquark Systems Research Articles

Probing the nature of the anticharmed-strange pentaquark states: Mass spectra, decays, and magnetic moments

Within the framework of the quark delocalization color screening model, a systematic investigation of the anticharmed-strange pentaquark system is performed using the resonance group method. The currently estimations predict three bound states with estimated masses to be 2886 MeV, 3039 MeV, and 3153 MeV, respectively. Additionally, three resonance states are identified in various scattering phase shifts processes. Among them, two resonance states ΣD¯ and Σ*D¯* with quantum number 12(12−) are detected in channels ND¯s* and ND¯, and ΣD¯* and ΛD¯, with masses and decay widths of (MR=3053–3055 MeV, Ttotal=13.0–13.4 MeV) and (MR=3389–3390 MeV, Ttotal=10.4 MeV), respectively. In the ΛD¯* and ΣD¯* channels, a resonance state with quantum number 12(32−) is discovered, with its mass and decay width being 3250–3252 MeV and 4.4,MeV, respectively. These predicted pentaquark states have c¯snnn quark compositions, allowing them to be recognized as genuine pentaquark states. To validate these predictions, it is expected that upcoming experiments will further explore the predicted resonance and bound states in these possible decay channels. Published by the American Physical Society 2024

Triply charm and bottom tetraquarks in a constituent quark model

Singly, doubly, and fully charmed tetraquark candidates, e.g., Tcs¯(2900), Tcc+(3875), and X(6900) have been recently reported by the LHCb collaboration. Therefore, it is timely to implement a theoretical investigation on triply heavy tetraquark systems; herein, the S-wave triply charm and bottom tetraquarks, Q¯Qq¯Q (q=u,d,s;Q=c,b), with spin-parity JP=0+, 1+, and 2+, isospin I=0 and 12, are systematically studied in a constituent quark model. Besides, all tetraquark configurations, i.e., meson-meson, diquark-antidiquark, and K-type arrangements, along with any allowed color structure, are comprehensively considered. The Gaussian expansion method (GEM), in combination with the complex-scaling method (CSM), which is quite ingenious in dealing with either bound or resonances, is the approach adopted in solving the complex scaled Schrödinger equation. This theoretical framework has already been applied in various tetra- and pentaquark systems. In a fully coupled-channel calculation within the GEM+CSM, narrow resonances are found in each I(JP) channel of the charm and bottom sector. In particular, triply charm and bottom tetraquark resonances are obtained in 5.6–5.9 GeV and 15.3–15.7 GeV, respectively. We provide also some insights of the compositeness of these exotic states, such as the inner quark distance, magnetic moment and dominant wave function component. All this may help to distinguish them in future high energy nuclear and particle experiments. Published by the American Physical Society 2024

Masses and decays of triply-heavy pentaquarks* *D. J. is Supported by the National Natural Science Foundation of China (12165017)

In this study, we analyzed masses and decays of triply-heavy pentaquarks in the unified MIT bag model. We construct the color-spin wave functions of the triply-heavy pentaquarks and use the numerical variational method to compute all the ground-state masses of these systems. By excluding the scattering states in configuration spsce, we computed the decay width ratios of each decay channel relative to the maximum width for the compact pentaquark states, obtaining the main decay modes of the triply-heavy pentaquark systems.

Spectrum of the molecular pentaquarks

We investigate the mass spectrum of the molecular pentaquarks composed of a baryon and a meson. We establish the underlying relations among the near-threshold interactions of the molecular tetraquark and pentaquark systems. We find the existence of the molecule candidates in the ΣcD¯(*), DD*, and DD¯* systems indicates a substantial presence of the hadronic molecules in the heavy baryon plus heavy meson systems ( refers to the hadrons with the c and/or s quarks). We make an exhaustive prediction of the possible bound/virtual molecular states in the systems: Σc(*)D¯(*), Σc(*)D(*), Ξc(′,*)D¯(*), Ξc(′,*)D(*), Σc(*)K*, Σc(*)K¯*, Ξc(′,*)K*, Ξc(′,*)K¯*, Ξcc(*)D¯(*), Ξcc(*)D(*), Ξcc(*)K*, Ξcc(*)K¯*, Σ(*)D¯(*), Σ(*)D(*), Ξ(*)D¯(*), Ξ(*)D(*), Σ(*)K*, Σ(*)K¯*, Ξ(*)K*, Ξ(*)K¯*. Hunting for the predicted states in experiments will significantly deepen our understanding of the formation mechanism of the hadronic molecules, and shed light on the manifestation of flavor symmetry in the low-energy residual strong interactions. Published by the American Physical Society 2024

