  We experimentally realize cavity cooling of all three translational degrees
of motion of a levitated nanoparticle in vacuum. The particle is trapped by a
cavity-independent optical tweezer and coherently scatters tweezer light into
the blue detuned cavity mode. For vacuum pressures around $10^{-5}\,{\rm
mbar}$, minimal temperatures along the cavity axis in the mK regime are
observed. Simultaneously, the center-of-mass (COM) motion along the other two
spatial directions is cooled to minimal temperatures of a few hundred $\rm mK$.
Measuring temperatures and damping rates as the pressure is varied, we find
that the cooling efficiencies depend on the particle position within the
intracavity standing wave. This data and the behaviour of the COM temperatures
as functions of cavity detuning and tweezer power are consistent with a
theoretical analysis of the experiment. Experimental limits and opportunities
of our approach are outlined.
