Matter profile effect in a neutrino factory

We point out that the matter profile effect—the effect of matter density fluctuation on the baseline—is very important to estimate the parameters in a neutrino factory with a very long baseline. To make it clear, we propose the method of Fourier series expansion of the matter profile. By using this method, we can take account of both the matter profile effect and its ambiguity. For very long baseline experiment, such as $L=7332\mathrm{}\mathrm{km},$ in the analysis of the oscillation phenomena we need to introduce a new parameter $a_1$—the Fourier coefficient of the matter profile—as a theoretical parameter to deal with the matter profile effects.