Transverse Deformation of Parton Distributions and Transversity Decomposition of Angular Momentum

TL;DR

This work links transverse distortion of impact-parameter dependent parton distributions to Ji's angular momentum sum rule, showing that transversity decomposes quark angular momentum into transversity eigenstates. It identifies a key linear combination of chirally odd GPDs, H_T + 2 tildeH_T + E_T, as governing both the transverse spin–angular momentum correlation and the transverse density distortion in unpolarized targets, and it proposes a mechanism by which this distortion can generate the Boer-Mulders effect via final-state interactions. The paper also provides an alternative derivation confirming gauge-invariant results and highlights lattice QCD as a route to determine the relevant chirally odd GPDs, with experimental measurements of Boer-Mulders offering complementary insights into quark spin–orbit correlations in the nucleon.

Abstract

Impact parameter dependent parton distributions are transversely distorted when one considers transversely polarized nucleons and/or quarks. This provides a physical mechanism for the T-odd Sivers effect in semi-inclusive deep-inelastic scattering. The transverse distortion can also be related to Ji's sum rule for the angular momentum carried by the quarks. The distortion of chirally odd impact parameter dependent parton distributions is related to chirally odd GPDs. This result is used to provide a decomposition of the quark angular momentum w.r.t. quarks of definite transversity. Chirally odd GPDs can thus be used to determine the correlation between quark spin and quark angular momentum in unpolarized nucleons. Based on the transverse distortion, we also suggest a qualitative connection between chirally odd GPDs and the Boer-Mulders effect.

Figures (1)

• Figure 1: Distribution of transversity in impact parameter space for a simple model (\ref{['model']}).