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.

arXiv comment7 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

References in corpus (31)

• Observation of a near-threshold enhancement in the e+e- -->Lambda_c+Lambda_c- cross section using initial-state radiation
• Final Analysis of Proton Form Factor Ratio Data at ${\mathbf{Q}}^2=4.0$, 4.8 and 5.6 GeV${}^2$
• Study of e+e- --> p anti-p via initial-state radiation at BABAR
• Study of e+e- --> Lambda anti-Lambda, Lambda anti-Sigma0, Sigma0 anti-Sigma0 using Initial State Radiation with BABAR
• Measurement of proton electromagnetic form factors in $e^{+}{e}^{-}\to p\bar{p}$ in the energy region 2.00-3.08 GeV
• Precision measurement of the $e^{+}{e}^{-}\to {\Lambda }_c^{+}{\bar{\Lambda }}_c^{-}$ cross section near threshold
• New Features in the Electromagnetic Structure of the Neutron
• Polarization Transfer Observables in Elastic Electron Proton Scattering at $Q^2=$2.5, 5.2, 6.8, and 8.5 GeV${}^2$
• New insights into the nucleon's electromagnetic structure
• The electromagnetic form factors of the proton in the timelike region
• Observation of a cross-section enhancement near mass threshold in $e^{+}{e}^{-}\to \Lambda \bar{\Lambda }$
• Nucleon Electromagnetic Form Factors in the Timelike Region
• Measurement of the e+e- --> p anti-p cross section in the energy range from 3.0 to 6.5 GeV
• Periodic interference structures in the time-like proton form factor
• Measurements of Sigma+ and Sigma- Time-like Electromagnetic Form Factors for center-of-mass energies from 2.3864 to 3.0200 GeV
• The electromagnetic form factors of $\Lambda$ hyperon in the vector meson dominance model
• On the electromagnetic form factors of hadrons in the time-like region near threshold
• Hyperon electromagnetic form factors in the timelike region
• New structures in the proton-antiproton system
• Measurement of cross-section for $e^{+}{e}^{-}\to {\Xi }^{-}{\bar{\Xi }}^{+}$ near threshold at BESIII
• Measurement of cross section for $e^{+}{e}^{-}\to {\Xi }^0{\bar{\Xi }}^0$ near threshold
• Phenomenological analysis of near threshold periodic modulations of the proton timelike form factor
• On relativization of the Sommerfeld-Gamow-Sakharov factor
• Re-examining the $X(4630)$ resonance in the reaction $e^{+}{e}^{-}\to {\Lambda }_c^{+}{\bar{\Lambda }}_c^{-}$
• Origin of the structures observed in $e^{+}{e}^{-}$ annihilation into multipion states around the $\bar{p}p$ threshold
• Vector mesons and electromagnetic form factor of the $\Lambda$ hyperon
• Electromagnetic form factors of $\Lambda$ hyperon in the vector meson dominance model and a possible explanation of the near-threshold enhancement of the $e^{+}{e}^{-}\to \Lambda \bar{\Lambda }$ reaction
• Timelike nucleon electromagnetic form factors: All about interference of isospin amplitudes
• $N\bar{N}$ production in $e^{+}{e}^{-}$ annihilation near the threshold revisited
• Isoscalar amplitude dominance in $e^{+}e-$ annihilation to $N\bar{N}$ pair close to the threshold
• Electromagnetic form factors of neutron and neutral stange hyperons in the oscillating view of point

Cited by in corpus (8)

• New insights into the oscillation of the nucleon electromagnetic form factors
• $e^{+}{e}^{-}\to {\Lambda }_c^{+}{\bar{\Lambda }}_c^{-}$ cross sections and the ${\Lambda }_c^{+}$ electromagnetic form factors within the extended vector meson dominance model
• 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 $e^{\pm }\gamma \to e^{\pm }B\bar{B}$