Anomalous Magnetic Moments and Quark Orbital Angular Momentum

TL;DR

This work establishes a model-independent inequality linking the nucleon's anomalous magnetic moment, via $E^q(x,0,0)$, to the presence of quark orbital angular momentum in light-cone wave functions. By expressing $E^q$ in impact-parameter space and applying Cauchy–Schwarz to the light-cone operator structure, the authors derive a lower bound on the norm of $L_z^q$ components, demonstrating that a nonzero $ ext{E}$ requires finite transverse size and positive-$L_z^q$ content. The central result, $(E^q(x,0,0)/(4M))^2 \nleq q_{L_z\uparrow ext{(}x)} b^{2}_{L_z ext{≤0}rrow(x)}$, provides a concrete, albeit modest, constraint on light-cone wave functions and clarifies the relationship between transverse distortions and orbital motion. The analysis also distinguishes the light-cone angular-momentum decomposition from Ji’s net $L_z$, with implications for interpreting Sivers-type effects and guiding future hadron structure modeling.

Abstract

We derive an inequality for the distribution of quarks with non-zero orbital angular momentum, and thus demonstrate, in a model-independent way, that a non-vanishing anomalous magnetic moment requires both a non-zero size of the target as well as the presence of wave function components with quark orbital angular momentum L_z>0.