On How Neutrino Protects the Axion

TL;DR

The paper recasts the axion solution to the strong-CP problem as a three-form Higgs mechanism, where a mass gap for the QCD Chern-Simons three-form $C$ ensures $\theta$-independence. It identifies gravity as a potential threat that can reintroduce a massless pole unless the gravitational sector is kept busy by additional structure; the authors propose a protection mechanism based on the Standard Model neutrino lepton-number anomaly, which, for vanishing or tiny neutrino mass $m_ν$, preserves the axion solution and yields a quantitative bound $m_ν\lesssim 10^{-9}\frac{\Lambda^4}{α_G^2\Lambda_G^3}$ linked to the non-perturbative gravity scale $\Lambda_G$. A nonzero $m_ν$ generates a pseudo-Goldstone $\eta_ν$ and a revised low-energy dynamics with a new pseudoscalar degree of freedom, $η_ν$, whose presence could have phenomenological and cosmological consequences. Overall, the work connects axion stability under quantum gravity to neutrino physics, offering a gauge-invariant framework and testable implications for both neutrino masses and gravity-sector scales.

Abstract

We show how the neutrino can sacrifice itself to quantum gravity and save the axion solution to the strong-CP problem. This mechanism puts an upper bound on the lightest neutrino mass.