An innovative model for coupled fermion-antifermion pairs

Abstract

Abstract Understanding the behavior of fermion-antifermion ( $$f\overline{f}$$ 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 $$f\overline{f}$$ f f ¯ pairs with an effective position-dependent mass (i.e., $$m \rightarrow m + \mathcal {S}(r)$$ 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, $$m(r) = m - \alpha /r$$ m ( r ) = m - α / r , where $$-\alpha /r$$ - α / r is the Lorentz scalar potential $$\mathcal {S}(r)$$ S ( r ) , our results match the well-established energy eigenvalues for $$f\overline{f}$$ f f ¯ pairs interacting through the Coulomb potential, without approximation. By applying adjustments based on the Cornell potential (i.e., $$\mathcal {S}(r) = kr - \alpha /r$$ 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 $$f\overline{f}$$ f f ¯ pairs under various interaction potentials, with potential applications in particle physics. Additionally, it could be extended to various $$f\overline{f}$$ 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.