Gluon transversity and TMDs for spin-1 hadrons

TL;DR

This paper explores gluon transversity and TMDs in spin-1 hadrons, revealing new distributions, sum rules, and measurement methods, which are crucial for understanding exotic components in deuterons beyond simple nucleon models.

Contribution

It introduces the concept of gluon transversity in spin-1 hadrons, details the full set of TMDs at various twists, and proposes experimental approaches for their measurement.

Findings

30 TMDs at twists 3 and 4 in tensor-polarized spin-1 hadrons

Existence of 3 collinear PDFs at twists 3 and 4

New sum rules for time-reversal odd TMDs

Abstract

We explain a gluon transversity, transverse-momentum-dependent parton distribution functions (TMDs), and parton distribution functions (PDFs) for spin-1 hadrons. The gluon transversity exists in hadrons with spin more than or equal to one, and it does not exist in the spin-1/2 nucleons. Since there is no direct contribution from the nucleons, it is an appropriate quantity to probe an exotic component in the spin-1 deuteron beyond a simple bound system of the nucleons. We show how the gluon transversity can be measured at hadron accelerator facilities by the Drell-Yan process in addition to lepton-accelerator experiments. Next, possible TMDs are explained for the spin-1 hadrons at the twists 3 and 4 in addition to twist-2 ones by considering tensor polarizations. We found that 30 TMDs exist in the tensor-polarized spin-1 hadron at the twists 3 and 4 in addition to 10 TMDs at the twist 2. There are 3 collinear PDFs at the twists 3 and 4. We also indicate that the corresponding TMD fragmentation functions exist at the twists 3 and 4. Due to the time-reversal invariance in the collinear PDFs, there are new sum rules on the time-reversal odd TMDs. In addition, we obtained a useful twist-2 relation, a sum rule, and relations with multiparton distribution functions by using the operator product expansion and the equation of motion for quarks. These findings are valuable for experimental investigations on polarized deuteron structure functions in 2020's and 2030's at world accelerator facilities.