New insights into the oscillations of the nucleon electromagnetic form factors.

The electromagnetic form factors of the proton and the neutron in the timelike region are investigated. Electron-positron annihilation into antinucleon-nucleon (N¯N) pairs is treated in distorted wave Born approximation, including the final-state interaction in the N¯N system. The latter is obtained by a Lippmann-Schwinger equation for N¯N potentials derived within SU(3) chiral effective field theory. By fitting to the phase shifts and (differential) cross section data, a high quality description is achieved. With these amplitudes, the oscillations of the electromagnetic form factors of the proton and the neutron are studied. It is found that each of them can be described by two fractional oscillators. One is characterized as "overdamped" and dominates near the threshold, while the other is "underdamped" and plays an important role in the high-energy region. These two oscillators are essential to understand the distributions of polarized electric charges induced by hard photons for the nucleons.