Right-Handed Neutrinos (RHNs)

• Right-Handed Neutrinos (RHNs) are gauge singlet Weyl fermions that extend the Standard Model to enable both Dirac and Majorana mass terms via the seesaw mechanism.
• They play a crucial role in explaining neutrino oscillations, generating the baryon asymmetry through leptogenesis, and offering a viable dark matter candidate in specific mass regimes.
• Current experimental probes, including beam-dump experiments and LHC displaced-vertex searches, are designed to constrain their mixing parameters and mass ranges while complementing cosmological bounds.

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 (Mermod, 2017).
• 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 (Mermod, 2017).
• 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 (Mermod, 2017).

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 (Mermod, 2017).