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Systematic study of baryon-baryon interactions in singly bottomed systems

This paper systematically investigates baryon-baryon interactions in singly bottomed dibaryon systems using the chiral quark model, revealing that low-isospin and decuplet-decuplet channels favor stronger attraction and identifying numerous potential bound states that warrant further experimental verification.

Original authors: Yuxuan Du, Yanyue Pan, Xinmei Zhu, Zhiyun Tan, Hongxia Huang, Jialun Ping

Published 2026-09-07

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CC BY 4.0

Original authors: Yuxuan Du, Yanyue Pan, Xinmei Zhu, Zhiyun Tan, Hongxia Huang, Jialun Ping

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep within the heart of every atom lies a bustling world of tiny particles called quarks. These fundamental building blocks usually stick together in small groups of three to form protons and neutrons, the heavy cores of atoms. However, physicists have long wondered if quarks could arrange themselves in other ways, perhaps forming larger, more exotic structures. One such possibility is the "dibaryon," a rare particle made of six quarks bound together. While scientists have found hints of these six-quark states in systems made of lighter particles, the question remains whether they can exist when heavy, bottom quarks are involved. Bottom quarks are much heavier than their lighter cousins, and this extra weight changes the rules of how they move and interact, potentially allowing them to stick together more tightly. Understanding these heavy six-quark systems is crucial because it tests our deepest theories about how the universe's fundamental forces work at the smallest scales.

In a new study, researchers set out to map out the landscape of these heavy six-quark possibilities. They focused specifically on "singly bottomed" systems, which contain exactly one bottom quark paired with five lighter quarks. Using a sophisticated computer model based on the chiral quark theory, they simulated the interactions between pairs of baryons (three-quark particles) to see if they would naturally clump together into a stable, bound state. The team systematically checked every possible combination of spin and isospin—a quantum property related to how the particles align—looking for the specific conditions where the attractive forces between the particles would overcome their natural tendency to fly apart. Their calculations revealed that while many combinations simply repel each other, several specific configurations do indeed form deep, stable bonds.

The researchers found that the likelihood of forming a bound state depends heavily on the "flavor" and arrangement of the particles involved. They discovered that systems composed of two heavy, spinning particles (known as decuplet baryons) tend to attract each other much more strongly than systems made of two lighter, slower-spinning particles. In fact, the most promising candidates for stable six-quark particles were found in these heavy-heavy pairings. Furthermore, the study showed that the "isospin" of the system plays a critical role: configurations with lower isospin values generally create deeper, more stable bonds, while higher isospin values tend to weaken the attraction, often preventing the particles from sticking together at all. This suggests that nature has a preference for specific, low-energy arrangements when these heavy quarks come together.

Among the many possibilities they explored, the team identified several specific candidates that appear to be bound states. These include combinations such as a delta baryon paired with a bottomed sigma-star baryon, and various pairings of bottomed sigma and sigma-star particles. For instance, they calculated that a specific pairing of a delta and a sigma-star baryon could be bound with an energy of roughly 38.81 MeV, while another configuration involving two sigma-star baryons could be bound by about 33.68 MeV. These numbers represent the energy required to pull the particles apart; the more negative the number, the tighter the bond. The study also examined a specific six-quark state known as the H-dibaryon, which contains a bottom quark, but their results suggest that this particular configuration does not form a stable bound state on its own, at least not within the limits of their single-particle calculations.

While the study provides a strong theoretical map of where these particles might hide, it stops short of confirming their existence in the real world. The researchers emphasize that their work is a simulation based on established physical models, and the next step requires experimental verification. They suggest that future experiments, such as those conducted at high-energy particle colliders, should look for these specific low-isospin, heavy-heavy combinations. If these particles are found, they would not only confirm the existence of these exotic six-quark states but also provide a clearer picture of how the strong nuclear force behaves when heavy quarks are involved. Until then, these calculated states remain the most promising targets for scientists searching for the next layer of complexity in the subatomic world.

Technical Summary: Systematic Study of Baryon-Baryon Interactions in Singly Bottomed Systems

Problem and Motivation
The search for dibaryon (hexaquark) states has a long history in hadron physics, with significant attention paid to candidates composed of light quarks (e.g., the $H$ -dibaryon, $d^*$ , $N\Omega$ , and $\Omega\Omega$ ). While experimental progress has been made in the bottom baryon sector (e.g., observations of $\Sigma_b$ , $\Sigma^*_b$ , $\Omega_b$ , and excited $\Xi_b$ states by CDF, LHCb, and CMS), no dibaryon state containing heavy quarks has been experimentally established. Theoretical motivation for extending these studies to heavy-flavor systems stems from the substantial reduction in kinetic energy due to the larger reduced mass of heavy quarks compared to light-baryon systems. Previous theoretical efforts using quark models, lattice QCD, and meson exchange models have yielded conflicting results regarding the stability of heavy-flavor dibaryons (e.g., $uuddsb$). This work aims to systematically investigate singly bottomed dibaryon systems to identify possible bound states and analyze the underlying baryon-baryon interactions.

Methodology
The authors employ the Chiral Quark Model (ChQM) extended to include a bottom quark. The theoretical framework is based on the dynamical breaking of chiral symmetry. The system is treated as a six-quark system using the Resonating Group Method (RGM) and the Generating Coordinate Method (GCM) for dynamical calculations.

