Parametric enhancement of flavor oscillation in a three-neutrino framework

Abstract

When neutrinos travel through matter with a periodic density profile, the neutrino oscillation probability can be enhanced if certain conditions are satisfied. In a two-neutrino framework, the condition for parametric resonance is known. Herein, we consider the analogous parametric resonance condition within the context of a full three-neutrino framework with two oscillation scales. For energies in the range of hundreds of MeV to a few GeV, we find that neutrino oscillation can be parametrically enhanced if two approximate relations are satisfied. The first is similar to the two-neutrino parametric resonance condition while the second involves the other oscillation scale. Treating the Earth's density as piecewise constant, we show that oscillations in this energy range can be enhanced between two-and threefold.

Parameter symmetries of neutrino oscillations in vacuum, matter, and approximation schemes

“…We have focused on the standard PDG parameterization of the lepton mixing matrix, but the results presented here apply to different parameterizations containing a different sequence of rotations after straightforward modifications. It may be interesting to explore connections to other parameterizations involving generators of SU(3) [39][40][41], four complex phases [42], five rotations and a complex phase [43], the exponential of a complex matrix [44].…”

The Impact of Different Parameterizations on the Interpretation of CP Violation in Neutrino Oscillations

“…In this paper, we are only considering parameterizations of the form U ijk ≡ U i U j U k for i, j, k = 1, 2, 3 in which i, j, and k are all different. Other parameterizations exist including those using the same rotation axis twice (U iji ) [8], three of the Gell-Mann matrices parameterizing the generators of SU(3) [9][10][11][12], or four complex phases [13]. In this article we focus on parameterizations containing three rotations and one complex phase although we anticipate that our conclusions qualitatively apply to other scenarios as well.…”

The impact of different parameterizations on the interpretation of CP violation in neutrino oscillations

“…In this paper, we are only considering parameterizations of the form U ijk ≡ U i U j U k for i, j, k = 1, 2, 3 in which i, j, and k are all different. Other parameterizations exist [33,34] including those using the same rotation axis twice (U iji ) [35], three of the Gell-Mann matrices parameterizing the generators of SU(3) [36][37][38][39], four complex phases [40], the exponential of a complex matrix [41], or five rotations and a complex phase [42]. 2 If one wanted to include the Majorana phases in the parameterization for U , the symmetric parameterization [43,44] is advantageous over the PDG method of including the Majorana phases, and it simplifies to the PDG parameterization in the context neutrino oscillations.…”