Forces within hadrons on the light front

TL;DR

This paper derives relativistically correct light front densities for momentum and internal forces within hadrons, linking them to gravitational form factors, and introduces new expressions for mechanical properties and stability conditions.

Contribution

It provides a novel light front formalism approach to define and analyze internal hadron densities and mechanical properties, improving upon previous instant form methods.

Findings

Derived expressions for hadron densities related to gravitational form factors.

Established the importance of light front formalism for internal structure analysis.

Illustrated findings using a multipole ansatz for form factors.

Abstract

In this work, we find the light front densities for momentum and forces, including pressure and shear forces, within hadrons. This is achieved by deriving relativistically correct expressions relating these densities to the gravitational form factors $A(t)$ and $D(t)$ associated with the energy momentum tensor. The derivation begins from the fundamental definition of density in a quantum field theory, namely the expectation value of a local operator within a spatially-localized state. We find that it is necessary to use the light front formalism to define a density that corresponds to internal hadron structure. When using the instant form formalism, it is impossible to remove the spatial extent of the hadron wave function from any density, and -- even within instant form dynamics -- one does not obtain a Breit frame Fourier transform for a properly defined density. Within the front formalism, we derive new expressions for various mechanical properties of hadrons, including the mechanical radius, as well as for stability conditions. The multipole ansatz for the form factors is used as an example to illustrate all of these findings.