Solving Schrödinger Equation Reveals Bound States and Resonances at 9 MeV and 1400 MeV

The interactions between subatomic particles reveal fundamental aspects of matter, and recent work explores the complex relationship between kaons and their antimatter counterparts. Bao-Xi Sun, Qin-Qin Cao, and Ying-Tai Sun, from Beijing University of Technology and North China University of Technology, investigate these interactions by solving the Schrödinger equation, a cornerstone of quantum mechanics. Their calculations predict not only one previously known bound state, but also a new one, lying just below the threshold for particle formation. Furthermore, the team identifies two resonance states near 1400 MeV, suggesting a connection to a particle listed in the Particle Data Group’s review, and demonstrates that this approach successfully predicts the properties of other related particles, confirming the spin and parity of these states. This research advances our understanding of hadron physics and provides a theoretical framework for interpreting experimental observations of these elusive particles.

New Bound States in Kaon and D Meson

Scientists have achieved a detailed understanding of interactions between kaons and anti-kaons, and subsequently, D mesons and anti-mesons, by solving the Schrödinger equation with a simplified approximation. This work reveals the existence of previously unconfirmed bound states and resonance states within these particle systems. The team meticulously modeled the interactions using a one-pion exchange potential, allowing them to predict the properties of these exotic states. Experiments based on this theoretical framework predict a second bound state of K̄K* in addition to the well-established particle f1(1285), with a binding energy approximately 9 MeV below the K̄K* threshold.

This newly predicted state, labeled f1(1378), shares the same spin and parity as f1(1285) and has not yet been observed in experimental data, presenting a clear target for future research. Calculations show that the binding energy of f1(1285) is 105 MeV, determined by a specific order of the mathematical function used in the model. These resonance states are distinguished by different coupling constants, calculated from the binding energies of 1425 −i41 MeV and 1428.

4+1. 5 −1. 3 MeV, respectively. Extending this approach to the D̄D* system, scientists predict similar behavior, assuming the particle χc1(3872) represents a bound state of D⁰ ̄D⁰ or ̄D⁰D⁰. This work provides a theoretical foundation for understanding the complex interactions within these particle systems and offers specific predictions for future experimental verification.

Kaon and D Meson States Predicted

By solving the Schrödinger equation with a simplified model of particle interactions, researchers have identified predicted states of matter involving kaons and anti-kaons, as well as their heavier counterparts involving D mesons. The study successfully predicts both bound states and resonance states, mirroring observations documented in the Particle Data Group, and specifically identifies solutions corresponding to the particles f1(1285) and f1(1420). The method involves approximating the interaction between particles as an exchange of pions, allowing for analytical solutions to the Schrödinger equation in certain conditions. This approach successfully models a deep bound state, with a binding energy of approximately 105 MeV, and a resonance state occurring around 1400 MeV.

The researchers acknowledge that the model relies on approximations, notably the simplification of the interaction potential and the restriction to S-wave interactions. Future work could extend the model to include more complex interactions and explore other particle combinations, potentially refining the understanding of exotic hadron states. The team suggests that this method provides a valuable framework for investigating the properties of these particles and could contribute to a more complete picture of strong force interactions within the Standard Model of particle physics.

Resonance and Bound State Analyses of Meson Interactions

The K̄K* and D̄D* systems are studied by solving the Schrödinger equation under specific boundary conditions, assuming a one-pion-exchange potential. This approach yields resonance states, which are interpreted as corresponding to particles documented in the Particle Data Group review, suggesting an intrinsic relation between bound and resonance states. By fitting the coupling constant with the binding energy of the bound state, resonance states are obtained as solutions of the Schrödinger equation when the boundary conditions are taken into account. The particle χc1(3872) is assumed to be a bound state of D⁰D̄⁰ or D̄⁰D̄⁰, allowing determination of the coupling constant. The analysis of the K̄K* and D̄D* systems yields resonance states corresponding to known particles, including Tc̄c1(3900), Tc̄c(4020), χc1(4274), χc1(4685), and X(3940).