Refractive neutrino masses in the solar DM halo: Can the dark-LMA solution be revived?

Abstract: Neutrinos can acquire "refractive masses" as a consequence of their interactions with ultralight dark matter (DM). We explore a model with two additional sterile neutrinos and an ultralight scalar field which acts as DM and interacts with all five neutrinos. We show that the effective $5 \times 5$ Hamiltonian for neutrino propagation can be diagonalized by a unitary matrix $\mathbb{P}$ parametrized by 6 mixing angles and 1 complex phase. When active-sterile mixing angles are small, we identify a parametrization for $\mathbb{P}$ that reduces neutrino propagation inside the Sun to a two-flavor problem for a uniform DM background. In the presence of a DM halo inside the Sun, however, the propagation shows additional features in the region of halo dominance. We derive approximate analytic expressions for the electron neutrino survival probability in the presence of the DM halo. We show that this probability has a strong dependence on the neutrino production region even for a fixed energy, and numerically calculate the effects of averaging over these production regions. Comparisons with the re-interpreted solar data, in the light of possible active-sterile neutrino conversions, would allow putting bounds on the halo parameters. Finally, we examine the possibility of reviving the dark-LMA solution in this context, where the survival probability spectrum can have attractive features aligned with the measurements at Super-Kamiokande.