---
title: Right-Handed Neutrinos (RHNs)
url: https://www.emergentmind.com/topics/right-handed-neutrinos-rhns
type: topic
---

# Right-Handed Neutrinos (RHNs)

A right-handed neutrino (RHN) is a Standard Model (SM) gauge singlet Weyl fermion with right-handed chirality, introduced as a minimal extension of the SM. They are motivated by multiple observations: the necessity of nonzero neutrino masses, the baryon asymmetry of the universe, and the dark matter (DM) problem. In the SM, only left-handed neutrino fields exist, rendering neutrinos massless. The addition of RHNs allows for the construction of both Dirac and Majorana mass terms and naturally generates sub-eV active neutrino masses via the seesaw mechanism. The Majorana nature of RHNs enables lepton-number violation, a precondition for generating the baryon asymmetry, and certain mass/mixing regimes of RHNs provide a compelling DM candidate. RHNs are parameterized by their Majorana mass eigenvalues $M_I$ and mixing with active flavors, and their phenomenology spans from laboratory constraints on rare processes and direct searches to cosmological and astrophysical bounds.

## 1. Theoretical Motivation and Model Structure

In the SM, neutrinos are strictly massless due to the absence of right-handed neutrino fields and the corresponding Yukawa terms. The observation of neutrino oscillations implies non-zero neutrino masses, prompting physics beyond the SM. The minimal and most predictive extension is the Type-I seesaw, where $n$ right-handed neutrinos $N_I$ ($I=1\ldots n$) are added as gauge singlets and allowed to possess large Majorana masses $M_I$:
\[
\mathcal{L} \supset -Y_{\alpha I}\,\overline{L}_\alpha\,\tilde{H}\,N_I - \tfrac{1}{2} M_I\,\overline{N_I^c}\,N_I + \text{h.c.}
\]
with Yukawa couplings $Y_{\alpha I}$ and $L_\alpha$ denoting the SM lepton doublets. After electroweak symmetry breaking ($\langle H\rangle = v/\sqrt 2$), the Dirac mass $m_D = Y v / \sqrt{2}$ mixes active and sterile neutrinos, giving rise to a $6 \times 6$ neutrino mass matrix:
\[
\mathcal{M} = \begin{pmatrix} 0 & m_D \\ m_D^T & M \end{pmatrix}
\]
Diagonalizing $\mathcal{M}$ for $M \gg m_D$ yields the classic seesaw relation:
\[
m_{\nu} \simeq - m_D M^{-1} m_D^T
\]
RHNs naturally allow processes forbidden in the SM, such as neutrinoless double-beta decay, and can provide mechanisms for baryogenesis via leptogenesis and for DM.

## 2. Parameter Space and Experimental and Cosmological Constraints

The phenomenology of RHNs is governed by their masses $M_I$ and their mixing with active neutrinos, $U_{\alpha I} \simeq (m_D M^{-1})_{\alpha I} \sim Y_{\alpha I} v / (\sqrt{2} M_I)$. The allowed parameter space is delineated by a combination of laboratory, astrophysical, and cosmological constraints:

- **Laboratory bounds**: Fixed-target (e.g., PS191, CHARM, NuTeV) and collider (DELPHI/LEP1) experiments constrain $|U_{\ell}|^2 \lesssim 10^{-8}\text{--}10^{-5}$ for $M \sim 0.03$–75 GeV. Prompt LHC same-sign dilepton searches extend to $M_N > 30$ GeV for larger mixings.
- **Big-Bang Nucleosynthesis (BBN)**: Requires that RHNs decayed before $t \sim 1$ s, setting a lower bound on $|U|^2$ of order $10^{-10}$–$10^{-12}$ for $1$ MeV $< m_N <$ 1 GeV.
- **Neutrino mass constraint**: The sum rule $\sum_I |U|^2 M_I \gtrsim 0.05$ eV is dictated by oscillation data and the seesaw relation.
- **Leptogenesis window**: Successful baryogenesis via leptogenesis for nearly degenerate RHNs in the mass range $0.5$–$5$ GeV and $|U|^2 \sim 10^{-11}$–$10^{-8}$.
- **Dark matter**: The lightest RHN (e.g., with mass $\sim$ keV) can be a warm DM candidate if $|U|^2 \sim 10^{-8}$. X-ray non-observation places stringent upper limits on $|U|^2$ for this mass scale.

