The Type-I Seesaw family

TL;DR

The paper addresses how neutrino masses arise within the Type-I Seesaw family, unifying conventional type-I, linear, and inverse seesaw mechanisms under explicit lepton-number violation, and then systematically classifies minimal models with spontaneous $U(1)_L$ breaking that produce a Majoron. It derives the general neutrino-mass formula in the seesaw expansion, demonstrates the texture-based equivalence for explicit breaking, and identifies three minimal spontaneous classes (Class 1–3) with distinct majoron phenomenology. A central finding is that some spontaneous models yield enhanced majoron couplings to charged leptons, enabling potentially observable lepton-flavor-violating decays such as $\mu \to e J$ even for high lepton-number-breaking scales, while many scenarios maintain neutrino-mass suppression for majoron interactions. The paper also provides comprehensive formulas for majoron–charged-lepton couplings and analyzes current and future experimental constraints, highlighting a complementary avenue to test lepton-number violation through majoron signatures and informing cosmological implications of a massless or light majoron.

Abstract

We provide a comprehensive analysis of the Type-I Seesaw family of neutrino mass models, including the conventional type-I seesaw and its low-scale variants, namely the linear and inverse seesaws. We establish that all these models essentially correspond to a particular form of the type-I seesaw in the context of explicit lepton number violation. We then focus into the more interesting scenario of spontaneous lepton number violation, systematically categorizing all inequivalent minimal models. Furthermore, we identify and flesh out specific models that feature a rich majoron phenomenology and discuss some scenarios which, despite having heavy mediators and being invisible in processes such as $μ\to e γ$, predict sizable rates for decays including the majoron in the final state.

Figures (4)

• Figure 1: Feynman diagrams leading to the 1-loop coupling of the majoron to a pair of charged leptons.
• Figure 2: Feynman diagrams relevant for the muon decay $\mu \rightarrow e \gamma$. The fermion mediators include the light and heavy neutral fermions. Left diagram: mediation by $W$ boson. Right diagram: mediation by scalar $\eta^+$.
• Figure 3: Lepton flavor violation predictions in the selected models. Left panel: Relationship between the lepton number breaking scale $v_\sigma$ and the flavor violating coupling $\widetilde{S}_{\mu e}$. Right panel: Comparison between the branching ratios of the non-standard muon decays with a majoron or a photon in the final state. In both panels we are imposing the seesaw condition $(M_D \cdot M_F^{-1})_{ij} < 10^{-2}$, the astrophysical constraints of Eqs. \ref{['eq:stellarcooling']} and \ref{['eq:stellarcooling2']}, as well as correct neutrino masses and mixing. The orange points have Yukawa couplings $y_N, \lambda \sim \mathcal{O}(1)$, while the blue points allow for more freedom, with the Yukawa couplings taking values in a wider range, $y_N, \lambda \sim \mathcal{O}(10^{-3}-1)$.
• Figure 4: Lepton flavor violation predictions for $\tau$ decays in the selected models. In both panels we are imposing the seesaw condition $(M_D \cdot M_F^{-1})_{ij} < 10^{-2}$, the astrophysical constraints of Eqs. \ref{['eq:stellarcooling']} and \ref{['eq:stellarcooling2']}, as well as correct neutrino masses and mixing. The orange points have Yukawa couplings $y_N, \lambda \sim \mathcal{O}(1)$, while the blue points allow for more freedom, with the Yukawa couplings taking values in a wider range, $y_N, \lambda \sim \mathcal{O}(10^{-3}-1)$. The rates for both processes $\tau \to J \, e/\mu$ are predicted to be several orders of magnitude below observational limits.