⚛️ phenomenology

The Dark Dimension and Majorana Neutrinos

This paper derives terrestrial constraints on Majorana bulk neutrinos within the Dark Dimension scenario by analyzing their mass spectrum and mixing, demonstrating that KATRIN beta-decay data provides the strongest limits on Yukawa couplings while the Kaluza-Klein tower effectively screens neutrinoless double beta decay signals.

Original authors: Arturo de Giorgi, Dhruv Pasari

Published 2026-09-11

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Arturo de Giorgi, Dhruv Pasari

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

For decades, physicists have been trying to reconcile two very different descriptions of the universe. On one side, we have the Standard Model, a highly successful theory that explains the behavior of the smallest known particles and the forces that govern them. On the other side is the theory of gravity, which describes the curvature of space and time on a cosmic scale. While both theories work perfectly in their own domains, they clash when scientists try to combine them into a single, unified framework. To resolve this tension, a new line of thinking called the Swampland program has emerged. It suggests that for our universe to be consistent with the laws of quantum gravity, it must possess certain hidden features. One of the most intriguing predictions from this program is the existence of a "Dark Dimension." This is not a dark place in the sense of being unlit, but rather a hidden, extra spatial dimension that is much larger than the tiny scales usually imagined in physics, yet still microscopic to human eyes.

The theory proposes that this extra dimension is roughly the size of a human hair, ranging from one-tenth of a micrometer to ten micrometers across. While the familiar particles of our world are stuck on a thin membrane, like a sheet of paper, this extra space is filled with a tower of invisible particles. These particles are special because they can move through the hidden dimension, and they are thought to be the missing pieces that give neutrinos their tiny mass. Neutrinos are ghostly particles that zip through the universe almost without interacting with anything. Understanding where their mass comes from is one of the biggest mysteries in modern physics. If the Dark Dimension exists, it would not only solve the mystery of neutrino mass but also explain why the universe is expanding at the rate it is. However, because this dimension is so small and the particles so elusive, proving its existence requires looking for very subtle signs in experiments conducted here on Earth.

A team of researchers at Durham University has taken a fresh look at this idea, focusing on a specific type of particle that might live in this hidden space. They investigated a scenario where these extra-dimensional particles are "Majorana" fermions, a unique kind of particle that is its own antiparticle. The researchers built a detailed mathematical model to describe how these particles would behave if they existed in a dimension of the size predicted by the Swampland program. They then asked a critical question: if these particles were real, what would they look like in our experiments? To answer this, they compared their model against data from three of the most sensitive neutrino experiments currently operating in the world. These experiments study neutrinos in different ways: one looks at how neutrinos change their identity as they travel, another measures the energy of electrons released during radioactive decay, and the third searches for a rare process where two neutrons turn into two protons without emitting any neutrinos.

The team discovered that the presence of these extra particles would leave a distinct fingerprint on the data, but the nature of that fingerprint depends heavily on the mass of the particles. They found that the hidden dimension acts like a filter. If the particles in the extra dimension are very light, they would cause the neutrinos to change their behavior in ways that current experiments have already ruled out. However, if the particles are heavier, within a specific range of thousands of electron volts, they create a different effect. In this heavier range, the many different versions of these particles, which arise from moving through the extra dimension, work together to cancel out certain signals. This cancellation makes the particles much harder to detect in some experiments, effectively hiding them from view. This screening effect is a crucial finding because it means that previous searches might have missed these particles simply because they were looking for the wrong kind of signal.

After running their calculations against the real-world data, the researchers found that the most powerful tool for testing this theory is an experiment called KATRIN, which measures the energy of electrons from tritium decay. Their analysis shows that for the Dark Dimension scenario to remain a viable possibility, the connection between the particles in our world and those in the hidden dimension must be extremely weak. Specifically, the strength of this connection, known as a coupling, must be very small, roughly one-thousandth of the strength of similar interactions in other theories. This result pushes the allowed parameters of the theory into a very narrow window. While the other two experiments, which study neutrino oscillations and the rare double beta decay, provide important supporting information, they are not as sensitive to this specific range of particle masses as the KATRIN experiment is. The oscillation experiments are better at ruling out lighter particles, while the double beta decay searches are more sensitive to very heavy ones, but the middle ground where the Dark Dimension theory lives is best probed by the beta decay measurements.

The study concludes that the Dark Dimension hypothesis is not yet dead, but it is under significant pressure. For the theory to survive, it requires a specific, somewhat unnatural setup where the particles in the hidden dimension have masses in the range of one to ten thousand electron volts, and their interaction with our world is surprisingly feeble. The researchers also explored what would happen if the masses of these particles were not all the same, but varied significantly from one another. They found that while this variation could open up a few more possibilities, it does not fundamentally change the conclusion that the KATRIN experiment provides the strongest test. If future updates to the KATRIN experiment, which will be able to look at a wider range of energies, do not find the subtle distortions predicted by this model, the Dark Dimension scenario as currently described will be effectively ruled out. Until then, the search continues, with the quiet hope that the next generation of data might reveal the hidden geometry of our universe.

Technical Summary: The Dark Dimension and Majorana Neutrinos

Problem Statement
Recent developments in the Swampland program suggest a scenario where the Standard Model (SM) is confined to a 4D brane, accompanied by a mesoscopic "Dark Dimension" (DD) of size $R_{DD} \sim 0.1 - 10$ $\mu$ m. This framework naturally predicts a tower of bulk fermions with masses in the keV range, potentially identifying them as right-handed neutrinos. However, the specific phenomenological implications of a 5D Lorentz-invariant (5DLI) Majorana mass term for these bulk fermions have not been rigorously derived. Previous literature often utilized the ordinary 4D charge-conjugation matrix, which fails to construct a valid 5DLI Majorana mass term due to the specific properties of 5D spinors (where double conjugation yields a minus sign). Furthermore, while neutrino oscillations have been used to probe extra dimensions, the interplay between the KK tower, Majorana masses, and terrestrial constraints (oscillations, neutrinoless double beta decay, and beta decay) within the specific DD parameter space remains unexplored.

