Hunting for Hidden Hadrons: A Search for Exotic Decay Paths

Author: Denis Avetisyan

New data from the BESIII experiment probes the decay of a mysterious particle, seeking evidence for its composition and furthering our understanding of exotic hadronic states.

The distributions of <span class="katex-eq" data-katex-display="false">M(\pi^{+}\pi^{-}J/\psi)</span> and <span class="katex-eq" data-katex-display="false">M(\eta_{h}\psi(2S))</span> at center-of-mass energies of 4.92 and 4.95 GeV reveal distinct signal regions for <span class="katex-eq" data-katex-display="false">\psi(2S)</span> and <span class="katex-eq" data-katex-display="false">\psi_{0}(4360)</span>, as demonstrated through a comparison of data-represented by black dots with error bars-with inclusive and signal Monte Carlo simulations of <span class="katex-eq" data-katex-display="false">e^{+}e^{-}\rightarrow\eta\psi_{0}(4360)</span>. — The distributions of $M(\pi^{+}\pi^{-}J/\psi)$ and $M(\eta_{h}\psi(2S))$ at center-of-mass energies of 4.92 and 4.95 GeV reveal distinct signal regions for $\psi(2S)$ and $\psi_{0}(4360)$ , as demonstrated through a comparison of data-represented by black dots with error bars-with inclusive and signal Monte Carlo simulations of $e^{+}e^{-}\rightarrow\eta\psi_{0}(4360)$ .

This paper reports a search for the ηψ₀(4360) → ηψ(2S) decay via the e⁺e⁻ → ηηψ(2S) process and sets upper limits on its production cross section.

The established framework of quarkonium spectroscopy continues to be challenged by observations of unexpected resonances, prompting ongoing investigation into the nature of exotic hadrons. This paper, ‘Search for $ψ_0(4360)\rightarrow ηψ(2S)$ through the process $e^+e^- \rightarrow ηηψ(2S)$’, reports a search for the $ψ_0(4360)$ resonance decaying into $ηψ(2S)$ using data collected with the BESIII detector. No significant signal for the $ψ_0(4360)$ was observed, and upper limits on the production cross section were determined at several center-of-mass energies. Do these results suggest a non-conventional decay mechanism or a need to refine theoretical models of these enigmatic particles?

Unveiling the Exotic: A New Landscape in Hadron Physics

The established understanding of matter’s building blocks, specifically hadrons – particles like protons and neutrons – rests upon the quark model, which categorizes them as combinations of three quarks or a quark-antiquark pair. However, the recent discovery of XYZ particles presents a significant challenge to this framework. These particles, observed as short-lived resonances in high-energy collisions, possess masses and decay patterns that cannot be adequately explained by conventional quark configurations. The existence of XYZ particles suggests a more complex internal structure, potentially involving arrangements like tetraquarks – four quarks bound together – or hybrid mesons, where quarks are connected by gluons in a manner beyond simple combinations. This finding necessitates a re-evaluation of the strong force, which governs interactions within hadrons, and prompts the development of new theoretical models capable of accommodating these unexpectedly massive and intricately structured particles, ultimately broadening the landscape of known matter.

The emergence of XYZ particles necessitates a fundamental re-evaluation of hadron structure, as these resonances defy explanation within the established quark model. Traditional classifications rely on mesons – quark-antiquark pairs – and baryons – triplets of quarks – but XYZ particles exhibit properties inconsistent with these configurations. This discrepancy suggests the existence of more complex internal structures, potentially involving tightly bound tetraquarks – four-quark combinations – pentaquarks – five-quark arrangements – or even molecules of conventional hadrons. Consequently, physicists are developing innovative theoretical frameworks, such as constituent quark models incorporating hidden color confinement and effective field theories designed to describe multi-quark interactions, to accommodate these exotic states and accurately predict their behavior. The pursuit of understanding XYZ particles is therefore driving advancements in quantum chromodynamics and challenging long-held assumptions about the strong nuclear force.

