Minimally coupled fermion-antifermion pairs via exponentially decaying potential

• URL: http://arxiv.org/abs/2408.02681v1
• Date: Wed, 31 Jul 2024 13:47:16 GMT
• Title: Minimally coupled fermion-antifermion pairs via exponentially decaying potential
• Authors: Abdullah Guvendi, Semra Gurtas Dogan, Omar Mustafa,
• Abstract summary: We study how a fermion-antifermion ($foverlinef$) pair interacts via an exponentially decaying potential. We find that such interacting $foverlinef$ systems are unstable and decay over time, with the decay time depending on the Compton wavelength of the fermions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this study, we explore how a fermion-antifermion ($f\overline{f}$) 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 $f\overline{f}$ systems are unstable and decay over time, with the decay time depending on the Compton wavelength of the fermions.

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