  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.
