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Lepton number violation at hadron colliders via pseudo-Dirac heavy neutral leptons

This paper demonstrates that damped heavy neutrino-antineutrino oscillations significantly alleviate the suppression of lepton number violation in symmetry-protected pseudo-Dirac heavy neutral leptons at hadron colliders, while showing that combining lepton-number-blind and lepton-number-violating searches can distinguish these models from the double-Majorana limit despite the sensitivity challenges posed by small mass splittings.

Original authors: Stefan Antusch, Jan Hajer, Bruno M. S. Oliveira

Published 2026-06-25

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Stefan Antusch, Jan Hajer, Bruno M. S. Oliveira

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

The Big Picture: Finding the "Ghost" Particles

Imagine the Standard Model of physics as a very complete, well-organized library. But there's a missing book: Neutrinos. We know they exist and have mass (because they change flavors), but the library's current rules say they should be massless. To fix this, scientists propose adding new, heavy "ghost" particles called Heavy Neutral Leptons (HNLs).

This paper asks: How do we find these ghosts at a giant particle collider (like the FCC-hh), and how do we tell if they are "real" ghosts or just a trick of the light?

The Problem: The "Twin" Confusion

In many theories, these heavy ghosts come in pairs that are almost identical, like Siamese twins who share a brain but have a tiny, almost invisible difference in their heartbeat.

The Symmetry: Nature has a rule (a symmetry) that tries to keep these twins identical. If they were perfectly identical, they would act like a single "Dirac" particle, and a specific type of physics violation (called Lepton Number Violation or LN violation) would be impossible to see.
The Tiny Crack: In reality, the twins aren't perfectly identical. There is a tiny crack in the symmetry. This crack allows them to violate the rules (LN violation), but standard physics calculations say this violation should be so small it's invisible.

The Paper's Twist: The authors realized that standard calculations treat these twins like perfect, endless waves. But in a real collider, these twins are created, they travel a short distance, and then they die (decay). Because they are so close in mass, they oscillate (switch back and forth between being twin A and twin B) as they travel.

The Solution: The "Damped Swing" Analogy

Imagine pushing a child on a swing.

The Oscillation: If the twins are very close in mass, they swing back and forth between two states. This swinging creates a "signal" that we can detect.
The Decoherence (The Damping): However, the swing doesn't go on forever. The air resistance (decoherence) and the fact that the twins are born from a messy collision (protons) eventually stop the perfect swinging.
The Surprise: The paper shows that this "damping" actually helps us! Instead of canceling out the signal (which is what happens in the standard "perfect wave" math), the damping creates a sweet spot where the signal becomes strong enough to see. It's like the swing hitting a wall and bouncing back in a way that makes a loud noise we can hear.

The Experiment: Two Ways to Look

The authors simulated what would happen if we built a super-powerful collider (the FCC-hh, which is much bigger than the current LHC) and looked for these particles. They used two different "flashlights" to search:

The "Blind" Search (LN-Blind):
- What it looks for: A specific pattern of three muons (a type of particle).
- The Metaphor: This is like looking for a specific type of car in a parking lot without caring about the license plate. It counts all the cars, regardless of whether they are "good" or "bad" according to the rules.
- Result: It finds a lot of cars, but it's hard to tell if they are the special twins we want because the background noise is high.
The "Violation" Search (LN-Violating):
- What it looks for: Two muons with the same electric charge (like two positive signs: ++).
- The Metaphor: This is like looking for a car with a very specific, illegal license plate. In the Standard Model, you almost never see two positive signs together. If you do, it's a "smoking gun" that the rules are broken.
- Result: This search is much cleaner (less background noise). If the "twin" effect is strong, this search is 10 times more sensitive than the blind search.

The Catch: The "Goldilocks" Zone

Here is the most important finding of the paper: The sensitivity depends entirely on how different the twins are.

