Dark Dimension Right-Handed Neutrinos

• Dark Dimension right-handed neutrinos are SM-singlet fermions in a hidden extra dimension that yield a Kaluza–Klein tower of sterile states.
• The models use brane-localized Yukawa couplings and bulk gauge symmetries to achieve anomaly cancellation and naturally suppressed Dirac neutrino masses.
• Experimental signatures include modified oscillation patterns, beta-decay spectrum kinks, and potential dark matter candidates from sterile neutrinos.

Dark Dimension right-handed neutrinos are Standard Model (SM)–singlet fermions that propagate in one or more extra spatial dimensions, most commonly a single “dark” dimension of micron-scale radius. These models embed the visible SM on a codimension-one brane within five-dimensional spacetime, where SM gauge and matter fields are brane-localized while right-handed neutrinos and select dark-sector fields reside in the bulk. This scenario leads to a tower of sterile right-handed neutrinos, nontrivial active–sterile mixing, and deep connections to anomaly cancellation, neutrino mass generation, and dark-matter/energy phenomenology.

1. Geometric and Gauge Structure of the Dark Dimension

In the canonical dark-dimension setup, the universe is described as a 3+1-dimensional SM brane embedded in $M^{4} \times S^{1}/\mathbb{Z}_2$ of radius $R$ (Montero et al., 9 Dec 2025, Bai et al., 2 Jan 2026, Antoniadis et al., 5 Sep 2025, Anchordoqui et al., 2023). Gauge fields such as $U(1)_{B-L}$ or novel dark symmetries propagate in the five-dimensional bulk, as do SM-neutral fermions (right-handed neutrinos, $\Psi_i$). The Standard Model fields—including $L$ (left-handed leptons) and $H$ (Higgs)—remain brane-bound at, e.g., $x^5 = 0$.

The orbifold parity assignments ensure that only the vector component $A_\mu$ and the scalar $\Phi$ harbor zero modes, corresponding to surviving 4D gauge and Higgs-like fields. The 5D fermions $\Psi_i$ yield a single right-handed Weyl neutrino zero mode per generation. All bulk fields couple to brane-localized matter via higher-dimensional operators, specifically Yukawa terms localized at $y=0$ on the brane (Montero et al., 9 Dec 2025, Bai et al., 2 Jan 2026, Antoniadis et al., 5 Sep 2025).

Bulk gauge symmetries play a central role. In one line of work, a bulk $U(1)_{B-L}$ anomaly cancellation is realized through the addition of three right-handed neutrino Dirac fermions, with proper charge normalization to ensure vanishing gauge and gravitational anomalies modulo 8, as required by six-dimensional bordism constraints (Montero et al., 9 Dec 2025). Alternative realizations may employ a dark $U(1)_D$ or additional “dark-family” groups as detailed in models extending the SM gauge group by $SU_f(3)\times SU_R(2)$ (Hwang, 2012, Dong et al., 2023).

2. Kaluza–Klein Tower and Sterile Right-Handed Neutrinos

Right-handed neutrino bulk fields $\Psi_i(x,y)$ decompose into a tower of 4D modes under the Kaluza–Klein (KK) procedure, with masses

$$m_n = \sqrt{M^2 + \left(\frac{n}{R}\right)^2},\quad n=0,1,2,\ldots$$

where $M$ is the bulk mass parameter (Antoniadis et al., 5 Sep 2025, Anchordoqui et al., 2023). The lowest ($n=0$) mode is purely right-handed due to orbifold boundary conditions, while $n>0$ modes are vector-like, sterile states. Depending on the model, the tower spacing $1/R$ may be of order meV (for $R \sim 10~\mu$m) or eV–keV, with cosmologically significant heavy sterile neutrinos for $n\gg1$.

The active neutrinos $\nu_{L}$ mix with the KK tower via brane-localized Yukawa couplings. The overlap between zero mode and brane yields a suppressed 4D Dirac mass,

$m_{D} \sim \frac{y_\nu v}{\sqrt{2\pi R}},$

as the right-handed zero-mode wavefunction normalization is volume-suppressed across the extra dimension (Anchordoqui et al., 2023). This mechanism permits naturally small neutrino masses without an ultra-heavy seesaw scale.

