Constraints on Decaying Sterile Neutrinos from Solar Antineutrinos

Solar neutrino experiments are highly sensitive to sources of $\nu\to\overline{\nu}$ conversions in the $^8$B neutrino flux. In this work we adapt these searches to non-minimal sterile neutrino models recently proposed to explain the LSND, MiniBooNE, and reactor anomalies. The production of such sterile neutrinos in the Sun, followed the decay chain $\nu_4 \to \nu \phi \to \nu \nu \overline{\nu}$ with a new scalar $\phi$ results in upper limits for the neutrino mixing $|U_{e4}|^2$ at the per mille level. We conclude that a simultaneous explanations of all anomalies is in tension with KamLAND, Super-Kamiokande, and Borexino constraints on the flux of solar antineutrinos. We then present other minimal models that violate parity or lepton number, and discuss the applicability of our constraints in each case. Future improvements can be expected from existing Borexino data as well as from future searches at Super-Kamiokande with added Gd.