  We develop a formalism for calculating resonant inelastic x-ray scattering
(RIXS) spectra in systems of itinerant electrons with arbitrary band
structures, accounting for the effect of the positively-charged core hole
exactly. We apply this formalism to the cuprate superconductors and obtain
quantitative agreement with experimental data over a wide range of dopings. We
reproduce the dispersing peaks and non-trivial polarization dependence found in
RIXS experiments on several materials. Thus we demonstrate that features
previously attributed to collective magnetic modes can be explained by band
structure alone.
