Minimally coupled fermion–antifermion pairs via exponentially decaying potential

Abdullah Guvendi; Semra Gurtas Dogan; Omar Mustafa

doi:10.1140/epjc/s10052-024-13181-y

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 801
https://doi.org/10.1140/epjc/s10052-024-13181-y

Regular Article – Theoretical Physics

Minimally coupled fermion–antifermion pairs via exponentially decaying potential

Abdullah Guvendi¹, Semra Gurtas Dogan²^b and Omar Mustafa³

¹ Department of Basic Sciences, Erzurum Technical University, 25050, Erzurum, Turkey
² Department of Medical Imaging Techniques, Hakkari University, 30000, Hakkari, Turkey
³ Department of Physics, Eastern Mediterranean University, G. Magusa, 99628, North Cyprus, Mersin 10, Turkey

^b semragurtasdogan@hakkari.edu.tr

Received: 11 May 2024
Accepted: 31 July 2024
Published online: 12 August 2024

Abstract

In this study, we explore how a fermion–antifermion ( $f \bar{f}$ $f\overline{f}$ ) pair interacts via an exponentially decaying potential. Using a covariant one-time two-body Dirac equation, we examine their relative motion in a three-dimensional flat background. Our approach leads to coupled equations governing their behavior, resulting in a general second-order wave equation. Through this, we derive analytical solutions by establishing quantization conditions for pair formation, providing insights into their dynamics. Notably, we find that such interacting $f \bar{f}$ $f\overline{f}$ systems are unstable and decay over time, with the decay time depending on the Compton wavelength of the fermions.

© The Author(s) 2024

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