Theory model zoo

The minimal seesaw extension of the Standard Model adds three right-handed neutrinos N with Majorana masses M and Dirac couplings y to the lepton doublet via the Higgs. Diagonalising the resulting mass matrix produces three light states with masses m_ν ≈ y² v² / M and three nearly-decoupled heavy states with masses ≈ M.

For y ~ 1 and M ~ 10¹⁴ GeV the framework naturally yields sub-eV neutrinos and connects to leptogenesis. Lower scales (M ~ TeV with smaller y) give phenomenology at the LHC, FCC and SHiP.

Type-II seesaw adds an SU(2)_L triplet scalar with hypercharge 2; its neutral component picks up a small induced VEV v_Δ that gives a Majorana mass directly to the left-handed neutrinos: m_ν = y_Δ v_Δ.

The doubly-charged component H^{++} of the triplet is a striking collider signature, with the same-sign-dilepton decay H^{++} → ℓ⁺ℓ⁺ providing direct access to the PMNS structure if the triplet is light enough.

Type-III seesaw uses fermionic triplets Σ = (Σ⁺, Σ⁰, Σ⁻) under SU(2)_L. The neutral Σ⁰ couples to the lepton doublet and Higgs analogously to a right-handed neutrino, generating the same m_ν ≈ y² v²/M structure.

The charged components Σ^± appear in collider production via electroweak couplings; their decays to ℓ + Z, ℓ + h or ν + W give multi-lepton signatures directly testable at LHC and beyond.

The inverse seesaw extends the SM by two singlet fields N and S per generation, with a small Majorana mass μ for S and a Dirac coupling between N and S. The light neutrino mass m_ν ≈ μ (m_D / M_N)² is suppressed by the small μ rather than a high M scale.

This allows heavy states at TeV with O(0.01) mixing, making them accessible at the LHC, FCC-ee and lepton-flavour-violation experiments. It also avoids the leptogenesis-via-decay constraint on M.

NSI provide a model-independent EFT description of how neutrinos may couple to matter beyond the Standard Model. The strength is parameterised by ε^f_{αβ} matrices for charged- and neutral-current operators with f = e, u, d.

NSI modify the matter effective Hamiltonian in long-baseline and atmospheric oscillations, can mimic δ_CP and the mass ordering, and produce coherent and incoherent scattering signals at CEνNS experiments. The COHERENT and CONUS+ programmes provide the leading direct constraints.

Leptoquarks (LQs) are bosons that simultaneously carry baryon and lepton number, mediating processes like q + ν → q + ν or q + ℓ → q + ν. They contribute to neutrino NSI, modify B-meson decay rates, and feature in many GUT-inspired completions of the Standard Model.

Direct LHC searches push generic-coupling LQ masses above ~1.5 TeV; the surviving parameter space generates ε^f_{αβ} of order 10^{-2} to 10^{-3}, observable in next-generation oscillation and CEνNS data.

Mass-mixing of a single ~7 keV sterile neutrino with active states reproduces the observed ν_e flavour fraction in solar/atmospheric data while being long-lived enough to be the cosmological dark matter. A radiative decay channel ν_4 → ν + γ produces a narrow X-ray line — the unidentified 3.5 keV line in galaxy-cluster spectra has been a much-discussed (and disputed) candidate.

KATRIN's TRISTAN upgrade and dedicated keV-sterile searches at upcoming β-decay experiments are the leading laboratory probes.

If lepton number is a spontaneously broken global symmetry, its Goldstone is a massless scalar called the majoron. It couples to neutrinos with strength m_ν / v_BL and would allow exotic two-Goldstone decays in 0νββ — A → A + 2e + n_majoron — distorting the summed-electron spectrum.

Modern constraints come primarily from KamLAND-Zen and GERDA spectral analyses; the majoron–neutrino coupling is bounded at the ~10⁻⁵ level.