Positivity bounds on gluon TMDs for hadrons of spin $\le$ 1

TL;DR

This paper derives positivity bounds on gluon transverse momentum dependent distributions for hadrons with spin up to 1, providing theoretical constraints useful for future experimental analyses, especially at small-x.

Contribution

It extends the analysis of gluon TMDs to tensor polarized targets and derives positivity bounds applicable to various polarization states, including the small-x limit with Wilson loop structures.

Findings

Derived positivity bounds for gluon TMDs with different polarization states.

Extended bounds to tensor polarized targets relevant for spin ≥1 hadrons.

Analyzed small-x behavior of bounds using Wilson loop matrix elements.

Abstract

We consider the transverse momentum dependent gluon distribution functions (called gluon TMDs) by studying the light-front gluon-gluon correlator, extending the results for unpolarized and vector polarized targets to also include tensor polarized targets -- the latter type of polarization is relevant for targets of spin $\ge1$. The light-front correlator includes process-dependent gauge links to guarantee color gauge invariance. As from the experimental side the gluon TMDs are largely unknown, we present positivity bounds for combinations of leading-twist gluon distributions that may be used to estimate their maximal contribution to observables. Since the gluonic content of hadrons is particularly relevant in the small-$x$ kinematic region, we also study these bounds in the small-$x$ limit for the dipole-type gauge link structure using matrix elements of a single Wilson loop.