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

TL;DR

This work investigates neutrinos acquiring refractive masses through interactions with an ultralight DM background, modeled by two sterile neutrinos and a light scalar. The authors diagonalize a $5\times5$ neutrino Hamiltonian with a unitary $\mathbb{P}$ parameterized by six mixing angles and one phase, enabling a reduction to an effective two-flavor problem inside the Sun for uniform DM. They then explore the impact of a solar DM halo, characterized by a radius $R_\star$ and overdensity, on Mixing angles, level crossings, and the electron-neutrino survival probability $P_{ee}$, showing that production region strongly influences the observed spectrum when a halo is present. The flux-averaged survival probability can exhibit distinctive features, including a flat spectrum in the $2$–$15$ MeV range and a jump near $15$ MeV in the dark-LMA scenario, which can be partially reconciled with SK/SNO data. The paper provides halo-parameter regions that can revive the dark-LMA solution and highlights testable predictions for upcoming solar neutrino experiments (JUNO, Hyper-K, DUNE).

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.

Figures (12)

• Figure 1: Mixing angles (upper panels) and mass-squared values (lower panels) in the 5-neutrino system for $E =0.5 \ \text{MeV (left panels) and}\ E =10\ \text{MeV (right panels)}$ when $m_\phi = 10^{-9}$ eV, $m_\chi^2 = 10^{-7}\, \text{eV}^2$ and $\dot{\Phi}=m_\phi$. The choice of parameters ensures small active-sterile mixing angles. We take $s_{12}^2 = 0.32$ in the uniform DM background. The vertical dotted line in the right panels represents the radial distance at which the MSW resonance occurs for $E = 10$ MeV. It is evident that in this scenario, the neutrino evolution can be treated effectively as a two-flavor problem.
• Figure 2: Mixing angles (upper panels) and mass-squared values (lower panels) in the 5-neutrino system for $E =0.5 \ \text{MeV (left panels) and}\ E =10\ \text{MeV (right panels)}$ when $m_\phi = 10^{-22}$ eV, $m_\chi^2 = 10^{-20}\, \text{eV}^2$ and $\dot{\Phi}=0$. The choice of parameters ensures small active-sterile mass-squared difference. We take $s_{12}^2 = 0.32$ in the uniform DM background. The vertical dotted line in the right panels represents the radial distance at which the MSW resonance occurs for $E = 10$ MeV. It is evident that in this scenario, the neutrino evolution can be treated effectively as a two-flavor problem.
• Figure 3: Mixing angles (upper panels) and mass-squared values (lower panels) in the 5-neutrino system for $E =0.5 \ \text{MeV (left panels) and}\ E =10\ \text{MeV (right panels)}$ when $m_\phi = 10^{-9}$ eV, $m_\chi^2 = 10^{-7}\, \text{eV}^2$ and $\dot{\Phi}=m_\phi$, $M_\star =10^{-8}\,M_\odot$. We take $s_{12}^2 = 0.32$ in the uniform DM background. The vertical dashed line indicates the boundary of RHD ($r = r_0$) and the shaded region represents the RHD core ($r \leq r_1$). Notice the sharp core-periphery transition. Beyond RHD, the plots mimic the standard MSW evolution.
• Figure 4: Mixing angles (upper panels) and mass-squared values (lower panels) in the 5-neutrino system for $E =0.5 \ \text{MeV (left panels) and}\ E =10\ \text{MeV (right panels)}$ when $m_\phi = 10^{-9}$ eV, $m_\chi^2 = 10^{-7}\, \text{eV}^2$, $\dot{\Phi}=m_\phi$ and $M_\star =10^{-25}\,M_\odot$. We take $s_{12}^2 = 0.32$ in the uniform DM background. The vertical dashed line indicates the boundary of RHD ($r = r_0$). Within RHD, there is no sharp core-periphery transition. Beyond RHD, the plots mimic the standard MSW evolution.
• Figure 5: Left panel: Survival probability of an electron neutrino produced at different radial distances $r=0.05\, R_\odot$, $r=0.085\, R_\odot$ and $r=0.1\, R_\odot$, for a DM halo with $m_\phi = 10^{-9}$ eV, $m_\chi^2 = 10^{-7}\, \text{eV}^2$ and $\dot{\Phi}=m_\phi$, $M_\star =10^{-8}\,M_\odot$. The three radial distances are chosen to correspond to regions within the RHD core, the RHD periphery and outside the RHD, respectively. Right panel: Survival probability of an electron neutrino produced at $r=0.05\, R_\odot$ for different halo parameters. We have taken $m_\chi^2 = 2\, E_R\, m_\phi$ with $E_R=50$ eV. The value of $s_{12}^2$ has been taken to be 0.32 for all scenarios, for illustration.