Realistic Earth matter density for CP violation in a very long baseline neutrino oscillation

We investigate three Earth density models for the measurement of the CP phase in very long baseline neutrino oscillation experiments to study the effect of the potential error due to Earth density uncertainties. Two of the density models which are commonly used are global models. The third provides a more realistic density profile which takes into account the local density variation along a specific 2100 km baseline. We find significant differences among these density models. The more realistic density model has a smaller intrinsic density fluctuation and hence allows better control of the error caused by the Earth density uncertainty. We also find that the conventional CP violation (CPV) variable, i.e., the CP odd difference, is in general small. Under the running conditions assumed in the present calculation, the differences of this CPV variable among the different density models and even the CPV variable itself can be dominated over by statistical and systematic errors. Therefore, other more suitable CPV variables have to be considered in the extraction of the CP phase