Transverse distortion of a relativistic composite system in impact parameter space

TL;DR

This paper explores the transverse distortion of a relativistic composite system's quark distribution in impact parameter space using light front wave functions, linking GPDs to nucleon spin and form factors.

Contribution

It introduces a detailed analysis of GPDs in impact parameter space with explicit LFWFs, connecting transverse distortions to nucleon spin and form factors, including a holographic QCD model.

Findings

Distortion sign correlates with anomalous magnetic moment.

Explicit relation between space and impact parameter distortions.

Simulated nucleon form factor with holographic LFWFs.

Abstract

We investigate the Generalized Parton Distributions (GPDs) in impact parameter space using the explicit light front wave functions (LFWFs) for the two-particle Fock state of the electron in QED. The Fourier transform (FT) of the GPDs gives the distribution of quarks in the transverse plane for zero longitudinal momentum transfer ($\xi=0$). We study the relationship of the spin flip GPD $E(x,0,-\vec{\Delta}_\perp^2)$ with the distortion of unpolarized quark distribution in the transverse plane when the target nucleon is transversely polarized and also determine the sign of distortion from the sign of anomalous magnetic moment. To verify the sign of distortion, we also compute it directly from the LFWFs by performing a FT in position space coordinate $\vec{f}_\perp$. The explicit relation between the deformation in the two spaces can also be obtained using the convolution integrals. To show the relation of the model LFWFs to a realistic model of nucleon physics, we have designed a specific weight function of our model LFWFs and integrated it over the mass parameter. Also we have simulated the form factor of the nucleon in the AdS/QCD holographic LFWFs model and studied the power-law behaviour at short distances.