Methodology
The authors construct a 5D model featuring a circular orbifolded $S^1/Z_2$ extra dimension of radius $R$ . The SM is confined to a brane at $y=0$ , while gravity and three generations of bulk Majorana fermions $\Psi_i$ propagate in the bulk.

Model Construction: The authors define the bulk action using the correct 5DLI Majorana mass term involving the operator $C_5 = \gamma_5 C_4$ , rather than the standard 4D $C_4$ . The bulk fermions couple to SM leptons via a Yukawa portal localized on the brane.
Spectrum Derivation: By performing a Kaluza-Klein (KK) expansion and integrating out the extra dimension, the authors derive the 4D effective mass matrix. This matrix mixes the SM active neutrinos with the entire KK tower. They solve the secular equation to determine the physical mass eigenvalues ( $\lambda_n$ ) and the mixing elements ( $N_\lambda$ ) between the mass eigenstates and the flavor eigenstates.
Observables: The study focuses on three laboratory constraints:
- Neutrino Oscillations: Using Daya Bay reactor data (3158-day dataset) to constrain deviations from standard 3-neutrino oscillations.
- Neutrinoless Double Beta Decay ( $0\nu\beta\beta$ ): Utilizing KamLAND-Zen limits on $^{136}$ Xe. The authors derive a closed-form "master formula" for the effective Majorana mass $m_{\beta\beta}$ by summing over the KK tower, accounting for the gauge-protected sum rules that lead to cancellations.
- Tritium Beta Decay: Applying KATRIN constraints on the effective electron neutrino mass $m_\beta$ , utilizing a simplified effective mass formula valid when heavy KK modes lie outside the experimental energy window.
Analysis Strategy: The authors scan the parameter space of the compactification scale ( $\mu_1 = 1/R$ ) and the bulk Majorana mass ( $M$ ). They consider three benchmark scenarios for the Majorana masses: (i) Universal ( $M_1=M_2=M_3$ ), (ii) Profiled (one free, others varied within $\pm 1$ decade), and (iii) Hierarchical (one non-zero, others negligible).

Key Contributions

Correct 5DLI Formalism: The paper fills a gap in the literature by deriving the 4D spectrum and phenomenology based on the correct 5DLI Majorana mass definition ( $C_5$ ), correcting previous treatments that relied on the 4D operator.
KK Screening Mechanism: The authors derive a closed-form expression for the effective Majorana mass in $0\nu\beta\beta$ . They demonstrate that the KK tower acts as an efficient screen: when the nuclear momentum scale $p$ exceeds the compactification and Majorana scales ( $p \gg M, \mu_1$ ), the gauge-invariant sum rule causes the contributions of the light KK states to cancel out, suppressing the $0\nu\beta\beta$ rate by a factor of $M/p$ .
Complementary Constraints: The study maps out how different observables probe different regions of the parameter space. Oscillations constrain the compactification scale at smaller $M$ , while $0\nu\beta\beta$ becomes relevant at larger $M$ (though suppressed by screening).
Beta Decay Dominance: The analysis identifies tritium beta decay (KATRIN) as the most stringent constraint within the DD-favored parameter space ( $M \gg \mu_1$ ).

Results

Constraints on Yukawa Couplings: In the Dark Dimension window ( $R \sim 0.1-10$ $\mu$ m, $M \sim 1-10$ keV), the KATRIN bound on the effective electron neutrino mass pushes the allowed Dirac Yukawa couplings ( $y_D$ ) down to $\mathcal{O}(10^{-3})$ . This implies a mild hierarchy in the model parameters, scaling as $R^{-1/6}$ .
Oscillation Limits: Daya Bay data provides complementary constraints, particularly for smaller Majorana masses ( $M \lesssim 1/R$ ). The constraints weaken as $M$ increases, scaling roughly as $1/M$ .
$0\nu\beta\beta$ Limits: Due to the KK screening effect, $0\nu\beta\beta$ constraints are generally weaker than beta decay constraints in the keV mass range. They only become competitive at significantly larger Majorana masses ( $M \gg p$ ). The constraints are highly sensitive to the assumption of universal vs. hierarchical masses; allowing for hierarchical masses can significantly weaken the $0\nu\beta\beta$ bounds due to phase cancellations.
Hierarchical Scenarios: In the hierarchical benchmark (outside the strict DD naturalness assumptions), the parameter space opens up significantly, particularly for $0\nu\beta\beta$ , as the cancellation mechanisms rely on the coherence of the tower which is disrupted if only one generation carries a significant mass.

Significance
The paper claims that neutrino physics offers a uniquely sensitive probe of the Dark Dimension, potentially surpassing direct gravitational tests. By rigorously applying the correct 5D formalism, the authors establish that the DD scenario is not ruled out but is tightly constrained by current beta decay data. The work highlights that viable DD scenarios require specific, albeit mild, hierarchies in the Yukawa couplings. The authors note that while current terrestrial data constrains the model, future improvements in beta decay sensitivity (e.g., TRISTAN) and the inclusion of cosmological bounds could further test or potentially rule out the scenario. The study emphasizes that the "screening" of $0\nu\beta\beta$ by the KK tower is a distinctive feature of this model, differentiating it from standard seesaw scenarios.

Technical Summary: The Dark Dimension and Majorana Neutrinos

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