Heavy Neutral Leptons: Searching for the Seesaw at the GeV Scale

The Standard Model contains three neutrinos, and they are all left-handed. There are no right-handed partner fields in the Standard Model — a fact that is responsible for the model’s prediction that neutrinos are massless. When experimental observations of neutrino oscillation in 1998 and 2001 demonstrated that neutrinos do have mass, the Standard Model needed modification.

The simplest modification is to add right-handed partner fields, with Yukawa couplings to the Higgs that produce small Dirac masses. But the required Yukawa couplings are unnaturally small — of order $10^{-12}$ — many orders of magnitude smaller than other Standard Model Yukawas. This is the neutrino-mass naturalness problem.

The standard theoretical resolution is the seesaw mechanism. The right-handed neutrino fields are given a Majorana mass term $M_R$ (which mixes the field with itself), in addition to the Yukawa coupling $y_{\nu }$ to the Higgs. The visible (light) neutrino masses are then $m_{\nu }\sim y_{\nu }^2{v}^2/M_R$, where $v=246$ GeV is the Higgs vacuum expectation value. For Yukawa couplings of order unity, $M_R$ in the range of $10^{14}$ GeV gives the observed light-neutrino masses. For smaller Yukawa couplings, $M_R$ can be smaller.

The seesaw mechanism naturally explains both the smallness of neutrino masses and (via leptogenesis) the matter-antimatter asymmetry of the universe. But it also predicts the existence of new heavy neutrino-like particles — heavy neutral leptons (HNLs) — in addition to the three light neutrinos.

These heavy neutrinos are the experimental target of a substantial current programme. If $M_R$ is at the high-scale (GUT) range — $10^{12}$–$10^{15}$ GeV — they are inaccessible to any current or planned experiment. But if $M_R$ is at the GeV-to-TeV scale, they can be searched for at modern accelerators. The “GeV-scale HNL window” — also known as the νMSM scenario in some theoretical frameworks — is the most experimentally interesting region.

This post is about the GeV-scale HNL search programme, what experiments are looking for, and what current limits look like.

The GeV-scale HNL theory

In the GeV-scale HNL scenario, the three right-handed neutrino fields have Majorana masses around 1-10 GeV — light compared to the electroweak scale, heavy compared to the visible neutrinos. The Yukawa couplings are small but non-negligible (typically $y_{\nu }\sim 10^{-7}$). The active-sterile mixing parameter $|U{|}^2$, which controls how often visible-neutrino events become HNL-related events, is small (typically $|U{|}^2<10^{-7}$).

The phenomenology:

• Production: HNLs are produced in meson decays, including charged-pion decays (${\pi }^{\pm }\to {\mu }^{\pm }+N$ for HNL mass below the pion-muon mass difference), kaon decays, D meson decays, and B meson decays. The branching ratio is proportional to $|U{|}^2$.

• Propagation: HNLs are weakly interacting and propagate distances of order 1-10 metres before decaying. The typical decay length is set by the HNL mass and mixing: $L\sim \hslash c/(G_F^2{m}_N^5|U{|}^2)$. For $m_N=1$ GeV and $|U{|}^2=10^{-8}$, $L\sim 10$ metres.

• Decay: HNLs decay back to Standard Model particles via the same mixing that produces them. Common decay channels include $N\to \nu \pi$, $N\to \mu \pi$, $N\to \nu e^{+}{e}^{-}$, etc.

• Signature in detectors: A displaced vertex — a Standard-Model decay (e.g., ${\pi }^{+}{\pi }^{-}$ pair, or a single charged lepton plus missing energy) appearing at a characteristic distance from the original production point. The displacement is the HNL’s flight distance.

The displacement signature is the key experimental handle. Standard-Model particles with similar decay products but produced promptly (no displacement) are the dominant background; rejecting prompt-vertex events while keeping displaced-vertex events is how HNL searches achieve sensitivity.

Theoretical motivation: νMSM

The νMSM (neutrino Minimal Standard Model) scenario, proposed by Asaka and Shaposhnikov in 2005, is a specific theoretical framework where three GeV-scale right-handed neutrinos provide:

1. The active-neutrino masses observed in oscillation experiments (via the seesaw mechanism)
2. The matter-antimatter asymmetry of the universe (via leptogenesis at the electroweak phase transition)
3. The dark matter (one of the heavy neutrinos at the keV scale could be the dark matter candidate)

In the νMSM, two of the three right-handed neutrinos have masses around 100-1000 MeV (these mediate baryogenesis) and the third has a much lower mass around 1-10 keV (this is the dark matter candidate). The two heavier ones are GeV-scale HNLs, accessible to accelerator searches.

This scenario gives a particular target for the experimental programme: HNL masses in the 100-1000 MeV range, with mixing parameters $|U{|}^2$ in the range $10^{-9}$–$10^{-12}$. Current experiments have not yet reached this sensitivity but are within an order of magnitude of relevant scales.

Current searches

LHC searches. Both ATLAS and CMS have searched for HNLs in proton-proton collisions. The dominant production at LHC energies is via W boson decay: $W^{\pm }\to {\ell }^{\pm }+N$. The HNL then decays via $N\to \ell q\bar{q}$. The displaced vertex signature is the basis for the search.

