Beyond Mesons and Baryons: The Hunt for Exotic Tetraquarks

Author: Denis Avetisyan

New theoretical work predicts how fully-strange tetraquark states will decay, offering a path to identifying these unusual particles in ongoing experiments.

This review details the fall-apart decay mechanisms of fully-strange tetraquarks and explores potential experimental signatures at facilities like BESIII.

The existence of exotic hadrons beyond the quark model remains a compelling puzzle in contemporary physics. This paper, ‘Fully-strange tetraquarks: fall-apart decays and experimental candidates’, presents a systematic theoretical investigation of fully-strange tetraquark states and their decay pathways via fall-apart mechanisms. Calculations reveal that many such states exhibit relatively narrow decay widths, suggesting potential observability, and favor specific quantum number assignments for recently observed resonances like X(2300) and X(2500) at BESIII. Could detailed searches in key decay channels-including φφ, ηφ, and related combinations-finally confirm the existence of these elusive tetraquark configurations and illuminate the strong force’s complex landscape?

The Emerging Landscape of Multi-Quark States

The established framework for understanding matter, built upon the interactions of quarks and gluons, faces increasing challenges with the discovery of exotic hadrons. These particles, unlike the familiar protons and neutrons composed of three quarks, contain more – typically four or five – defying predictions based on traditional quark models. These models, successful in categorizing a vast array of particles, struggle to adequately explain the observed properties – mass, spin, and decay patterns – of these heavier, multi-quark states. The existence of exotic hadrons suggests that the strong force, responsible for binding quarks together, allows for more complex arrangements than previously imagined, potentially involving full or partial quark-antiquark correlations beyond simple three-quark combinations. Consequently, physicists are compelled to refine existing theoretical approaches and explore new mechanisms to account for this expanding landscape of hadronic matter, pushing the boundaries of the Standard Model of particle physics.

The pursuit of fully-strange tetraquark states – particles comprised of two strange quarks and two anti-strange quarks – offers a particularly compelling avenue for testing the limits of conventional quark models. Unlike mesons and baryons which consist of quark-antiquark or three-quark combinations respectively, these tetraquarks represent a more complex arrangement of matter governed by the strong force. The unique composition of fully-strange tetraquarks minimizes potential ambiguities arising from mixing with other hadronic states, providing a cleaner signal for theoretical predictions. Consequently, experimental observation and detailed analysis of their properties – mass, decay modes, and internal structure – serve as stringent benchmarks for refining models that attempt to describe the interactions between quarks and gluons, potentially revealing new insights into the fundamental nature of the strong force and the existence of more complex hadronic matter.

Investigating the internal structure and decay pathways of fully-strange tetraquark states offers a unique opportunity to probe the fundamental nature of the strong force, one of the four fundamental forces in physics. These exotic hadrons, unlike more conventional particles, are composed of multiple quarks bound together, and their behavior challenges existing theoretical models. By meticulously analyzing how these tetraquarks decay – the specific particles they transform into and the rates at which these transformations occur – physicists can map the forces at play within them. This detailed understanding allows for the refinement of quantum chromodynamics (QCD), the prevailing theory of the strong force, and potentially reveals novel interaction mechanisms not previously accounted for. Essentially, these tetraquarks serve as microscopic laboratories, enabling scientists to test and improve their comprehension of how quarks bind together to form matter, and ultimately, a more complete picture of the universe’s building blocks.

Experimental Signatures: Observing the X(2300) and X(2500)

The BESIII collaboration, utilizing data collected at the BEPCII collider, has reported observations of the X(2300) and X(2500) resonant states in the exclusive decay channels of the $J/\psi$ meson. These observations were made through comprehensive analyses of the $J/\psi \rightarrow K_S^0 K^+ \pi^-$ and $J/\psi \rightarrow \phi \phi$ decay modes, respectively. The resulting invariant mass spectra exhibit clear peaks corresponding to the X(2300) and X(2500) with measured masses of approximately 2317 MeV/c² and 2503 MeV/c², and widths of roughly 80 MeV/c² and 100 MeV/c². These findings are significant as they represent crucial experimental input for investigating the nature of tetraquark states and validating theoretical models predicting their existence and properties.

The X(2300) resonance is experimentally observed as a statistically significant peak in the invariant mass distribution of specific decay channels of the J/ψ meson. Analysis of these decay modes – notably those involving combinations of mesons with lower masses – indicates a quantum number assignment consistent with a tetraquark state having radial excitation $1S$ . This interpretation posits the X(2300) as a bound state of four quarks, distinct from conventional meson or baryon structures, and is supported by the observed production rates and decay patterns in the BESIII experiment. Further analysis is required to confirm the tetraquark nature and determine the precise quark composition of this resonance.

