Singlet Charged Neutral Fermion

• Singlet charged neutral fermions are gauge-singlet spin-1/2 fields that serve as key components in neutrino mass generation, dark matter models, and baryogenesis.
• They acquire Majorana or Dirac masses through mechanisms such as the type-I seesaw, radiative corrections, and exotic quantum gravitational effects.
• Their diverse roles in collider experiments, lepton-number violation, and global symmetry breaking provide a minimal yet versatile portal to new physics.

A singlet charged neutral fermion—more precisely, a gauge-singlet neutral fermion—denotes a spin-1/2 field that is a singlet under non-Abelian gauge groups of the Standard Model and electrically neutral. Such objects, typically denoted $N_R$ or $\psi$, have been intensively studied in neutrino mass generation, dark matter, baryogenesis, and beyond-Standard-Model (BSM) frameworks. While intrinsically “neutral,” they may acquire additional conserved charges (e.g., lepton, baryon, Peccei–Quinn) or dark-sector parities that play substantive roles in phenomenology. The term encompasses right-handed neutrinos, dark matter singlets, and other exotic, SM-sterile fermions admitting nontrivial mass-generation mechanisms and new physics signatures.

1. Quantum Numbers and Gauge Structure

Singlet neutral fermions are characterized by their quantum numbers under both gauge and potential global symmetries. Under the Standard Model $SU(3)_c \times SU(2)_L \times U(1)_Y$ the minimal assignment is

$N_R \sim (\mathbf{1}, \mathbf{1}, 0)$

indicating absence of SM color, weak isospin, or hypercharge (Ma, 2017). Global charges can include lepton number $L(N_R) = 0, \pm1$, baryon number $B(N_R) = 0, \pm 1$, dark parity $D(N_R) = \pm1$, matter parity $M = (-1)^{3B+L}$, or charges under additional $U(1)_F$ group factors. In BSM left–right symmetric models, further structure arises, e.g. under $SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ (Patra et al., 2015, Borboruah et al., 11 Apr 2025). Singlet fermions can be Majorana or Dirac types, often dictated by symmetry breaking or explicit model construction (e.g., Peccei–Quinn models (Carvajal et al., 2021)).

2. Mass Generation Mechanisms

The mass of a singlet neutral fermion can arise via several mechanisms depending on couplings and symmetry structure. In type-I seesaw, Majorana masses $M_N$ are allowed for gauge singlets: $$\mathcal L \supset \frac{1}{2} M_{ij} N_{iR}^T C^{-1} N_{jR} + y_{ij} \overline{L}_i \tilde{\Phi} N_{jR} + \text{h.c.}$$ The Majorana term violates lepton number and, after electroweak symmetry breaking, leads to a suppressed light neutrino mass $m_\nu \sim (yv)^2/M_N$.

Exotic, non-perturbative origins are also possible. In the D-particle foam model, quantum gravitational space–time fluctuations generate a dynamically large $M_N$ via the minimal coupling of the singlet fermion to a massless vector ("phonon") field $\mathcal A_\mu$. The effective Lagrangian is

$$\mathcal L = -\frac{1}{4} F^{\mu\nu}(1-\Delta/M^2) F_{\mu\nu} + \overline{\psi} \gamma^\mu(i\partial_\mu + \tilde g_V \mathcal A_\mu)\psi$$

with the dynamical mass gap equation yielding $m_N = M \exp(-2\pi / (3\alpha_V))$, where $M$ depends on string and foam parameters and $\alpha_V = \tilde g_V^2/4\pi$ (Ellis et al., 2017). Such masses can be dynamically suppressed yet remain in the typical $10^{12}$–$10^{15}$ GeV range required for standard seesaw fits.

In Dirac frameworks, singlet masses may arise radiatively through Yukawa couplings involving inert scalars and additional symmetry breaking, as in the scotogenic mechanism associated with Peccei–Quinn symmetry breaking, which forbids bare masses and generates them after $\Phi$ acquires a vacuum expectation value (Carvajal et al., 2021).