Current LHC limits, for HNL masses below the W mass (about 80 GeV), exclude $|U{|}^2$ at the level of $10^{-2}$–$10^{-4}$. Above the W mass, the limits become weaker because HNL production is suppressed by phase-space considerations.

Beam-dump experiments. Fixed-target experiments at proton beam dumps produce HNLs through cascade decays of secondary mesons. Past examples include CHARM (CERN, 1980s) and PS191 (CERN, 1980s). Current limits from these experiments exclude $|U{|}^2$ at levels of $10^{-4}$–$10^{-7}$ for HNL masses in the 0.1-2 GeV range.

Dedicated HNL experiments. The proposed SHiP experiment at CERN would dump 400 GeV protons into a dedicated target, producing HNLs through D meson decays at high rate. SHiP would have approximately a 100-metre evacuated decay region behind the target, allowing HNLs to fly far before decaying into a downstream spectrometer. The sensitivity goal is $|U{|}^2$ at $10^{-9}$–$10^{-10}$ — well below the νMSM target region.

SHiP is currently in advanced design at CERN. If approved, it would begin running in approximately 2030. It would be the first dedicated HNL search facility.

FASER and SND@LHC (the LHC forward neutrino experiments) can also search for HNLs through their decays during transit through the experimental volume. Both have reported preliminary limits, though they are not as stringent as those from CHARM and similar dedicated searches.

Recent results and status

By 2025, the experimental status is roughly:

• LHC limits cover HNL masses 5-80 GeV at $|U{|}^2>10^{-3}$.
• CHARM and PS191 limits cover masses 0.1-2 GeV at $|U{|}^2>10^{-6}$.
• T2K, MicroBooNE, and other accelerator-neutrino experiments have set limits on HNLs from kaon decays.
• ATLAS and CMS have specifically searched for displaced-vertex topologies in long-lived-particle searches.

In 2024, the ATLAS collaboration published a specific HNL search using LHC Run 3 data, setting limits around $|U{|}^2<10^{-3}$ for HNL masses in the 4-15 GeV range. CMS has reported similar results for their parameter space.

For the νMSM target region ($|U{|}^2\sim 10^{-9}$–$10^{-12}$ at GeV mass scales), the current experimental limits are still 3-4 orders of magnitude away. This is the gap that the next generation of experiments — SHiP, dedicated detector upgrades, and improved long-lived-particle searches at the LHC — will close.

What an HNL discovery would mean

If a heavy neutral lepton is detected in any of these experiments, the implications are substantial:

1. Direct evidence for the seesaw mechanism. The HNL would be the right-handed partner whose existence is required by the seesaw. This would establish that neutrino masses arise through the seesaw, not through some other mechanism.

2. Active-sterile mixing measurement. The mixing parameter $|U{|}^2$ would be measured, providing constraints on the leptonic CP phases and the Yukawa couplings.

3. Leptogenesis becomes a much stronger explanation for the matter-antimatter asymmetry. If HNLs exist at the GeV scale with the predicted properties, their CP-violating decays in the early universe could naturally produce the observed baryon asymmetry.

4. A new portal to beyond-Standard-Model physics. The HNL would be a particle that can be produced at accelerators, propagated through the laboratory environment, and used as a calibration probe of weak interaction physics at energies where direct measurements are otherwise difficult.

The first HNL discovery would be major news for the field and would substantially clarify the picture of beyond-Standard-Model physics.

What no detection would mean

If the next generation of experiments — SHiP, LHC long-lived-particle searches, and others — find no HNLs in the GeV mass range, the implications are also significant:

1. The νMSM scenario is excluded in its standard form. Other variants (with different mass scales, different mixing patterns) might still survive.

2. Low-scale leptogenesis is disfavored. If GeV-scale HNLs do not exist, leptogenesis must operate at higher scales — typically requiring a high reheating temperature after inflation, which is constrained by other cosmological observations.

3. Either neutrinos are Dirac, with the right-handed partners simply being weakly coupled and at very high mass scales (GUT-style seesaw), or the seesaw operates at even smaller mixings than the experimental sensitivity reaches.

The non-detection scenarios are not as definitive as a discovery would be, but they constrain a substantial part of the theoretical landscape.

The bigger picture

The HNL search is currently one of the most active frontiers in beyond-Standard-Model physics. The motivation is strong: HNLs are the simplest theoretical resolution of the neutrino-mass problem, and their discovery would have implications across multiple subfields (neutrino physics, baryogenesis, dark matter, beyond-Standard-Model theory).

The experimental approach has evolved substantially over the past decade. Early searches were limited to kinematic decays of pions and kaons; modern searches use heavy-meson decays at colliders and beam-dump facilities, accessing much higher masses. The forthcoming SHiP experiment, if approved, will be the first dedicated HNL search facility and will probe the most theoretically motivated parameter region.

By 2030-2035, the GeV-scale HNL window should be substantially explored. Either an HNL discovery is in the cards, or the seesaw mechanism operates at higher scales (and is therefore harder to test directly). Either outcome will substantially clarify the picture of how neutrino masses arise.

For now, the search continues. Each new generation of experiments incrementally extends the parameter space probed. The eventual answer — discovery or strong null — will be a milestone in the path from oscillation observations to the underlying mass-generating mechanism. Heavy neutral leptons, if they exist at the GeV scale, will be the most direct experimental window into that mechanism.