---
title: GeV-Scale Heavy Neutral Leptons
url: https://www.emergentmind.com/topics/gev-scale-heavy-neutral-leptons-hnls
type: topic
---

# GeV-Scale Heavy Neutral Leptons

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 $M \sim 1\,\text{GeV}$ and $m_\nu \sim 0.05\,\text{eV}$, this implies $m_D \sim 10\,\text{keV}$ and $Y \sim 10^{-7}$ [1310.1762].

Active–sterile mixing is parameterized as $U_{I\alpha} = (Y_{I\alpha} v)/(\sqrt{2} M_I)$, with total mixing strength $U^2 = \sum_{I,\alpha} |U_{I\alpha}|^2$. Signal and background yields in fixed-target experiments generally scale as $U^4$ in the long-lifetime regime.

The νMSM requires:
- One HNL at $O(\text{keV})$ as a DM candidate (subject to X-ray decay constraints),
- Two nearly degenerate HNLs at $O(\text{GeV})$ for leptogenesis and baryonic asymmetry,
- Seesaw-motivated active–sterile mixing: for $m_\nu \sim 0.05$ eV and $M_N \sim 1$ GeV, $|U|^2 \sim 5 \times 10^{-11}$ to $10^{-7}$ [1310.1762, 1607.07880, 1805.08567].

## 2. Production and Decay Channels

### Production Mechanisms

GeV-scale HNLs are produced dominantly via:
- **Meson decays:** $D \to \ell N X$, $B \to \ell N X$
- **Kaon and pion decays:** $K \to \ell N$, $\pi \to \ell N$
- **Tau decays:** $\tau \to N + X$ for $m_N < m_\tau$
- **Proton–nucleus Drell–Yan and deep inelastic processes:** subdominant for $M_N \lesssim 2$ GeV [1805.08567, 2103.11494]

Branching ratios are suppressed by $|U_\alpha|^2$ and relevant phase-space factors, sensitively depending on $m_N$ [1805.08567]. For example, $\mathcal{B}(D\to N X)\sim10^{-8}$–$10^{-12}$ for $U^2$ in the seesaw/νMSM range [1310.1762].

### Decay Modes

HNL decays proceed via charged-current (CC) and neutral-current (NC) weak interactions:
- **Two-body decays:** $N \to \ell^- h^+$ ($h^+=\pi^+,K^+,\ldots$), $N\to\nu h^0$ ($h^0=\pi^0,\eta,\ldots$)
- **Three-body leptonic decays:** $N \to \ell^- \ell'^+ \nu$, $N\to 3\nu$
- **Semileptonic decays:** $N \to \ell^- (\text{hadrons})$, $N\to\nu (\text{hadrons})$
- **Multi-meson decays:** open up above $M_N \sim 1.5$ GeV [1805.08567].

Decay widths scale as $\Gamma\propto G_F^2 M_N^5 |U_{\alpha N}|^2$ times channel-dependent phase space.

Typical branching ratios shift rapidly with $m_N$: below pion threshold, HNLs decay only leptonically; above, hadronic modes dominate [1805.08567, 2405.07330]. For $M_N \sim 400$ MeV, $\mathrm{BR}(N\to\mu\pi)\sim50\%$; $\mathrm{BR}(N\to\pi^0\nu)\sim30\%$ [2211.10210].

HNL total lifetimes are macroscopically long for $|U|^2\lesssim10^{-8}$: $\tau_N \sim 3\times10^{-5}\,\text{s}\,(1\,\text{GeV}/M_N)^5/|U|^2$ [1805.08567]. This underpins the importance of displaced-vertex and decay-in-flight searches.

## 3. Cosmological and Astrophysical Constraints

Cosmological observations constrain the allowed window in $(M_N,|U|^2)$:
- **Big Bang Nucleosynthesis (BBN):** Long-lived HNLs (with $\tau_N \gtrsim 0.03$–$0.05$ s for $m_N \gtrsim m_\pi$) disrupt light element formation, excluding $|U|^2\lesssim10^{-7}$ for $m_N\lesssim200$–$450$ MeV, depending on mixing pattern [2006.07387].
- **Baryogenesis bounds ("BAU limit"):** To preserve lepton asymmetry, $|U|^2\lesssim10^{-7}$ for $M_N\sim1$ GeV [1310.1762].
- **Seesaw lower bound:** To explain observed $\Delta m_\nu^2$, $|U|^2 \gtrsim 10^{-11}$ (normal hierarchy) [1310.1762, 1607.07880].
- **Dark matter (keV HNL):** Requires radiative decay lifetime consistent with X-ray bounds [1310.1762].

