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.

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

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• Understanding oscillating features of the timelike nucleon electromagnetic form factors within the extending vector meson dominance model
• Higher strangeonium decays into light flavor baryon pairs like $\Lambda \bar{\Lambda }$, $\Sigma \bar{\Sigma }$, and $\Xi \bar{\Xi }$
• The electromagnetic form factors and spin polarization of ${\Lambda }_c^{+}$ in the process $e^{+}{e}^{-}\to {\Lambda }_c^{+}{\bar{\Lambda }}_c^{-}$
• Observation of Transverse Polarization and Determination of Psionic Form Factors of the $\Lambda$ Hyperon at $\sqrt{s}=3.773$ GeV
• Baryon Form Factors
• Accessing baryon-antibaryon generalized distribution amplitudes in $e^{\pm }\gamma \to e^{\pm }B\bar{B}$