Tensor-polarized parton distribution functions for spin-1 hadrons

TL;DR

This work surveys tensor-polarized PDFs and TMDs for spin-1 hadrons, focusing on the leading-twist structure function $b_1$, its sum rule, and the potential tensor-polarized antiquark content modeled through a LO parametrization. It shows that the standard deuteron convolution underestimates $b_1$ relative to data, motivating a $\chi^2$-based extraction of tensor-polarized PDFs and acknowledging possible nonzero tensor-polarized antiquarks. The article further develops the formalism for PDFs, TMDs, and fragmentation functions up to twist-4, providing covariant definitions, operator structures, and mapping between TMDs and collinear functions, while highlighting the unique spin-1 gluon transversity $\Delta_T g(x)$ and its experimental prospects. With upcoming tensor-polarized deuteron measurements at JLab and complementary facilities, this framework aims to uncover novel hadron dynamics beyond simple nucleon-nucleon bound states and to clarify the role of higher-twist effects at moderate $Q^2$. Overall, it offers a roadmap for exploring high-energy spin-1 physics through structured observables, model tests, and planned experiments.

Abstract

Spin-1 hadrons contain different aspects of spin physics from the ones of the spin-1/2 nucleon because of the existence of tensor-polarized structure functions. In the charged-lepton deep inelastic scattering from a spin-1 hadron or nucleus, such as the deuteron, there are leading-twist structure functions $b_1$ and $b_2$. In addition, there exists a gluon transversity which does not exist in the spin-1/2 nucleon. In the deuteron, these observables could probe interesting dynamical aspects beyond a simple bound system of a proton and a neutron. In addition, there are recent theoretical studies on higher-twist distributions. Tensor-polarized deuteron experiments are now under preparation at the Thomas Jefferson National Accelerator Facility, so that the topic of polarized deuteron is expected to become one of exciting fields in hadron physics. This paper is a brief overview on the tensor-polarized parton distribution functions, including transverse-momentum-dependent parton distributions and fragmentation functions up to twist 4.

Figures (2)

• Figure 1: The distribution $xb_1(x)$ by the standard deuteron model in comparison with the HERMES data.
• Figure 2: Tensor-polarized PDFs $x \delta_T q_v(x)$ and $x \delta_T \bar{q}(x)$ are shown at $Q^2=2.5$ GeV$^2$.