Chiral dynamics and peripheral transverse densities

TL;DR

This paper investigates the peripheral transverse densities of the nucleon using chiral effective field theory, linking low-t form factors to high-energy scattering and providing insights into the nucleon's chiral structure at large distances.

Contribution

It derives the asymptotic behavior of isovector transverse densities, includes Delta states, and explores the spatial dominance of chiral components in nucleon structure.

Findings

Derived the Yukawa tail of transverse densities in chiral regions

Quantified the spatial dominance of chiral components

Calculated chiral divergences of charge and magnetic radii

Abstract

In the partonic (or light-front) description of relativistic systems the electromagnetic form factors are expressed in terms of frame-independent charge and magnetization densities in transverse space. This formulation allows one to identify the chiral components of nucleon structure as the peripheral densities at transverse distances b = O(M_pi^{-1}) and compute them in a parametrically controlled manner. A dispersion relation connects the large-distance behavior of the transverse charge and magnetization densities to the spectral functions of the Dirac and Pauli form factors near the two-pion threshold at timelike t = 4 M_pi^2. Using relativistic chiral effective field theory in the leading-order approximation, we (a) derive the asymptotic behavior (Yukawa tail) of the isovector transverse densities in the "chiral" region b = O(M_pi^{-1}) and the "molecular" region b = O(M_N^2/M_pi^3); (b) perform the heavy-baryon expansion; (c) explain the relative magnitude of the peripheral charge and magnetization densities in a simple mechanical picture; (d) include Delta intermediate states and study the densities in the large-N_c limit of QCD; (e) quantify the spatial region where the chiral components are numerically dominant; (f) calculate the chiral divergences of the b^2-weighted moments of the transverse densities (charge and magnetic radii) and determine their spatial support. Our approach provides a concise formulation of the spatial structure of the nucleon's chiral component and offers new insights into basic properties of the chiral expansion. It relates the information extracted from low-t elastic form factors to the generalized parton distributions probed in peripheral high-energy scattering processes.