Oscillation into the KK tower potentially yields observable deviations from 3-flavor oscillation phenomenology and has phenomenological signatures distinguishing these models from standard sterile-neutrino extensions (Bai et al., 2 Jan 2026, Antoniadis et al., 5 Sep 2025).

3. Neutrino Mass Generation and Anomaly Cancellation

Multiple routes to generating neutrino masses arise in dark-dimension models. In the $U(1)_{B-L}$ scenario, with three bulk Dirac fermions and a bulk scalar $\Phi$ that acquires a VEV $v_\Phi$, the following features are realized (Montero et al., 9 Dec 2025):

• The $B-L$ gauge anomaly of the chiral SM is canceled by the bulk zero modes' contributions, provided bulk charge quantization satisfies $\sum q_i \equiv 0$ mod 8.
• Spontaneous breaking of $B-L$ via bulk $\Phi$ yields a 4D massive gauge boson with $m_{B-L} \sim 100$ GeV, $g_{B-L} \sim 10^{-10}$.
• The neutrino Dirac mass structure,

$$m_\nu \sim y^2 \left(\frac{v_H}{v_\Phi}\right)^2 m_{KK} \sim m_{KK} \sim \Lambda^{1/4},$$

is set by the compactification scale tied to the dark energy (cosmological constant) via the Swampland Distance Conjecture ($m_{KK} \sim \Lambda^{1/4}$), explaining the empirical proximity of neutrino masses to the dark energy scale.

Alternative extensions (e.g., $U(1)_D$ with three right-handed neutrinos carrying $D=0,-1,+1$) employ a hybrid seesaw (“scotoseesaw”) mechanism, where type-I seesaw from $D=0$ and one-loop (scotogenic) diagrams mediated by dark-sector inert scalars generate the observed pattern of active neutrino masses (Dong et al., 2023). Anomaly cancellation strictly determines the dark U(1) charges for right-handed neutrinos to be $\{0,-1,+1\}$.

4. Experimental and Observational Signatures

The presence of a KK tower of mostly sterile right-handed neutrinos manifests in various direct and indirect experimental searches, with current and projected limits spanning oscillations, $\beta$-decay, cosmology, and gravity tests.

Long-baseline oscillation experiments: T2K and NOvA place stringent exclusion limits on the parameter space ($R, c_i, \mu_i$), ruling out compactification radii $R=10\,\mu$m and dimensionless bulk masses $|c_i R| \lesssim 5-6$ at 90% C.L. No evidence for the additional KK tower has been found, with sensitivity to zero-mode mass shifts and sterile mixing (Bai et al., 2 Jan 2026).

KATRIN $\beta$-decay spectrum: Right-handed neutrinos in the dark-dimension model predict either multiple kinks in the tritium $\beta$ spectrum (if $M \ll 1/R$) at $E_0-n/R$, or a single kink (if $M \gg 1/R$) at $E_0-M$. KATRIN constraints exclude significant regions of $(M, \lambda)$ for $R\ll10~\mu$m, and project future sensitivity to effective mixings $\sin^2\theta_{\rm eff}\sim10^{-4}$ (Antoniadis et al., 5 Sep 2025).

Cosmological and fifth-force constraints: KK sterile neutrinos with masses in the ${\rm keV}$ range can contribute as warm dark matter, with bounds from structure formation on production mechanisms (Montero et al., 9 Dec 2025). Compactification radii $R \lesssim 0.1~\mu{\rm m}$ are required to avoid oscillation disappearance constraints; this pushes the lightest KK mode masses above 5 eV, precluding impact on the stabilization of the radion potential (Anchordoqui et al., 2023).

Collider and dark sector searches: The B-L gauge boson with $m_{B-L} \sim 100$ GeV and $g_{B-L} \sim 10^{-10}$ easily evades LHC bounds. The full KK tower may become accessible only at future high-energy colliders via apparent power-law running of effective couplings, but all new gauge and scalar states in the dark sector are otherwise neutral and highly decoupled from visible matter (Montero et al., 9 Dec 2025, Dong et al., 2023, Hwang, 2012).

