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arXiv · 2211.11555

Toy model to understand oscillatory behavior in timelike nucleon form factors

Ri-Qing Qian·Zhan-Wei Liu·Xu Cao·Xiang Liu
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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.

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Ri-Qing Qian, Zhan-Wei Liu, Xu Cao, Xiang Liu. 2022-11-21. Toy model to understand oscillatory behavior in timelike nucleon form factors. https://doi.org/10.1103/physrevd.107.l091502

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