In models with dominant invisible decay channels (e.g., $N\to a\nu$ with an axion-like particle $a$), BBN constraints can be significantly relaxed, opening parameter space for $1\,$MeV $\lesssim m_N \lesssim 1\,$GeV and $|U|^2 \sim 10^{-9}$–$10^{-6}$ [2410.06970].

## 4. Laboratory Search Strategies and Experimental Sensitivities

### Fixed-Target and Beam-Dump Facilities

- **CERN SPS/SHiP:** Exploits high-intensity $400\,$GeV proton beams. Sensitivity to $0.3\,$GeV $\lesssim M_N \lesssim 7\,$GeV, $|U|^2 \gtrsim 10^{-10}$ (muon flavor) [1811.00930].
- **ICARUS/DUNE/SBND/DarkQuest:** Use LArTPCs near high-energy beams. Sensitivity to $|U|^2 \sim 3 \times 10^{-10}$ at $1.6$ GeV (muon flavor, ICARUS) [2408.03383]; DUNE ND projects $|U|^2 \sim 10^{-8}$ at $0.3$–$2$ GeV [2212.14690, 2410.08981].
- **Current reach:** PS191, CHARM, BEBC exclude $|U_{e,\mu}|^2 \gtrsim 10^{-8}$–$10^{-7}$ in $0.1$–$2$ GeV [1607.07880].

### Collider Experiments

- **HL-LHC:** For $M_N \lesssim 50$ GeV, searches targeting prompt trilepton signatures with $\tau$-enrichment reach $|U_{\tau N}|^2 \simeq 2 \times 10^{-6}$ [2004.11537].
- **Electron-Ion Collider (EIC):** Probes $m_N \simeq 1$–$100$ GeV; $|U_e|^2 \gtrsim 10^{-4}$–$10^{-3}$ (prompt), $10^{-6}$–$10^{-4}$ (displaced vertex) [2210.09287].
- **TeV-scale Muon Collider:** For $m_N = 200$–$1000$ GeV, reach down to $|U_{\ell N}|^2 \sim 10^{-6}$–$10^{-7}$; same-sign dilepton and kinematic asymmetries allow Majorana/Dirac discrimination [2301.05177].

### Future Lepton Colliders

- **FCC-ee ($Z$-factory):** Ultimate sensitivity to $|U|^2 \sim 10^{-11}$–$10^{-10}$ at $m_N \lesssim 45$ GeV via $Z \to \nu N$ decays, flavor-independent [1607.07880].

### Summary Table of Projected Sensitivity

| Facility        | Mass Range (GeV) | $|U|^2$ Reach  | Flavor          | Note                                   |
|-----------------|------------------|---------------|-----------------|----------------------------------------|
| SHiP           | 0.3–7            | $10^{-10}$    | $e$, $\mu$, $\tau$ | D, B decays; beam-dump                 |
| DUNE ND        | 0.1–2            | $10^{-8}$     | $e$, $\mu$, $[\tau]$ | kaon/charm production; fixed-target    |
| FASER2         | 0.2–4            | $10^{-9}$–$10^{-6}$ | all        | forward LHC, multiple couplings        |
| HL-LHC         | 10–150           | $10^{-6}$–$10^{-4}$ | $\tau$   | 3-lepton, $2\tau$ prompt signature     |
| EIC            | 1–100            | $10^{-6}$–$10^{-3}$ | $e$      | prompt/displaced; hadronic channels    |
| FCC-ee         | 1–45             | $10^{-11}$–$10^{-10}$ | all    | $Z\to\nu N$ 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** ($\mathcal{O}_{\rm LNH}$): modifies $U_{\alpha N}$,
- **Bosonic currents** ($\mathcal{O}_{\rm HN}$, $\mathcal{O}_{\rm HN\ell}$): provide $Z/W$-like couplings,
- **Dipole operators** ($\mathcal{O}_{\rm NB}$, $\mathcal{O}_{\rm NW}$): induce $N\to\nu\gamma$ decays,
- **Four-fermion contact terms** (charged and neutral currents): affect production and decay, can lift mixing suppression for pair production [2304.06772, 2105.13851].

Production via contact interactions or new vector mediators ($Z'$) can vastly enhance sensitivity, especially at fixed-target setups:
- **$U(1)_{B-L}$ or other $U(1)'$ extensions:** $Z'$ produced via Drell–Yan, decays promptly to $NN$, dramatically increasing HNL flux if $g' \gtrsim 10^{-5}$ [2410.08981, 2601.18874].
- **Projected reach**: DUNE ND, SHiP, SBND can access $|U|^2 \sim 10^{-9}$–$10^{-8}$ in the seesaw band for $m_N = 0.2$–$2$ GeV provided additional $Z'$ production [2410.08981, 2601.18874].

