Testing sterile neutrino mixing with present and future solar neutrino data

We investigate the sensitivity of solar neutrino data to mixing of sterile neutrinos with masses $\gtrsim$ eV. For current data, we perform a Feldman-Cousins analysis to derive a robust limit on the sterile neutrino mixing. The solar neutrino limit excludes significant regions of the parameter space relevant to hints from reactor and radioactive gallium source experiments. We then study the sensitivity of upcoming solar neutrino data, most notably elastic neutrino-electron scattering in the DARWIN and DUNE experiments as well as coherent neutrino-nucleus scattering in DARWIN. These high precision measurements will increase the sensitivity to sterile neutrino mixing by about a factor of 4.5 compared to present limits. As a by-product, we introduce a simplified solar neutrino analysis using only four data points: the low- and high-energy $\nu_e$ survival and transition probabilities. We show that this simplified analysis is in excellent agreement with a full solar neutrino analysis; it is very easy to handle numerically and can be applied to any new physics model in which the energy dependence of the $\nu_e$ transition probabilities is not significantly modified.