Oscillating Neutrinos vs. Oscillating Scalars: Constraining Scalar Dark Matter-Induced Neutrino Mass

We consider the hypothesis that neutrino masses are generated by a coupling to an ultra-light (pseudo-)scalar field, which provides the dark matter in the universe. This leads to time-varying neutrino masses with a frequency set by the dark matter mass, with implications for neutrino oscillation data. We use that dark matter is in a virialised state in the galaxy and provide a detailed discussion of the relevant time scales. Using data from the T2K, RENO and JUNO experiments, we show that for dark matter masses smaller than about $3\times 10^{-8}$eV down to the smallest allowed dark matter mass of about $10^{-21}$eV only a fraction of between 9\% to 54\% of the total neutrino mass can arise from the coupling to the background scalar, depending on the value of the scalar mass. Future data from JUNO may improve these limits down to 1\% in certain regions of scalar masses. We focus on a real scalar field, but most of our results hold also for a complex scalar.