Abstract
It is known in vacuum that the three-flavor neutrino survival probability can be approximated by the effective two-flavor form to first orders in ϵ≡Δm 221 /Δm 231 , with introduction of the effective Δm 2 αα (α = e, μ, τ), in regions of neutrino energy E and baseline L such that Δm 231 L/2E ∼ π. Here, we investigate the question of whether the similar effective two-flavor approximation can be formulated for the survival probability in matter. Using a perturbative framework with the expansion parameters ϵ and \( {s}_{13}\propto \sqrt{\upepsilon} \), we give an affirmative answer to this question and the resultant two-flavor form of the probability is valid to order ϵ. However, we observe a contrived feature of the effective Δm 2 αα (a) in matter. It ceases to be a combination of the fundamental parameters and has energy dependence, which may be legitimate because it comes from the matter potential. But, it turned out that Δm 2 μμ (a) becomes L-dependent, though Δm 2 ee (a) is not, which casts doubt on adequacy of the concept of effective Δm 2 in matter. We also find that the appearance probability in vacuum admits, to order ϵ, the similar effective two-flavor form with a slightly different effective Δm 2 βα from the disappearance channel. A general result is derived to describe suppression of the matter effect in the oscillation probability.
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Minakata, H. An effective two-flavor approximation for neutrino survival probabilities in matter. J. High Energ. Phys. 2017, 43 (2017). https://doi.org/10.1007/JHEP05(2017)043
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DOI: https://doi.org/10.1007/JHEP05(2017)043