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17 pages, 1739 KiB

Open AccessArticle

Masses of Hadrons, Tetraquarks, and Pentaquarks Through a Tsallis-Entropy Approach in the MIT Bag Model

by Vanesa Fernández, Gerardo Herrera Corral, Manuel A. Matías Astorga and Jesús M. Sáenz

Entropy 2025, 27(7), 681; https://doi.org/10.3390/e27070681 - 26 Jun 2025

Viewed by 652

We propose a new approach to describe hadrons and new forms of quark matter in the MIT bag model. The proposal is an extension that integrates a Tsallis nonextensive statistics description of quarks and gluons and is shown to capture the main features underlying mass spectroscopy. While the traditional bag model successfully accounts for the masses of light hadrons, it has not been widely used to describe exotic quark configurations. We compute the system’s internal energy and derive expressions for hadronic masses, showing how they depend on the Tsallis parameter. The model reasonably reproduces known mass spectra of conventional hadrons and naturally extends to exotic states such as tetraquarks and pentaquarks. Additionally, we provide estimates of hadron radii within this framework. Our results suggest that nonextensive statistics provide a meaningful generalization of the bag model, capturing both conventional and exotic features of hadronic matter within a unified formalism. Full article

(This article belongs to the Section Statistical Physics)

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24 pages, 515 KiB

Open AccessArticle

Hidden-Charm Pentaquarks with Strangeness in a Chiral Quark Model

by Gang Yang, Jialun Ping and Jorge Segovia

Symmetry 2024, 16(3), 354; https://doi.org/10.3390/sym16030354 - 14 Mar 2024

Cited by 7 | Viewed by 1528

Abstract

The LHCb collaboration has recently announced the discovery of two hidden-charm pentaquark states with strange quark content,

P_{c s} (4338)

and

P_{c s} (4459)

; its analysis points towards having both hadrons’ isospins equal to zero and [...] Read more.

The LHCb collaboration has recently announced the discovery of two hidden-charm pentaquark states with strange quark content,

P_{c s} (4338)

and

P_{c s} (4459)

; its analysis points towards having both hadrons’ isospins equal to zero and spin-parity quantum numbers

{\frac{1}{2}}^{-}

and

{\frac{3}{2}}^{-}

, respectively. Herein, we perform a systematical investigation of the

q q s c \bar{c}

(q = u, d)

system by means of a chiral quark model, along with a highly accurate computational method, the Gaussian expansion approach combined with the complex scaling technique. baryon-meson configurations in both singlet- and hidden-color channels are considered. The

P_{c s} (4338)

and

P_{c s} (4459)

signals can be well identified as molecular bound states with dominant components

Λ J / ψ

(60 %)

and

Ξ_{c} D

(23 %)

for the lowest-energy case and

Ξ_{c} D^{*}

(72 %)

for the highest-energy one. In addition, it seems that some narrow resonances can also be found in each allowed

I (J^{P})

channel in the energy region of

4.6

–

5.5

GeV, except for the

1 ({\frac{1}{2}}^{-})

channel where a shallow bound state with dominant

Ξ_{c}^{*} D^{*}

structure is obtained at 4673 MeV with binding energy

E_{B} = - 3

MeV. These exotic states are expected to be confirmed in future high-energy experiments. Full article

(This article belongs to the Section Physics)

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76 pages, 2612 KiB

Open AccessFeature PaperEditor’s ChoiceReview

Tetraquarks and Pentaquarks from Quark Model Perspective

by Hongxia Huang, Chengrong Deng, Xuejie Liu, Yue Tan and Jialun Ping

Symmetry 2023, 15(7), 1298; https://doi.org/10.3390/sym15071298 - 22 Jun 2023

Cited by 25 | Viewed by 3865

Abstract

According to the classification of the quark model, the hadrons going beyond three-quark baryon and quark-antiquark meson pictures are called exotic hadrons. Many new hadrons have been observed since 2003, some of which exhibit exotic behaviors. There are a lot of excellent review articles on exotic hadrons available so far; the present article tries to focus on the recent experimental and theoretical progress on the exotic states from the perspective of the quark model. Although lattice quantum chromodynamics may give the final answer of the problem, the phenomenological models are still powerful tools to explore the exotic states and to provide insight on the phenomenology of hadrons. The spatial and color structures of multiquark states and the channel coupling calculation are emphasized through reviewing some bound states, molecular and color structure resonances. Finally, the unquench effects of some exotic states are reviewed. With the accumulation of experimental data on multiquark states and inspiration of underlying theory developments, more reasonable phenomenological models incorporating multi-body interactions and high Fock components to unify the description of normal hadrons and exotic hadrons are expectable. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2022)

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14 pages, 380 KiB

Open AccessArticle

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

by Xinmei Zhu, Yuheng Wu, Hongxia Huang, Jialun Ping and Youchang Yang

Universe 2023, 9(6), 265; https://doi.org/10.3390/universe9060265 - 31 May 2023

Cited by 3 | Viewed by 1366

Abstract

Inspired by the LHCb observation of hidden-charm pentaquarks, i.e.,

P_{c} (4312)

P_{c} (4440)

, and

P_{c} (4457)

in the

J / ψ p

invariant mass spectrum, a calculation of the [...] Read more.

