Novel twist-three transverse-spin sum rule for the proton and related generalized parton distributions

TL;DR

This paper derives a new twist-3 sum rule for the proton's transverse spin, linking partonic distributions and orbital angular momentum, and discusses its implications for measurable distributions and proton structure.

Contribution

It introduces a novel twist-3 transverse spin sum rule for the proton, connecting generalized parton distributions with orbital angular momentum in a transverse polarization context.

Findings

Derived a new twist-3 sum rule for proton transverse spin

Related orbital angular momentum densities to measurable GPDs

Analyzed transverse-space distributions in polarized protons

Abstract

We derive a new twist-3 partonic sum rule for the transverse spin of the proton, which involves the well-know quark spin structure function $g_T(x)=g_1(x)+g_2(x)$, the less-studied but known transverse gluon polarization density $\Delta G_T(x)$, and quark and gluon canonical orbital angular momentum densities associated with transverse polarization. This is the counter part of the sum rule for the longitudinal spin of the proton derived by Jaffe and Manohar previously. We relate the partonic canonical orbital angular momentum densities to a new class of twist-3 generalized parton distribution functions which are potentially measurable in deep-virtual exclusive processes. We also discuss in detail an important technicality related to the transverse polarization in the infinite momentum frame, i.e., separation of intrinsic contributions from the extrinsic ones. We apply our finding to the transverse-space distributions of partons, angular momentum, and magnetic moment, respectively, in a transversely polarized proton.