Pseudo-Goldstone Neutrinos and Majoron Phenomenology from Spontaneous $U(1){Lμ-L_τ}$ Breaking

TL;DR

This work develops a SUSY framework where spontaneous breaking of a leptonic $U(1)_{L_\mu-L_\tau}$ symmetry yields a Majoron-like ALP and a pseudo-Goldstone RH neutrino, naturally generating a low-scale seesaw and a full-rank light-neutrino mass matrix. The model predicts characteristic correlations among the symmetry-breaking scale $U$, heavy neutrino masses, Majoron couplings, and neutrino lifetimes, and identifies benchmark points spanning $U$ from $10^3$ to $10^6$ GeV. Majoron-induced invisible neutrino decays can relax cosmological mass bounds and lead to observable effects in long-baseline experiments and displaced-vertex collider signatures. The framework is testable via a combination of neutrino oscillation/decay experiments, cosmological surveys, and collider searches, with a coherent set of predictions linking laboratory, astrophysical, and cosmological probes to the mechanism of neutrino mass generation and axion-like physics.

Abstract

We present a predictive framework for neutrino mass generation based on the spontaneous breaking of a leptonic $U(1)_{L_μ-L_τ}$ symmetry within a supersymmetric setting. The breaking of the global symmetry gives rise to a Majoron-like axion-like particle and a pseudo-Goldstone right-handed neutrino whose mass is naturally suppressed by supersymmetry-breaking effects. The interplay between the pseudo-Goldstone neutrino and the low-scale seesaw mechanism leads to a structured neutrino mass matrix capable of reproducing the observed neutrino masses, mixing angles, and CP-violating phase without invoking extreme parameter hierarchies. We perform a numerical fit to current neutrino oscillation data and identify representative benchmark solutions consistent with laboratory constraints as well as cosmological and astrophysical bounds. A characteristic outcome of the framework is the emergence of correlated relations linking the symmetry breaking scale, heavy neutrino masses, Majoron couplings, and neutrino lifetimes. Majoron-induced invisible neutrino decay arises generically and can significantly modify cosmological neutrino mass constraints for sufficiently low symmetry breaking scales. We discuss the phenomenological implications across neutrino oscillation experiments, cosmology, and collider searches for long-lived heavy neutrinos. While a detailed experimental simulation is beyond the scope of this work, existing sensitivity projections indicate that portions of the parameter space may become accessible in future facilities. The combined interplay of laboratory probes and cosmological observations provides a consistent and testable picture of neutrino mass generation tied to spontaneous leptonic symmetry breaking and axion-like physics.

Figures (9)

• Figure 1: Broad parameter scan of the Majoron--neutrino coupling $g_{a\nu\nu}$ as a function of the $U(1)$ symmetry breaking scale $U$. The shaded regions are excluded by cosmological constraints from Planck Planck2018 and stellar cooling bounds Raffelt1996. The star symbols indicate the benchmark points BP1--BP4 obtained in Section 4.
• Figure 2: Neutrino lifetime as a function of the symmetry breaking scale $U$ obtained from the parameter scan. Shaded regions denote excluded cosmological and astrophysical domains Planck2018Raffelt1996Hannestad2005. Star markers correspond to BP1--BP4.
• Figure 3: Scatter plot showing the correlation between the Majoron coupling and neutrino mass for representative values of $U$. Benchmark points BP1--BP4 are highlighted by star symbols.
• Figure 4: Neutrino lifetime as a function of neutrino mass for the scanned parameter space. Stars denote the benchmark points BP1--BP4.
• Figure 5: Projected sensitivity of future neutrino experiments to the neutrino lifetime parameter $\tau_\nu/m_\nu$. Shaded bands represent experimental reach of JUNO, DUNE and Hyper-Kamiokande Foguel2019. Star symbols indicate benchmark points of the present model.