The groundwork for uncovering exotic hadrons was subtly laid by experiments at the BaBar and Belle facilities. These studies, initially focused on precision measurements of known particles and decay processes, began to reveal slight, yet persistent, deviations from theoretical predictions. Signals exceeding expected mass ranges appeared as fleeting resonances within the copious data, hinting at structures beyond the standard quark model. Though not immediately recognized as a new class of particles, these anomalies prompted a systematic re-examination of existing data and spurred dedicated experiments designed to confirm and characterize these unexpected signals. This initial period of discovery wasn’t characterized by a single, definitive finding, but rather by the accumulation of intriguing hints that collectively demanded a deeper investigation into the fundamental building blocks of matter and the forces that govern their interactions.

The exploration of XYZ particles necessitates a tightly integrated approach, where experimental observations are meticulously coupled with advanced theoretical modeling and rigorous data analysis. Simply detecting these unusual resonances is insufficient; physicists must develop and refine theoretical frameworks-often extending beyond the Standard Model-to interpret the particles’ properties and decay patterns. This involves complex calculations, often utilizing $QCD$ and related techniques, to predict expected signals and differentiate them from background noise. Robust data analysis then plays a crucial role in extracting meaningful information from vast datasets, validating theoretical predictions, and ultimately, unveiling the underlying structure of these exotic hadrons – a process demanding both computational power and innovative statistical methods to confirm their existence and characteristics.

Mapping the Internal Structure: Theoretical Models for Exotic Hadrons

Following the observation of XYZ particles – a class of hadrons not fitting the quark-antiquark meson or three-quark baryon models – several theoretical frameworks were proposed to account for their existence. These models include the ‘hadronic molecule’ picture, suggesting bound states of conventional mesons and baryons; the ‘compact tetraquark’ model, which posits that these particles are tetraquarks-bound states of four quarks; and the ‘hybrid meson’ interpretation, wherein the particle consists of a quark-antiquark pair plus a gluon. Each model differs in its predicted internal structure and dynamics, requiring specific quark configurations and interaction mechanisms to explain the observed particle properties such as mass, spin, and decay modes. Further experimental investigation is needed to differentiate between these competing explanations and definitively determine the underlying structure of XYZ particles.

The hadronic molecule model explains XYZ particles as weakly bound states of two conventional hadrons – a meson and a baryon, or two mesons – interacting through residual strong force interactions. This picture avoids the need to postulate entirely new quark configurations; instead, it relies on known hadronic constituents and their established interactions. Binding energies are expected to be relatively small, on the order of a few MeV, due to the weak coupling between the constituent hadrons. The observed properties of XYZ particles, such as their decay patterns, are then interpreted as arising from the combined dynamics of these pre-existing hadronic components, offering a comparatively straightforward explanation for their existence and characteristics.

The compact tetraquark model proposes that certain exotic hadrons, specifically XYZ particles, are not composed of quark-antiquark pairs or conventional hadron combinations, but instead consist of four valence quarks – two quarks and two antiquarks – tightly bound together. This configuration differs from mesons and baryons, which contain two or three valence quarks, respectively. The strong force interactions between these four quarks necessitate a complex quantum mechanical treatment to predict the particle’s properties, including its mass, spin, and decay modes. Unlike the hadronic molecule picture, which relies on a separable structure, the compact tetraquark assumes a fully combined and interacting four-quark system, resulting in a distinct internal structure and differing observable characteristics.

Hybrid mesons represent a distinct configuration for XYZ particles, differing from tetraquarks and hadronic molecules through the inclusion of a gluon in addition to a quark-antiquark pair. This gluon introduces a more complex internal dynamical structure, as it mediates the interaction between the quarks and contributes to the meson’s overall quantum numbers. Unlike conventional mesons composed solely of a quark-antiquark system, the gluon’s presence necessitates consideration of its excitation modes and its contribution to the observed decay patterns. Theoretical calculations suggest that the gluon can exist in various excited states, leading to a spectrum of hybrid meson candidates with differing masses and decay characteristics, and distinguishing them from states formed by simpler quark configurations.

