Two Photon Exchange in Impact Parameter Space in the Relativistic Eikonal Approximation for Elastic e - N Scattering

TL;DR

This paper investigates the impact of two-photon exchange processes in elastic electron-nucleon scattering using the relativistic Eikonal approximation, revealing azimuthal asymmetries linked to nucleon transverse polarization.

Contribution

It introduces a convolution-based method to evaluate two-photon exchange amplitudes in impact parameter space, highlighting azimuthal asymmetries in scattering cross sections.

Findings

Interference term shows azimuthal asymmetry.

Results align with existing data on single spin asymmetry.

Transverse charge density distortion causes asymmetries.

Abstract

Using the relativistic Eikonal approximation, we study the one and two photon exchange amplitudes in elastic electron-nucleon scattering for the case of transversely polarized nucleons with unpolarized electrons beam. In our approach, we utilize the convolution theory of Fourier transforms and the transverse charge density in transverse momentum space to evaluate the one and two photon exchange Eikonal amplitudes. The results obtained for the $2\gamma$ amplitude in impact parameter space are compared to the corresponding 4D case. We show that while the one and two photon cross sections are azimuthally symmetric, the interference term between them is azimuthally asymmetric, which is an indication of an azimuthal single spin asymmetry for proton and neutron which can be attributed to the fact that the nucleon charge density is transversely (azimuthally) distorted in the transverse plane for transversely polarized nucleons. In addition, the calculations of the interference term for proton and neutron show agreement in sign and magnitude of the existence data and calculations for transverse target single spin asymmetry.