Radiative Seesaw Mechanism in Neutrino Physics

• Radiative seesaw mechanism is a class of models where suppressed neutrino masses emerge via quantum loop effects, involving extra scalars, fermions, and discrete symmetries.
• These models use loop-induced corrections to generate Dirac or Majorana mass submatrices, lowering the new-physics scale and enabling potential collider and LFV experimental tests.
• Phenomenologically, the mechanism naturally yields sub-eV neutrino masses, connects neutrino mass generation to dark matter candidates, and predicts distinct signals in precision and collider experiments.

The radiative seesaw mechanism refers to a broad class of models in which suppressed neutrino masses—typically of Majorana type—are generated via quantum loop effects rather than at the tree level, often in association with extended symmetries, additional scalars or fermions, and new sources of lepton-number violation. While conventionally the term “seesaw mechanism” describes tree-level suppression of the light neutrino masses by integrating out heavy right-handed Majorana neutrinos, in radiative variants, the loop-induced structure accounts for one or more crucial submatrices (Dirac or Majorana) in the neutrino sector, thereby lowering the physical scale at which new particles appear and linking neutrino mass generation to dark matter and flavor phenomena. Radiative suppression not only yields naturally small neutrino masses but also provides novel signatures testable at colliders, lepton flavor violation experiments, and dark matter searches.

1. Loop-Level Realization of the Seesaw Principle

A central tenet of the radiative seesaw mechanism is that the effective Dirac or Majorana neutrino mass terms are forbidden or highly suppressed at tree level by additional discrete or gauge symmetries, and are only generated via loop diagrams involving new particles—commonly extra scalars (e.g., inert doublets, charged singlets, or triplets) and/or heavy vector-like fermions.

Representative formulas appear across models:

• In TeV-scale frameworks such as (Chao, 2010), the effective Dirac mass matrix $M_D$ arises at one loop:

$$(M_D)_{ab}^{\rm loop} = \frac{\lambda_n \langle H_n \rangle}{32\pi^2} (Y_S)_{ac} (Y_N^\dagger)_{cb} M_{S_c} \mathcal{F}(M_H^2, M_\Phi^2, M_{S_c}^2)$$

where $\mathcal{F}$ denotes the loop function depending on the masses of the exchanged fields.

• In models incorporating radiative inverse seesaw structures (Guo et al., 2012, Baldes et al., 2013), a tiny lepton-number violating parameter $\mu_L$ is induced as

$m_\nu \sim m_D M^{-1} \mu_L (M^{-1})^T m_D^T$

with $\mu_L$ itself being generated at the two-loop level, e.g., through mixing of scalar singlets and triplets.

• In radiative type-I seesaw constructions (Kanemura et al., 2012), spontaneous symmetry breaking (e.g. $U(1)_{B-L}$ at TeV scale) leads to right-handed neutrino Majorana masses generated at tree level and Dirac masses generated only radiatively (often by one-loop diagrams involving inert scalars and dark fermions), resulting in light neutrino masses emerging at two-loop order:

$$m_\nu \sim \frac{(\text{1-loop Dirac mass})^2}{M_R}$$

Radiative suppression confers an additional factor $1/(16\pi^2)^n$ ($n=1$ for one loop, $n=2$ for two loops), further reducing $m_\nu$ and enabling the new-physics mass scale to be as low as $\mathcal{O}$(TeV), in contrast to traditional high-scale type-I seesaw realizations.

