⚛️ phenomenology

Archimedean Seesaw: Small Neutrino Masses and Large Lepton-number Violation

This paper proposes a class of seesaw models where a symmetry-protected texture-zero structure allows for arbitrarily large lepton-number violation in the heavy sector while naturally yielding sub-eV neutrino masses, thereby predicting observable signatures of heavy neutral leptons at current and future experiments.

Original authors: Tao Han, Alejandro Ibarra, Subhojit Roy, Martina Sabová

Published 2026-08-12

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CC0 1.0

Original authors: Tao Han, Alejandro Ibarra, Subhojit Roy, Martina Sabová

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ 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

Imagine the universe as a giant, invisible puzzle where every piece of matter has a hidden twin. For decades, physicists have been trying to figure out why some of these twins, called neutrinos, are so incredibly light—so light that they barely have any weight at all. In the standard story, there's a rule called "lepton number" that acts like a cosmic accounting system. Usually, if you break this rule to give neutrinos a little mass, the universe demands a heavy price: the process that breaks the rule should be so rare and weak that we'd never see it in a lab. It's like trying to hear a whisper from across a stadium; the signal is there, but it's drowned out by the noise. This has made it incredibly hard to find the heavy cousins of neutrinos, known as "Heavy Neutral Leptons," because the math says they should be so shy and quiet that no machine could ever catch them. But what if the universe has a loophole? What if the rules of the game allow for a loud, noisy party in the heavy sector while keeping the light neutrinos perfectly silent? That is the big question this paper asks, and it suggests a surprisingly clever way the universe might be bypassing the system.

The authors of this paper, Tao Han, Alejandro Ibarra, Subhojit Roy, and Martina Sabová, propose a new way to build the "seesaw" mechanism—the famous theory that explains why neutrinos are so light. In the old, standard version of the seesaw, the lightness of the neutrino is directly tied to how weak the heavy particles are; if the neutrino is light, the heavy particles must be invisible. This new paper suggests a different design, which they whimsically call the "Archimedean seesaw." They show that it is possible to have heavy particles that are very "loud" (meaning they break the lepton number rule strongly and can be easily spotted in experiments) while the light neutrinos remain "silent" (massless or nearly massless).

How do they do this? Imagine a playground seesaw. In the standard version, if you put a giant weight on one side (the heavy neutrino), the other side (the light neutrino) has to be tiny to balance it. But the authors found a special arrangement where the seesaw has a secret "texture-zero" structure. Think of this like a seesaw where the fulcrum (the pivot point) is placed in a very specific spot, or where the weights are arranged in a pattern that cancels out perfectly. In their model, the heavy particles interact in a way that violates the lepton number rule, but because of a hidden symmetry (a kind of invisible rulebook), these interactions perfectly cancel each other out when it comes to giving mass to the light neutrinos. It's as if the heavy particles are shouting at the top of their lungs, but their voices are arranged in a circle so that the sound cancels out at the center, leaving the light neutrinos in perfect silence.

The paper explicitly argues against the "common lore" that observable lepton-number violation must be suppressed by tiny neutrino masses. They don't just suggest this is possible; they construct a mathematical model with specific equations to prove it. They show that if you arrange the heavy neutrino masses and their connections (Yukawa couplings) in a specific pattern with zeros in the right places, the light neutrino mass vanishes completely, even if the heavy sector is breaking the rules with full force. They further suggest that if you slightly tweak this perfect arrangement (by adding tiny "perturbations"), you get the small, non-zero neutrino masses we actually observe in nature, without ruining the ability to see the heavy particles.

The result is a framework that is surprisingly testable. The authors calculate that these heavy particles could have masses ranging from 1 MeV to 10 TeV and could mix with normal matter much more strongly than the old theories allowed. This means that instead of being invisible ghosts, these Heavy Neutral Leptons could be produced in large numbers at particle colliders like the Large Hadron Collider (LHC). They predict that we could see them through "same-sign dilepton" signatures—basically, seeing two particles with the same electric charge appear out of nowhere, a clear sign that lepton number has been violated. The paper shows that current experiments, like those by ATLAS, have already started looking for these signals, and future experiments will be able to probe a huge range of possibilities.

In short, this paper suggests that the universe doesn't have to choose between having light neutrinos and having visible heavy ones. By using a clever "Archimedean" balance, nature could be hiding the light neutrinos behind a wall of zeros while letting the heavy ones dance in the spotlight. It turns a problem that seemed like a dead end into a roadmap for discovery, inviting scientists to look for these heavy neutrinos in places they previously thought were too quiet to matter. The authors are confident in their mathematical construction, showing that this "texture-zero" mechanism is a robust way to protect light neutrino masses while allowing for large, observable effects in the heavy sector, opening up a new and exciting window into the secrets of the universe.

