Minimally coupled fermion–antifermion pairs via exponentially decaying potential

Abstract In this study, we explore how a fermion–antifermion ( $$f\overline{f}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mover> <mml:mi>f</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> ) 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 $$f\overline{f}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mover> <mml:mi>f</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> systems are unstable and decay over time, with the decay time depending on the Compton wavelength of the fermions.