The tetraquark system in a chiral quark model* *Partially supported by the National Natural Science Foundation of China (12305093, 11535005, 11775118), the Natural Science Foundation of Zhejiang Province, China(LQ22A050004), the Ministerio Español de Ciencia e Innovación (PID2019-107844GB-C22, PID2022-140440NB-C22), the Junta de Andalucía under contract Nos. Operativo FEDER Andalucía (2014-2020 UHU-1264517, P18-FR-5057 and also PAIDI FQM-370)

The S-wave tetraquarks, with spin-parities , , and , in both isoscalar and isovector sectors, are systematically studied using a chiral quark model. The meson-meson, diquark-antidiquark, and K-type arrangements of quarks and all possible color wave functions are comprehensively considered. The four-body system is solved using the Gaussian expansion method, a highly efficient computational approach. Additonally, a complex-scaling formulation of the problem is established to disentangle bound, resonance, and scattering states. This theoretical framework has already been successfully applied in various tetra- and penta-quark systems. For the complete coupled channel and within the complex-range formulation, several narrow resonances of and systems are obtained, in each allowed -channel, within the energy regions of GeV and GeV, respectively. The predicted exotic states, which indicate a richer color structure when going towards multiquark systems beyond mesons and baryons, are expected to be confirmed in future high-energy particle and nuclear experiments.

Prediction of Pcc states in a quark model

Inspired by the observation of hidden-charm pentaquark Pc and Pcs states by the LHCb Collaboration, we explore the qqcc¯c (q=u or d) pentaquark systems in the quark delocalization color screening model. The interaction between baryons and mesons and the influence of channel coupling are studied in this work. Three compact qqcc¯c pentaquark states are obtained, whose masses are 5259 MeV with I(JP)=0(1/2−), 5396 MeV with I(JP)=1(1/2−), and 5465 MeV with I(JP)=1(3/2−). Two molecular states are obtained, which are I(JP)=0(1/2−)ΛcJ/ψ with 5367 MeV and I(JP)=0(5/2−) Ξcc*D¯* with 5690 MeV. These predicted states may provide important information for future experimental search. Published by the American Physical Society 2024

Charmoniumlike tetraquarks in a chiral quark model

The lowest-lying charmonium-like tetraquarks c{bar{c}}q{bar{q}}(q=u,,d) and c{bar{c}}s{bar{s}}, with spin-parity J^P=0^+, 1^+ and 2^+, and isospin I=0 and 1, are systematically investigated within the theoretical framework of complex-scaling range for a chiral quark model that has already been successfully applied in former studies of various tetra- and penta-quark systems. A four-body S-wave configuration which includes meson–meson, diquark–antidiquark and K-type arrangements of quarks, along with all possible color wave functions, is comprehensively considered. Several narrow resonances are obtained in each tetraquark channel when a fully coupled-channel computation is performed. We tentatively assign theoretical states to experimentally reported charmonium-like signals such as X(3872), Z_c(3900), X(3960), X(4350), X(4685) and X(4700). They can be well identified as hadronic molecules; however, other exotic components which involve, for instance, hidden-color channels or diquark–antidiquark structures play a considerable role. Meanwhile, two resonances are obtained at 4.04 GeV and 4.14 GeV which may be compatible with experimental data in the energy interval 4.0–4.2 GeV. Furthermore, the X(3940) and X(4630) may be identified as color compact tetraquark resonances. Finally, we also find few resonance states in the energy interval from 4.5 to 5.0 GeV, which would be awaiting for discovery in future experiments.

Prediction of charmed-bottom pentaquarks in quark model

Inspired by the fully heavy tetraquark states reported by the LHCb, ATLAS and CMS Collaborations, we perform a systematical investigation of the low-lying fully heavy pentaquark systems composed of charm and bottom quarks (anti-quark) in the chiral quark model. With the help of the channel-coupling, we obtain several fully heavy pentaquark candidates, which are ccccbar{b} and bbbbbar{c} systems with J^P = 1/2^- and 3/2^-, cccbbar{c}, bbbcbar{b}, cccbbar{b} and bbbcbar{c} systems with J^P = 5/2^-. The binding energies of these states are all below 10 MeV and the root mean square (RMS) are around 1.8 fm, which indicates that these states are likely to be molecular states. These predicted exotic states may provide new ideas for experimental searches and we expect more experimental and theoretical researches to study and understand the fully heavy states in future.

Discovery of Tcs¯0a(2900)0,++ implies new charmed-strange pentaquark system

Inspired by the very recently discovered tetraquark states $T_{c\bar s 0}^a(2900)^{0,++}$ from the LHCb Collaboration, we predict the existence of a new charmed-strange pentaquark system, $c\bar s nnn$, which is closely connected to $c\bar s n\bar n$ by exchanging $\bar n$ into $nn$ with $n=u,d$. Especially, it is suggested to experimentally search for the predicted new pentaquark system via the weak decays of $B$ mesons or $b$-baryons, with the support from the study of the mass spectrum and the decay properties. The predicted new pentaquark system must attract extensive attention from experimentalists and theorists when it constructs the ``particle zoo 2.0" in the near future.

