New insights into the oscillation of the nucleon electromagnetic form factors

TL;DR

This paper investigates the oscillatory behavior of nucleon electromagnetic form factors in the timelike region, revealing they can be modeled by two fractional oscillators with distinct damping characteristics.

Contribution

It introduces a novel model describing nucleon form factor oscillations using two fractional oscillators, incorporating final-state interactions derived from chiral effective field theory.

Findings

Proton and neutron form factors exhibit oscillations describable by two fractional oscillators.

One oscillator is overdamped near threshold, the other underdamped at high energies.

The model helps understand polarized charge distributions in nucleons.

Abstract

The electromagnetic form factors of the proton and the neutron in the timelike region are investigated. Electron-positron annihilation into antinucleon-nucleon ($\bar NN$) pairs is treated in distorted wave Born approximation, including the final-state interaction in the $\bar NN$ system. The latter is obtained by a Lippmann-Schwinger equation for $\bar{N}N$ 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 \lq overdamped' and dominates near the threshold, while the other is \lq 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.