Small neutrino masses from gravitational $θ$-term
Gia Dvali, Lena Funcke
TL;DR
The paper argues that a physical gravitational θ-term, via gravitational anomalies, induces a bound neutrino state η_ν and a neutrino vacuum condensate, providing a nonperturbative mechanism for generating small neutrino masses. This is implemented through a three-form Higgs mechanism that yields a mass gap analogous to the QCD η′ story, with the condensate acting as the order parameter. The resulting framework predicts a late-time phase transition at the meV scale, which removes cosmological neutrino mass bounds and creates light scalar degrees of freedom that affect high-energy neutrino processes, relic neutrinos, and possibly dark matter. It also anticipates observable consequences in IceCube flavor distributions, KATRIN measurements, gravitational-wave signals, and potential short-distance gravity tests, while remaining agnostic about UV completion due to anomaly-insensitivity at low energies.
Abstract
We present how a neutrino condensate and small neutrino masses emerge from a topological formulation of gravitational anomaly. We first recapitulate how a gravitational $θ$-term leads to the emergence of a new bound neutrino state analogous to the $η'$ meson of QCD. Then we show the consequent formation of a neutrino vacuum condensate, which effectively generates small neutrino masses. Afterwards we outline several phenomenological consequences of our neutrino mass generation model. The cosmological neutrino mass bound vanishes since we predict the neutrinos to be massless until the phase transition in the late Universe, $T\sim {\rm meV}$. Deviations from an equal flavor rate due to enhanced neutrino decays in extraterrestrial neutrino fluxes can be observed in future IceCube data. The current cosmological neutrino background only consists of the lightest neutrinos, which, due to enhanced neutrino-neutrino interactions, either bind up, form a superfluid, or completely annihilate into massless bosons. Strongly coupled relic neutrinos could provide a contribution to cold dark matter in the late Universe, together with the new proposed particles and topological defects, which may have formed during neutrino condensation. These enhanced interactions could also be a source of relic neutrino clustering in our Galaxy, which possibly makes the overdense cosmic neutrino background detectable in the KATRIN experiment. The neutrino condensate provides a mass for the hypothetical $B-L$ gauge boson, leading to a gravity-competing force detectable in short-distance measurements. Gravitational waves detections have the potential to probe our neutrino mass generation mechanism.