# Off-forward gluonic structure of vector mesons

## TL;DR

This study uses lattice QCD to explore the gluonic structure of the $$ meson, revealing differences in spatial distributions of gluons and quarks, advancing understanding of hadronic internal structure.

## Contribution

First lattice QCD calculation of the gluonic GFFs of the $$ meson, providing new insights into gluon distributions and their spatial characteristics.

## Key findings

- Quantitative differences between gluon and quark distributions.
- First determination of transversity gluon GFFs for the $$ meson.
- Comparison with quark GFFs and electromagnetic form factors.

## Abstract

The spin-independent and transversity generalised form factors (GFFs) of the $\phi$ meson are studied using lattice QCD calculations with light quark masses corresponding to a pion mass $m_\pi\sim450(5)$ MeV. One transversity and three spin-independent GFFs related to the lowest moments of leading-twist spin-independent and transversity gluon distributions are obtained at six non-zero values of the momentum transfer up to 1.2 GeV$^2$. These quantities are compared with the analogous spin-independent quark GFFs and the electromagnetic form factors determined on the same lattice ensemble. The results show quantitative distinction between the spatial distribution of transversely polarised gluons, unpolarised gluons, and quarks, and point the way towards further investigations of the gluon structure of nucleons and nuclei.