Toy model to understand the oscillatory behavior in timelike nucleon form factors

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 NN over bar 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 over 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 thorn e- -> nn over bar , ? over bar ?, and ?c over bar ?c can also be understand within this scenario.

Automated summary

In order to understand the oscillatory behavior in the timelike electromagnetic form factors of nucleons, a toy model is proposed based on the Jost function of the NN over bar pair. By using the distorted-wave Born approximation and constructing a simple square-well potential to reflect the final-state interaction of N over bar N, the damped oscillatory phenomenon in the timelike electromagnetic form factors of nucleons is naturally represented. The study also reveals that the period of oscillation is approximately determined by the Yukawa interaction range 1/m pi. Other possible potentials are also discussed.