Logarithmic corrections and soft photon phenomenology in the multipole model of the nucleon form factors

TL;DR

This paper presents a multipole model with logarithmic corrections for nucleon form factors, incorporating soft photon emission to explain experimental discrepancies and achieving a good fit to data with specific predictions for different measurement types.

Contribution

It introduces a novel multipole model with logarithmic functions and superconvergence relations, accounting for soft photon effects to reconcile various experimental data on nucleon form factors.

Findings

Good fit to experimental data with χ²/dof=0.86.

Predicted differences in proton form factor ratios across experiments.

Neutron form factor ratios are nearly identical across measurement types.

Abstract

We analyzed the presently available experimental data on nucleon electromagnetic form factors within a multipole model based on dispersion relations. A good fit of the data is achieved by considering the coefficients of the multipole expansions as logarithmic functions of the momentum transfer squared. The superconvergence relations, applied to this coefficients, makes the model agree with unitary constraints and pQCD asymptotics for the Dirac and Pauli form factors. The soft photon emission is proposed as a mechanism responsible for the difference between the Rosenbluth, polarization and beam--target--asymmetry data. It is shown, that the experimentally measured cross sections depend not only on the Dirac and Pauli form factors, but also on the average number of the photons emitted. For proton this number is shown to be different for different types of experimental measurements and then estimated phenomenologically. For neutron the same mechanism predicts, that the data form different types of experiments must coincide with high accuracy. A joint fit of all the experimental data reproduce the $Q^2-$dependence with the accuracy $\chi^2/dof=0.86$. Predictions of the model, that 1) the ratios of the proton form factors $G_E/G_M$ are different for Rosenbluth, polarization and beam--target--asymmetry experiments and 2) similar ratios are nearly the same for neutron, can be used for experimental verification of the model.