Transverse single-spin asymmetries in $γ$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 ($γ$SIDIS), $A_{UT}^{γ{\rm SIDIS}}$, provide an unprecedented opportunity to extract the quark-gluon-quark correlators $F_{FT}(x,x')$ and $G_{FT}(x,x')$ point-by-point in their full support $x,x'$. 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 $A_{UT}^{γ{\rm SIDIS}}$ 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 $10\%$ or larger for certain kinematics. Given that $F_{FT}(x,x')$ and $G_{FT}(x,x')$ are basically unknown, $A_{UT}^{γ{\rm SIDIS}}$ will be an important future measurement to learn about multi-parton correlations in the nucleon.