Three-Body Dynamics Achieves Resonance Reproduction in -Wave Charmed Mesons

Researchers are delving into the enigmatic world of hidden-charm tetraquark states, seeking to understand the forces binding these exotic particles together. Jian-Bo Cheng (China University of Petroleum), Zi-Yang Lin and Jun-Zhang Wang (Peking University) et al. present a systematic investigation into these states, focusing on those composed of – and – mesons, and utilising a sophisticated hadronic molecular picture. This work is significant because it rigorously accounts for the unstable nature of the constituent mesons, employing a novel approach to three-body decay effects which accurately reproduces experimentally observed decay widths. By identifying potential resonance candidates in the and sectors, and providing predictions for open-charm decay modes, this study offers crucial guidance for future experimental searches and promises to deepen our understanding of strongly coupled physics.

Hidden-charm tetraquarks and unstable meson dynamics

Scientists have unveiled a systematic investigation into hidden-charm tetraquark states, focusing on systems composed of S-wave and P-wave charmed mesons. The research team meticulously examined these exotic states within the framework of the hadronic molecular picture, employing the One-Boson Exchange potential to solve the Schrödinger equation in momentum space via the Complex Scaling Method. A key innovation of this work lies in the rigorous treatment of unstable constituents, specifically P-wave charmed mesons, by incorporating three-body decay effects through self-energy corrections and the static limit approximation. These three-body dynamics, the study reveals, play a crucial role in accurately determining the pole positions and, importantly, reproducing the large decay widths observed in experimental data.
The team identified several broad resonances within the D∗D1(2420) and D∗D∗2(2460) systems as potential candidates for the Zc(4430), while resonances in the DD∗0(2300) and DD1(2430) sectors are proposed as candidates for the Zc(4200). As a specific case study, the researchers focused on the assignment of the Zc(4430), performing a detailed analysis of its line shape using a Flatté-like parametrization with energy-dependent self-energy terms. This analysis yielded predictions for the open-charm decay modes of the Zc(4430), offering valuable guidance for future experimental searches and confirming the theoretical framework. The observation of the X(3872) in 2003 initiated a new era in hadron physics, revealing a spectrum of exotic candidates defying the conventional quark model.

Subsequent discoveries of charged charmonium-like states, including the Zc(3900) and Zc(4020), provided compelling evidence for the existence of multiquark states with a minimal content of charmed quarks and light quarks. More recently, the LHCb Collaboration reported the T+cc, a double-charm tetraquark candidate, further enriching the landscape of exotic hadrons. The prevailing theoretical interpretation posits that the Zc(3900) and Zc(4020) are S-wave hadronic molecules, though their precise nature remains under investigation. This study addresses a critical puzzle: the anomalous ratio of branching fractions for the Zc(4430) and related states, which exhibit a strong preference for decaying into ψ(2S)π over J/ψπ, with a ratio of approximately 10.

This behaviour contrasts sharply with the Zc(3900), where J/ψπ is the dominant decay mode, suggesting a distinct internal structure for the higher-mass states. The researchers propose that these states are likely composed of excited P-wave charmed mesons, with the spatial extension due to the P-wave centrifugal barrier facilitating overlap with the ψ(2S) wave function and enhancing the decay width. However, accurately modelling systems involving P-wave constituents necessitates accounting for the significant decay widths of these mesons and the resulting three-body dynamics, a challenge this work directly addresses.

Hidden-charm tetraquarks via complex scaling and decay effects

Scientists undertook a systematic investigation of hidden-charm tetraquark states, focusing on systems composed of an S-wave meson and a P-wave meson. The study employed the One-Boson Exchange potential to solve the Schrödinger equation in momentum space using the Complex Scaling Method, a technique crucial for handling unstable particles. A key innovation within this work was the rigorous treatment of unstable P-wave constituents, incorporating three-body decay effects via self-energy corrections and the static limit approximation, this directly addresses the observed large decay widths in experimental data. Researchers meticulously calculated these corrections to accurately model the behaviour of short-lived particles within the tetraquark system.

The team solved the Schrödinger equation in momentum space, a departure from traditional coordinate-space approaches, enabling a more efficient and accurate description of the system’s dynamics. This method facilitated the precise determination of pole positions, which are essential for understanding the resonance properties of the tetraquark states. Furthermore, the study identified several broad resonances within the D∗D1(2420) and D∗D∗2(2460) systems as potential candidates for the Zc(4430), while resonances in the DD∗0(2300) and DD1(2430) sectors were proposed as candidates for the Zc(4200). To refine the analysis, scientists focused on the D∗D∗2(2460) assignment as a case study, employing a Flatté-like parametrization with energy-dependent self-energy terms to model the line shape of the Zc(4430) candidate.

This parametrization allowed for detailed predictions regarding the open-charm decay modes, providing valuable guidance for future experimental searches. The research meticulously analyzed the Zc(4430) candidate, determining its mass as 4.452 ±0.016+0.055−0.033 GeV and its width as 0.174 ±0.019+0.083−0.020 GeV, values consistent with recent experimental observations. The approach enables a deeper understanding of the internal structure of these exotic hadrons, suggesting a composition of excited P-wave charmed mesons, a hypothesis supported by the observed decay patterns. By incorporating three-body decay effects, the study successfully reproduces the anomalous branching fraction ratio of ψ(2S)π to J/ψπ, a long-standing puzzle in the field, and provides a robust theoretical framework for interpreting the properties of these complex particles.

Three-body decay defines tetraquark properties and composition

Scientists have achieved a detailed investigation into hidden-charm tetraquark states, focusing on systems composed of an S-wave meson and a P-wave meson. The research team solved the Schrödinger equation in momentum space using the Complex Scaling Method, adopting a One-Boson Exchange potential to model interactions between the constituent particles. A crucial aspect of this work was the rigorous treatment of unstable constituents, incorporating three-body decay effects through self-energy corrections and the static limit approximation, essential for accurately modelling the system’s behaviour. Results demonstrate that these three-body dynamics are critical in determining the pole positions and, importantly, in reproducing the large decay widths observed in experimental data.

Experiments revealed several broad resonances within the D∗D1(2420) and D∗D∗2(2460) systems, identifying them as potential candidates for the Zc(4430) tetraquark. Conversely, significantly broader resonances in the DD∗0(2300) and DD1(2430) sectors are proposed as candidates for the Zc(4200) state. The team measured the mass of the Zc(4430) to be 4.452 ±0.016+0.055−0.033 GeV, with a decay width of 0.174 ±0.019+0.083−0.020 GeV, confirming recent experimental observations. These measurements provide crucial parameters for understanding the internal structure of this exotic hadron. Focusing specifically on the D∗D∗2(2460) assignment for the Zc(4430), scientists analysed the candidate’s line shape using a Flatté-like parametrization incorporating energy-dependent self-energy terms.

This detailed analysis yielded predictions for the open-charm decay modes, offering guidance for future experimental searches aimed at confirming the tetraquark’s composition. The study highlights the importance of accounting for the inherent instability of P-wave constituents, as their decay into D(∗)π significantly impacts the overall molecular system. Data shows that the three-body decay effects, arising from static limit corrections and self-energy diagrams, dramatically amplify the widths of the resonances, a finding particularly pronounced in systems involving P-wave mesons. This work provides a systematic study of 1+(1+−) Zc systems, explicitly incorporating these open-charm three-body decay effects and analysing the resulting line shapes.