  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.
