Matter Effects in Active-Sterile Solar Neutrino Oscillations

TL;DR

The paper addresses solar neutrino oscillations in the presence of an arbitrary number of sterile neutrinos (3+N_s framework) under a realistic mass-hierarchy, deriving an analytic MSW-based expression for flavor transitions. By decoupling the heavy-sterile states, the authors reduce the problem to an effective two-state system in the solar 1-2 sector, characterized by an effective mixing angle $ξ$ and a crossing probability $P_{12}$, with the evolution governed by the adiabaticity parameter $γ$. The key result is a general formula for the averaged flavor probabilities $\overline{P}_{ν_e→ν_β}$ that reduces to familiar two-neutrino results in the appropriate limit and remains valid for arbitrary sterile admixtures; this analytic solution is validated against numerical solutions in three four-neutrino mixing examples. The findings show that active-sterile mixing can significantly alter the electron-neutrino survival and sterile transition probabilities in solar data, offering a practical framework to constrain sterile neutrino properties from solar observations, while remaining robust to modest variations in solar density parameters.

Abstract

The matter effects for solar neutrino oscillations are studied in a general scheme with an arbitrary number of sterile neutrinos, without any constraint on the mixing, assuming only a realistic hierarchy of neutrino squared-mass differences in which the smallest squared-mass difference is effective in solar neutrino oscillations. The validity of the analytic results are illustrated with a numerical solution of the evolution equation in three examples of the possible mixing matrix in the simplest case of four-neutrino mixing.

Figures (4)

• Figure 1: Hydrogen mass fraction $X_{\text{H}}$, electron number fraction $Y_{e}=(1+X_{\text{H}})/2$, and neutral-current to charged-current ratio $R_{\text{NC}}$ [Eq. (\ref{['025']})] in the BP04 Standard Solar Model astro-ph/0402114. $R_{\text{SUN}} \simeq 6.7 \times 10^{10} \, \text{cm}$ is the radius of the Sun.
• Figure 2: Averaged probability of $\nu_{e}$ survival as a function of the neutrino energy $E$ for the three examples of mixing matrices M1, M2, and M3 in Tab. \ref{['tab01']}. For each of them we consider the two values of the electron fraction $Y_{e}$ in Tab. \ref{['tab01']}. In each plot, the solid line is obtained with the analytic expression in Eq. (\ref{['068']}), the points are obtained with a numerical solution of the evolution equation, the horizontal dashed line shows the value of $\overline{P}_{\nu_{e}\to\nu_{e}}^{\text{VAC}}$, and the horizontal dotted line shows the value of $\overline{P}_{\nu_{e}\to\nu_{e}}^{(\gamma_{\text{R}} \ll 1)}$.
• Figure 3: Averaged probability of $\nu_{e}\to\nu_{s}$ transitions as a function of the neutrino energy $E$ for the three examples of mixing matrices M1, M2, and M3 in Tab. \ref{['tab01']}. For each of them we consider the two values of the electron fraction $Y_{e}$ in Tab. \ref{['tab01']}. In each plot, the solid line is obtained with the analytic expression in Eq. (\ref{['068']}), the points are obtained with a numerical solution of the evolution equation, the horizontal dashed line shows the value of $\overline{P}_{\nu_{e}\to\nu_{s}}^{\text{VAC}}$, and the horizontal dotted line shows the value of $\overline{P}_{\nu_{e}\to\nu_{s}}^{(\gamma_{\text{R}} \ll 1)}$.
• Figure 4: Averaged probability of $\nu_{e}$ survival and $\nu_{e}\to\nu_{s}$ transitions as functions of the neutrino energy $E$ for the three examples of mixing matrices M1, M2, and M3 in Tab. \ref{['tab01']} calculated for the BP04 Standard Solar Model density astro-ph/0402114. For each of the three examples the lines are obtained with the analytic expression in Eq. (\ref{['068']}) and the overlapping points are obtained with a numerical solution of the evolution equation. In the left panel we also plotted the standard three-neutrino mixing value of $\overline{P}_{\nu_{e}\to\nu_{e}}(E)$ in the case of negligible $U_{e3}$ (dash-dotted line).