⚛️ phenomenology

Interpretation of the excited $\Omega_c$ family via mass and width in the chiral quark model

This study utilizes the chiral quark model combined with the $^3P_0$ decay mechanism to provide a coherent interpretation of the low-lying $\Omega_c$ spectrum, successfully identifying most observed states as $\lambda$ -mode $1P$ excitations while suggesting that $\Omega_c(3119)$ is not a pure three-quark state and assigning $\Omega_c(3185)$ and $\Omega_c(3327)$ to $2S$ and $1D$ configurations, respectively.

Original authors: Xiao-Huang Hu, Zhe-Tao Miu, Yue Tan, Qi Huang, Ye Yan, Jia-Lun Ping

Published 2026-09-15

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CC0 1.0

Original authors: Xiao-Huang Hu, Zhe-Tao Miu, Yue Tan, Qi Huang, Ye Yan, Jia-Lun Ping

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ 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 particles called quarks, the fundamental building blocks of matter. These tiny constituents are bound together by the strong force, the most powerful interaction in nature, to form larger particles known as hadrons. Among these, a special family called baryons is made of three quarks. While some baryons are common, others are rare and exotic, containing heavy quarks like the charm quark alongside lighter ones. Understanding how these heavy and light quarks dance together is crucial for physicists, as it reveals the hidden rules of the strong force that governs the universe. For decades, scientists have tried to map out the energy levels, or "spectrum," of these particles, much like identifying the notes on a musical instrument. However, a specific family of baryons containing one charm quark and two strange quarks, known as the Omega-c, remained a puzzle. Recent experiments had discovered several new, short-lived versions of this particle, but their internal structure and exact nature were unknown.

In a recent study, a team of physicists set out to solve this mystery by building a detailed theoretical model of the Omega-c family. They focused on the low-lying excited states of these particles, which are versions where the internal quarks are vibrating or moving in more complex patterns than in the ground state. The researchers used a framework called the chiral quark model, which treats the interactions between quarks as being mediated by the exchange of light particles known as Goldstone bosons. This approach allows scientists to calculate the expected mass and how quickly these particles should decay into other, more stable particles. To test their calculations, they compared their predicted numbers against the latest experimental data collected by the LHCb collaboration at the Large Hadron Collider, which had recently observed five narrow excited states and two additional broader ones.

The study successfully identified the internal structure of four of the five narrow states observed in 2017. The researchers found that the particles known as Omega-c(3000), Omega-c(3050), Omega-c(3065), and Omega-c(3090) fit perfectly into a specific pattern of motion where the two strange quarks move together in a coordinated way while the charm quark orbits them. In their calculations, these four particles correspond to specific quantum states with distinct spins and parities, matching the masses measured by the experiments with high precision. The team also determined the likely decay widths, or how fast these particles break apart, finding that their theoretical predictions align well with the narrow lifetimes observed in the lab. This consistent picture suggests that these four particles are indeed the lowest energy excitations of the Omega-c system, confirming a long-held hypothesis about how these three-quark systems organize themselves.

However, the story becomes more complex when looking at the fifth narrow state, Omega-c(3119). The researchers found that this particle cannot be explained as a simple three-quark system vibrating in a standard way. While their model predicted the existence of similar states with masses close to 3119, those predicted states should have decayed instantly or not at all in the specific way the experiment observed. The fact that the observed particle exists and decays as it does suggests it is not a pure three-quark object. Instead, the authors propose that this state might be a more exotic configuration, such as a molecule formed by two other particles sticking together, or perhaps a pentaquark containing five quarks. This finding highlights a gap in the standard three-quark picture and points toward more complex forms of matter that require further investigation.

The team also turned their attention to two heavier states, Omega-c(3185) and Omega-c(3327), which were discovered more recently. Their calculations suggest that the Omega-c(3185) is likely a radially excited state, meaning the quarks are vibrating in a higher energy mode, similar to a guitar string vibrating at a higher harmonic. They identified two possible spin configurations for this particle, but could not yet distinguish between them without more data. For the heaviest observed state, Omega-c(3327), the researchers concluded it is likely a state where the quarks are moving in a more complex orbital shape, known as a D-wave state. They ruled out one specific possibility for this particle because their model predicted it would not decay in the way the experiment saw it, leaving a different configuration as the most probable candidate.

