Tensor-polarized structure functions: Tensor structure of deuteron in 2020's

TL;DR

This paper explores the tensor structure functions of the deuteron, introduces new functions, derives formulas, discusses sum rules, and proposes experimental measurements to advance understanding of tensor polarization in hadrons.

Contribution

It introduces and formalizes new tensor structure functions for spin-one hadrons, relating them to deep inelastic scattering and proposing experimental tests and theoretical models.

Findings

Introduction of new tensor structure functions $b_1$-$b_4$

Derivation of projection operator formulas

Discussion of sum rules and experimental prospects

Abstract

We explain spin structure for a spin-one hadron, in which there are new structure functions, in addition to the ones ($F_1$, $F_2$, $g_1$, $g_2$) which exist for the spin-1/2 nucleon, associated with its tensor structure. The new structure functions are $b_1$, $b_2$, $b_3$, and $b_4$ in deep inelastic scattering of a charged-lepton from a spin-one hadron such as the deuteron. Among them, twist-two functions are related by the Callan-Gross type relation $b_2 = 2 x b_1$ in the Bjorken scaling limit. First, these new structure functions are introduced, and useful formulae are derived for projection operators of $b_{1-4}$ from a hadron tensor $W_{\mu\nu}$. Second, a sum rule is explained for $b_1$, and possible tensor-polarized distributions are discussed by using HERMES data in order to propose future experimental measurements and to compare them with theoretical models. A proposal was approved to measure $b_1$ at the Thomas Jefferson National Accelerator Facility (JLab), so that much progress is expected for $b_1$ in the near future. Third, formalisms of polarized proton-deuteron Drell-Yan processes are explained for probing especially tensor-polarized antiquark distributions, which were suggested by the HERMES data. The studies of the tensor-polarized structure functions will open a new era in 2020's for tensor-structure studies in terms of quark and gluon degrees of freedom, which is much different from ordinary descriptions in terms of nucleons and mesons.