Probing the polarized photon content of the proton in $ep$ collisions at the EIC

We study the single-inclusive production of prompt photons in electron proton collisions, $ep \to \gamma X$, for kinematics relevant at the Electron-Ion Collider (EIC). We perform a perturbative calculation of the differential cross section to next-to-leading order in QCD and to lowest order in QED. We consider unpolarized collisions as well as scattering of longitudinally polarized incident electrons and protons. We show that the cross sections are sensitive to the parton distribution functions of photons inside the proton, which we find to generate the dominant contributions in certain kinematical regions at the EIC. We also investigate the effects of photon isolation on the unpolarized and polarized cross sections.