Parameter degeneracies in neutrino oscillation measurement of leptonicCPandTviolation
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Abstract
The measurement of the mixing angle ${\ensuremath{\theta}}_{13},$ sign of $\ensuremath{\Delta}{m}_{13}^{2},$ and the $\mathrm{CP}$ or T violating phase $\ensuremath{\delta}$ is fraught with ambiguities in neutrino oscillation. In this paper we give an analytic treatment of the paramater degeneracies associated with measuring the ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{e}$ probability and its $\mathrm{CP}$ and/or T conjugates. For $\mathrm{CP}$ violation, we give explicit solutions to allow us to obtain the regions where there exist twofold and fourfold degeneracies. We calculate the fractional differences, $(\ensuremath{\Delta}\ensuremath{\theta}/\overline{\ensuremath{\theta}}),$ between the allowed solutions which may be used to compare with the expected sensitivities of the experiments. For T violation we show that there is always a complete degeneracy between solutions with positive and negative $\ensuremath{\Delta}{m}_{13}^{2}$ which arises due to a symmetry and cannot be removed by observing one neutrino oscillation probability and its T conjugate. Thus there is always a fourfold parameter degeneracy apart from exceptional points. Explicit solutions are also given and the fractional differences are computed. The biprobability $CP/T$ trajectory diagrams are extensively used to illuminate the nature of the degeneracies.