Effects of random matter density fluctuations on the neutrino oscillation transition probabilities in the Earth

In this Letter, we investigate the effects of random fluctuations of the Earth matter density for long baselines on the neutrino oscillation transition probabilities. We especially identify relevant parameters characterizing the matter density noise and calculate their effects by averaging over statistical ensembles of a large number of matter density profiles. For energies and baselines appropriate to neutrino factories, absolute errors on the relevant appearance probabilities are at the level of |ΔPαβ|∼10−4 (with perhaps |ΔPμe|/Pμe∼1% for neutrinos), whereby a modest improvement in understanding of the geophysical data should render such effects unimportant.