2. Model Structures and the Role of New Fields

Radiative seesaw models ubiquitously extend the Standard Model by several types of particles:

• Inert or Extra Higgs Doublets/Singlets: These do not develop VEVs (e.g., inert doublets in the Ma model) or are responsible for controlled mixing (e.g., singlet scalars providing the phase transition trigger (Ahriche et al., 2016), or mixing with scalar triplets (Guo et al., 2012)).
• Singly Charged/Scalar Triplets: Participate in closing the loop diagrams (e.g., $\Phi$ in (Chao, 2010), triplet $\Delta$ in (Guo et al., 2012)) and can mediate lepton-flavor-violating processes.
• Vector-like Fermions: Serve as mediators in the loops that connect SM leptons to new neutral fermions, induce non-unitarity in the lepton mixing matrix, and often serve as decay products of new scalars accessible at colliders.
• Right-Handed Majorana or Dirac Neutrinos: Lowered in mass scale due to radiative suppression, leading to possible collider accessibility and sizable electromagnetic moments.
• Discrete Symmetries: $Z_2$ (or global $U(1)$) symmetries are crucial, forbidding the offending tree-level terms and guaranteeing stability of dark matter candidates by ensuring the lightest $Z_2$-odd particle cannot decay.

These ingredients also facilitate experimental signatures beyond neutrino physics, such as dark matter, lepton flavor violation, and baryogenesis.

3. Phenomenology: Neutrino Masses, Mixing, and Non-Unitarity

The unique structure of the radiative seesaw mechanism leads to several phenomenological consequences:

• Neutrino Masses: Light neutrino masses are suppressed both by loop factors and heavy scales. For example, with $M_D$ loop-suppressed to the MeV scale and $M_R$ at the 100 GeV–TeV scale, $M_\nu$ readily attains the sub-eV range (Chao, 2010, Guo et al., 2012).
• Non-unitarity in PMNS Matrix: The mixing of SM leptons with heavy vector-like states distorts the PMNS matrix:

$$U \approx \left(1 - \frac{1}{2}|M_C M_S^{-1}|^2\right) V$$

leading to deviations probed in oscillation and precision electroweak measurements.

• Mixing Patterns and Predictivity: In symmetry-guided frameworks (e.g., $A_4 \otimes Z_2 \otimes Z'_2$ (Hernández et al., 2013), $\Delta(27)$ (Bernal et al., 2017)), the texture of the loop-induced neutrino mass matrix provides correlations between mixing angles and CP phases, with some models predicting nearly tribimaximal mixing, small CP violation, and fixed effective neutrino masses for $0\nu\beta\beta$.

4. Connections to Dark Matter

Radiative seesaw models often inherently link neutrino mass generation and a stable dark matter candidate:

• Dark Sector Fields as Loop Participants: The same $Z_2$-odd fields that run in the neutrino mass-generating loop (e.g., inert scalars, dark fermions) are potential WIMP or FIMP dark matter candidates. Their stability is a consequence of the symmetry protecting the loop structure (Guo et al., 2012, Hernández et al., 2013, Bernal et al., 2017, Ma et al., 2021).
• Relic Density and Direct Detection: Scalar dark matter annihilating via Higgs portal couplings can account for observed relic abundance but must respect increasingly stringent direct detection bounds (e.g., for some models only $m_\mathrm{DM} \gtrsim 130$ GeV remains allowed (Guo et al., 2012)); in other constructions with extremely small couplings (FIMP scenarios), the freeze-in mechanism is realized.
• Collider and Indirect Signatures: Loop-induced couplings of dark matter to SM Higgs or $Z'$ bosons can result in missing energy signals or affect Higgs invisible decays and diphoton rates.

5. Lepton Flavor Violation and Electromagnetic Properties

Because the radiative mechanism involves new charged states and mixing with heavy fermions, signatures arise in lepton flavor-violating (LFV) decays and electromagnetic moments:

• LFV Decays: Branching ratios for processes like $\mu \to 3e$ (tree) and $\mu \to e \gamma$ (loop) directly constrain off-diagonal entries of Yukawa matrices and the inverse mass scale of new vector-like fermions/scalars (Chao, 2010, Guo et al., 2012, Binh et al., 20 Apr 2024).
• Muon Anomalous Magnetic Moment: Loops with heavy charged fermions and scalars can contribute to the muon $g-2$, and parameter regions compatible with experimental anomalies may be found in multiple radiative seesaw models (Hernández et al., 2021, Hernández et al., 8 Mar 2024).
• Electromagnetic Form Factors of Heavy Neutrinos: Large transition magnetic moments for TeV-scale Majorana neutrinos (~$10^{-2}$) can facilitate pair production at colliders through electromagnetic interactions (Chao, 2010).

