Toy model to understand oscillatory behavior in timelike nucleon form factors

Abstract: To understand the oscillatory behavior exhibited in the timelike electromagnetic form factors of nucleons, we propose a toy model based on the Jost function of the $N\bar N$ pair into the timelike form factors with the help of the distorted-wave Born approximation. By constructing a simple square-well potential reflecting the final-state interaction of $N\bar N$, we naturally represent the damped oscillatory phenomenon in the timelike electromagnetic form factors of nucleons. Especially, our study reveals that the ``period" of the oscillation is approximately determined by the Yukawa interaction range $1/m_\pi$. Other possible potentials are also discussed. The threshold enhancements of the cross sections for $e^+e^-\to n\bar n$, $\Lambda\bar\Lambda$, and $\Lambda_c\bar\Lambda_c$ can also be understand within this scenario.