Probing the absolute density of the Earth's core using a neutrino beam

We demonstrate that one could measure the absolute matter density of the Earth's core with a vertical neutrino factory baseline at the per cent level for $\sin^2 2 \theta_{13} \gtrsim 0.01$, where we include all correlations with the oscillation parameters in the analysis. We discuss the geographical feasibility of such an approach, and illustrate how the results change as a function of the detector location. We point out the complementarity to geophysics.