Beyond explaining the known particles, the study offers a roadmap for future discoveries. The researchers predicted the existence of several other excited states that have not yet been seen, estimating their masses to be between 3253 and 3305 MeV. They also identified the specific ways these missing particles should decay, providing clear targets for experimentalists to search for. By mapping out these invisible states, the study provides a coherent and detailed picture of the Omega-c family, turning a collection of mysterious peaks in experimental data into a structured family of particles. This work not only clarifies the nature of the particles we have found but also guides the search for the ones that are still hiding, deepening our understanding of the fundamental forces that hold the universe together.

Technical Summary: Interpretation of the excited $\Omega_c$ family via mass and width in the chiral quark model

Problem Statement
The $\Omega_c$ baryon system, composed of one charm quark and two identical strange quarks ($ssc$), offers a unique laboratory for investigating heavy-quark symmetry and non-perturbative QCD dynamics. Unlike the $\Xi_c$ family, which contains both flavor-antitriplet and flavor-sextet light-diquark configurations, the $\Omega_c$ system possesses a simpler flavor structure with a symmetric flavor wave function. This symmetry imposes strict constraints on allowed spin-space configurations, making it an ideal platform for testing quark models.

Following the 2017 discovery of five narrow excited states ( $\Omega_c(3000)$ , $\Omega_c(3050)$ , $\Omega_c(3065)$ , $\Omega_c(3090)$ , and $\Omega_c(3119)$ ) by the LHCb Collaboration, and subsequent observations of $\Omega_c(3185)$ and $\Omega_c(3327)$ , the assignment of their quantum numbers ( $J^P$ ) and internal structures (radial vs. orbital excitations, $\lambda$ -mode vs. $\rho$ -mode) remains a subject of debate. Previous theoretical studies using the chiral quark model on the $\Omega_c$ system failed to resolve fine splittings among the $1P$ multiplet members because spin-orbit and tensor interactions were omitted. Furthermore, a consistent description of both the mass spectrum and strong decay widths was lacking.

Methodology
This work investigates the low-lying orbital excitations ( $2S$ , $1P$ , and $1D$ ) of the $\Omega_c$ baryons using a unified theoretical framework:

Mass Spectrum Calculation: The authors employ the chiral quark model, which incorporates kinematic terms, color confinement, one-gluon exchange (OGE), and Goldstone-boson exchange (GBE). The Hamiltonian includes spin-orbit and tensor interactions to resolve fine splittings.
- Parameters: To ensure consistency and enhance predictive power, the model parameters are inherited directly from the authors' previous successful study of the $\Xi'_c$ system [32], without further adjustment.
- Wave Functions: The spatial wave functions are solved using the Gaussian Expansion Method (GEM) within the Rayleigh-Ritz variational method. The system is treated in both $S-L$ coupling and $J_l-S_Q$ (heavy quark symmetry) coupling schemes.
Decay Width Calculation: Strong decay widths are evaluated using the $^3P_0$ $^{3} P_{0}$ quark-pair-creation mechanism. The transition operator includes convergence and damping factors to address mass shift issues found in earlier applications.
- Decay Channels: The primary decay modes considered are $\Xi_c \bar{K}$ , $\Xi'_c \bar{K}$ , and $\Xi^*_c \bar{K}$ .
Analysis Strategy: The calculated masses and decay widths are compared against experimental data from the LHCb and Belle Collaborations to assign quantum numbers and interpret the nature of the observed states.

