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

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.

💡 Research Summary

The authors present a supersymmetric model in which a global leptonic U(1){L_μ‑L_τ} symmetry is spontaneously broken at a low scale. The breaking generates a complex scalar sector with vacuum expectation values (VEVs) for two singlet superfields (N and N′) while the third singlet (Y) remains at zero in the supersymmetric limit. This pattern yields a massless Goldstone boson (the Majoron‑like axion) and its fermionic partner, a Goldstone fermion. Soft supersymmetry breaking (e.g., gravity‑mediated) introduces a small VEV for Y, parametrised by ε≪1, which lifts the Goldstone fermion mass to M{N1}≈2|ελU sinφ cosφ|. The resulting spectrum contains one pseudo‑Goldstone right‑handed neutrino (N1) with a naturally suppressed mass (sub‑TeV) and two heavier RH neutrinos (N2, N3) with masses ≈|λU|.

Yukawa interactions W_D=λ_{αβ} L_α N_β H_2 generate Dirac masses after electroweak symmetry breaking, while bilinear R‑parity‑violating terms ε_α=−λ_α⟨˜N_α⟩ arise from the same VEVs. The full neutral‑fermion mass matrix is a 10×10 block matrix comprising three active neutrinos, three singlet RH neutrinos, and four MSSM neutralinos. In the seesaw limit (m_D, m_{νχ}≪M_N, M_χ) the effective light‑neutrino mass matrix is m_ν≈−m_{3×7} M_{7×7}^{−1} m_{3×7}^T.

A crucial observation is that a flavour‑independent U(1) (acting only on the singlet sector) leads to a rank‑1 neutrino mass matrix, insufficient to reproduce the observed mixing pattern. By contrast, the flavour‑dependent L_μ‑L_τ charge assignment (L_e=0, L_μ=+1, L_τ=−1) yields a structured Dirac matrix m_D=diag(λ_e, λ_μ, λ_τ) v_2 and a pseudo‑Goldstone RH neutrino mass matrix with off‑diagonal entries proportional to sinφ and cosφ. This structure produces a full‑rank light‑neutrino mass matrix already at leading order, allowing a fit to the measured mass‑splittings, mixing angles and the CP‑violating phase without extreme hierarchies among the Yukawa couplings.

The authors perform a numerical χ² fit to current oscillation data, scanning over the symmetry‑breaking scale U, the mixing angle φ, the coupling λ, and the soft‑breaking parameter ε. Representative benchmark points are identified with U∼(0.5–5) TeV, ε∼10^{−5}–10^{−3}, and RH‑neutrino masses M_{N2,3}∼(1–10) TeV, while the pseudo‑Goldstone neutrino mass lies in the 10 MeV–1 GeV range. These points satisfy laboratory bounds on heavy‑neutrino mixing, lepton‑flavour‑violating processes, and direct searches for long‑lived neutral particles.

The Majoron‑like axion couples derivatively to neutrinos with strength g_{Jνν}∝(m_ν/U). For low U, the coupling can be sizable, leading to invisible neutrino decays ν_i→ν_j+J with lifetimes τ∼(g_{Jνν}^2 Δm^3)^{−1}. The authors map the (U, g_{Jνν}) and (U, τ) planes, showing that for U≲1 TeV the decay can be fast enough to affect cosmological neutrino‑mass limits, relaxing the bound from Σ m_ν<0.12 eV.

Phenomenologically, the model predicts several correlated signatures:

1. Neutrino oscillation experiments – the presence of invisible decay modifies the survival probability, potentially observable as a distortion of the energy spectrum in long‑baseline experiments (e.g., DUNE, Hyper‑K).

2. Cosmology – altered neutrino free‑streaming and reduced effective neutrino mass impact CMB anisotropies and large‑scale structure; upcoming surveys (CMB‑S4, Euclid) could probe the predicted decay rates.

3. Collider searches – the heavy RH neutrinos can be produced via their mixing with active neutrinos or through the new gauge‑invariant interactions induced by the symmetry‑breaking sector. Because the pseudo‑Goldstone neutrino has enhanced couplings, it can lead to displaced‑vertex signatures (decay lengths from millimetres to metres) at the LHC or future lepton colliders.

4. Rare decays – the Majoron‑like particle can mediate processes such as μ→eJ or τ→μJ, providing complementary constraints from MEG‑II and Belle‑II.

The authors discuss the complementarity of these probes, emphasizing that a combined analysis can test the correlated parameter space. They also outline future directions, including a full simulation of displaced‑vertex signatures, a detailed study of the Majoron cosmology (including its contribution to ΔN_eff), and extensions to gauge‑U(1)_{L_μ‑L_τ} models with a Z′ boson. Overall, the paper offers a coherent framework linking low‑scale seesaw neutrino masses, pseudo‑Goldstone fermions, and axion‑like phenomenology, with clear experimental avenues for verification.