From seesaw suppression to radiative testability
The baseline problem is well established: in the minimal type-I seesaw, the smallness of neutrino masses forces either extremely heavy right-handed neutrinos or tiny Dirac Yukawa couplings, which in turn makes active-sterile mixing negligible and charged-lepton flavor violation unobservably small [1]. Inverse seesaw models were introduced to relax that tension by attributing the small neutrino mass to a tiny lepton-number-violating Majorana parameter μ, allowing TeV-scale mediators and potentially observable flavor violation [1]. Radiative seesaw models then made μ itself a loop-generated quantity, tying the origin of neutrino mass to a dark sector stabilized by a discrete symmetry [1][3].
The anchor paper takes that logic one step further by realizing the inverse seesaw μ term at two loops, with the same topology as the Zee-Babu mechanism [1]. The model adds two real singlet scalars and four electrically neutral leptons, with a spontaneously broken global U(1)_X and an exact Z3 symmetry [1]. The Z3 is the key: it forbids tree-level and one-loop neutrino masses, fixes the dominant two-loop topology, and stabilizes the dark matter candidates [1]. This is a different structural choice from the three-loop inverse scotogenic construction in [3], which uses a Z2⊗Z3 symmetry and generates μ at three loops with a novel topology.
What the two-loop model actually predicts
The anchor paper fits a representative benchmark to neutrino oscillation data and finds two pseudo-Dirac heavy pairs with small active-sterile mixing [1]. The effective Majorana mass for neutrinoless double beta decay is predicted in the range m_ee = 2.1–4.4 meV for normal ordering [1]. For the same benchmark, BR(μ→eγ) ≈ 1.6×10⁻¹⁴, with correlated predictions BR(μ→eee) ≈ 8.35×10⁻¹⁶, CR(μ–e, Au) ≈ 2.69×10⁻¹⁴, and CR(μ–e, Ti) ≈ 1.3×10⁻¹⁴ [1]. These numbers are not discoveries; they are benchmark-point predictions that lie below current bounds but within the projected reach of next-generation experiments such as MEG II, Mu2e, and COMET [1].
The dark matter analysis considers both a scalar candidate ρ and a fermionic candidate Ω, with the lightest Z3-nontrivial state being stable [1]. For scalar dark matter, annihilation proceeds mainly through the Higgs portal, and current XENON1T/LZ limits already push the Higgs-portal coupling λ_φρ ≲ 0.1 across most of the 1–3.5 TeV mass range [1]. For fermionic dark matter, annihilation proceeds through t-channel ρ exchange into sterile neutrinos, with a one-loop-generated effective Higgs coupling well below present bounds for masses around 1–5 TeV [1]. The fermionic option is therefore less constrained by direct detection, but that also means it is harder to test with current nuclear-recoil experiments [1].
How it compares with precursor and competing frameworks
The closest precursor is the three-loop inverse scotogenic seesaw of [3], which also uses an inverse seesaw with a radiatively generated μ term and a preserved discrete symmetry for dark matter stabilization. That model employs a Z2⊗Z3 symmetry, generates μ at three loops, and finds multi-component dark matter scenarios including single-, two-, and three-component domination [3]. Its scan shows that many points satisfying the observed baryon asymmetry lie within Mu2e and COMET sensitivity, while escaping MEG II [3]. The anchor paper's two-loop realization is therefore a different point in the same model space: it predicts a benchmark BR(μ→eγ) that is explicitly within MEG II's projected reach, whereas the three-loop construction's baryogenesis-viable points tend to evade MEG II [1][3].
A competing approach is the type-I Dirac cogenesis framework of [4], which generates neutrino masses through a Dirac seesaw and simultaneously produces dark matter and baryon asymmetry from out-of-equilibrium decays of heavy vector-like fermions. That model realizes asymmetric dark matter in the mass range 100 MeV ≲ m_χ ≲ 39 TeV, with the lower bound from requiring the symmetric component to annihilate before BBN and the upper bound from unitarity [4]. The anchor paper instead relies on thermal freeze-out of a WIMP-like scalar or fermionic candidate at the TeV scale, with relic abundance determined by annihilation and coannihilation processes [1]. These are different cosmological histories: cogenesis ties the dark matter abundance to the baryon asymmetry, while the two-loop inverse seesaw treats dark matter as a separate thermal relic [1][4].
