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

Quasiparticle Theory of Resonant Inelastic X-ray Scattering in high-T$_c$ cuprates