Probing Competing and Intertwined Orders with Resonant Inelastic x-ray Scattering in the Hole-Doped Cuprates

We develop a formalism to study indirect resonant inelastic x-ray scattering (RIXS) in systems with itinerant electrons, accounting for the attraction between valence electrons and the positively-charged core hole exactly, and apply this formalism to the hole-doped cuprate superconductors. We focus on the relationship between RIXS lineshapes and band structure, including broken symmetries. We show that RIXS is capable of distinguishing between competing order parameters, establishing it as a useful probe of the pseudogap phase.