Journal of High Energy Physics

, 2014:92

Chiral dynamics and peripheral transverse densities

Open Access
Article

DOI: 10.1007/JHEP01(2014)092

Cite this article as:
Granados, C. & Weiss, C. J. High Energ. Phys. (2014) 2014: 92. doi:10.1007/JHEP01(2014)092

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-Nc 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 b2-weighted moments of the isovector transverse densities (charge and anomalous magnetic radii) in the limit Mπ → 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.

Keywords

Chiral Lagrangians Parton Model 1/N Expansion 
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Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Theory CenterJefferson LabNewport NewsU.S.A.
  2. 2.Department of Physics and Astronomy, Nuclear PhysicsUppsala UniversityUppsalaSweden

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