Minding the gap between hard and diffractive structure functions at the EIC

Diffraction is characterized by forward scattering and a large rapidity gap. Ordinary hard scattering also produces gapped events and presents a significant background to identification of diffractively produced events. We present a fully differential factorization of gapped hard $ep$ scattering. We find that the unpolarized azimuthally-dependent structure functions $F_{3,4}^{\mathrm{g}\mathrm{a}\mathrm{p}}$ and the longitudinal $F_L^{\mathrm{g}\mathrm{a}\mathrm{p}}$ vanish at leading power for hard scattering. Azimuthal dependence is thus a pure diffractive signature. This is borne out in Monte Carlo simulations.