GeV-Scale Heavy Neutral Leptons

Updated 24 April 2026

GeV-scale HNLs are hypothetical singlet fermions that mix with SM neutrinos, underpinning seesaw models to explain neutrino masses and baryogenesis.
They are produced via meson, tau, and other decays in accelerator setups like SHiP, DUNE, and FCC-ee, where branching ratios depend on active-sterile mixing.
Cosmological and laboratory constraints, including BBN and oscillation data, tightly bound their mixing strength and decay rates, guiding the search for new physics.

Heavy Neutral Leptons (HNLs) at the GeV scale are hypothetical singlet fermions that mix with Standard Model (SM) neutrinos, providing a minimal and theoretically robust extension to address neutrino masses, baryogenesis via leptogenesis, and dark matter within and beyond the Standard Model. In this mass regime, HNLs can be thoroughly explored at accelerator-based laboratories, beam-dump experiments, future lepton colliders, and other fixed-target facilities. GeV-scale HNLs are central to the phenomenology of the Neutrino Minimal Standard Model (νMSM) and related seesaw-motivated scenarios, and are subject to precise cosmological, astrophysical, and laboratory constraints.

1. Theoretical Motivation and Seesaw Framework

The inclusion of GeV-scale HNLs is strongly motivated by the type-I seesaw mechanism. The SM is extended by right-handed gauge-singlet fermions $N_I$ ( $I=1,2,3$ ), yielding the Lagrangian

$\mathcal{L} \supset i \bar{N}_I \slashed{\partial} N_I - (Y_{I\alpha} \bar{N}_I^c \tilde{H} L_\alpha + \text{h.c.}) - \frac{1}{2} M_I \bar{N}_I^c N_I$

where $Y_{I\alpha}$ are Yukawa couplings, $L_\alpha$ the SM lepton doublets ( $\alpha=e,\mu,\tau$ ), and $M_I$ the Majorana masses. After electroweak symmetry breaking, the Dirac mass matrix $m_D=Yv/\sqrt{2}$ mediates mixing between $N_I$ and the active neutrinos, leading to light neutrino masses via

$m_\nu \simeq - m_D^2 / M$

For $I=1,2,3$ 0 and $I=1,2,3$ 1, this implies $I=1,2,3$ 2 and $I=1,2,3$ 3 (Bonivento et al., 2013).

Active–sterile mixing is parameterized as $I=1,2,3$ 4, with total mixing strength $I=1,2,3$ 5. Signal and background yields in fixed-target experiments generally scale as $I=1,2,3$ 6 in the long-lifetime regime.

The νMSM requires:

One HNL at $I=1,2,3$ 7 as a DM candidate (subject to X-ray decay constraints),
Two nearly degenerate HNLs at $I=1,2,3$ 8 for leptogenesis and baryonic asymmetry,
Seesaw-motivated active–sterile mixing: for $I=1,2,3$ 9 eV and $\mathcal{L} \supset i \bar{N}_I \slashed{\partial} N_I - (Y_{I\alpha} \bar{N}_I^c \tilde{H} L_\alpha + \text{h.c.}) - \frac{1}{2} M_I \bar{N}_I^c N_I$0 GeV, $\mathcal{L} \supset i \bar{N}_I \slashed{\partial} N_I - (Y_{I\alpha} \bar{N}_I^c \tilde{H} L_\alpha + \text{h.c.}) - \frac{1}{2} M_I \bar{N}_I^c N_I$1 to $\mathcal{L} \supset i \bar{N}_I \slashed{\partial} N_I - (Y_{I\alpha} \bar{N}_I^c \tilde{H} L_\alpha + \text{h.c.}) - \frac{1}{2} M_I \bar{N}_I^c N_I$2 (Bonivento et al., 2013, Rasmussen et al., 2016, Bondarenko et al., 2018).

