Off-axis beams and detector clusters: Resolving neutrino parameter degeneracies

There are three parameter degeneracies inherent in the three-neutrino analysis of long-baseline neutrino experiments. We develop a systematic method for determining whether or not a set of measurements in neutrino oscillation appearance experiments with approximately monoenergetic beams can completely resolve these ambiguities. We then use this method to identify experimental scenarios in which the parameter degeneracies may be efficiently resolved. Generally speaking, with two appearance measurements degeneracies can occur over wide areas of the $(\delta ,{\theta }_{13})$ parameter space; with three measurements they occur along lines in the parameter space and with four measurements they occur only at isolated points. If two detectors are placed at the same distance from the source but at different locations with respect to the main axis of the beam (a detector cluster), each detector will measure neutrinos at different energies. Then one run with neutrinos and one run with antineutrinos will give the four independent measurements that in principle can resolve all of the parameter degeneracies if ${\sin }^{2}2{\theta }_{13}>~\mathrm{0.002.}$ We also examine scenarios with detector clusters using only neutrino beams. Without detector clusters, the measurement of neutrinos and antineutrinos at a short distance and only neutrinos at a longer distance may also work.