Parton distribution functions and fragmentation functions of spin-1 hadrons

TL;DR

This paper surveys the theoretical status of structure functions for spin-1 hadrons, focusing on parton distribution functions, tensor-polarized PDFs, TMDs, and fragmentation functions up to twist 4. It highlights unique observables such as the tensor structure function $b_1$ and the gluon transversity $\Delta_T g$, and presents parametrizations and convolution-based models for the deuteron. The authors develop twist-2 through twist-4 relations, including Wandzura-Wilczek–like and Lorentz-invariance relations, and discuss multiparton distributions and quark equations of motion. They outline experimental opportunities at JLab, Fermilab SpinQuest, NICA, and future electron-ion colliders as potential avenues to uncover new hadron physics in tensor-polarized spin-1 systems.

Abstract

Structure functions of the spin-1 deuteron will be investigated experimentally from the late 2020's at various facilities such as Thomas Jefferson National Accelerator Facility, Fermi National Accelerator Laboratory, nuclotron-based ion collider facility, and electron-ion colliders. We expect that a new high-energy spin-physics field could be created by these projects. In this paper, the current theoretical status is explained for the structure functions of spin-1 hadrons, especially on parton distribution functions, transverse-momentum dependent parton distributions, and fragmentation functions. Related multiparton distribution functions are also shown.

Figures (7)

• Figure 1: New hadron physics by structure function $b_1$.
• Figure 2: New hadron physics by gluon transversity $\Delta_T g$.
• Figure 3: Relation between the first moment of a structure function and an elastic form factor.
• Figure 4: HERMES data and parametrized $b_1$ structure function with its uncertainty band given by $\Delta \chi^2=1$. The data with $Q^2<1$ GeV$^2$ is shown by the open circle.
• Figure 6: $S$ and $D$ wave contributions to $xb_1$. The SD and DD indicate S-D interference and the pure D-wave terms, respectively.