The complete tree-level result up to order $1/Q$ for polarized deep-inelastic leptoproduction

TL;DR

The paper develops a complete tree-level framework for polarized semi-inclusive deep-inelastic leptoproduction that includes intrinsic quark transverse momenta. It derives the hadronic tensor up to order $1/Q$, including both twist-two and twist-three quark distributions and fragmentation functions, and shows how quark-quark-gluon correlators ensure gauge invariance via QCD equations of motion. A wealth of azimuthal asymmetries and final-state polarization observables emerge, revealing access to the full set of transverse-momentum dependent distributions and their relations. The results provide a structured path toward three-dimensional nucleon structure studies and set the stage for incorporating QCD corrections like Sudakov effects and higher-order ladder diagrams.

Abstract

We present the results of the tree-level calculation of deep-inelastic leptoproduction, including polarization of target hadron and produced hadron. We also discuss the dependence on transverse momenta of the quarks, which leads to azimuthal asymmetries for the produced hadrons.

Figures (5)

• Figure 1: Kinematics for $\ell H$ scattering.
• Figure 2: Quark-quark correlation functions $\Phi(P,S;p)$ (left) and $\Delta(P_h,S_h;k)$ (right) giving quark distributions and fragmentation functions, respectively.
• Figure 3: Quark-quark-gluon correlation functions $\Phi_A$ (left) and $\Delta_A$ (right) contributing in hard scattering processes at subleading order.
• Figure 4: Quark diagram contributing to $\ell H$ scattering in leading order. There is a similar antiquark contribution.
• Figure 5: Quark diagrams contributing to $\ell H$ scattering at order $1/Q$.