Abstract
Motivated by tremendous progress in neutrino oscillation experiments, we derive a new set of simple and compact formulas for three-flavor neutrino oscillation probabilities in matter of a constant density. A useful definition of the η-gauge neutrino mass-squared difference Δ∗ ≡ ηΔ31 + (1 − η)Δ32 is introduced, where Δ ji ≡m 2 j − m 2 i for ji = 21, 31, 32 are the ordinary neutrino mass-squared differences and 0 ≤ η ≤ 1 is a real and positive parameter. Expanding neutrino oscillation probabilities in terms of α ≡ Δ21 /Δ∗, we demonstrate that the analytical formulas can be remarkably simplified for η = cos2 θ 12, with θ 12 being the solar mixing angle. As a by-product, the mapping from neutrino oscillation parameters in vacuum to their counterparts in matter is obtained at the order of \( \mathcal{O}\left({\alpha}^2\right) \). Finally, we show that our approximate formulas are not only valid for an arbitrary neutrino energy and any baseline length, but also still maintaining a high level of accuracy.
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Li, YF., Zhang, J., Zhou, S. et al. Looking into analytical approximations for three-flavor neutrino oscillation probabilities in matter. J. High Energ. Phys. 2016, 109 (2016). https://doi.org/10.1007/JHEP12(2016)109
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DOI: https://doi.org/10.1007/JHEP12(2016)109