Too Similar (Tiny Mass Splitting): If the twins are almost identical, the "violation" signal is too weak. The "Violation Search" fails, and we are stuck with the "Blind Search."
Too Different (Large Mass Splitting): If the twins are too different, they stop oscillating and act like two completely separate, independent particles. The signal becomes strong, but we can no longer tell if they were "twins" or just two random particles. The "Violation Search" works, but we lose the ability to prove they were a special pair.
Just Right (Intermediate): There is a "Goldilocks zone" in the middle. Here, the twins are different enough to create a signal, but similar enough that we can still distinguish them from random particles.

The Conclusion

The paper concludes that:

Future Colliders are Essential: The current LHC is too small to find these particles if they are in the "Goldilocks zone." We need the massive FCC-hh (Future Circular Collider) to have a chance.
Don't Ignore the "Twins": If we find these particles, we can't just assume they are standard "Majorana" particles. We have to look at the ratio of same-charge to opposite-charge events. This ratio tells us if the particles are "twins" (pseudo-Dirac) or "independent" (double-Majorana).
The Damping Effect is Key: The "noise" (decoherence) in the experiment isn't a bug; it's a feature that makes the signal visible in the first place.

In short: The paper argues that to find these heavy neutrino "twins," we need a bigger collider, and we must look for a specific "Goldilocks" balance where the particles are just different enough to be seen, but just similar enough to prove they are a special pair.

Technical Summary: Lepton Number Violation at Hadron Colliders via Pseudo-Dirac Heavy Neutral Leptons

Problem Statement
Symmetry-protected low-scale seesaw models (SPSS), such as the inverse and linear seesaws, offer a natural explanation for small neutrino masses without fine-tuning by invoking an approximate lepton number (LN) symmetry. In these models, heavy neutral leptons (HNLs) form quasi-degenerate pseudo-Dirac pairs. While standard quantum field theory (QFT) plane-wave calculations predict that LN-violating (LNV) amplitudes are suppressed by the small symmetry-breaking parameters (mass splittings), making them unobservable, this approach neglects the finite lifetime and propagation of the HNLs. The paper addresses the discrepancy between the suppressed amplitude-level expectations and the potential for observable LNV signals arising from heavy neutrino-antineutrino oscillations (NNOs) and decoherence effects in a realistic collider environment.

Methodology
The authors employ a comprehensive framework combining theoretical derivation with phenomenological simulation:

Theoretical Framework:
- Mass Spectrum: The SPSS Lagrangian is defined with two heavy Majorana neutrinos ( $N_1, N_2$ ) forming a pseudo-Dirac pair. The mass splitting $\Delta m$ is governed by small LN-violating parameters.
- Oscillations and Decoherence: The paper utilizes the QFT with external wave packets formalism to describe NNOs. It incorporates decoherence effects arising from the finite spatial localization of the incoming proton wave packets at the interaction point. This introduces a damping parameter $\lambda$ dependent on the mass splitting $\Delta m$ and the proton wave packet width.
- Regimes: The analysis identifies four distinct regimes for LNV based on the interplay between the HNL decay width ( $\Gamma_N$ ), the mass splitting ( $\Delta m$ ), and the damping threshold ( $\Delta m_\lambda$ ): small/large LN-ratio oscillation-enhanced and small/large LN-ratio damping-enhanced regimes.
Simulation and Analysis:
- Event Generation: Signal and background processes are simulated using MadGraph5_aMC@NLO, Pythia 8, and Delphes 3.5. The study focuses on the Future Circular Hadron Collider (FCC-hh) at $\sqrt{s} = 100$ TeV with an integrated luminosity of 30 ab $^{-1}$ .
- Signal Channels:
  - LN-Blind: Tri-muon final states ( $\mu^\pm \mu^\mp \mu^\pm \nu$ ) from charged current (CC) production and leptonic decay.
  - LN-Violating (LNV): Same-sign (SS) dimuon final states ( $\mu^\pm \mu^\pm j(j)$ ) from CC production and semi-leptonic decay.
- Backgrounds: Dominant backgrounds include multi-boson production ( $3\ell\nu, 4\ell, 3W, WW\ell\ell$ ) and top-quark processes ( $tq\ell\ell, t\bar{t}\ell\nu, t\bar{t}\ell\ell$ ). Misidentification backgrounds are neglected as they are subleading for muon-based searches.
- Statistical Analysis: A two-stage analysis is performed: cut-based preselection followed by a Boosted Decision Tree (BDT) using TMVA. Statistical significance is calculated using the Asimov dataset approach for 95% CL exclusion and 5 $\sigma$ discovery.
Reinterpretation of Bounds:
- Existing LHC limits are reinterpreted by mapping them onto an effective active-sterile mixing parameter that accounts for the suppression of the LNV signal rate due to the LN ratio $R = N_{SS}/N_{OS}$ . The paper distinguishes between s-channel resonant production (where NNOs apply) and t-channel processes (where symmetry protection suppresses LNV).