Technical Summary: The Archimedean Seesaw

Problem Statement
The prevailing understanding in neutrino physics posits a rigid correlation between the smallness of observed neutrino masses ( $m_\nu$ ) and the suppression of observable Lepton-Number Violation (LNV). In the standard Type-I seesaw mechanism, the active-sterile mixing ( $U_{\ell N}$ ) and the heavy neutrino mass ( $M_N$ ) are constrained by the relation $U_{\ell N}^2 M_N \approx m_\nu$ . Consequently, for heavy neutrinos at the electroweak scale, the mixing is suppressed to $\sim 10^{-13}$ , rendering LNV processes (such as neutrinoless double-beta decay or same-sign dilepton production at colliders) unobservable. While scenarios like the inverse and linear seesaws allow for larger mixing by introducing approximate lepton number conservation, this approximation simultaneously suppresses the very LNV signals experiments seek to detect. The central problem addressed is whether it is possible to construct a model where neutrino masses remain naturally small (sub-eV) while allowing for arbitrarily large LNV and sizeable active-sterile mixing, decoupling the two phenomena.

Methodology and Framework
The authors propose a novel class of seesaw models termed the "Archimedean seesaw." The methodology involves:

Texture-Zero Construction: The authors construct a specific texture-zero structure in the neutrino Yukawa couplings and the heavy Majorana mass matrix. In a simplified model with one lepton doublet and two right-handed neutrinos ( $N_{R1}, N_{R2}$ ), they impose a structure where specific entries in the mass matrix vanish (e.g., $m_1 = 0$ and $M_{11} = 0$ ).
Symmetry Protection: They demonstrate that these texture zeros are not arbitrary but arise from an accidental global symmetry ( $U(1)_{acc}$ ) inherent to the mass matrix structure. This symmetry protects the light neutrino mass, ensuring it vanishes identically at all orders, even in the presence of large LNV in the heavy sector.
Symmetry Breaking: To generate non-zero but naturally small neutrino masses, the authors introduce small perturbations (mass parameters $\mu_1, \mu_2$ ) that lift the texture zeros. These perturbations are generated by higher-dimensional operators in an ultraviolet completion involving an extra $U(1)_X$ symmetry and a singlet scalar $\phi$ .
Theoretical Realization: A specific model is constructed using an additional $U(1)_X$ symmetry. The charge assignments forbid the leading-order terms that would generate light neutrino masses, allowing only specific renormalizable terms. Higher-dimensional operators, suppressed by a heavy scale $\Lambda$ , break the accidental symmetry softly, generating the small observed neutrino masses.

Key Contributions and Results

Decoupling of Mass and LNV: The primary result is the identification of a mechanism where the light neutrino mass $m_\nu$ is protected by an accidental symmetry, while the heavy sector possesses large LNV. Unlike the standard seesaw relation (Eq. 2), the active-sterile mixing in this framework is determined by heavy-sector parameters and can be sizeable, independent of the smallness of $m_\nu$ .
The "Archimedean" Analogy: The authors derive a mass-mixing relation analogous to the lever principle: $m_\nu V_{\ell\nu}^2 + M_1 V_{\ell N_1}^2 + M_2 V_{\ell N_2}^2 = 0$ . In the texture-zero limit ( $m_\nu=0$ ), the system balances with two heavy masses ( $M_1, M_2$ ) acting as counterweights. This allows for large mixing angles (long lever arms) without requiring the heavy masses to be infinitesimally close to the pivot (small mixing), a constraint that plagues single-heavy-neutrino seesaws.
Phenomenological Predictions:
- Heavy Neutral Leptons (HNLs): The model predicts HNLs with sizeable active-sterile mixing over a broad mass range (from MeV to TeV scales).
- LNV Signatures: The framework predicts observable $\Delta L = 2$ signatures, including same-sign dilepton production ( $pp \to \ell^\pm \ell^\pm jj$ ) at the LHC and neutrinoless double-beta decay.
- Experimental Sensitivity: The paper analyzes current constraints from ATLAS (same-sign vector boson scattering and resonant Drell-Yan production) and projected sensitivities for the High-Luminosity LHC (HL-LHC). It shows that current data excludes specific regions of the parameter space (e.g., $M_2 \sim 10^8$ GeV for $y_2 \gtrsim 1$ ), but a vast region remains open for future exploration.
- Predictive Trajectories: The model maps the observable plane ( $M_N$ vs. $|V_{\mu N}|^2$ ) to the underlying heavy-sector mass scale $M_2$ via constant- $M_2$ trajectories, offering a direct way to test the underlying physics scale.

Significance and Claims
The paper claims to challenge the "common lore" that observable LNV is inevitably suppressed by tiny neutrino masses. It argues that this suppression is an artifact of restricted realizations (like the minimal Type-I seesaw) rather than an intrinsic feature of the seesaw mechanism. By identifying a class of models where an accidental symmetry protects the light neutrino mass while allowing large LNV in the heavy sector, the authors open a "qualitatively new direction" for constructing experimentally testable seesaw theories.

The significance lies in the potential for simultaneous observation of:

Naturally small neutrino masses.
Sizeable active-sterile mixing.
Observable LNV signatures at colliders and intensity-frontier experiments.

The authors note that while the current work focuses on a single active flavor, the framework naturally extends to three generations, potentially accommodating low-scale leptogenesis and charged-lepton flavor violation (e.g., $\mu \to e\gamma$ ), though these specific applications are reserved for future study. The "Archimedean seesaw" is presented as a versatile, symmetry-protected framework that makes the heavy sector accessible to current and near-future experimental probes.

Technical Summary: The Archimedean Seesaw

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