The Hamiltonian includes four components:

Mass and Kinetic Terms: Including individual quark masses and kinetic energy, minus the center-of-mass kinetic energy.
Potential Terms ( $V_{ij}$ ):
- Confinement Potential ( $V_{CON}$ ): A quadratic term dependent on the Gell-Mann matrices.
- One-Gluon Exchange (OGE) Potential ( $V_{OGE}$ ): Describes short-range interactions, including spin-spin and tensor forces (though tensor forces are neglected for S-wave states).
- Scalar $\sigma$ Meson Exchange ( $V_{\sigma}$ ): Provides intermediate-range attraction between $u$ and $d$ quarks.
- One-Boson Exchange (OBE) Potential ( $V_{OBE}$ ): Originally an $SU(3)$ framework involving $\pi, K, \eta$ exchanges. The authors extend this to an $SU(5)$ framework to explicitly include heavy meson exchanges ( $B, B_s, \eta_b$ ) necessary for systems containing a bottom quark.

Model parameters (quark masses, coupling constants, cutoffs) are fitted to reproduce the ground-state spectra of light and singly heavy baryons. The study focuses on S-wave states with isospin $I = 0, 1/2, 1, 3/2, 2, 5/2$ and total angular momentum $J = 0, 1, 2, 3$ .

Key Contributions and Results
The study systematically calculates binding energies ( $B_{sc} = E_{sc} - E_{th}$ ) for all possible singly bottomed dibaryon configurations. The primary findings are:

Identification of Bound States: Several bound states are predicted across various baryon multiplet combinations:
- $\Delta\Sigma^*_b$ : Bound for $IJ = 1/2_0, 1/2_1, 1/2_2, 1/2_3, 3/2_3$ with binding energies ranging from $-12.25$ to $-38.81$ MeV.
- $\Delta\Sigma_b$ : Bound for $IJ = 1/2_1, 3/2_1, 1/2_2, 3/2_2$ with binding energies from $-0.31$ to $-38.43$ MeV.
- $N\Sigma^*_b$ : Bound for $IJ = 1/2_2$ ($-1.59$ MeV).
- $\Sigma\Sigma_b$ : Bound for $IJ = 0_0, 0_1, 1_1$ (deeply bound at $-43.13$ MeV for $0_0$ ).
- $\Sigma\Sigma^*_b$ and $\Sigma^*\Sigma_b$ : Bound states found in low-isospin channels (e.g., $0_1, 0_2$ ).
- $\Sigma^*\Sigma^*_b$ : Bound for $IJ = 0_0, 0_1, 0_2, 0_3, 1_3$ with binding energies from $-2.27$ to $-33.68$ MeV.
Systematic Trends in Binding:
- Isospin Dependence: Low-isospin channels consistently exhibit deeper attractive interactions and are more prone to forming bound states. As isospin increases, attraction weakens, often leading to unbound states.
- Multiplet Structure: Decuplet-decuplet systems (e.g., $\Delta\Sigma^*_b, \Sigma^*\Sigma^*_b$ ) generally support the strongest attraction and the largest number of bound states. Octet-octet systems (e.g., $\Sigma\Sigma_b$ ) typically show weaker attraction, though exceptions like the deeply bound $\Sigma\Sigma_b$ ( $0_0$ ) exist. Octet-decuplet systems display intermediate behavior.
- Angular Momentum Dependence: For a fixed isospin, the relationship between binding energy and total angular momentum $J$ is not universal. While lower- $J$ states are often more bound, specific channels (e.g., $\Delta\Sigma^*_b$ with $I=1/2$ ) show deeper binding at $J=1$ compared to $J=0$ .
Interaction Mechanism Analysis:
- Effective Potentials: The study analyzes effective potentials $V(S_i)$ , revealing that bound states correspond to channels with deep attractive minima (often exceeding 100 MeV in depth at $\sim 0.5$ fm).
- Origin of Attraction: The attractive interaction arises from a competition between terms. The scalar $\sigma$ meson exchange provides the dominant intermediate-range attraction. The one-gluon exchange (OGE) interaction is crucial at short distances; its contribution can be attractive or repulsive depending on the isospin and spin configuration.
- Microscopic Origin: Matrix element analysis in spin-flavor-color space shows that the direct color interaction between two color-singlet clusters is zero. The interaction is driven by exchange terms induced by the antisymmetrization operator. The sign and magnitude of the OGE contribution are determined by the exchange matrix elements $\langle H^{cs}_{ij} \rangle_E$ . For high-isospin states (e.g., $I=5/2$ ), these matrix elements become positive, turning the OGE contribution repulsive, which, combined with Pauli blocking effects, suppresses bound state formation.

Significance and Claims
The paper claims to provide a systematic search for singly bottomed dibaryon states, offering a guide for future experimental searches. The authors emphasize that while low-isospin channels and decuplet-decuplet configurations are the most promising targets, the formation of bound states depends on the complex interplay of isospin, spin, and detailed baryon-baryon interactions.

The authors explicitly state that their single-channel results do not support a bound $H_b$ ($uuddsb$) state, contrasting with some previous quark-diquark model predictions, though they acknowledge that a full coupled-channel calculation is necessary to definitively rule out or confirm this possibility. They conclude that the identified states deserve further experimental investigation, noting that determining whether these candidates are resonances requires further study of scattering processes and decay properties (e.g., $\Delta\Sigma^*_b \to N\Sigma^*_b, N\Sigma_b, N\Lambda_b$ ), which is left for future work.

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