Determination of the Pattern of Neutrino Masses at a Neutrino Factory

We study the precision with which the sign of δm232 can be determined at a neutrino factory, as a function of stored muon energies and baselines. This is done by simultaneously fitting the channels νμ → νμ , ν̄e → ν̄μ from μ− decays and the channels ν̄μ → ν̄μ , νe → νμ from μ decays. For a 20 GeV muon storage ring we investigate as a function of the baseline length and the magnitude of δm232, the minimum value of the parameter sin 2θ13 for which the sign of δm 2 32 can be determined to at least 3 standard deviations. We find that for baselines longer than ∼ 3000 km, the sign of δm232 can be determined for sin 2θ13 down to the 10 −3 level with 10 decays of 20 GeV muons.