2. Production and Decay Channels

Production Mechanisms

GeV-scale HNLs are produced dominantly via:

Meson decays: $\mathcal{L} \supset i \bar{N}_I \slashed{\partial} N_I - (Y_{I\alpha} \bar{N}_I^c \tilde{H} L_\alpha + \text{h.c.}) - \frac{1}{2} M_I \bar{N}_I^c N_I$3, $\mathcal{L} \supset i \bar{N}_I \slashed{\partial} N_I - (Y_{I\alpha} \bar{N}_I^c \tilde{H} L_\alpha + \text{h.c.}) - \frac{1}{2} M_I \bar{N}_I^c N_I$4
Kaon and pion decays: $\mathcal{L} \supset i \bar{N}_I \slashed{\partial} N_I - (Y_{I\alpha} \bar{N}_I^c \tilde{H} L_\alpha + \text{h.c.}) - \frac{1}{2} M_I \bar{N}_I^c N_I$5, $\mathcal{L} \supset i \bar{N}_I \slashed{\partial} N_I - (Y_{I\alpha} \bar{N}_I^c \tilde{H} L_\alpha + \text{h.c.}) - \frac{1}{2} M_I \bar{N}_I^c N_I$6
Tau decays: $\mathcal{L} \supset i \bar{N}_I \slashed{\partial} N_I - (Y_{I\alpha} \bar{N}_I^c \tilde{H} L_\alpha + \text{h.c.}) - \frac{1}{2} M_I \bar{N}_I^c N_I$7 for $\mathcal{L} \supset i \bar{N}_I \slashed{\partial} N_I - (Y_{I\alpha} \bar{N}_I^c \tilde{H} L_\alpha + \text{h.c.}) - \frac{1}{2} M_I \bar{N}_I^c N_I$8
Proton–nucleus Drell–Yan and deep inelastic processes: subdominant for $\mathcal{L} \supset i \bar{N}_I \slashed{\partial} N_I - (Y_{I\alpha} \bar{N}_I^c \tilde{H} L_\alpha + \text{h.c.}) - \frac{1}{2} M_I \bar{N}_I^c N_I$9 GeV (Bondarenko et al., 2018, Gorkavenko et al., 2021)

Branching ratios are suppressed by $Y_{I\alpha}$ 0 and relevant phase-space factors, sensitively depending on $Y_{I\alpha}$ 1 (Bondarenko et al., 2018). For example, $Y_{I\alpha}$ 2– $Y_{I\alpha}$ 3 for $Y_{I\alpha}$ 4 in the seesaw/νMSM range (Bonivento et al., 2013).

Decay Modes

HNL decays proceed via charged-current (CC) and neutral-current (NC) weak interactions:

Two-body decays: $Y_{I\alpha}$ 5 ( $Y_{I\alpha}$ 6), $Y_{I\alpha}$ 7 ( $Y_{I\alpha}$ 8)
Three-body leptonic decays: $Y_{I\alpha}$ 9, $L_\alpha$ 0
Semileptonic decays: $L_\alpha$ 1, $L_\alpha$ 2
Multi-meson decays: open up above $L_\alpha$ 3 GeV (Bondarenko et al., 2018).

Decay widths scale as $L_\alpha$ 4 times channel-dependent phase space.

Typical branching ratios shift rapidly with $L_\alpha$ 5: below pion threshold, HNLs decay only leptonically; above, hadronic modes dominate (Bondarenko et al., 2018, Feng et al., 2024). For $L_\alpha$ 6 MeV, $L_\alpha$ 7; $L_\alpha$ 8 (Plows et al., 2022).

HNL total lifetimes are macroscopically long for $L_\alpha$ 9: $\alpha=e,\mu,\tau$ 0 (Bondarenko et al., 2018). This underpins the importance of displaced-vertex and decay-in-flight searches.

