Predictions of the neutrino oscillations parameters

Abstract

We demonstrate that the observed parameters, related to the flavor oscillation of the neutrinos, are consistent with a system with three degenerate ground states. These ground states must have the same energy and they are connected by a symmetry with its corresponding generator. This symmetry is not spontaneously broken because the neutrino never selects a specific vacuum state. Instead, the neutrino keeps oscillating between the three ground states as it moves through spacetime. The order parameter in this case is the neutrino flavor and then the superposition of all the possible vacuum flavor states for one neutrino gives a trivial (zero) result. From this trivial condition, we can find constraints over the observed mixing angles ${\theta }_{ij}$. By using these constraints we make the predictions of the mixing angles which are in agreement with the observations. Subsequently, complementing these arguments with a triangular formulation of the neutrino oscillation, we find relations between the the mass eigenvalues and the mixing angles, making again predictions consistent with the observations and consistent with a normal order in hierarchy with $m_3>>m_2\approx m_1$. Finally, we analyze the symmetry related to the flavor oscillation.

21 pages in its published version, 3 figures

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