Title:Neutrino mass and ultralight dark matter mass from the Higgs mechanism

Abstract:We propose a model in which small neutrino masses are generated via Yukawa coupling to a self-interacting ultralight dark matter (ULDM) field, treated as a pseudo-Nambu-Goldstone boson associated with a heavy Higgs-like field. ULDM has a mass \( m \gtrsim 10^{-22}~\text{eV} \) and a characteristic energy scale \( \tilde{m} \simeq 10~\text{eV} \). The resulting neutrino mass, as well as the mass and self-interaction strength of ULDM, align with cosmological observations. A quantum stability condition for an ULDM effective potential demands a small mass for neutrinos roughly bounded by $\tilde{m}$. The phase transition temperature for the Higgs mechanism can approach the grand unified theory (GUT) scale, potentially inducing the electroweak scale by reverting the type I seesaw mechanism for Majonara neutrinos. In this framework, neutrino masses can vary with spacetime, a feature that may be experimentally detectable through neutrino oscillation experiments. We also explore a scenario in which the tiny ULDM mass arises through radiative corrections via the Coleman-Weinberg mechanism, beginning from a massless field theory.
Our model addresses both the neutrino mass and ULDM mass puzzles through a unified approach, providing insights into possible extensions of the Standard Model.