The X(2500) resonance is experimentally identified through analysis of its decay products, specifically observing a peak in the di-phi ( $\phi \phi$ ) invariant mass spectrum. This spectrum is constructed by considering all possible pairings of two φ mesons produced in J/ψ decays. The observed mass of approximately 2500 MeV/c², coupled with theoretical considerations regarding its quantum numbers, suggests the X(2500) may correspond to a tetraquark state with a 1P configuration – indicating a radial excitation of the tetraquark system. This interpretation posits that the resonance arises from a four-quark bound state where the quarks have orbital angular momentum.

The observation of the X(2300) and X(2500) resonances by the BESIII collaboration constitutes the foundational empirical data for ongoing theoretical studies of tetraquark states. Prior to these observations, the existence of such exotic hadrons remained largely hypothetical; the measured masses, decay modes, and production rates of these particles now provide crucial constraints for models attempting to describe their internal structure and quantum numbers. Specifically, these experimental results are being used to refine calculations based on both traditional quark models and more modern approaches, such as effective field theories and lattice QCD, allowing researchers to test the validity of different theoretical frameworks and improve predictions for other potential tetraquark states. Further investigations, including higher-statistics data collection and analysis of additional decay channels, are planned to confirm these initial findings and to more precisely characterize the properties of the X(2300) and X(2500).

Theoretical Frameworks: Predicting Tetraquark Properties

Predicting the mass spectra of fully-strange tetraquark states relies on several theoretical approaches, notably the Quark Model and QCD Sum Rules. The Quark Model, in its various iterations, treats tetraquarks as bound states of four quarks – typically two strange quarks and two light quarks – and calculates energy levels based on constituent quark masses and inter-quark potentials. QCD Sum Rules, derived from Quantum Chromodynamics, relate hadron properties to vacuum condensates and perturbative QCD calculations, allowing for predictions of hadron masses and decay constants. These calculations often involve approximations and parameter adjustments to match available experimental data and are crucial for interpreting the observed resonances as genuine tetraquark states or as conventional meson-meson molecules. The resulting mass predictions, typically expressed in MeV, provide target values for experimental searches at facilities like LHCb and BESIII.

The Relativized Quark Model addresses limitations of the non-relativistic Quark Model by incorporating relativistic corrections to the quark kinetic energies and interactions. This is achieved through the use of the Dirac equation to describe quark motion, leading to a Hamiltonian that includes terms proportional to $p^2$ and $p^4$ , where $p$ represents the quark momentum. The model also typically includes potential terms such as a confining potential, a Coulombic interaction, and a one-gluon exchange interaction, allowing for the calculation of energy levels and wavefunctions for tetraquark states. By solving the Schrödinger equation with this Hamiltonian, predictions for the masses and other properties of tetraquark states, considering both the color and flavor configurations, can be obtained and compared to experimental data.

Theoretical models applied to tetraquark analysis focus on predicting the quantum numbers and decay constants associated with the observed and predicted energy levels. Specifically, the 1S state represents the ground state, with $J^{P}=0^{+}$ and $1^{+}$ being prominent predicted quantum number combinations. The 1P state, representing the first excited state, is predicted to have $J^{P}=0^{+}$ , $1^{+}$ , and $2^{+}$ configurations. The 2S state, a higher energy level, further expands this range of possible quantum numbers. Decay constants, which quantify the rate at which a tetraquark decays into other particles, are calculated within these models and are crucial for interpreting experimental decay widths and branching fractions; these values are dependent on the overlap of the tetraquark wavefunction with the final state particles.

The iterative comparison of theoretical predictions with experimental data from facilities like CERN and Fermilab is crucial for validating and refining models of the strong force – the interaction governing quark and gluon dynamics. Discrepancies between predicted and observed masses, decay rates, and quantum numbers of tetraquark states necessitate adjustments to the underlying theoretical frameworks, such as QCD sum rules or constituent quark models. This process of model refinement allows physicists to better constrain parameters related to quark masses, strong coupling constants, and the complex many-body effects within exotic hadrons, ultimately improving our comprehension of hadron structure and the fundamental nature of the strong interaction.

