Transverse charge distributions of the nucleon and their Abel images

June-Young Kim,Hyun-Chul Kim

doi:10.1103/physrevd.104.074003

Abstract

We investigate the two-dimensional transverse charge distributions of the transversely polarized nucleon. As the longitudinal momentum (${P}_{z}$) of the nucleon increases, the electric dipole moment is induced, which causes the displacement of the transverse charge and magnetization distributions of the nucleon. The induced dipole moment of the proton reaches its maximum value at around ${P}_{z}\ensuremath{\approx}3.2\text{ }\text{ }\mathrm{GeV}$ due to the kinematical reason. We also investigate how the Abel transformations map the three-dimensional charge and magnetization distributions in the Breit frame onto the transverse charge and magnetization ones in the infinite momentum frame.

Highlights

The electromagnetic (EM) structure of the nucleon has been one of the most important issues well over decades since Hofstadter’s experiments [1]
We investigate how the Abel transformations map the three-dimensional charge and magnetization distributions in the Breit frame onto the transverse charge and magnetization ones in the infinite momentum frame
Employing the formalism developed in Ref. [22], we extend the Abel transformations to the charge and magnetization distributions of the nucleon and show how the Abel transformations can be used to map the 3D charge distributions onto the 2D transverse ones in the infinite momentum frame (IMF)

Summary

INTRODUCTION

The electromagnetic (EM) structure of the nucleon has been one of the most important issues well over decades since Hofstadter’s experiments [1] (see a recent review [2] and references therein). Since Lorentz invariance ensures that the (n þ 1)th Mellin moments of a GPD should consist of an order-(n þ 1) polynomial, one can define the generalized form factors corresponding to the matrix elements of the twist-2 and spin(n þ 1) local operators This indicates that the EM form factors of the nucleon can be considered the first (n 1⁄4 0) Mellin moment of the vector GPDs. The GPDs in the case of the purely transverse momentum transfer, i.e., Δþ 1⁄4 0 ðξ 1⁄4 0Þ, have naturally led to the impact-parameterdependent parton distribution functions (PDFs) [6,7], which can be obtained by the two-dimensional (2D) Fourier transform of the GPDs. the first moment of the impactparameter-dependent PDFs yields the 2D transverse charge distribution in the plane perpendicular to the longitudinal momentum direction in the IMF. When the neutron is Lorentz boosted— i.e., its longitudinal momentum approaches infinity—the magnetic contribution dominates over the electric ones and the central part of the transverse charge distributions turns negative. As concluded in Refs. [22,28], the

Formalism

Results and discussion

ABEL TRANSFORMATION BETWEEN THE 3D BREIT AND 2D DRELL-YAN FRAMES

Findings

SUMMARY AND CONCLUSIONS