Probing Resonances: Experimental Insights from BESIII

The BESIII Collaboration investigated the $e^+e^- \rightarrow \pi^+\pi^-J/\psi$ reaction to identify potential resonance structures, specifically targeting the Y(4230) and Y(4360). This analysis utilized data collected with the BESIII detector at the BEPCII collider. The chosen reaction channel provides a sensitive probe for these resonances due to the expected decay modes and production mechanisms. By meticulously reconstructing the $\pi^+\pi^-J/\psi$ final state, the collaboration aimed to observe enhancements in the cross-section corresponding to the mass of these hypothesized particles, thus confirming their existence and characterizing their properties. The search involved detailed control of background processes and systematic uncertainties to ensure the reliability of any observed signals.

The extraction of resonance signals from the $e^+e^- \rightarrow \pi^+ \pi^- J/\psi$ data required specialized analytical techniques. The Partial Reconstruction Method was utilized to identify events where only one of the two pions was fully detected, allowing for a larger sample size despite incomplete information. To maximize the sensitivity of the analysis, optimization was performed using the Punzi Figure of Merit, a statistical measure that balances the number of signal events observed with the associated background contamination; this approach effectively minimizes uncertainties in signal yields and improves the precision of resonance parameter measurements. These techniques were essential for discerning subtle signals from the complex background environment present in the data.

Monte Carlo simulations were central to the BESIII analysis, specifically utilizing GEANT4 for detailed modeling of particle interactions within the detector and reconstruction of particle trajectories. KKMC was employed to generate simulated events for the e⁺e^– → π⁺π^–J/ψ process, including the production of background events, while EVTGEN handled the decays of resonance states and other particles. These simulations were crucial for understanding and correcting for detector effects, such as acceptance and efficiency, and for accurately estimating the background contribution to the observed signal, ultimately enabling precise measurements of resonance properties and the establishment of upper limits on specific cross-sections.

The analysis employed the PHOTOS package to model final state radiation, increasing the precision of resonance parameter measurements. A luminosity measurement with 0.6% uncertainty was achieved, which is essential for calculating accurate cross-sections. Consequently, the BESIII collaboration established 90% confidence level upper limits on the cross-sections for $σ(e+e-\toηηψ(2S))$ at 4.84 GeV and $σ(e+e-\toηψ0(4360))\cdotB(ψ0(4360)\toηψ(2S))$ at 4.92 and 4.95 GeV, demonstrating the analysis’s capacity to probe rare decay modes and constrain theoretical models.

Combined distributions of <span class="katex-eq" data-katex-display="false">M(\eta\_{2})</span> and <span class="katex-eq" data-katex-display="false">M(\pi^{+}\pi^{-}J/\psi)</span> from all center-of-mass energies show agreement between real data (black dots), inclusive Monte Carlo simulations (green dashed histograms), and signal Monte Carlo simulations (red histograms) for <span class="katex-eq" data-katex-display="false">e^{+}e^{-}\rightarrow\eta\eta\psi(2S)</span>, with signal regions indicated by blue vertical lines. — Combined distributions of $M(\eta\_{2})$ and $M(\pi^{+}\pi^{-}J/\psi)$ from all center-of-mass energies show agreement between real data (black dots), inclusive Monte Carlo simulations (green dashed histograms), and signal Monte Carlo simulations (red histograms) for $e^{+}e^{-}\rightarrow\eta\eta\psi(2S)$ , with signal regions indicated by blue vertical lines.

Beyond the Quark Model: Implications for Hadron Structure

Recent experimental evidence increasingly supports a “molecular picture” of certain hadronic resonances, challenging the traditionally simple quark models. Specifically, observations suggest that states like ψ(4230), ψ(4360), and ψ(4415) aren’t simply individual quarks bound together, but rather compact structures formed by the association of vector mesons and charm quarks. These resonances appear to be composed of pairs such as $D^* \overline{D}$ , $D_1 \overline{D}$ , $D_{12}(2420) \overline{D}$ , and $D_2 \overline{D}$ , functioning almost as molecules held together by the strong force. This implies a more complex internal structure than previously assumed, where heavier hadrons can exhibit bound states of other hadrons, significantly broadening the understanding of how matter assembles under the principles of quantum chromodynamics and prompting further investigation into the diverse configurations possible within the Standard Model.

