On the energy and baseline optimization to study effects related to the δ-phase (CP-/T-violation) in neutrino oscillations at a neutrino factory

In this paper we discuss the detection of CP- and T-violation effects in the framework of a neutrino factory. We introduce three quantities, which are good discriminants for a non-vanishing complex phase (δ) in the 3x3 neutrino mixing matrix: Δδ, ΔCP and ΔT. We find that these three discriminants (in vacuum) all scale with L/Eν, where L is the baseline and Eν the neutrino energy. Matter effects modify the scaling, but these effects are large enough to spoil the sensitivity only for baselines larger than 5000 km. So, in the hypothesis of constant neutrino factory power (i.e., number of muons inversely proportional to muon energy), the sensitivity on the δ-phase is independent of the baseline chosen. Specially interesting is the direct measurement of T-violation from the 'wrong-sign' electron channel (i.e., the ΔT discriminant), which involves a comparison of the νe→νμ and νμ→νe oscillation rates. However, the νμ→νe measurement requires magnetic discrimination of the electron charge, experimentally very challenging in a neutrino detector. Since the direction of the electron curvature has to be estimated before the start of the electromagnetic shower, low-energy neutrino beams and hence short baselines, are preferred. In this paper we show, as an example, the exclusion regions in the Δm212-δ plane using the ΔCP and ΔT discriminants for two concrete cases keeping the same L/Eν ratio (730 km/7.5 GeV and 2900 km/30 GeV). We obtain a similar excluded region provided that the electron detection efficiency is ∼20% and the charge confusion 0.1%. The Δm212 compatible with the LMA solar data can be tested with a flux of 5x1021 muons. We compare these results with the fit of the visible energy distributions