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.

Comments: 7 pages, 3 figures. We provide supplemental materials to show that the new data from the BESIII collaboration (arXiv:2303.07629) are consistent with our earlier description