6. Collider Signatures and Experimental Tests

Radiative seesaw models present distinct signals at high-energy colliders:

• Exotic Scalar and Fermion Production: New singly-charged scalars, inert scalars, or vector-like charged fermions with masses of $\mathcal{O}$(100 GeV–1 TeV) can be produced in hadronic ($pp$) or lepton ($e^+e^-$) collisions, leading to signatures such as multi-lepton plus missing energy, multi-jet states, or non-standard final states through decay chains (Chao, 2010, Kanemura et al., 2012, Guo et al., 2012, Hernández et al., 8 Mar 2024).
• Gauge Bosons and Extended Higgs Sector: Presence of additional vector bosons (e.g., $Z'$ from $U(1)_{B-L}$ breaking) and nearly degenerate Higgs states with sizable mixing can be probed through Drell-Yan and Higgs precision measurements (Kanemura et al., 2012).
• Signals in Leptogenesis and Baryogenesis: Models with (loop-induced) lepton number violation enable resonant leptogenesis in the presence of nearly degenerate heavy neutrinos (Baldes et al., 2013), with the possibility of directly testing the theory by combining low-energy and collider data.

7. Theoretical Implications and Future Research

Radiative seesaw constructions resolve the neutrino mass puzzle while positioning the associated new physics within current or near-future experimental reach:

• Hierarchy Problem and Vacuum Stability: Certain variants exploit radiative corrections to not only generate small neutrino masses but also induce electroweak symmetry breaking and stabilize the Higgs potential, as in scale-invariant models utilizing the Coleman-Weinberg or Gildener-Weinberg mechanism (Ahmed et al., 17 Apr 2025).
• Unified Solution to Multiple Puzzles: The suppression of tree-level terms by discrete symmetries yields natural stability for dark matter candidates, enables strong electroweak phase transitions, and links the neutrino mass origin to baryogenesis.
• Distinctiveness from Standard Seesaw: By employing radiative suppression, the new particle spectra and couplings are accessible at the sub-TeV–few TeV scale, in contrast to the high-scale seesaw, and can be systematically disentangled by detailed experimental paper.
• Parameter Space Exploration: Viable scenarios are characterized by correlations between lepton flavor violation rates, collider signatures, dark matter relic abundance, and oscillation data, requiring coordinated parameter-space analyses (Guo et al., 2012, Baldes et al., 2013, Binh et al., 20 Apr 2024).
• Open Directions: Further investigation includes probing loop-induced deviations from unitarity, nonstandard Higgs and gauge interactions, interplay with cosmological observables (e.g., baryon asymmetry, dark matter direct and indirect signals), and constructing ultraviolet completions or embeddings in grand-unified frameworks.

The radiative seesaw mechanism has led to a diverse landscape of models where the dynamical origin of neutrino masses, the identity of dark matter, and the flavor structure of the Standard Model become intertwined and accessible to a wide spectrum of experiments—a theme consistently underlined across the research literature (Chao, 2010, Guo et al., 2012, Kanemura et al., 2012, Baldes et al., 2013, Hernández et al., 2013, Ahriche et al., 2016, Arbeláez et al., 2016, Nomura et al., 2016, Khalil, 2016, Bernal et al., 2017, Diaz et al., 2017, Rojas et al., 2018, Chiang et al., 2021, Ma et al., 2021, Hernández et al., 2021, Hernández et al., 8 Mar 2024, Binh et al., 20 Apr 2024, C. et al., 20 May 2024, Ahmed et al., 17 Apr 2025).