An innovative model for coupled fermion-antifermion pairs

• Published in: The European physical journal. C, Particles and fields Particles and fields, 2024-08, Vol.84 (8), p.866-11, Article 866
• Main Authors: Guvendi, Abdullah, Mustafa, Omar
• Format: Article
• Language: English
• Subjects: Astronomy; Astrophysics and Cosmology; Coulomb potential; Dirac equation; Eigenvalues; Elementary Particles; Excitons; Fermions; Graphene; Hadrons; Heavy Ions; Measurement Science and Instrumentation; Mesons; Metal sheets; Monolayers; Nuclear Energy; Nuclear Physics; Particle physics; Physics; Physics and Astronomy; Positronium; Quantum Field Theories; Quantum Field Theory; Regular Article – Theoretical Physics; Solid state physics; String Theory; Transition metal compounds
• ISSN: 1434-6052; 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-024-13192-9

Understanding the behavior of fermion-antifermion ( f f ¯ ) pairs is crucial in modern physics. These systems, governed by fundamental forces, exhibit complex interactions essential for particle physics, high-energy physics, nuclear physics, and solid-state physics. This study introduces a novel theoretical model using the many-body Dirac equation for f f ¯ pairs with an effective position-dependent mass (i.e., m → m + S ( r ) ) under the influence of an external magnetic field. To validate our model, we show that by modifying the mass with a Coulomb-like potential, m ( r ) = m - α / r , where - α / r is the Lorentz scalar potential S ( r ) , our results match the well-established energy eigenvalues for f f ¯ pairs interacting through the Coulomb potential, without approximation. By applying adjustments based on the Cornell potential (i.e., S ( r ) = k r - α / r ), we derive a closed-form energy expression. We believe this unique model offers significant insights into the dynamics of f f ¯ pairs under various interaction potentials, with potential applications in particle physics. Additionally, it could be extended to various f f ¯ systems, such as positronium, relativistic Landau levels for neutral mesons, excitons in monolayer transition metal dichalcogenides, and Weyl pairs in monolayer graphene sheets.