Solar neutrino spectrum, sterile neutrinos and additional radiation in the Universe

TL;DR

The paper tackles the absence of the expected low-energy upturn in the solar neutrino spectrum and cosmological hints of extra radiation by proposing a very light sterile neutrino that mixes with active states. It develops a four-neutrino framework in which sterile mixing in the $\nu_1/\nu_2$ sector creates a dip in the electron-neutrino survival probability $P_{ee}$, potentially removing the upturn, while mixing into $\nu_3$ can yield $\Delta N_{eff} \approx 1$ before BBN, linking solar physics with early-Universe cosmology. The analysis yields constraints from Borexino Be-line measurements and boron-spectrum data, showing that allowed regions include $R_\Delta \sim 0.07-0.25$ with $\sin^2 2\alpha \sim 10^{-3}$, though very small $\Delta m^2_{01}$ are disfavored by Be data. The work further predicts phenomenology in atmospheric, accelerator, and SN neutrinos through resonances and potential wiggles in $P_{ee}$, as well as cosmological signatures from $\nu_s$ in $\nu_3$ that could produce observable $\Delta N_{eff}$ prior to BBN. Overall, the framework provides testable predictions for upcoming solar, atmospheric, and cosmological observations, linking subleading neutrino mixing to both terrestrial and cosmic probes.

Abstract

Recent results from the SNO, Super-Kamiokande and Borexino experiments do not show the expected upturn of the energy spectrum of events (the ratio $R \equiv N_{obs}/N_{SSM}$) at low energies. At the same time, cosmological observations testify for possible existence of additional relativistic degrees of freedom in the early Universe: $ΔN_{eff} = 1 - 2$. These facts strengthen the case of very light sterile neutrino, $ν_s$, with $Δm^2_{01} \sim (0.7 - 2) \cdot 10^{-5}$ eV$^2$, which mixes weakly with the active neutrinos. The $ν_s$ mixing in the mass eigenstate $ν_1$ characterized by $\sin^2 2α\sim 10^{-3}$ can explain an absence of the upturn. The mixing of $ν_s$ in the eigenstate $ν_3$ with $\sin^2 β\sim 0.1$ leads to production of $ν_s$ via oscillations in the Universe and to additional contribution $ΔN_{eff} \approx 0.7 - 1$ before the big bang nucleosynthesis and later. Such a mixing can be tested in forthcoming experiments with the atmospheric neutrinos as well as in future accelerator long baseline experiments. It has substantial impact on conversion of the supernova neutrinos.

Figures (14)

• Figure 1: The level crossing scheme for the neutrino energy $E = 10$ MeV. Dependence of the eigenvalues of total Hamiltonian in matter, $\lambda_i$, on distance from the center of the Sun. The LMA neutrino oscillation parameters are taken as $\Delta m^2_{21} = 8\times 10^{-5}$ eV$^2$ and $\tan^2\theta_{12} =0.44$, while sterile neutrino parameters are $R_\Delta = 0.25$ and $\sin^22\alpha=10^{-3}$.
• Figure 2: Flavor content of the mass eigenstates in matter for the same neutrino parameters as in fig. \ref{['fig:eigenvalues']}.
• Figure 3: The survival probability of the electron neutrino as function of neutrino energy for different values of the sterile-active mixing parameter $\sin^2 2\alpha$ and mass scale $R_\Delta \ll 1$. The active neutrino parameters are $\Delta m^2_{21}=8\times 10^{-5}$ eV$^2$ and $\tan^2\theta=0.44$.
• Figure 4: The same as in fig. \ref{['fig:psurv']} for higher values of mixing angle $\alpha$.
• Figure 5: The same as in fig. \ref{['fig:psurv']} for $R_\Delta > 1$.