Light-front representation of chiral dynamics in peripheral transverse densities

TL;DR

This paper presents a light-front quantum-mechanical framework for understanding chiral dynamics in the peripheral transverse densities of nucleons, linking low-energy form factors to high-energy scattering insights.

Contribution

It introduces a novel light-front wave function representation of chiral EFT results, providing a unified, relativistic view of chiral dynamics in nucleon structure.

Findings

Explains the parametric order of peripheral transverse densities.

Establishes an inequality between spin-independent and -dependent densities.

Reveals a large left-right asymmetry in transversely polarized nucleons.

Abstract

The nucleon's electromagnetic form factors are expressed in terms of the transverse densities of charge and magnetization at fixed light-front time. At peripheral transverse distances $b = O(M_\pi^{-1})$ the densities are governed by chiral dynamics and can be calculated model-independently using chiral effective field theory (EFT). We represent the leading-order chiral EFT results for the peripheral transverse densities as overlap integrals of chiral light-front wave functions, describing the transition of the initial nucleon to soft pion-nucleon intermediate states and back. The new representation (a) explains the parametric order of the peripheral transverse densities; (b) establishes an inequality between the spin-independent and -dependent densities; (c) exposes the role of pion orbital angular momentum in chiral dynamics; (d) reveals a large left-right asymmetry of the current in a transversely polarized nucleon and suggests a simple interpretation. The light-front representation enables a first-quantized, quantum-mechanical view of chiral dynamics that is fully relativistic and exactly equivalent to the second-quantized, field-theoretical formulation. It relates the charge and magnetization densities measured in low-energy elastic scattering to the generalized parton distributions probed in peripheral high-energy scattering processes. The method can be applied to nucleon form factors of other operators, e.g. the energy-momentum tensor.