Electroweak Axion as the Fuzzy Dark Matter -- A Proposal for the Mixed Fuzzy and Cold Dark Matters

The electroweak axion is identified with the fuzzy dark matter of a mass $m\simeq {10}^{-20}$–${10}^{-19}\mathrm{e}\mathrm{V}$. The model predicts two components of dark matter, one is ultralight and the other is WIMP-like. The Chern-Simons-type interaction between the fuzzy dark matter and photon and the $B+L$ breaking proton decays are predicted.