3. Phenomenological Roles and Model Implementations

3.1. Neutrino Mass and Mixing

Singlet neutral fermions enable neutrino mass generation via:

• Type-I seesaw (Majorana, tree-level or loop-suppressed, e.g., one-loop with no scalar bidoublet (Borboruah et al., 11 Apr 2025))
• Radiative (e.g., scotogenic one-loop) Dirac masses in PQ-symmetric models (Carvajal et al., 2021).

These frameworks can accommodate both normal and inverted mass hierarchies, with neutrino mass matrices constrained by oscillation data, requiring sub-eV masses for the active neutrinos.

3.2. Dark Matter Candidates

Gauge-singlet neutral fermions can serve as viable dark matter (DM) in multiple BSM scenarios:

• As a Dirac WIMP stabilized by $\mathbb{Z}_2$, coupled via new gauge bosons $Z_{B,\ell}$ in left–right models (Patra et al., 2015).
• As the lightest PQ-charged singlet in multi-component PQ frameworks, where it is stabilized by a remnant parity from PQ breaking and annihilates via t-channel exchange or one-loop Higgs-mediated processes (Carvajal et al., 2021).
• As a warm DM candidate (keV–few keV masses) in left–right models with no scalar bidoublet, with appropriate suppression of couplings and lifetimes far exceeding the age of the Universe (Borboruah et al., 11 Apr 2025).

3.3. Heavy Neutral Leptons and Collider Phenomenology

At colliders, singlet neutral fermions appear as heavy neutral leptons (HNLs), with mass-dependent production and decay channels. In the $N_R$SMEFT framework, dimension-6 four-fermion operators of the form $(\bar d_R \gamma^\mu u_R)(\bar N_R \gamma_\mu e_R)$ or $(\bar L N_R)\varepsilon (\bar Q d_R)$ drive contact interactions, enabling LHC and HL-LHC to probe new physics scales up to $\sim$20 TeV for first-generation quarks and electrons (Beltrán et al., 2021). Displaced-vertex signatures and lepton-number–violating decays are classic probes of HNLs.

3.4. Baryogenesis and Leptogenesis

CP-violating decays of heavy singlet Majorana fermions in the early Universe can generate the observed matter–antimatter asymmetry via leptogenesis, even at TeV scales via resonant mechanisms if singlet mass splittings are appropriately tuned (Borboruah et al., 11 Apr 2025). Some variants exploit baryon-number–charged singlets to catalyze baryogenesis from out-of-equilibrium decays (Ma, 2017).

3.5. Spontaneous Global Symmetry Breaking

Singlet neutral fermions allow realization of spontaneous breaking of lepton or baryon number, leading to massless Nambu–Goldstone bosons: the majoron (leptonic case) or “sakharon” (baryonic case). Phenomenology includes invisible Higgs decays, highly suppressed couplings to SM states, and specific astrophysical and laboratory constraints (Ma, 2017).

4. Theoretical Model Variants and Lagrangian Structures

The diversity of roles for singlet neutral fermions is reflected in the permissible Lagrangian terms:

• Majorana and Dirac mass terms, with structures dictated by symmetry and charge assignments.
• Yukawa interactions with SM doublets, inert scalars, or other BSM states.
• Higher-dimensional operators in effective field theory (e.g., $d=6$ four-fermion operators discussed above (Beltrán et al., 2021)), often implemented to maintain lepton-number conservation or invoke new BSM gauge invariances.
• Dark-matter–related couplings, such as those mediated via new vector gauge bosons ($Z_{B,\ell}$), or radiative couplings to the SM Higgs via scalar mixing.
• Spontaneous symmetry breaking terms involving singlet scalar sectors with global symmetry charges, yielding new Goldstone bosons or stabilizing parities for dark sector components (Ma, 2017, Carvajal et al., 2021).

