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 − 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.
Highlights
At peripheral transverse distances b = O(Mπ−1) the densities are governed by chiral dynamics and can be calculated model-independently using chiral effective field theory (EFT)
QCD the transverse densities correspond to a projection of the generalized parton distributions (GPDs) describing the transverse spatial distribution of quarks and antiquarks [2, 5]; as such they connect the information gained from low-energy elastic scattering with the partonic content probed by high-momentum-transfer processes in high-energy scattering
At transverse distances b = O(Mπ−1), where the pion mass is regarded as parametrically small compared to the typical inverse hadronic size, the densities are governed by the universal dynamics resulting from the spontaneous breaking of chiral symmetry and can be computed from first principles using the methods of chiral effective field theory (EFT)
Summary
The transition matrix element of the electromagnetic current between nucleon states is parametrized in terms of two invariant form factors (we follow the notation and conventions of ref. [8]). The transition matrix element of the electromagnetic current between nucleon states is parametrized in terms of two invariant form factors In a state where the nucleon is localized in transverse space at the origin, and polarized in the y-direction, the matrix element of the current J+ at light-front time x+ = 0 and light-front coordinates x− = 0 and xT = b is given by. Be interpreted as the left-right asymmetry of the J+ current in a nucleon polarized in the positive y direction. We note that eq (2.6) and its interpretation can be generalized to the case of arbitrary nucleon polarization states in the rest frame, including non-diagonal transitions; see ref. The electromagnetic current matrix element and the transverse densities have two isospin components. The isoscalar component is defined by the same expression with the + sign
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