The recent detection of tetraquark candidates, most notably Tcc4020 and Tcc13900, significantly complicates the established picture of hadron structure. These states, composed of four quarks rather than the conventional three, demonstrate that baryons and mesons are not the only types of particles formed by the strong force. The existence of Tcc4020 and Tcc13900, along with theoretical predictions for other exotic hadrons, suggests a far richer spectrum of possible quark configurations than previously imagined. Researchers are now actively investigating whether these tetraquarks represent compact, tightly bound structures, or looser, more molecular-like arrangements of diquarks and antidiquarks. This ongoing work is not only expanding the catalog of known particles but also challenging the fundamental assumptions of quantum chromodynamics and demanding refinements to existing theoretical models of hadron formation.

The elusive $\Psi_0(4360)$ remains a focal point for high-energy physics research due to its predicted quantum numbers, which deviate significantly from conventional meson expectations. Theoretical models suggest this state isn’t a simple quark-antiquark pairing, but potentially a tetraquark or even a more exotic configuration involving tightly bound quarks and gluons. Its continued absence from definitive experimental observation challenges current understandings of hadron structure and necessitates refined search strategies. Researchers are actively pursuing this particle through analyses of proton-proton collision data, hoping to uncover its decay signatures and confirm its existence – a discovery that could reshape the landscape of quantum chromodynamics and reveal previously unknown forces governing the strong interaction.

Recent discoveries in hadron spectroscopy are fundamentally reshaping the established understanding of particle composition. For decades, the quark model-positing that hadrons are built from combinations of just a few types of quarks-provided a successful, if incomplete, framework. However, the consistent observation of exotic hadrons-tetraquarks and pentaquarks-and resonant states that don’t fit neatly into traditional configurations, demonstrates the model’s limitations. These findings necessitate a move beyond simple quark-antiquark or three-quark pictures, compelling physicists to explore more complex arrangements governed by the strong force, as described by quantum chromodynamics (QCD). This shift isn’t merely an addition to existing knowledge; it’s a catalyst for renewed theoretical investigation and experimental searches, driving the development of more sophisticated QCD-based calculations and prompting the design of experiments specifically tailored to probe the internal structure of these unusual particles and reveal the full richness of hadron physics.

The search for the ηψ₀(4360) necessitates a meticulous examination of decay patterns, mirroring the investigative spirit of discerning underlying structures. Each observed interaction, or lack thereof, contributes to a growing map of hadronic states. As John Locke observed, “All mankind… being all equal and independent, no one ought to harm another in his life, health, liberty, or possessions.” Though seemingly disparate, this principle resonates with the scientific pursuit; just as individuals possess inherent rights, so too do fundamental particles adhere to defined physical laws. Establishing upper limits on the production cross section, as detailed in this study, defines the boundaries of what is possible, and clarifies the parameters within which further investigation must occur. The absence of a significant signal, while not a discovery, is itself a vital piece of data, rigorously defining the constraints of potential models.

Where Do We Go From Here?

The absence of a clear signal for $ψ_0(4360)\rightarrow ηψ(2S)$ is, predictably, not a null result. It is, rather, a sharpening of the question. The established framework for understanding hadronic interactions continues to be tested, and each non-detection reveals the subtle ways in which reality resists simple categorization. The current upper limits on the cross section, while not definitive, constrain theoretical models and direct future searches toward less conventional decay modes or production mechanisms.

The persistent search for exotic hadrons-molecules, tetraquarks, glueballs-relies on a willingness to embrace the unexpected. Every deviation from predicted behavior, every outlier in the data, represents not an error to be corrected, but an opportunity to uncover hidden dependencies. It is increasingly clear that the “standard” picture of quark-antiquark confinement may be incomplete, and that the strong force allows for structures far more complex than initially imagined.

Continued exploration, particularly with experiments capable of higher luminosity and improved particle identification, will be crucial. The focus should expand beyond seeking confirmation of existing models and toward designing experiments specifically aimed at disproving them. Only through rigorous, skeptical inquiry-and a genuine appreciation for the beauty of the anomalous-can the underlying architecture of hadronic matter be revealed.

Original article: https://arxiv.org/pdf/2601.21190.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

Unveiling the Exotic: A New Landscape in Hadron Physics

Mapping the Internal Structure: Theoretical Models for Exotic Hadrons

Probing Resonances: Experimental Insights from BESIII

Beyond the Quark Model: Implications for Hadron Structure

Where Do We Go From Here?

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