We present an exploratory study of the gluonic structure of the $\varphi$ meson using lattice QCD (LQCD). This includes the first investigation of gluonic transversity via the leading moment of the twist-2 double-helicity-flip gluonic structure function $\mathrm{\Delta }(x,Q^2)$. This structure function only exists for targets of spin $J\ge 1$ and does not mix with quark distributions at leading twist, thereby providing a particularly clean probe of gluonic degrees of freedom. We also explore the gluonic analogue of the Soffer bound which relates the helicity flip and nonflip gluonic distributions, finding it to be saturated at the level of 80%. This work sets the stage for more complex LQCD studies of gluonic structure in the nucleon and in light nuclei where $\mathrm{\Delta }(x,Q^2)$ is an “exotic glue” observable probing gluons in a nucleus not associated with individual nucleons.

• Received 17 June 2016

DOI:https://doi.org/10.1103/PhysRevD.94.014507