Constraining super-light sterile neutrinos at Borexino and KamLAND

The presence of a super-light sterile neutrino can lead to a dip in the survival probability of solar neutrinos, and explain the suppression of the upturn in the low energy solar neutrino data. In this work, we systematically study the survival probabilities in the 3+1 framework by taking into account of the non-adiabatic transitions and the coherence effect. We obtain an analytic equation that can predict the position of the dip. We also place constraints on the parameter space of sterile neutrinos by using the latest Borexino and KamLAND data. We find that the low and high energy neutrino data at Borexino are sensitive to different regions in the sterile neutrino parameter space. In the case with only $\theta_{01}$ being nonzero, the $\rm{{}^{8}B}$ data sets the strongest bounds at $\Delta m_{01}^{2} \approx (1.1\sim2.2)\Delta m_{21}^{2}$, while the low energy neutrino data is more sensitive to other mass-squared regions. The lowest bounds on $\Delta m_{01}^{2}$ from the $\rm{pp}$ data can reach $10^{-12} \ \rm{eV^{2}}$ because of the coherence effect. Also, due to the presence of non-adiabatic transitions, the bounds in the range of $10^{-9} \ \textrm{eV}^{2} \lesssim \Delta m_{01}^{2} \lesssim 10^{-5} \ \textrm{eV}^{2}$ become weaker as $\Delta m_{01}^{2}$ or $\sin^{2}2\theta_{01}$ decreases. We also find that in the case with only $\theta_{02}$ or $\theta_{03}$ being nonzero, the low energy solar neutrino data set similar but weaker bounds as compared to the case with only $\theta_{01}$ being nonzero. However, the bounds from the high energy solar data and the KamLAND data are largely affected by the sterile mixing angles.