Energy-momentum tensor form factors and spin density distribution in the nucleon calculated in a quantized Skyrme model with vector mesons

TL;DR

This paper explores how different pseudogauge choices in a quantized Skyrme model affect local spin and momentum densities in the nucleon, highlighting the ambiguity in spatial interpretations of nucleon structure.

Contribution

It provides a detailed analysis of pseudogauge dependence in energy-momentum tensor form factors and spin densities within a Skyrme model including vector mesons.

Findings

Pseudogauge choice significantly alters local spin and momentum densities.

Canonical EMT encodes spin density via antisymmetric tensor structure.

Belinfante EMT reflects total angular momentum but not local spin density.

Abstract

We investigate energy-momentum tensor (EMT) form factors and the spatial spin density distribution in the nucleon within a framework of the quantized Skyrme model with vector mesons. We construct both the canonical and Belinfante improved EMTs and analyze how pseudogauge uncertainty influences local spin and momentum densities while leaving the global nucleon properties unchanged. Using the inversion formulas from nucleon matrix elements in the forward limit, we extract the form factors, $A(t)$, $D(t)$, and $J(t)$, in both pseudogauges and the additional antisymmetric form factor associated with the canonical EMT. We find that the pseudogauge choice leads to sizable differences in the local spin and momentum densities. In particular, the canonical EMT naturally encodes spin density through the antisymmetric tensor structure, while the Belinfante EMT is sensitive to the total angular momentum only. Our results illustrate explicitly how different pseudogauges correspond to different spatial interpretations of nucleon spin structure within the same underlying dynamics. These findings provide a concrete model realization of the pseudogauge ambiguity in QCD-inspired nucleon structure and offer useful intuition for interpreting spatial distributions.