Physical region for three-neutrino mixing angles

Abstract

We derive a set of symmetry relations for the three-neutrino mixing angles, including the MSW matter effect. Though interesting in their own right, these relations are used to choose the physical region of the mixing angles such that oscillations are parameterized completely and uniquely. We propose that the preferred way of setting the bounds on the mixing angles should be ${\theta }_{12}\in [0,\pi /2]$, ${\theta }_{13}\in [-\pi /2,\pi /2]$, ${\theta }_{23}\in [0,\pi /2]$, and $\delta \in [0,\pi )$. No CP violation then results simply from setting $\delta =0$. In the presence of the MSW effect, this choice of bounds is a new result. Since the size of the asymmetry about ${\theta }_{13}=0$ is dependent on the details of the data analysis and is a part of the results of the analysis, we argue that the negative values of ${\theta }_{13}$ should not be ignored.

arXiv comment4 pages

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Cited by in corpus (9)

• The Physical Range of Majorana Neutrino Mixing Parameters
• Atmospheric, long baseline, and reactor neutrino data constraints on ${\theta }_{13}$
• Implications of the Super-K atmospheric data for the mixing angles ${\theta }_{13}$ and ${\theta }_{23}$
• Neutrino oscillations: measuring ${\theta }_{13}$ including its sign
• Correlations between ${\theta }_{13}$ and ${\theta }_{23}$ in a very long baseline neutrino oscillation experiment
• Parameterizing Majorana Neutrino Couplings in the Higgs Sector
• On detecting CP violation in a single neutrino oscillation channel at very long baselines
• The impact of hierarchy upon the values of neutrino mixing parameters
• Implications of nonzero ${\theta }_{13}$ for the neutrino mass hierarchy