Key Contributions and Results
The study provides a simultaneous description of the mass spectrum and decay widths for the observed $\Omega_c$ states, leading to the following assignments:

The $\lambda$ -mode $1P$ Multiplet:
- $\Omega_c(3000)$ : Identified as the $J^P = 1/2^-$ state of the $\lambda$ -mode $1P$ excitation. The calculated mass (2999 MeV) agrees well with the experimental value (3000.44 MeV). The predicted width (8.89 MeV) is larger than the measured value (3.83 MeV), a discrepancy attributed to intrinsic uncertainties in the $^3P_0$ model (30–50% level).
- $\Omega_c(3050)$ and $\Omega_c(3065)$ : Assigned to the two $J^P = 3/2^-$ states of the $\lambda$ -mode $1P$ multiplet. Their calculated masses (3042 MeV and 3053 MeV) align with experimental values (3050.18 MeV and 3065.63 MeV). The calculated partial widths to $\Xi_c \bar{K}$ are small (0.02 MeV and 0.1 MeV), consistent with experimental upper limits. This assignment is supported by helicity angle measurements that disfavor $J=1/2$ .
- $\Omega_c(3090)$ : Assigned to the $J^P = 5/2^-$ state of the $\lambda$ -mode $1P$ multiplet. The calculated mass (3078 MeV) is within the typical accuracy of the model relative to the experimental value (3090.15 MeV).
The $\Omega_c(3119)$ Anomaly:
- The authors find that the $\Omega_c(3119)$ cannot be described as a pure three-quark excitation. While $\rho$ -mode $1P$ states ( $\tilde{\Omega}_c(1/2^-, 1P)$ and $\tilde{\Omega}_c(3/2^-, 1P)$ ) have masses close to the experimental value (3119 MeV), their predicted decay widths within the $^3P_0$ model are strictly zero.
- This incompatibility suggests that $\Omega_c(3119)$ likely possesses a molecular, pentaquark, or mixed three-quark/pentaquark structure, rather than being a conventional quark-model state.
Higher Excitations ( $2S$ and $1D$ ):
- $\Omega_c(3185)$ : Assigned to the $2S$ radial excitation. The calculated masses for the $J^P = 1/2^+$ (3168 MeV) and $3/2^+$ (3219 MeV) states are close to the experimental value (3185 MeV). The authors note that theoretical widths are generally underestimated compared to the experimental width (50 MeV), a feature observed across the sector. Future measurements of $\Xi'_c \bar{K}$ and $\Xi^*_c \bar{K}$ channels are required to distinguish between the $1/2^+$ and $3/2^+$ assignments.
- $\Omega_c(3327)$ : Assigned to the $\lambda$ -mode $1D$ excitation. The $J^P = 7/2^+$ state ( $\Omega_c3(7/2^+, 1D)$ ) is identified as the candidate, with a calculated mass of 3305 MeV. The alternative $J^P = 3/2^+$ candidate ( $\tilde{\Omega}_c2(3/2^+, 1D)$ ), which is also a $\lambda$ -mode state, is excluded because its predicted decay to $\Xi_c \bar{K}$ is nearly zero, contradicting experimental observation.
Predictions:
- The study predicts the existence of other $\lambda$ -mode $D$ -wave $\Omega_c$ states with masses ranging from 3253 to 3305 MeV. Their dominant decay channels are identified (e.g., $\Xi_c \bar{K}$ , $\Xi^*_c \bar{K}$ , $\Xi D$ ), offering specific targets for future experimental searches.

Significance
The paper claims to offer a "coherent picture" of the low-lying $\Omega_c$ spectrum by successfully describing the observed states within a single theoretical framework (chiral quark model + $^3P_0$ mechanism) using parameters fixed from the $\Xi_c$ system. The work highlights the importance of including spin-orbit and tensor interactions to resolve fine splittings in the $1P$ multiplet.

Crucially, the study demonstrates that while the $\lambda$ -mode $1P$ assignment works well for the first four narrow states, the $\Omega_c(3119)$ requires an exotic interpretation, thereby motivating further experimental tests to distinguish between conventional three-quark, molecular, and pentaquark scenarios. The results serve as a benchmark for understanding heavy-light baryon dynamics and the role of Goldstone-boson exchange in baryon spectroscopy.

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