Relativistic spin sum rules and the role of the pivot

TL;DR

This paper investigates how the choice of pivot affects relativistic spin sum rules, introducing a phase-space approach to derive a general rule that clarifies previous contradictions.

Contribution

It develops a phase-space method to compute the impact of the nucleon's center motion on spin sum rules in relativistic theories.

Findings

Derived a general relativistic spin sum rule.

Clarified the role of the pivot in spin sum rules.

Connected the new results to established formulas.

Abstract

Spin sum rules depend on the choice of a pivot, i.e. the point about which the angular momentun is defined, usually identified with the center of the nucleon. The latter is however not unique in a relativistic theory and has led to apparently contradictory results in the literature. Using the recently developed phase-space approach, we compute for the first time the contribution associated with the motion of the center of the nucleon, and we derive a general spin sum rule which reduces to established results after appropriate choices for the pivot and the spin component.