Light front synchronization and rest frame densities of the proton: Electromagnetic densities

TL;DR

This paper clarifies the physical basis of light front relativistic densities, showing they originate from a different synchronization convention and providing explicit charge and current densities for the proton and neutron.

Contribution

It introduces tilted light front coordinates to interpret densities at rest and derives detailed electromagnetic densities for nucleons using empirical form factors.

Findings

Densities describe a system at rest, not infinite momentum.

Explicit charge and current densities for proton and neutron are obtained.

Angular modulations are explained by quark motion effects.

Abstract

We clarify the physical origin and meaning of the two-dimensional relativistic densities of the light front formalism. The densities are shown to originate entirely from the use of light front time instead of instant form time, which physically corresponds to using an alternative synchronization convention. This is shown by using tilted light front coordinates, which consist of light front time and ordinary spatial coordinates, and which are also used to show that the obtained densities describe a system at rest rather than at infinite momentum. These coordinates allow all four components of the electromagnetic current density to be given clear physical meanings. We explicate the formalism for spin-half targets, obtaining charge and current densities of the proton and neutron using empirical form factor parametrizations, as well as up and down quark densities and currents. Angular modulations in the densities of transversely-polarized states are explained as originating from redshifts and blueshifts due to quarks moving in different longitudinal directions.