An effective twoflavor approximation for neutrino survival probabilities in matter
Abstract
It is known in vacuum that the threeflavor neutrino survival probability can be approximated by the effective twoflavor form to first orders in ∊≡ ∆m _{21} ^{2} / ∆m _{31} ^{2} , with introduction of the effective ∆m _{ αα } ^{2} ( α = e, μ, τ), in regions of neutrino energy E and baseline L such that ∆m _{31} ^{2} L/2 E ̃ π. Here, we investigate the question of whether the similar effective twoflavor approximation can be formulated for the survival probability in matter. Using a perturbative framework with the expansion parameters ∊ and {s}_{13}∝ √{∊} , we give an affirmative answer to this question and the resultant twoflavor form of the probability is valid to order ∊. However, we observe a contrived feature of the effective ∆m _{ αα } ^{2} ( 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 ∆m _{ μμ } ^{2} ( a) becomes Ldependent, though ∆m _{ ee } ^{2} ( a) is not, which casts doubt on adequacy of the concept of effective ∆ m ^{2} in matter. We also find that the appearance probability in vacuum admits, to order ∊, the similar effective twoflavor form with a slightly different effective ∆m _{ βα } ^{2} from the disappearance channel. A general result is derived to describe suppression of the matter effect in the oscillation probability.
 Publication:

Journal of High Energy Physics
 Pub Date:
 May 2017
 DOI:
 10.1007/JHEP05(2017)043
 arXiv:
 arXiv:1702.03332
 Bibcode:
 2017JHEP...05..043M
 Keywords:

 Neutrino Physics;
 Beyond Standard Model;
 High Energy Physics  Phenomenology
 EPrint:
 Discussion on appearance effective $\Delta m^2$ added. Version to appear in JHEP. 26 pages, 3 figures