Inspired by the LHCb observation of hidden-charm pentaquarks, i.e.,

P_{c} (4312)

P_{c} (4440)

, and

P_{c} (4457)

in the

J / ψ p

invariant mass spectrum, a calculation of the

J / ψ p

scattering cross-section was performed using the quark-delocalization color screening model. The results show that

P_{c} (4312)

can be identified as a hidden-charm molecular state

Σ_{c} D

with

J^{P} = {\frac{1}{2}}^{-}

. The two-peak structure can be reproduced around 4450 MeV, which corresponds to

P_{c} (4440)

and

P_{c} (4457)

. They are the resonances molecular states

Σ_{c} D^{*}

J^{P} = {\frac{1}{2}}^{-}

and

J^{P} = {\frac{3}{2}}^{-}

. Moreover, the

Σ_{c}^{*} D^{*}

of both

J^{P} = {\frac{1}{2}}^{-}

and

J^{P} = {\frac{3}{2}}^{-}

are possible molecular pentaquarks. Moreover, in the same theoretical frame, the calculation is extended to the

P_{c}

-like molecular pentaquarks, denoted as

P_{b}

. 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. Full article

(This article belongs to the Special Issue Universe: Feature Papers 2024—High Energy Nuclear and Particle Physics)

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78 pages, 1348 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Tetra- and Penta-Quark Structures in the Constituent Quark Model

by Gang Yang, Jialun Ping and Jorge Segovia

Symmetry 2020, 12(11), 1869; https://doi.org/10.3390/sym12111869 - 13 Nov 2020

Cited by 114 | Viewed by 5570

Abstract

With the development of high energy physics experiments, a large amount of exotic states in the hadronic sector have been observed. In order to shed some light on the nature of the tetraquark and pentaquark candidates, a constituent quark model, along with the Gaussian expansion method, has been employed systematically in real- and complex-range investigations. We review herein the double- and fully-heavy tetraquarks, but also the hidden-charm, hidden-bottom and doubly charmed pentaquarks. Several exotic hadrons observed experimentally were well reproduced within our approach; moreover, their possible compositeness and other properties, such as their decay widths and general patterns in the spectrum, are analyzed. Besides, we report also some theoretical predictions of tetra- and penta-quark states which have not seen by experiment yet. Full article

(This article belongs to the Special Issue Advances in Chiral Quark Models)

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13 pages, 473 KiB

Open AccessEditor’s ChoiceArticle

Exploring Possible Triangle Singularities in the Ξ b − → K − J / ψ Λ Decay

by Chao-Wei Shen, Hao-Jie Jing, Feng-Kun Guo and Jia-Jun Wu

Symmetry 2020, 12(10), 1611; https://doi.org/10.3390/sym12101611 - 28 Sep 2020

Cited by 30 | Viewed by 3388

Abstract

We analyze possible singularities in the

J / ψ Λ

invariant mass distribution of the

Ξ_{b}^{-} \to K^{-} J / ψ Λ

process via triangle loop diagrams. Triangle singularities in the physical region are found in 18 different triangle loop [...] Read more.

We analyze possible singularities in the

J / ψ Λ

invariant mass distribution of the

Ξ_{b}^{-} \to K^{-} J / ψ Λ

process via triangle loop diagrams. Triangle singularities in the physical region are found in 18 different triangle loop diagrams. Among those with

Ξ^{*}

-charmonium-

Λ

intermediate states, the one from the

χ_{c 1} Ξ (2120) Λ

loop, which is located around 4628 MeV, is found the most likely to cause observable effects. One needs S- and P-waves in

χ_{c 1} Λ

and

J / ψ Λ

systems, respectively, when the quantum numbers of these systems are

1 / 2^{+}

3 / 2^{+}

. When the quantum numbers of the

Ξ (2120)

are

J^{P} = 1 / 2^{+}

1 / 2^{-}

3 / 2^{+}

, the peak structure should be sharper than the other

J^{P}

choices. This suggests that although the whole strength is unknown, we should pay attention to the contributions from the

Ξ^{*}

-charmonium-

Λ

triangle diagram if structures are observed in the

J / ψ Λ

invariant mass spectrum experimentally. In addition, a few triangle diagrams with the

D_{s 1}^{*} (2700)

as one of the intermediate particles can also produce singularities in the

J / ψ Λ

distribution, but at higher energies above 4.9 GeV. Full article

(This article belongs to the Special Issue Advances in Chiral Quark Models)

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12 pages, 368 KiB

Open AccessArticle

Exotic Baryons in Chiral Soliton Models

by Herbert Weigel

Universe 2018, 4(12), 142; https://doi.org/10.3390/universe4120142 - 6 Dec 2018

Cited by 2 | Viewed by 3388

Abstract

We cautiously review the treatment of pentaquark exotic baryons in chiral soliton models. We consider two examples and argue that any consistent and self-contained description must go beyond the mean field approximation that only considers the classical soliton and the canonical quantization of [...] Read more.

(This article belongs to the Special Issue Selected Papers from the 7th International Conference on New Frontiers in Physics (ICNFP 2018))

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