A critical assessment of the 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.

Comments: 14 pages. This version contains the following corrections to V2: Eq.~(23} is replaced by Eqs.~(23) and (24). Numerical factors have been corrected in various equations and, crucially, corrected in the old Eq.~(50), which now becomes (51)