3. Cosmological and Astrophysical Constraints

Cosmological observations constrain the allowed window in $\alpha=e,\mu,\tau$ 1:

Big Bang Nucleosynthesis (BBN): Long-lived HNLs (with $\alpha=e,\mu,\tau$ 2– $\alpha=e,\mu,\tau$ 3 s for $\alpha=e,\mu,\tau$ 4) disrupt light element formation, excluding $\alpha=e,\mu,\tau$ 5 for $\alpha=e,\mu,\tau$ 6– $\alpha=e,\mu,\tau$ 7 MeV, depending on mixing pattern (Sabti et al., 2020).
Baryogenesis bounds ("BAU limit"): To preserve lepton asymmetry, $\alpha=e,\mu,\tau$ 8 for $\alpha=e,\mu,\tau$ 9 GeV (Bonivento et al., 2013).
Seesaw lower bound: To explain observed $M_I$ 0, $M_I$ 1 (normal hierarchy) (Bonivento et al., 2013, Rasmussen et al., 2016).
Dark matter (keV HNL): Requires radiative decay lifetime consistent with X-ray bounds (Bonivento et al., 2013).

In models with dominant invisible decay channels (e.g., $M_I$ 2 with an axion-like particle $M_I$ 3), BBN constraints can be significantly relaxed, opening parameter space for $M_I$ 4MeV $M_I$ 5GeV and $M_I$ 6– $M_I$ 7 (Deppisch et al., 2024).

4. Laboratory Search Strategies and Experimental Sensitivities

Fixed-Target and Beam-Dump Facilities

CERN SPS/SHiP: Exploits high-intensity $M_I$ 8GeV proton beams. Sensitivity to $M_I$ 9GeV $m_D=Yv/\sqrt{2}$ 0GeV, $m_D=Yv/\sqrt{2}$ 1 (muon flavor) (Collaboration, 2018).
ICARUS/DUNE/SBND/DarkQuest: Use LArTPCs near high-energy beams. Sensitivity to $m_D=Yv/\sqrt{2}$ 2 at $m_D=Yv/\sqrt{2}$ 3 GeV (muon flavor, ICARUS) (Chatterjee et al., 2024); DUNE ND projects $m_D=Yv/\sqrt{2}$ 4 at $m_D=Yv/\sqrt{2}$ 5– $m_D=Yv/\sqrt{2}$ 6 GeV (Bolton et al., 2022, Capozzi et al., 2024).
Current reach: PS191, CHARM, BEBC exclude $m_D=Yv/\sqrt{2}$ 7– $m_D=Yv/\sqrt{2}$ 8 in $m_D=Yv/\sqrt{2}$ 9– $N_I$ 0 GeV (Rasmussen et al., 2016).

Collider Experiments

HL-LHC: For $N_I$ 1 GeV, searches targeting prompt trilepton signatures with $N_I$ 2-enrichment reach $N_I$ 3 (Cheung et al., 2020).
Electron-Ion Collider (EIC): Probes $N_I$ 4– $N_I$ 5 GeV; $N_I$ 6– $N_I$ 7 (prompt), $N_I$ 8– $N_I$ 9 (displaced vertex) (Batell et al., 2022).
TeV-scale Muon Collider: For $m_\nu \simeq - m_D^2 / M$ 0– $m_\nu \simeq - m_D^2 / M$ 1 GeV, reach down to $m_\nu \simeq - m_D^2 / M$ 2– $m_\nu \simeq - m_D^2 / M$ 3; same-sign dilepton and kinematic asymmetries allow Majorana/Dirac discrimination (Kwok et al., 2023).

Future Lepton Colliders

FCC-ee ( $m_\nu \simeq - m_D^2 / M$ 4-factory): Ultimate sensitivity to $m_\nu \simeq - m_D^2 / M$ 5– $m_\nu \simeq - m_D^2 / M$ 6 at $m_\nu \simeq - m_D^2 / M$ 7 GeV via $m_\nu \simeq - m_D^2 / M$ 8 decays, flavor-independent (Rasmussen et al., 2016).