Key Contributions

Damping-Enhanced LNV: The paper demonstrates that decoherence effects can significantly enhance observable LNV in the "damping-enhanced" regimes, allowing LNV signals to be observable even when the symmetry-breaking parameters are small, provided the mass splitting exceeds a specific threshold relative to the proton wave packet width.
Regime Classification: It establishes a detailed classification of LNV regimes, showing that the transition from Dirac-like behavior (suppressed LNV) to double-Majorana behavior (maximal LNV) is not abrupt but depends on the ratio of $\Delta m$ to $\Gamma_N$ and the damping threshold.
Distinguishability Criterion: A novel statistical criterion is proposed to distinguish a pseudo-Dirac HNL pair from the double-Majorana limit. This requires simultaneous exclusion sensitivity in both LN-blind and LNV channels, combined with a significant separation between the predicted SS rates of the two hypotheses.
Inverse Seesaw Application: The results are applied to the inverse seesaw scenario, linking the pseudo-Dirac mass splitting directly to the light neutrino mass, thereby projecting sensitivity to light neutrino masses down to $\sim 0.1$ meV.

Results

Sensitivity: At the FCC-hh, LNV searches (SS dimuons) outperform LN-blind searches (tri-muons) by up to one order of magnitude in active-sterile mixing sensitivity, primarily due to lower Standard Model backgrounds.
Mass Splitting Dependence: The sensitivity of LNV searches is highly dependent on the pseudo-Dirac mass splitting. In the small LN-ratio regimes (small $\Delta m$ ), sensitivity is drastically reduced compared to the double-Majorana limit. However, in the large LN-ratio regimes (large $\Delta m$ or strong damping), sensitivity approaches the maximal reach.
Distinguishability: The ability to distinguish pseudo-Dirac HNLs from double-Majorana HNLs is restricted to an intermediate regime of mass splittings. If $\Delta m$ is too small, the LNV signal is too suppressed to be detected; if $\Delta m$ is too large, the pseudo-Dirac pair becomes phenomenologically indistinguishable from two independent Majorana neutrinos.
LHC Bounds: Existing LHC bounds, often interpreted under the assumption of maximal LNV (double-Majorana), must be reinterpreted for SPSS. In the symmetry-protected regime with small mass splittings, these bounds are significantly weaker than the standard interpretation suggests.

Significance
The paper argues that a consistent interpretation of current and future collider searches for HNLs requires accounting for the quantum dynamics of pseudo-Dirac neutrinos. Specifically, the interplay between symmetry protection, NNOs, and decoherence effects dictates the observable LN ratio. The authors conclude that while future hadron colliders like the FCC-hh offer a unique opportunity to probe these scenarios, the reach of LNV searches is not universal but is critically dependent on the specific mass splitting of the pseudo-Dirac pair. Furthermore, the ability to experimentally distinguish between pseudo-Dirac and double-Majorana scenarios provides a unique probe into the nature of lepton number violation and the underlying symmetry structure of neutrino mass generation.