Role of matter density uncertainties in the analysis of future neutrino factory experiments

Matter density uncertainties can affect the measurements of the neutrino oscillation parameters at future neutrino factory experiments, such as the measurements of the mixing parameters ${\theta }_{13}$ and ${\delta }_{\mathrm{CP}}.$ We compare different matter density uncertainty models and discuss the possibility to include the matter density uncertainties in a complete statistical analysis. Furthermore, we systematically study in which measurements and where in the parameter space matter density uncertainties are most relevant. We illustrate this discussion with examples that show the effects as functions of different magnitudes of the matter density uncertainties. We find that matter density uncertainties are especially relevant for large ${\sin }^{2}2{\theta }_{13}\gtrsim {10}^{-3}.$ Within the KamLAND-allowed range, they are most relevant for the precision measurements of ${\sin }^{2}2{\theta }_{13}$ and ${\delta }_{\mathrm{CP}},$ but less relevant for “binary” measurements, such as for the sign of $\Delta m_{31}^2,$ the sensitivity to ${\sin }^{2}2{\theta }_{13},$ or the sensitivity to maximal $\mathrm{CP}$ violation. In addition, we demonstrate that knowing the matter density along a specific baseline better than to about $1\%$ precision means that all measurements will become almost independent of the matter density uncertainties.