Summary Table of Projected Sensitivity

Facility	Mass Range (GeV)	$m_\nu \simeq - m_D^2 / M$ 9 Reach	Flavor	Note
SHiP	0.3–7	$I=1,2,3$ 00	$I=1,2,3$ 01, $I=1,2,3$ 02, $I=1,2,3$ 03	D, B decays; beam-dump
DUNE ND	0.1–2	$I=1,2,3$ 04	$I=1,2,3$ 05, $I=1,2,3$ 06, $I=1,2,3$ 07	kaon/charm production; fixed-target
FASER2	0.2–4	$I=1,2,3$ 08– $I=1,2,3$ 09	all	forward LHC, multiple couplings
HL-LHC	10–150	$I=1,2,3$ 10– $I=1,2,3$ 11	$I=1,2,3$ 12	3-lepton, $I=1,2,3$ 13 prompt signature
EIC	1–100	$I=1,2,3$ 14– $I=1,2,3$ 15	$I=1,2,3$ 16	prompt/displaced; hadronic channels
FCC-ee	1–45	$I=1,2,3$ 17– $I=1,2,3$ 18	all	$I=1,2,3$ 19 direct measurement

5. Effective Field Theory, Portals, and New Gauge Interactions

GeV-scale HNLs may couple to the SM through higher-dimension operators in the neutrino SMEFT (νSMEFT), classified as:

Higgs-dressed mixing ( $I=1,2,3$ 20): modifies $I=1,2,3$ 21,
Bosonic currents ( $I=1,2,3$ 22, $I=1,2,3$ 23): provide $I=1,2,3$ 24-like couplings,
Dipole operators ( $I=1,2,3$ 25, $I=1,2,3$ 26): induce $I=1,2,3$ 27 decays,
Four-fermion contact terms (charged and neutral currents): affect production and decay, can lift mixing suppression for pair production (Fernández-Martínez et al., 2023, Cottin et al., 2021).

Production via contact interactions or new vector mediators ( $I=1,2,3$ 28) can vastly enhance sensitivity, especially at fixed-target setups:

$I=1,2,3$ 29 or other $I=1,2,3$ 30 extensions: $I=1,2,3$ 31 produced via Drell–Yan, decays promptly to $I=1,2,3$ 32, dramatically increasing HNL flux if $I=1,2,3$ 33 (Capozzi et al., 2024, Burk et al., 26 Jan 2026).
Projected reach: DUNE ND, SHiP, SBND can access $I=1,2,3$ 34– $I=1,2,3$ 35 in the seesaw band for $I=1,2,3$ 36– $I=1,2,3$ 37 GeV provided additional $I=1,2,3$ 38 production (Capozzi et al., 2024, Burk et al., 26 Jan 2026).

In the SMEFT, current bounds on operator coefficients of dimension-6 CC-type operators reach $I=1,2,3$ 39 GeV $I=1,2,3$ 40 in the sub–10 GeV region, corresponding to new-physics scales up to $I=1,2,3$ 41 TeV (Fernández-Martínez et al., 2023, Cottin et al., 2021).

6. Flavor Structure, Parameter Scans, and Model Discrimination

Mixing patterns $I=1,2,3$ 42 are heavily model-dependent:

Generic seesaw models (Casas–Ibarra/random scans): yield $I=1,2,3$ 43– $I=1,2,3$ 44 for $I=1,2,3$ 45– $I=1,2,3$ 46 GeV, with BBN and laboratory bounds truncating extreme regions (Rasmussen et al., 2016).
Flavor-symmetry models: predict hierarchies (e.g., $I=1,2,3$ 47, etc.), providing robust discrimination if all flavors are probed (Rasmussen et al., 2016).
Experimental flavor-resolved sensitivity: Essential to separate models since $I=1,2,3$ 48, $I=1,2,3$ 49, and $I=1,2,3$ 50 couplings may differ by orders of magnitude. Modern experiments (e.g., SHiP, DUNE, HL-LHC) provide or plan such discrimination.

Dedicated simulation frameworks (e.g., HNLCalc) now allow general coupling configurations to all flavors, enabling robust, assumption-free experimental projections (Feng et al., 2024).

