A novel two loop inverse seesaw model

TL;DR

This work introduces a minimal SM extension with a spontaneously broken global $U(1)_X$ and an exact $\mathbb{Z}_3$ symmetry, adding two real singlet scalars $\rho,\sigma$ and two generations of neutral leptons to realize a two-loop inverse seesaw that radiatively generates the lepton-number-violating submatrix $\mu$. The preserved $\mathbb{Z}_3$ simultaneously stabilizes dark matter candidates, allowing either a scalar $\rho$ or a fermionic $\Omega$ DM depending on mass ordering, while connecting neutrino masses to dark matter and charged-lepton flavor violation. Neutrino masses and mixings are fitted to oscillation data, predicting $m_{ee}$ in the NO range $(2.1-4.4)\text{ meV}$, and implying two nearly degenerate heavy pseudo-Dirac neutrinos with small splittings set by $\mu$. The model yields testable CLFV rates near current and next-generation sensitivities and maps viable DM parameter space under relic-density, direct, and indirect detection constraints, offering concrete targets for MEG II, Mu2e/COMET, and HL-LHC, while remaining distinct from conventional inverse- and radiative-seesaw models.

Abstract

We propose a Standard Model (SM) extension where neutrinos get masses through a two-loop inverse seesaw mechanism. This naturally explains the smallness of the neutrino masses and allows seesaw mediators to be at the TeV scale with testable phenomenology. The model adds two real singlet scalars and four electrically neutral leptons to the SM. The extension considers the existence of two global Abelian symmetries, a continuous $U(1)$ and a discrete $Z_3$. The latter, remains unbroken after spontaneous symmetry breaking and forbids tree-level and one-loop neutrino masses, and stabilizes the dark matter (DM) candidates. This setup accommodates neutrino-oscillation data, yields two pseudo-Dirac heavy pairs with small active-sterile mixing, and predicts an effective Majorana mass $m_{ee}$ in the $2.1$-$4.4$ meV range for normal ordering. Charged-lepton flavor violation is naturally suppressed yet testable: for a representative benchmark we obtain BR$(μ\to e γ)\simeq 1.6 \times 10^{-14}$, with correlated signals in $μ\to eee$ and $μ$-$e$ conversion within next-generation experimental reach. Altogether, the radiative origin of neutrino masses links low-energy flavor observables to collider signatures, delineating discovery targets for MEG II, Mu2e/COMET, and the HL-LHC and distinguishing this framework from conventional inverse- and radiative-seesaw models. Moreover, the $Z_3$ guarantees a stable DM candidate, either scalar ($ρ$) or fermionic ($Ω$). Then, here we analyze and identify the viable parameter space that is consistent with the observed DM relic abundance for both situations.

Figures (14)

• Figure 1: Two-loop Feynman diagram contributing to the Majorana neutrino mass submatrix $\mu$.
• Figure 2: Correlation plot between the effective mass parameter of the neutrinoless double beta decay $(0\nu \beta \beta)$$m_{ee}$ and a) CP violation phase $\delta^(l)_{\rm CP}$, for different values of the mixing angle $\sin^2\theta_{13}$ and b) for the mixing angle $\sin^2\theta_{12}$ and different values of the mixing angle $\sin^2\theta_{13}$.
• Figure 3: Feynman diagram for the $\Omega$ decay into the $\rho$-singlet and the fermion $N$.
• Figure 4: Some Feymann diagrams contributing to $\rho\rho$ annihilation to SM particles.
• Figure 5: Feynman diagram for the dark matter contribution to spin-independent direct detection at tree-level.