⚛️ phenomenology

Investigating the Molecular Nature of $\Lambda_b(6146)$ and $\Lambda_b(6152)$ via Strong Decays and Predicting Their Heavy-Quark Symmetry Partners

This study investigates the molecular nature of $\Lambda_b(6146)$ and $\Lambda_b(6152)$ by calculating their strong decay widths, concluding that while $\Lambda_b(6146)$ is likely a $\bar{B}^{*}N$ molecule, $\Lambda_b(6152)$ may not be, and subsequently predicting the existence of their heavy-quark symmetry partners in the charm sector and as higher-spin states to guide future experimental searches.

Original authors: Jing-wen Feng, Cai Cheng, Yin Huang

Published 2026-09-03

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Jing-wen Feng, Cai Cheng, Yin Huang

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 matter, protons and neutrons are not the smallest building blocks, but rather complex structures made of even smaller particles called quarks. For decades, physicists have understood that these quarks usually group together in threes to form ordinary particles like protons, or in pairs of a quark and an antiquark to form mesons. However, nature is often more creative than our simple rules suggest. Scientists have long suspected that quarks can also arrange themselves into more exotic, temporary clusters, behaving like molecules where two distinct particles orbit each other loosely before breaking apart. This idea, known as the hadronic molecule, suggests that some of the heavy, short-lived particles observed in high-energy collisions are not single, tight-knit units, but rather fragile associations of a heavy meson and a baryon. Understanding whether these particles are tight knots of three quarks or loose molecular bonds is crucial, because it reveals how the fundamental forces of nature hold the universe together at its most basic level.

In a recent study, researchers Jing-wen Feng, Cai Cheng, and Yin Huang set out to solve a specific mystery involving two such particles, named $\Lambda_b(6146)$ and $\Lambda_b(6152)$ . These particles were first spotted by the LHCb collaboration at the Large Hadron Collider, appearing as fleeting resonances in a spectrum of mass and energy. They are heavy baryons containing a bottom quark, and their existence has sparked a debate: are they traditional three-quark particles, or are they the molecular structures that theory predicts might exist? The researchers decided to test the molecular hypothesis by looking at how these particles decay, or break apart, into lighter particles. They focused on the idea that if these particles are indeed molecules made of a specific combination of a bottom meson and a neutron, they should decay in very specific ways and at specific rates.

To investigate this, the team built a detailed theoretical model that treated the $\Lambda_b(6146)$ and $\Lambda_b(6152)$ as if they were composed primarily of a $\bar{B}^*$ meson and a neutron. They then calculated the probability of these molecular states breaking apart into a pion and a bottom Sigma baryon, a process that involves complex interactions known as hadronic loops. The researchers had to account for the size and shape of these molecular bonds, adjusting a parameter that represents the spatial distribution of the components within the molecule. By running these calculations across a range of plausible values, they generated predictions for how wide the decay should be, which is a measure of how quickly the particle disappears.

The results of this investigation were strikingly different for the two particles. For the $\Lambda_b(6146)$ , the calculations aligned remarkably well with what the LHCb experimenters had actually observed. The predicted rate at which the particle decays into a pion and a Sigma baryon matched the experimental data, and the specific channel where it breaks down into a Sigma baryon rather than a heavier Sigma-star baryon was the dominant one. This strong agreement suggests that the $\Lambda_b(6146)$ is indeed a molecular state, a loose binding of a $\bar{B}^*$ meson and a neutron. However, the story changed completely for the $\Lambda_b(6152)$ . When the researchers applied the same molecular model to this second particle, the predicted decay rate was far too small to match reality. The model predicted it would decay almost instantly, but the experimental data showed it lasting much longer. Furthermore, the model predicted it would break down into the wrong type of particles compared to what was seen in the lab. This mismatch indicates that the $\Lambda_b(6152)$ is likely not a molecule, but rather a conventional three-quark particle, or perhaps a mix of both structures.

