  We develop a theory for cavity cooling of the center-of-mass motion of a
levitated nanoparticle through coherent scattering into an optical cavity. We
analytically determine the full coupled Hamiltonian for the nanoparticle,
cavity, and free electromagnetic field. By tracing out the latter, we obtain a
Master Equation for the cavity and the center of mass motion, where the
decoherence rates ascribed to recoil heating, gas pressure, and trap
displacement noise are calculated explicitly. Then, we benchmark our model by
reproducing published experimental results for three-dimensional cooling.
Finally, we use our model to demonstrate the possibility of ground-state
cooling along each of the three motional axes. Our work illustrates the
potential of cavity-assisted coherent scattering to reach the quantum regime of
levitated nanomechanics.
