In situ determination of Earth matter density in a neutrino factory

We point out that an accurate in situ determination of the earth matter density ρ is possible in neutrino factory by placing a detector at the magic baseline, L=√(2)π/GFNe where Ne denotes electron number density. The accuracy of matter density determination is excellent in a region of relatively large θ13 with fractional uncertainty δρ/ρ of about 0.43%, 1.3%, and < or approx. 3% at 1σ CL at sin22θ13=0.1, 10-2, and 3x10-3, respectively. At smaller θ13 the uncertainty depends upon the CP phase δ, but it remains small, 3%-7% in more than 3/4 of the entire region of δ at sin22θ13=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 θ13 and δ. It may provide a test for the geophysical model of the earth, or it may serve as a method for a stringent test of the Mikheyev-Smirnov-Wolfenstein theory of neutrino propagation in matter once an accurate geophysical estimation of the matter density is available