A critical assessment of the angular momentum sum rules

TL;DR

This paper critically examines five different angular momentum sum rules in nucleon physics, clarifying their interpretations, limitations, and the inaccuracies in recent claims about their frame independence, thus addressing ongoing controversies.

Contribution

The paper provides a detailed analysis of existing angular momentum sum rules, clarifies misconceptions, and corrects the interpretation of the Pauli-Lubanski vector relation.

Findings

Ji, Xiong, and Yuan's claim of frame independence is incorrect.

An energy-dependent term was overlooked in the Pauli-Lubanski relation.

The paper clarifies the interpretation of various angular momentum sum rules.

Abstract

There are now five angular momentum relations or sum rules in the literature: the Jaffe, Manohar relation for a longitudinally polarized nucleon, and the Bakker, Leader, Trueman result for the case of transverse polarization; the Ji relation for longitudinal polarization, and the Leader result for transverse polarization, both involving generalized parton distributions; and a new sum rule due to Ji, Xiong and Yuan dealing with the transverse component of the Pauli-Lubanski vector. I discuss these various relations and examine their precise interpretation in the light of the so-called "angular momentum controversy". In particular, I show that the claim of Ji, Xiong and Yuan that their Pauli-Lubanski relation is frame or energy independent is incorrect, and that they have missed an energy dependent term in their expression.