Chiral dynamics and peripheral transverse densities

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.