On in situ Determination of Earth Matter Density in Neutrino Factory

Abstract

We point out that an accurate in situ determination of the earth matter density \rho is possible in neutrino factory by placing a detector at the magic baseline, L = \sqrt{2} \pi / G_{F} N_{e} where N_{e} denotes electron number density. The accuracy of matter density determination is excellent in a region of relatively large theta_{13} with fractional uncertainty \delta \rho / \rho of about 0.43%, 1.3%, and \lsim 3% at 1 sigma CL at sin^2 2theta_{13}=0.1, 10^{-2}, and 3 x 10^{-3}, respectively. At smaller theta_{13} the uncertainty depends upon the CP phase delta, but it remains small, 3%-7% in more than 3/4 of the entire region of delta at sin^2 2theta_{13} = 10^{-4}. The results would allow us to solve the problem of obscured CP violation due to the uncertainty of earth matter density in a wide range of theta_{13} and delta. It may provide a test for the geophysical model of the earth, or it may serve as a method for stringent test of the MSW theory of neutrino propagation in matter once an accurate geophysical estimation of the matter density is available.