Revising the Solution of the Neutrino Oscillation Parameter Degeneracies at Neutrino Factories

In the context of neutrino factories, we review the solution of the degeneracies in the neutrino oscillation parameters. In particular, we have set limits to $\sin^2 2\theta_{13}$ in order to accomplish the unambiguous determination of $\theta_{23}$ and $\delta$. We have performed two different analysis. In the first, at a baseline of 3000 km, we simulate a measurement of the channels $\nu_e\to\nu_\mu$, $\nu_e\to\nu_\tau$ and $\bar{\nu}_\mu\to\bar{\nu}_\mu$, combined with their respective conjugate ones, with a muon energy of 50 GeV and a running time of five years. In the second, we merge the simulated data obtained at L=3000 km with the measurement of $\nu_e\to\nu_\mu$ channel at 7250 km, the so called 'magic baseline'. In both cases, we have studied the impact of varying the $\nu_\tau$ detector efficiency-mass product, $(\epsilon_{\nu_\tau}\times M_\tau)$, at 3000 km, keeping unchanged the $\nu_\mu$ detector mass and its efficiency. At L=3000 km, we found the existance of degenerate zones, that corresponds to values of $\theta_{13}$, which are equal or almost equal to the true ones. These zones are extremely difficult to discard, even when we increase the number of events. However, in the second scenario, this difficulty is overcomed, demostrating the relevance of the 'magic baseline'. From this scenario, the best limits of $\sin^2 2\theta_{13}$, reached at $3\sigma$, for $\sin^2 2\theta_{23}=0.95$, 0.975 and 0.99 are: 0.008, 0.015 and 0.045, respectively, obtained at $\delta=0$, and considering $(\epsilon_{\nu_\tau}\times M_\tau) \approx 125$, which is five times the initial efficiency-mass combination.Comment: 40 pages, 18 figures; added references, corrected typos, updated Eq (15c