Transverse single-spin asymmetries in $\gamma$SIDIS as a direct probe of quark-gluon-quark longitudinal momentum structure

Transverse single-spin asymmetries in the semi-inclusive deep-inelastic production of isolated photons ($\gamma$SIDIS), $A_{UT}^{\gamma \mathrm{S}\mathrm{I}\mathrm{D}\mathrm{I}\mathrm{S}}$, provide an unprecedented opportunity to extract the quark-gluon-quark correlators $F_{FT}(x,x^{\mathrm{\prime }})$ and $G_{FT}(x,x^{\mathrm{\prime }})$ point-by-point in their full support $x,x^{\mathrm{\prime }}$. We utilize realistic models for these functions, based on input from the Sivers transverse momentum dependent parton distribution function and imposing constraints from the $d_2$ matrix element calculated in lattice QCD, in order to provide numerical estimates for $A_{UT}^{\gamma \mathrm{S}\mathrm{I}\mathrm{D}\mathrm{I}\mathrm{S}}$ at the Electron-Ion Collider (EIC). We thoroughly explore the EIC phase space in order to isolate in which regions the asymmetry can be sizable, finding it can be as much as $10\mathrm{\%}$ or larger for certain kinematics. Given that $F_{FT}(x,x^{\mathrm{\prime }})$ and $G_{FT}(x,x^{\mathrm{\prime }})$ are basically unknown, $A_{UT}^{\gamma \mathrm{S}\mathrm{I}\mathrm{D}\mathrm{I}\mathrm{S}}$ will be an important future measurement to learn about multi-parton correlations in the nucleon.