In the SMEFT, current bounds on operator coefficients of dimension-6 CC-type operators reach $|C/\Lambda^2| \lesssim 10^{-7}$ GeV$^{-2}$ in the sub–10 GeV region, corresponding to new-physics scales up to $\sim10$ TeV [2304.06772, 2105.13851].

## 6. Flavor Structure, Parameter Scans, and Model Discrimination

Mixing patterns $U_e^2:U_\mu^2:U_\tau^2$ are heavily model-dependent:
- **Generic seesaw models (Casas–Ibarra/random scans):** yield $|U|^2 \sim 10^{-10}$–$10^{-6}$ for $M_N=0.3$–$10$ GeV, with BBN and laboratory bounds truncating extreme regions [1607.07880].
- **Flavor-symmetry models:** predict hierarchies (e.g., $U_e^2 \gg U_\mu^2$, etc.), providing robust discrimination if all flavors are probed [1607.07880].
- **Experimental flavor-resolved sensitivity:** Essential to separate models since $\nu_e$, $\nu_\mu$, and $\nu_\tau$ 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 [2405.07330].

## 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 ($0\nu\beta\beta$) is sensitive to Majorana-violating couplings and phases [2212.14690].
- **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 [2410.06970].
- **Majorana/Dirac discrimination:** Accessible via same-sign dilepton ratios, forward-backward and energy asymmetries, and event topology at colliders and muon colliders [2301.05177].

### Summary Table: Constraints and Sensitivity by Experiment

| Constraint          | $m_N$ Range   | $|U|^2$ Range     | Experiment(s)/Method        | Reference          |
|---------------------|--------------|------------------|----------------------------|--------------------|
| BBN                 | 3 MeV–1 GeV  | $10^{-7}$–$10^{-9}$ | Primordial elemental ratios | [2006.07387]     |
| Direct searches (past)| 0.1–2 GeV   | $10^{-8}$–$10^{-7}$ | PS191, CHARM, BEBC         | [1607.07880]     |
| Direct (future/ongoing)| 0.3–7 GeV  | $10^{-10}$–$10^{-8}$ | SHiP, DUNE, FCC-ee         | [1811.00930][2410.08981] |
| Collider (HL-LHC)   | $<$50 GeV    | $2 \times 10^{-6}$   | τ-enriched trileptons      | [2004.11537]     |
| EIC (prompt/displaced) | 1–100 GeV | $10^{-6}$–$10^{-4}$ | $e$-flavor only            | [2210.09287]     |
| SMEFT contact      | $\leq 10$ GeV | $10^{-7}$ GeV$^{-2}$ | inclusive                  | [2304.06772]     |

The allowed region remains open predominantly in the $10^{-11} \lesssim |U|^2 \lesssim 10^{-7}$ band for $M_N\sim0.3$–$2$ 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 [1310.1762]
- Phenomenology of GeV-scale Heavy Neutral Leptons [1805.08567]
- Sensitivity of the SHiP experiment to Heavy Neutral Leptons [1811.00930]
- Perspectives for tests of neutrino mass generation at the GeV scale [1607.07880]
- Modelling Heavy Neutral Leptons in Accelerator Beamlines [2211.10210]
- Simulating Heavy Neutral Leptons with General Couplings at Collider and Fixed Target Experiments [2405.07330]
- Heavy Neutral Leptons at the Electron-Ion Collider [2210.09287]
- Probing the Nature of Heavy Neutral Leptons in Direct Searches and Neutrinoless Double Beta Decay [2212.14690]
- Relaxing Limits from Big Bang Nucleosynthesis on Heavy Neutral Leptons with Axion-like Particles [2410.06970]
- Enhancing the Sensitivity to Seesaw Predictions in Gauged $B-L$ Scenarios [2410.08981]
- Drell-Yan Production of New Particles at Fixed-Target Experiments: Heavy Neutral Lepton as a Case Study [2601.18874]
- Heavy neutral leptons in effective field theory and the high-luminosity LHC [2105.13851]
- Effective portals to heavy neutral leptons [2304.06772]
- Heavy Neutral Lepton searches at an ICARUS-like detector using NuMI beam [2408.03383]
- Searching for Heavy Neutral Leptons at A Future Muon Collider [2301.05177]

Source: https://www.emergentmind.com/topics/gev-scale-heavy-neutral-leptons-hnls