Testing the dark side of neutrino oscillations with the solar neutrino fog at dark matter experiments

The recent detection of the solar neutrino background at dark matter direct detection experiments paves the way to fully explore an important degeneracy in neutrino oscillations in the presence of new interactions, named the LMA-Dark degeneracy. This degeneracy makes it impossible to determine the neutrino mass ordering in oscillation experiments if neutrinos have new vectorial interactions with matter. As the composition of solar neutrinos at the Earth consists of all three neutrino flavors, testing the presence of new neutrino interactions in the muon and tau neutrino sector in scatterings can fully probe the LMA-Dark region for the first time. In this paper we show that current data from XENONnT and PandaX-4T do not yet exclude the LMA-Dark region with equal couplings of a new mediator to muon and tau neutrinos and quarks, and we identify the possible experimental scenarios to do so in the future. We also show that dark matter experiments can distinguish new interactions in the muon or tau sector only from new interactions affecting both sectors.