The following table summarizes several representative model frameworks involving singlet neutral fermions:

Framework / Paper	Mass Type	Key Interactions	Phenomenology
D-particle Foam (Ellis et al., 2017)	Majorana	Phonon-like vector	Dynamical $M_N$ for seesaw
Scotogenic PQ Model (Carvajal et al., 2021)	Dirac	Yukawa+scalars/PQ	WIMP DM, 1-loop Dirac $\nu$ mass
LR Symmetric (Borboruah et al., 11 Apr 2025)	Majorana (TeV)	Yukawa+one-loop	1-loop seesaw, leptogenesis, warm DM
$U(1)_B \times U(1)_L$ (Patra et al., 2015)	Dirac	$Z_{B, \ell}$ vector	WIMP DM via $Z'$ portal
$N_R$ SMEFT (Beltrán et al., 2021)	Dirac/Majorana	$d=6$ 4-fermion	Displaced LHC signatures, EFT reach
Sakharon scenario (Ma, 2017)	Majorana	Spont. baryon break	Massless Goldstone, rare decays

5. Experimental Constraints and Probes

Experimental probes of singlet neutral fermions are model-dependent and span multiple frontiers:

• Collider limits from LEP and LHC on $Z', Z_B, Z_\ell$ masses ($M_{Z'}/g_{Z'} \gtrsim 6$ TeV), direct searches for HNLs with displaced-vertex topologies, and rare lepton flavor–violating decays (Patra et al., 2015, Beltrán et al., 2021).
• Direct and indirect DM detection, exploiting WIMP–quark couplings via $Z$, Higgs, or loop-induced processes. Next-generation experiments like XENONnT and LZ will probe predicted cross sections (Carvajal et al., 2021).
• Neutrino oscillation and double-beta decay constraints, with $m_{\beta\beta}$ limits from KamLAND-Zen for heavy-neutrino exchange (Borboruah et al., 11 Apr 2025).
• Cosmological and astrophysical observations, such as DM relic abundance, structure formation bounds on warm DM candidates, and bounds on the lifetime of keV-scale singlets.

A plausible implication is that the parameter space for singlet neutral fermion models with cosmologically significant roles (DM, baryogenesis) is increasingly constrained but not excluded, with forthcoming searches at colliders, rare-decay, and DM direct-detection experiments providing decisive tests for many scenarios.

6. Model Variants: Beyond Minimal Constructions

A single neutral fermion singlet can be embedded into extended gauge or global symmetry schemes:

• With additional $U(1)_F$ or $U(1)_{B-L}$ factors, enforcing anomaly cancellation and new $Z'$ gauge bosons.
• In left–right symmetric or universal seesaw models (often without scalar bidoublets), which generate small neutrino masses only at loop level (Borboruah et al., 11 Apr 2025).
• As dark-matter candidates stabilized by discrete symmetries (e.g., matter parity or remnant $\mathbb{Z}_2$ from spontaneous PQ breaking) (Carvajal et al., 2021).
• Facilitating alternative baryogenesis pathways, e.g., via baryon-number–charged fermions and diquark scalars or baryon-number–preserving extensions (the “sakharon” mechanism) (Ma, 2017).
• In scotogenic variants, coupling singlet fermions and auxiliary inert scalars via $Z_2$ symmetry and loop-induced neutrino masses, with the lightest singlet or scalar as the DM (Ma, 2017, Carvajal et al., 2021).

This flexibility renders the singlet neutral fermion a central element in the theoretical exploration of neutrino physics, DM, and BSM signatures, serving as a minimal and versatile portal to new sectors.

7. Summary and Outlook

Gauge singlet neutral fermions, whether Dirac or Majorana, function as essential mediators and protagonists in neutrino mass generation, dark matter, baryogenesis, and spontaneous symmetry breaking. Their mass origin ranges from explicit Yukawa or Majorana terms, radiative corrections, to quantum gravitational foam dynamics. Phenomenological consequences are diverse, with implications for collider searches, rare processes, DM detection, and cosmology. The convergence of high-precision experiments—collider, astrophysical, and cosmological—is expected to probe or tightly constrain most viable parameter spaces for such singlets in the coming years (Ellis et al., 2017, Carvajal et al., 2021, Borboruah et al., 11 Apr 2025, Patra et al., 2015, Beltrán et al., 2021, Ma, 2017).