These findings have important consequences for how physicists view the family of heavy particles. Because the $\Lambda_b(6146)$ appears to be a molecule while the $\Lambda_b(6152)$ does not fit that description, the two cannot be simple "twins" related by a symmetry that usually pairs particles with similar masses and spins. This forces scientists to look elsewhere for the molecular partner of the $\Lambda_b(6146)$ . Using the principles of heavy quark symmetry, the authors predicted that a new, heavier molecular state should exist with a mass between 6195 and 6200 MeV. This hypothetical particle would be the spin partner of the $\Lambda_b(6146)$ and should decay primarily into a pion and a Sigma-star baryon. The study also suggests that similar molecular structures might exist in the charm sector, potentially corresponding to particles like the $\Lambda_c(2860)^+$ , while others like the $\Lambda_c(2880)^+$ might remain conventional three-quark states.

Ultimately, this work highlights that the internal structure of heavy baryons is more diverse than a simple list of masses might suggest. While the $\Lambda_b(6146)$ stands as a strong candidate for a hadronic molecule, the $\Lambda_b(6152)$ resists that explanation, pointing instead toward a more traditional quark arrangement. The researchers conclude that these particles may not be pure examples of one type or the other, but could be mixed states, containing both molecular and three-quark components. This nuanced view provides a clearer path for future experiments, guiding scientists on where to look for the missing molecular partners and helping to refine our understanding of the forces that bind the subatomic world.

Technical Summary: Investigating the Molecular Nature of $\Lambda_b(6146)$ and $\Lambda_b(6152)$

Problem Statement
The internal structure of the recently observed bottom baryons $\Lambda_b(6146)$ and $\Lambda_b(6152)$ remains a subject of debate. While the LHCb Collaboration identified these states with masses around 6146 MeV and 6152 MeV and spin-parity assignments of $J^P = 3/2^+$ and $5/2^+$ respectively, their nature as either conventional three-quark ($qqq$) states or hadronic molecules is unresolved. Previous theoretical studies using the quark model and QCD sum rules have provided explanations for these states as $1D$ -wave excitations, yet discrepancies exist between calculated decay widths and experimental data. Specifically, some quark model calculations yield decay widths larger than observed, suggesting these states might possess complex structures, potentially involving molecular components such as $\bar{B}^{(*)}N$ . Furthermore, the relationship between these bottom baryons and their charm counterparts ( $\Lambda_c$ ) under heavy quark symmetry (HQS) requires clarification to predict the existence of new partners.

Methodology
The authors investigate the strong decay modes of $\Lambda_b(6146)$ and $\Lambda_b(6152)$ under the hypothesis that they are predominantly $\bar{B}^*N$ molecular states, building upon the mass spectrum analysis in Ref. [11]. The study employs an effective Lagrangian approach to calculate partial decay widths into $\pi\Sigma_b$ and $\pi\Sigma_b^*$ final states via hadronic loops.

Key methodological elements include:

Effective Lagrangians: The interaction vertices for the coupling of the molecular states to their constituents ( $\bar{B}^*N$ ) are modeled using $P$ -wave and $F$ -wave Lagrangians for $J^P=3/2^+$ and $5/2^+$ states, respectively. Additional Lagrangians describe the interactions of $\bar{B}^{(*)}$ , $N$ , $\Sigma_b^{(*)}$ , and pions.
Form Factors: To ensure ultraviolet finiteness and account for the spatial distribution of the molecular constituents, a Gaussian form factor $\Phi(p_E^2/\Lambda^2) = \exp(-p_E^2/\Lambda^2)$ is introduced. The size parameter $\Lambda$ is varied between 0.9 and 1.1 GeV.
Coupling Constants: The unknown coupling constants $g_{\Lambda_b^* N \bar{B}^*}$ are determined using the compositeness condition, which sets the renormalization constant of the molecular wave function to zero.
Decay Calculation: The decay amplitudes are computed using Feynman diagrams involving $t$ -channel exchanges of $B$ and $B^*$ mesons. The total decay widths are derived by summing the contributions from $\pi\Sigma_b$ and $\pi\Sigma_b^*$ channels.

