, 2014:92,
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Date: 17 Jan 2014

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 \( b=O\left( {\mathrm{M}_{\pi}^{-1 }} \right) \) 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 time-like \( t=4M_{\pi}^2 \) , which can be computed in relativistic chiral effective field theory. Using the leading-order approximation we (a) derive the asymptotic behavior (Yukawa tail) of the isovector transverse densities in the “chiral” region \( b=O\left( {\mathrm{M}_{\pi}^{-1 }} \right) \) and the “molecular” region \( b = O\left( {{{{M_N^2}} \left/ {{M_{\pi}^3}} \right.}} \right) \) ; (b) perform the heavy-baryon expansion of the transverse densities; (c) explain the relative magnitude of the peripheral charge and magnetization densities in a simple mechanical picture; (d) include Δ isobar intermediate states and study the peripheral transverse densities in the large-N c limit of QCD; (e) quantify the region of transverse distances where the chiral components of the densities are numerically dominant; (f) calculate the chiral divergences of the b 2-weighted moments of the isovector transverse densities (charge and anomalous magnetic radii) in the limit M π → 0 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.

ArXiv ePrint: 1308.1634