Analysis of Ω(2012) as a molecule in the chiral quark model

Inspired by the updated information on $\Omega(2012)$ by the Belle Collaboration, we conduct a study of all possible $S$-wave pentaquark systems with quark contents $sssq\bar{q},q=u,d$ in a chiral quark model with the help of Gaussian expansion method. Channel coupling is also considered. The real-scaling method (stabilization method) is employed to identify and check the bound states and the genuine resonances. In addition, the decay widths of all resonances are given. The results show that $\Omega(2012)$ can be interpreted as a $\Xi^*K$ molecular state with quantum number of $IJ^P=0(\frac{3}{2})^-$. Other resonances are obtained: $\Xi^* K^*$ with $IJ^P=0(\frac{1}{2})^-$ and$0(\frac{3}{2})^-$, $\Omega\pi$ with $IJ^P=1(\frac{3}{2})^-$. These pentaquark states is expected to be further verified in future experiments.

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.

Fully heavy pentaquark states in constituent quark model

The LHCb collaboration reported a fully charmed tetraquark state X(6900) in the invariant mass spectrum of $J/\psi$ pairs in 2020. This discovery inspires us to further study the fully heavy pentaquark system. In this work, we investigate systematically all possible configurations for ground fully heavy pentaquark system via the variational method in the constituent quark model. According to our calculations, we further analyze the relative lengths between quarks and the contributions to the pentaquark masses from different terms of the Hamiltonian. We think no stable states exist in fully heavy pentaquark system. We hope that our study will be helpful to explore for fully heavy pentaquark states.

Fully heavy pentaquarks in quark models

The fully heavy pentaquarks $cccc\bar{c}$ and $bbbb\bar{b}$ are systematically investigated within the chiral quark model and quark delocalization color screening model. The results are consistent in both two moelds, and the effect of the channel-coupling is crucial for forming a bound state of the fully heavy pentaquark system. Three possible fully heavy pentaquarks are obtained, which are the $cccc\bar{c}$ state with $J^P = 1/2^-$ and the mass of $7891.9 \sim 7892.7$ MeV, the $bbbb\bar{b}$ state with $J^P=1/2^-$ and the mass of $23810.1 \sim 23813.8$ MeV, and the $bbbb\bar{b}$ state with $J^P = 3/2^-$ and the mass of $23748.2 \sim 23752.3$ MeV. All these fully heavy pentaquark states are worth searching in future experiments.

Study of qqq{bar{q}}Q pentaquark system in the chiral quark model

With the discovery of some hidden-charm pentaquark resonances by the LHCb Collaboration, investigations of pentaquark states containing heavy quarks have aroused the interest of theorists. We study herein qqq{bar{q}}Q (q = u or d, Q=c or b) pentaquark system, in the framework of the chiral quark model. In consequence, some charmed and bottomed pentaquarks are considered to exist by five-body dynamical calculations. In the charm sector, Sigma _cpi (IJ^P=0frac{1}{2}^-) and Sigma _c^*pi (IJ^P=0frac{3}{2}^-) are possible candidates of Lambda _c(2595) and Lambda _c(2625), respectively. Besides, two high-spin states, Sigma _c^*rho (IJ^P=0frac{5}{2}^-) and Delta D^*(IJ^P=1frac{5}{2}^-), are also found in the energy region of 3.2 sim 3.3 GeV. In the bottom sector, Sigma _bpi (IJ^P=0frac{1}{2}^-), Sigma _b^*pi (IJ^P=0frac{3}{2}^-) could be candidates of Lambda _b(5912) and Lambda _b(5920), respectively. And Sigma _b^*rho (IJ^P=0frac{5}{2}^-) and Delta B^*(IJ^P=1frac{5}{2}^-) are found in the energy region of 6.5 sim 6.6 GeV. Sigma _c^{(*)}pi and Sigma _b^{(*)}pi are expected as compact states, while Sigma _c^*rho , Sigma _b^*rho , Delta D^* and Delta B^* are expected as molecular states.

