On the energy and baseline optimization to study effects related to the $\delta$-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 ($\delta$) in the $3\times 3$ neutrino mixing matrix. We find that these three discriminants (in vacuum) all scale with $L/E_{\nu}$. 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, the sensitivity on the $\delta$-phase is independent of the baseline chosen. Specially interesting is the direct measurement of T-violation from the ``wrong-sign'' electron channel, which involves a comparison of the $\nue\ra\numu$ and $\numu\ra\nue$ oscillation rates. However, the $\numu\ra\nue$ measurement requires magnetic discrimination of the electron charge, experimentally very challenging in a neutrino detector: low-energy neutrino beams and hence short baselines, are preferred. In this paper we show the exclusion regions in the $\Delta m^2_{12} - \delta$ plane for two concrete cases. We obtain a similar excluded region provided that the electron detection efficiency is $\sim$20% and the charge confusion 0.1%. The $\Delta m^2_{12}$ compatible with the LMA solar data can be tested with a flux of 5$\times 10^{21}$ muons. We compare these results with the fit of the visible energy distributions.