7. Complementarity, Model Status, and Open Directions

Direct searches and indirect/probe physics are complementary. DUNE, FASER2, SBND/ICARUS probe visible HNL decays; neutrinoless double-beta decay ( $I=1,2,3$ 51) is sensitive to Majorana-violating couplings and phases (Bolton et al., 2022).
Displaced-vertex and invisible signatures: Both are essential for full parameter-space coverage. Models with new invisible decay modes (e.g., via ALPs) can escape detection in standard visible channels, requiring synergy with BBN and laboratory constraints (Deppisch et al., 2024).
Majorana/Dirac discrimination: Accessible via same-sign dilepton ratios, forward-backward and energy asymmetries, and event topology at colliders and muon colliders (Kwok et al., 2023).

Summary Table: Constraints and Sensitivity by Experiment

Constraint	$I=1,2,3$ 52 Range	$I=1,2,3$ 53 Range	Experiment(s)/Method	Reference
BBN	3 MeV–1 GeV	$I=1,2,3$ 54– $I=1,2,3$ 55	Primordial elemental ratios	(Sabti et al., 2020)
Direct searches (past)	0.1–2 GeV	$I=1,2,3$ 56– $I=1,2,3$ 57	PS191, CHARM, BEBC	(Rasmussen et al., 2016)
Direct (future/ongoing)	0.3–7 GeV	$I=1,2,3$ 58– $I=1,2,3$ 59	SHiP, DUNE, FCC-ee	(Collaboration, 2018, Capozzi et al., 2024)
Collider (HL-LHC)	$I=1,2,3$ 6050 GeV	$I=1,2,3$ 61	τ-enriched trileptons	(Cheung et al., 2020)
EIC (prompt/displaced)	1–100 GeV	$I=1,2,3$ 62– $I=1,2,3$ 63	$I=1,2,3$ 64-flavor only	(Batell et al., 2022)
SMEFT contact	$I=1,2,3$ 65 GeV	$I=1,2,3$ 66 GeV $I=1,2,3$ 67	inclusive	(Fernández-Martínez et al., 2023)

The allowed region remains open predominantly in the $I=1,2,3$ 68 band for $I=1,2,3$ 69– $I=1,2,3$ 70 GeV, precisely the domain targeted by the next generation of fixed-target, collider, and beam-dump experiments.

References

Proposal to Search for Heavy Neutral Leptons at the SPS (Bonivento et al., 2013)
Phenomenology of GeV-scale Heavy Neutral Leptons (Bondarenko et al., 2018)
Sensitivity of the SHiP experiment to Heavy Neutral Leptons (Collaboration, 2018)
Perspectives for tests of neutrino mass generation at the GeV scale (Rasmussen et al., 2016)
Modelling Heavy Neutral Leptons in Accelerator Beamlines (Plows et al., 2022)
Simulating Heavy Neutral Leptons with General Couplings at Collider and Fixed Target Experiments (Feng et al., 2024)
Heavy Neutral Leptons at the Electron-Ion Collider (Batell et al., 2022)
Probing the Nature of Heavy Neutral Leptons in Direct Searches and Neutrinoless Double Beta Decay (Bolton et al., 2022)
Relaxing Limits from Big Bang Nucleosynthesis on Heavy Neutral Leptons with Axion-like Particles (Deppisch et al., 2024)
Enhancing the Sensitivity to Seesaw Predictions in Gauged $I=1,2,3$ 71 Scenarios (Capozzi et al., 2024)
Drell-Yan Production of New Particles at Fixed-Target Experiments: Heavy Neutral Lepton as a Case Study (Burk et al., 26 Jan 2026)
Heavy neutral leptons in effective field theory and the high-luminosity LHC (Cottin et al., 2021)
Effective portals to heavy neutral leptons (Fernández-Martínez et al., 2023)
Heavy Neutral Lepton searches at an ICARUS-like detector using NuMI beam (Chatterjee et al., 2024)
Searching for Heavy Neutral Leptons at A Future Muon Collider (Kwok et al., 2023)