Key Results

$\Lambda_b(6146)$ as a Molecular State: The calculated total decay width for $\Lambda_b(6146)$ , assuming a $P$ -wave $\bar{B}^*N$ molecular structure, ranges from 1.20 to 2.23 MeV for $\Lambda \in [0.9, 1.1]$ GeV. This range is consistent with the experimental value of $2.9 \pm 1.3 \pm 0.3$ MeV. The dominant decay channel is predicted to be $\pi\Sigma_b$ , which aligns with experimental observations. These results support the interpretation of $\Lambda_b(6146)$ as primarily a $\bar{B}^*N$ molecule.
$\Lambda_b(6152)$ Disfavored as a Molecule: In contrast, the calculation for $\Lambda_b(6152)$ as an $F$ -wave $\bar{B}^*N$ molecule yields a total decay width that is orders of magnitude smaller than the experimental value of $2.1 \pm 0.8 \pm 0.3$ MeV. Furthermore, the calculation predicts $\pi\Sigma_b$ as the dominant channel, whereas experiments indicate the primary contribution comes from $\pi\Sigma_b^*$ . Consequently, the molecular interpretation for $\Lambda_b(6152)$ is not supported by this framework.
Mixed Structure Implications: The discrepancy between the calculated molecular width for $\Lambda_b(6146)$ (1.59 MeV at $\Lambda=1.0$ GeV) and the experimental central value suggests that $\Lambda_b(6146)$ may not be a pure molecule but a mixed state containing both molecular and three-quark components. Similarly, the failure of the molecular model for $\Lambda_b(6152)$ , combined with quark model results that better fit the data, suggests $\Lambda_b(6152)$ is likely a conventional three-quark state with a possible small molecular admixture.

Predictions and Heavy Quark Symmetry
Based on the findings and heavy quark symmetry principles, the authors make the following predictions:

Heavy Quark Spin Partners: Since $\Lambda_b(6146)$ is identified as a $P$ -wave $\bar{B}^*N$ molecule, its heavy quark spin symmetry partner should be a $\bar{B}^*N$ molecule with $J^P = 5/2^+$ . The authors predict this state exists in the mass range of 6195–6200 MeV, with a dominant decay channel of $\pi\Sigma_b^*$ .
Heavy Quark Flavor Partners: Under heavy quark flavor symmetry, the existence of $\Lambda_b(6146)$ as a molecule implies a corresponding $D^*N$ molecule with $J^P = 3/2^+$ , potentially corresponding to the experimentally observed $\Lambda_c(2860)^+$ . Conversely, if $\Lambda_c(2880)^+$ is the flavor partner of $\Lambda_b(6152)$ (which appears to be a conventional baryon), it should also possess a three-quark structure.
Search for New States: The authors propose searching for a $D^*N$ molecule with $J^P = 5/2^+$ , which would be the heavy-quark spin partner of the $\Lambda_c(2860)^+$ .

Significance
The paper claims that its results aid in exploring the internal structure of these baryons by providing a rigorous test of the molecular hypothesis through strong decay widths, rather than relying solely on mass spectra. The study highlights that not all hadron pairs with small mass splittings and similar widths necessarily form heavy quark spin symmetry doublets; in this case, $\Lambda_b(6146)$ and $\Lambda_b(6152)$ likely have distinct internal structures (molecular vs. conventional). The work provides specific mass ranges and decay characteristics for future experimental searches of heavy-quark symmetry partners, thereby refining the understanding of hadronic molecules and the applicability of heavy quark symmetry in the bottom sector.

Technical Summary: Investigating the Molecular Nature of Λb(6146)\Lambda_b(6146)Λb​(6146) and Λb(6152)\Lambda_b(6152)Λb​(6152)

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Technical Summary: Investigating the Molecular Nature of $\Lambda_b(6146)$ and $\Lambda_b(6152)$