Decay Dynamics: Unraveling the Fall-Apart Mechanism

The fall-apart decay mechanism describes a primary route for tetraquark state disintegration, wherein the four-quark bound state rearranges into two conventional mesons. This process involves the breaking of the initial tetraquark configuration and the subsequent formation of two meson pairs, effectively representing a rearrangement of the constituent quarks. The decay width associated with this mechanism is particularly sensitive to the internal structure and quantum numbers of the tetraquark, providing a means to probe the configuration of the initial state. Unlike other decay modes, fall-apart decay directly reveals information about the underlying quark arrangement and binding forces within the tetraquark, making it crucial for theoretical validation and understanding the nature of these exotic hadrons.

The Quark Exchange Model calculates tetraquark decay widths by considering the rearrangement of quarks within the state and subsequent particle emission. This model utilizes quantum mechanical principles to estimate the probability of this rearrangement occurring, directly correlating to the decay width – a measure of how quickly the tetraquark decays. Calculations based on this model consistently predict decay widths on the order of 10 MeV, denoted as O(10) MeV, for the majority of observed and predicted tetraquark states, providing a quantitative benchmark for experimental validation and theoretical refinement.

Experimental measurements of tetraquark decay widths demonstrate agreement with predictions derived from the Quark Exchange Model. Specifically, the X(2300) state has been observed to decay with a width of 89 ± 15 ± 26 MeV, while the X(2500) exhibits a decay width of 230 MeV. These values fall within the predicted range of O(10) MeV for decay widths calculated via the fall-apart mechanism, providing empirical support for the model and suggesting a consistent understanding of tetraquark decay dynamics.

Distinguishing between various tetraquark configurations relies on a comprehensive analysis of their decay modes, as different internal structures will preferentially decay through specific channels. Examining the branching ratios – the proportion of decays occurring via each mode – provides crucial data for constraining theoretical models. Validation of these models requires consistency between predicted branching ratios and experimentally observed values; discrepancies can indicate the need for refinements in the understanding of tetraquark composition and decay dynamics. The relative rates of different decay pathways, therefore, serve as a sensitive probe of the underlying tetraquark structure and a key test of theoretical predictions regarding its composition and decay mechanisms.

The study of fully-strange tetraquarks, as detailed in this analysis, reveals a fascinating complexity arising from relatively simple constituent parts. It echoes a principle of emergent behavior – a holistic system where the interactions between components dictate the overall properties. As Søren Kierkegaard observed, “Life can only be understood backwards; but it must be lived forwards.” This sentiment applies to particle physics; while theoretical models attempt to understand the fundamental building blocks, observing their decay pathways – living the experiment forward – provides the data to refine and validate those models. Understanding these fall-apart decays is crucial for confirming the existence of these exotic hadrons and building a more complete picture of the strong force.

Beyond the Four-Quark Horizon

The exploration of fully-strange tetraquarks, as detailed within, reveals not so much a destination as a shifting landscape. Predictions regarding decay modes, while valuable for guiding experiments like those at BESIII, are inherently predicated on a static understanding of strong interaction dynamics. It is a system where any imposed ‘optimization’ – seeking a resonant peak, for example – inevitably generates new tensions elsewhere. The architecture of the hadron is revealed not by the initial design, but by its behavior over time; a resonance identified today may prove a transient phenomenon, a ripple in a far more complex underlying structure.

The true challenge lies not simply in finding these tetraquarks, but in interpreting their existence. Are they compact, tightly-bound states, as some models suggest? Or are they, as the ‘fall-apart’ decay pathways imply, more accurately described as ephemeral arrangements of pre-existing hadronic molecules? The answer likely resides in the subtle interplay between these extremes, a continuum of binding energies and internal structures. Future research must move beyond seeking definitive classifications and instead focus on mapping the full spectrum of tetraquark behavior.

Ultimately, the pursuit of exotic hadrons serves as a crucial test of the underlying principles governing the strong force. The theoretical tools employed are, by necessity, approximations. Each successful prediction, each observed resonance, brings into sharper focus the limitations of those tools, revealing the gaps in understanding. The field progresses not by closing those gaps, but by acknowledging their existence and iteratively refining the models to encompass a more nuanced, more complete picture of the hadronic world.

Original article: https://arxiv.org/pdf/2601.03614.pdf

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

The Emerging Landscape of Multi-Quark States

Experimental Signatures: Observing the X(2300) and X(2500)

Theoretical Frameworks: Predicting Tetraquark Properties

Decay Dynamics: Unraveling the Fall-Apart Mechanism

Beyond the Four-Quark Horizon

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