Where the experimental test gets complicated
The flavor-violation predictions are the most concrete testable handle, but they come with important caveats. The benchmark values in [1] are obtained for a specific parameter point, and the paper notes that the exact central experimental values of neutrino oscillation parameters can be reproduced by perturbing around that benchmark [1]. The quoted ranges for BR(μ→eee), CR(μ–e, Au), and CR(μ–e, Ti) come from perturbing the benchmark by about 20% while requiring agreement with oscillation data [1]. This means the predictions are not parameter-space-wide; they are benchmark-anchored, and the full viable parameter space may contain regions with different flavor signatures [1].
A further limitation comes from the dark matter side. The scalar dark matter option is already being squeezed by XENON1T/LZ, and future multi-ton detectors such as XENONnT and DARWIN will probe most of the remaining parameter space [1]. The fermionic option avoids those bounds through suppressed nuclear scattering, but that same suppression makes direct detection difficult [1]. The paper also notes that a one-loop renormalization group study of vacuum stability and Landau poles, a systematic exploration of CP phases including EDM constraints, and collider recasts targeting mono-X and displaced signatures remain to be done [1]. Until those are completed, the model's viability across the full parameter space is not established.
There is also a broader interpretive caution from the flavor-violation literature. The effective-field-theory study of [5] shows that MEG II and Mu3e can probe TeV-scale new physics through μ→eχχ decays, but the sensitivity depends strongly on the Lorentz structure of the interaction and on the dark matter mass [5]. For purely left-handed interactions, the energy and angular distributions approach the Standard Model Michel spectrum as m_χ→0, leading to progressive loss of sensitivity [5]. This means that a null result in one channel does not rule out the anchor paper's framework; it constrains specific operator structures and mass regions [1][5].
What remains open and what would settle it
The anchor paper's central claim is that a two-loop inverse seesaw with Z3 symmetry can simultaneously accommodate neutrino oscillation data, a stable dark matter candidate, and testable charged-lepton flavor violation [1]. That claim is supported by a benchmark fit and by consistency checks against relic abundance, direct detection, and collider constraints [1]. But the paper does not demonstrate that the full parameter space is viable; it identifies a viable region and shows that it can satisfy current bounds [1]. The three-loop precursor [3] performs a global numerical scan with MultiNest and finds a rich variety of dark matter compositions, which suggests that the two-loop model's parameter space may also contain more diverse phenomenology than the benchmark reveals [1][3].
The most decisive near-term tests are the ones the paper itself highlights: MEG II for μ→eγ, Mu2e and COMET for μ–e conversion, and future direct-detection experiments for scalar dark matter [1]. If MEG II observes a signal near the predicted benchmark, that would strengthen the case for a TeV-scale radiative inverse seesaw; if it does not, the model can still survive in regions with smaller active-sterile mixing or different CP phases [1]. The fermionic dark matter option is harder to test directly, but collider searches for displaced vertices or mono-X signatures could provide complementary coverage [1]. Until those searches report, the framework remains a well-motivated but unconfirmed possibility.
About These Sources
This research page is built on 5 peer-reviewed studies — published in 2026, 5 from 2024 or later — selected as the most relevant from 10 studies that passed quality screening, drawn from 71 papers retrieved from a database of over 500 million.
Sources used in this answer
A novel two loop inverse seesaw model
The anchor paper proposes a two-loop inverse seesaw with Z3 symmetry, predicting m_ee = 2.1–4.4 meV and benchmark BR(μ→eγ) ≈ 1.6×10⁻¹⁴, with scalar or fermionic dark matter stabilized by the same discrete symmetry.
TeV-scale origin of light dark matter and neutrino mass
This foundational paper demonstrates that a minimal inverse seesaw extension can simultaneously determine neutrino mass and collider-accessible TeV-scale physics, establishing the baseline concept that the anchor paper extends to two loops.
Multi-component Dark Matter in a Novel Three-Loop Inverse Scotogenic Seesaw Model
This precursor three-loop inverse scotogenic seesaw uses Z2⊗Z3 symmetry and a novel topology for μ, finding multi-component dark matter and CLFV signals that often evade MEG II while falling within Mu2e/COMET reach.
Cogenesis of visible and dark matter in type-I Dirac seesaw
This competing type-I Dirac cogenesis framework generates dark matter and baryon asymmetry together from heavy fermion decays, realizing asymmetric dark matter in the range 100 MeV ≲ m_χ ≲ 39 TeV.
Flavor-violating dark matter at MEG-II and Mu3e
This limitation paper shows that MEG II and Mu3e sensitivity to μ→eχχ depends strongly on Lorentz structure and dark matter mass, with left-handed interactions losing sensitivity as m_χ→0.