Regresar

An effective two-flavor approximation for neutrino survival probabilities in matter

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≡Δm212/Δm312, with introduction of the effective Δmαα2(α = e, μ, τ), in regions of neutrino energy E and baseline L such that Δm312L/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 s13∝ϵ, 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 Δmαα2(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 Δmμμ2(a) becomes L-dependent, though Δmee2(a) is not, which casts doubt on adequacy of the concept of effective Δm2 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 Δmβα2 from the disappearance channel. A general result is derived to describe suppression of the matter effect in the oscillation probability.