An innovative model for coupled fermion-antifermion pairs

Abdullah Guvendi; Omar Mustafa

doi:10.1140/epjc/s10052-024-13192-9

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 866
https://doi.org/10.1140/epjc/s10052-024-13192-9

Regular Article – Theoretical Physics

An innovative model for coupled fermion-antifermion pairs

Abdullah Guvendi¹ and Omar Mustafa²^b

¹ Department of Basic Sciences, Erzurum Technical University, 25050, Erzurum, Türkiye
² Department of Physics, Eastern Mediterranean University, G. Magusa, North Cyprus, Mersin 10, Türkiye

^b omar.mustafa@emu.edu.tr

Received: 29 May 2024
Accepted: 31 July 2024
Published online: 29 August 2024

Abstract

Understanding the behavior of fermion-antifermion ( $f \bar{f}$ $f\overline{f}$ ) 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 $f \bar{f}$ $f\overline{f}$ pairs with an effective position-dependent mass (i.e., $m \to m + S (r)$ $m \rightarrow m + \mathcal {S}(r)$ ) under the influence of an external magnetic field. To validate our model, we show that by modifying the mass with a Coulomb-like potential, $m (r) = m - α / r$ $m(r) = m - \alpha /r$ , where $- α / r$ $-\alpha /r$ is the Lorentz scalar potential $S (r)$ $\mathcal {S}(r)$ , our results match the well-established energy eigenvalues for $f \bar{f}$ $f\overline{f}$ pairs interacting through the Coulomb potential, without approximation. By applying adjustments based on the Cornell potential (i.e., $S (r) = k r - α / r$ $\mathcal {S}(r) = kr - \alpha /r$ ), we derive a closed-form energy expression. We believe this unique model offers significant insights into the dynamics of $f \bar{f}$ $f\overline{f}$ pairs under various interaction potentials, with potential applications in particle physics. Additionally, it could be extended to various $f \bar{f}$ $f\overline{f}$ systems, such as positronium, relativistic Landau levels for neutral mesons, excitons in monolayer transition metal dichalcogenides, and Weyl pairs in monolayer graphene sheets.

© The Author(s) 2024

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