## 3. Experimental Probes and Detection Strategies

Contemporary and proposed searches pursue a dual approach exploiting the macroscopic lifetime and weak coupling of sub-electroweak scale RHNs:

- **Beam-dump experiments (SHiP at CERN)**: 400 GeV protons on target yield a copious flux of heavy-flavor mesons. Decays $D\to \ell N_I$ or $D_s\to \tau N_I$ produce $N_I$ up to $m_N\lesssim5$ GeV. A 50 m vacuum vessel with background rejection via timing and tracking enables detection by reconstructing displaced vertices. SHiP can probe $|U|^2\sim 10^{-10}$ at $m_N\sim 1$ GeV, reaching up to $10^{-9}$ at $m_N = 5$ GeV and completely covering the low-scale leptogenesis window [1704.08635].

- **Displaced-vertex searches at LHC (ATLAS/CMS)**: $W\to \ell N$ production, with $\sigma(pp\to W)\approx20$ nb at $\sqrt{s}=14$ TeV. For $m_N=5$–$30$ GeV and $|U|^2=10^{-8}$--$10^{-6}$, the RHN decay length in the lab is mm to meters. Triggers on prompt leptons and vertex displacement in the inner detector allow background-free searches down to $|U|^2\sim 10^{-8}$ for $m_N=3$--$30$ GeV [1704.08635].

- **Summary table**:

| Mass range (GeV)   | $|U|^2$ Sensitivity  | Current Bound               | Favored by BAU         |
|--------------------|---------------------|-----------------------------|------------------------|
| 0.1–0.5            | $10^{-10}$–$10^{-9}$ (SHiP) | PS191/CHARM: $10^{-8}$–$10^{-7}$ | Partly                |
| 0.5–5              | $10^{-9}$–$10^{-8}$ (SHiP) | DELPHI: $10^{-5}$                | Yes                   |
| 3–30               | $10^{-8}$–$10^{-7}$ (LHC)  | DELPHI: $10^{-5}$                | Yes                   |
| 30–80              | $10^{-6}$–$10^{-5}$ (LHC)  | DELPHI: $10^{-5}$                | No                    |

- **SHiP and LHC complementarity**: SHiP accesses the leptogenesis window for $m_N < 5$ GeV with sensitivity several orders of magnitude below current bounds, while LHC displaced-vertex searches probe up to $m_N \sim 30$ GeV where prior limits are orders of magnitude weaker.

## 4. Cosmological and Astrophysical Implications

RHNs address three separate sources of SM incompleteness:

- **Neutrino mass**: The seesaw mechanism generated by the RHN Majorana and Dirac masses provides a natural explanation for observed mass splittings and mixings.
- **Baryogenesis via leptogenesis**: Out-of-equilibrium, CP-violating RHN decays in the early universe create a lepton asymmetry which sphaleron transitions convert into the observed baryon asymmetry. The favored mass and mixing region, $m_N\sim 0.5$–5 GeV, $|U|^2\sim10^{-11}$–$10^{-8}$, is broadly accessible to SHiP and LHC searches.
- **Dark matter**: The neutrino minimal Standard Model ($\nu$MSM) utilizes three RHNs; the lightest, $N_1$ with $m_N\sim$ keV, serves as DM, with the heavier two providing light-neutrino mass and facilitating leptogenesis. The mixing required for $N_1$ to be sufficiently long-lived and cosmologically stable is limited by X-ray and structure-formation constraints [1704.08635].

## 5. Synthesis: Status and Future Prospects

A combined program at high-intensity and high-energy frontiers will, within the next decade, decisively probe the parameter space for RHNs relevant to neutrino mass, baryogenesis, and DM. SHiP will fully test the low-mass, small-mixing region crucial for leptogenesis, while the LHC (and proposed future colliders) can directly explore higher-mass states and test the next mass decade. In conjunction, limits from cosmology (BBN, structure formation), laboratory rare process searches, and astroparticle signals cross-validate discoveries and exclusion regions.

- **Discovery of RHNs** at the predicted mass and mixing scales would simultaneously reveal the mechanism of neutrino mass generation, the origin of cosmic baryon excess, and (at keV scale) the DM candidate.
- **Null results** will exclude large portions of theoretically motivated parameter space and substantially constrain alternatives to the seesaw + leptogenesis + sterile DM paradigm. Absence of a signal in proposed experiments such as SHiP and ATLAS/CMS would push the viable scenarios towards either more exotic couplings (non-minimal interactions) or higher mass scales inaccessible to current facilities.

This synthesis establishes right-handed neutrinos as a central focus for both experimental searches and theoretical constructions beyond the SM [1704.08635].

Source: https://www.emergentmind.com/topics/right-handed-neutrinos-rhns