Forces inside the nucleon on the light front from 3D Breit frame force distributions: Abel tomography case

TL;DR

This paper establishes a mathematical link between 3D Breit frame force distributions and 2D light front force distributions using Abel transformations, enabling unambiguous conversion and analysis of internal nucleon forces.

Contribution

It introduces invertible Abel transformation relations that connect 3D Breit frame and 2D light front force distributions, ensuring stability conditions are maintained.

Findings

Derived explicit Abel transformation relations.

Applied the relations to large nucleus and nucleon models.

Demonstrated the stability of the transformed distributions.

Abstract

We derive simple relations which express 2D light front force distributions in terms of 3D Breit frame pressure and shear force distributions. Mathematically the relations correspond to invertible Abel transformation and they establish one-to-one mathematical equivalence of 3D Breit frame force distributions and 2D light front ones. Any knowledge (model calculation, experimental measurement, etc.) about pressure and shear force distributions in Breit frame can be unambiguously transformed into light front force distributions with the help of Abel transformation. It is important that the transformation ensures 2D stability conditions if the 3D stability conditions are satisfied. As an illustration of how the relations work, we calculated the light front force distributions for a large nucleus as a liquid drop, and for large $N_c$ nucleon as a chiral soliton.