Yet another correlation in the analysis of CP violation using a neutrino oscillation experiment

We investigate the effect induced by variations in the density profile of the Earth's interior using a long-baseline neutrino oscillation experiment. At first, we point out two facts. (i) The most essential part of the matter profile is the first Fourier mode of the matter profile function; and (ii) The Earth models based on the study of seismology include a large uncertainty for the first Fourier mode. Next, we show that there is a strong correlation between the average density value and the first Fourier coefficient in the analysis of oscillation probability. This means that the matter profile effect induces added uncertainty for the average matter parameter. %although the average density can be determined at a few percent accuracy. Taking into account this extra uncertainty, we make numerical calculations for the sensitivity to CP violation search and show that CP sensitivity is impaired by this added uncertainty within a large $U_{e3}$ region.