Probe	Model Parameter	Experimental Reach / Bound
Oscillations (T2K/NOvA)	$R, c_i, \mu_i$	$R\lesssim 10~\mu$m, $c_i\gtrsim 0.1$ eV
KATRIN $\beta$-decay	$M, R, \lambda$	$M\lesssim 10$ eV (for $\sin^2\theta_{\rm eff} \gtrsim 10^{-2}$)
Gravity, Casimir	$R$	$R\lesssim 30~\mu$m
Cosmology	$\sum m_\nu$	$\sum m_\nu \lesssim 0.12$ eV (Planck)

5. Dark Matter and Cosmological Implications

The KK tower of sterile right-handed neutrinos generates warm dark matter candidates with masses $m_n \sim n\Lambda^{1/4}$. For $n\sim10^6$, $m_n\sim$ keV, enabling a population of sterile states potentially detectable via X-ray lines, subject to mixing- and production-dependent limits (Montero et al., 9 Dec 2025).

In “scotoseesaw” realizations ($U(1)_D$ models), the lightest $P_D$-odd Majorana right-handed neutrino or inert scalar can be cosmologically stable, serving as a viable dark matter candidate. The relic density, annihilation cross-sections, and spin-independent nuclear scattering rates can saturate the observed abundance while remaining below direct detection limits (e.g., LZ) (Dong et al., 2023).

The dark-dimension scenario further relates neutrino physics to the stabilization of compactified dimensions. If the right-handed neutrino KK tower is light enough (first KK mode mass $m_{\rm KK}\sim$ meV), it can compensate the negative contribution to the radion potential from the graviton KK tower, ensuring a metastable three-dimensional de Sitter vacuum. Oscillation limits, however, require heavy KK neutrinos ($m_{\rm KK}^{(1)}\gtrsim$ 5 eV), so only the addition of a meV-scale gravitino KK tower can further raise the neutrino mass bound in the context of the swampland conjecture ($m_{1,{\rm max}}\sim 50$ meV) (Anchordoqui et al., 2023).

6. Model Variants and Theoretical Considerations

Variants on the dark-dimension right-handed neutrino paradigm include:

• Dark-sector gauge groups ($SU_f(3), SU_R(2)$) under which only $\nu_R$ transforms (Hwang, 2012). Here, all neutrinos are Dirac, with masses set by small Yukawa couplings or large dark VEV scales; no light sterile state beyond $\nu_{L,R}$ is present.
• Dark $U(1)_D$ models with anomaly-fixed assignments $D=\{0, -1, +1\}$ for $\nu_{iR}$ (Dong et al., 2023). These allow combined seesaw and radiative mass mechanisms, residual stabilizing parities, and controlled mixing-induced LFV rates.
• The role of bulk Dirac (or Majorana) masses in suppressing active–sterile mixing, thus weakening oscillation bounds at the expense of raising the whole KK spectrum above the Casimir compensation window (Anchordoqui et al., 2023).

The interplay between anomaly cancellation, phenomenological signatures, and swampland-compatibility constraints combines to tightly constrain model-building in the dark-dimension framework.

7. Outlook and Projections

Future experimental initiatives—T2HK, DUNE, JUNO, upgraded short-baseline and $\beta$-decay searches—aim to improve sensitivity to the defining parameters: extra dimension size, bulk mass terms, and brane–bulk mixing strengths. High-energy colliders could probe the B-L KK tower or new dark-sector gauge bosons if energy thresholds permit. Next-generation cosmological experiments may distinguish between scenarios with and without light gravitinos, by resolving $\sum m_\nu$ at the $\mathcal{O}$(10\,meV) level.

A plausible implication is that if no deviations from three-flavor neutrino oscillations or multi-kink $\beta$-decay spectra are observed, the scale of the dark dimension (if present) and associated KK towers must be pushed to even higher masses and smaller mixing angles. This would strengthen the argument for volume-suppressed, Dirac-neutrino masses as a dynamically explained feature of extra-dimensional physics, tightly entwined with dark energy, dark matter, and constraints from quantum gravity (Montero et al., 9 Dec 2025, Anchordoqui et al., 2023, Bai et al., 2 Jan 2026, Antoniadis et al., 5 Sep 2025, Dong et al., 2023, Hwang, 2012).