Minimally coupled fermion-antifermion pairs via exponentially decaying potential

TL;DR

This paper investigates the interaction and stability of fermion-antifermion pairs under an exponentially decaying potential using a covariant two-body Dirac framework, revealing their inherent instability and decay characteristics.

Contribution

It introduces a covariant two-body Dirac equation approach to analyze fermion-antifermion pairs with an exponential potential, deriving analytical solutions and quantization conditions.

Findings

Fermion-antifermion pairs are unstable and decay over time.

Decay time depends on the fermions' Compton wavelength.

Analytical solutions for the pair dynamics are obtained.

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.