Investigating Ω(2012) as a molecular state

We conduct a dynamical calculation of pentaquark systems with quark contents $sssu\bar{u}$ in the framework of two quark models: the chiral quark model(ChQM) and quark delocalization color screening model(QDCSM). The effective potentials between baryon and meson clusters are given, and the possible bound states are also investigated. Besides, the study of the scattering process of the open channels is also performed to look for any resonance state. The results show that the $\Omega(2012)$ is not suitable for the interpretation as a $\Xi^{*} \bar{K}$ molecular state in present quark models. Two resonance states: the $\Xi^{*}\bar{K}^{*}$ with $IJ^{P}=0\frac{3}{2}^{-}$ ($M=2328\sim2374$ MeV, $\Gamma=57\sim65.5$ MeV) and $IJ^{P}=1\frac{3}{2}^{-}$ ($M=2341\sim2386$ MeV, $\Gamma=31.5\sim100$ MeV) are obtained in both QDCSM and ChQM, which indicates that both of these two states are more possible to be existed and worthy of being searched by future experiments.

Investigation of multi-quark systems

In this study, the researcher decided to study Tetraquark and Pentaquark systems. We introduce the Pentaquark system as a meson-baryon system and Tetraquark as a diquark-antidiquark system. A diquark consists of two quarks. The interaction potential between these particles is considered as a combination of two color charge potentials and the confinement potential is considered as harmonic and linear sentences. Solve the Schrodinger equation by considering the effects of spin-spin, isospin- isospin, spin-isospin, and then obtain the mass of the diquark and the heavy tetraquuarks with charm quarks and bottom. These calculations are calculated using the approach of diquark - antidiquark within the framework of the non-relativistic quark model. In the following, we calculate the mass of Pentaquark systems in the same way.

Triply charmed dibaryons in the one boson exchange model

The pentaquark states, $P_{c}(4312)$, $P_{c}(4440)$ and $P_{c}(4450)$, can be nicely arranged into a multiplet of seven molecules of $\bar{D}^{(\ast)}\Sigma_{c}^{(\ast)}$ dictated by heavy quark spin symmetry, while the $\Xi_{cc}^{(\ast)}\Sigma_{c}^{(\ast)}$ system can be related to the $\bar{D}^{(\ast)}\Sigma_{c}^{(\ast)}$ system via heavy antiquark diquark symmetry. In this work we employ the one boson exchange model to study the interactions between $\Xi_{cc}^{(\ast)}$ and $\Sigma_{c}^{(\ast)}$ with constraints from the pentaquark system. We show that a multiplet of ten triply charmed dibaryons emerge naturally in the isospin-1/2 sector, while only three appear in the isospin-3/2 sector. In addition, we study their heavy quark flavor partners. Ten triply bottom diybaryons are found in the isospin-1/2 sector, while only nine are likely in the isospin-3/2 sector. Furthermore, the predicted mass splitting between the $0^{+}$ $\Xi_{cc}\Sigma_{c}$ state and its $1^{+}$ counterpart is found to be consistent with the correlation implied by heavy antiquark diquark symmetry recently pointed out in Pan $et$ $al$..

Calculation of masses of heavy pentaquark using the NU Method

In this paper, the bound states of pentaquark systems are studied by solving the Schrodinger equation containing Van der Waals potential via Nikiforov–Uvarov method. The binding energies, wave functions and the masses of heavy pentaquarks are calculated. The results are in agreement with the existing ones in the literature.

Hidden charm pentaquarks Λcc¯ above 4 GeV

A dynamical calculation of the strange hidden charm pentaquark systems $\Lambda_{c\bar{c}}$ is performed in the framework of the quark delocalization color screening model. The effective potentials between two clusters are calculated to investigate the interaction between the baryons and mesons. The dynamic calculations indicate that the strange hidden charm pentaquark system with $IJ^{P}=0\frac{1}{2}^{-}$ and $IJ^{P}=0\frac{3}{2}^{-}$ can form bound states with the help of the channel-coupling. The energies of these two system are 4094.3 MeV and 4207.4 Mev, respectively. These two $\Lambda_{c\bar{c}}$ states are possible to be intriguing pentaquark candidates which are worth searching in experiments. Whereas, for the systems with isospin $I=1$, the effective potentials of all channels are repulsive, and there is no any bound state for these systems.

Investigation of the pentaquark resonance in the NK system

A dynamical calculation of pentaquark systems with quark contents $uudd\bar{s}$ is performed in the framework of quark delocalization color screening model with the help of resonating group method. The effective potentials between baryon and meson clusters are given, and the possible bound states or resonances are investigated. The single calculations show that the $NK^{*}$ with $I=0, J^{P}=\frac{1}{2}^{-}$, $\Delta K^{*}$ with $I=1, J^{P}=\frac{1}{2}^{-}$, and $\Delta K^{*}$ with $I=2, J^{P}=\frac{3}{2}^{-}$ are all bound, but they all turns into scattering states by coupling with the corresponding open channels. A possible resonance state $\Delta K^{*}$ with $I=1, J^{P}=\frac{5}{2}^{-}$ is proposed. The mass is around $2110.5$ MeV, and the decay modes are $NK$ in $D$-wave or $NK\pi\pi$ in $P$-waves.