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Heavy Neutral Lepton at Same-Sign Muon Collider

This paper investigates the discovery potential of heavy neutral leptons at the proposed $\mu$ TRISTAN same-sign muon collider, demonstrating that its high-energy lepton-number-violating and lepton-flavor-violating signatures could significantly surpass current electroweak precision bounds on HNL mixing, particularly for masses in the 5–10 TeV range.

Original authors: Ryuichiro Kitano, Ian Low, Ryutaro Matsudo, Shohei Okawa, Subhojit Roy

Published 2026-08-25

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CC0 1.0

Original authors: Ryuichiro Kitano, Ian Low, Ryutaro Matsudo, Shohei Okawa, Subhojit Roy

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

The universe is built on a foundation of particles, most of which fit neatly into a standard catalog known as the Standard Model. This model has been remarkably successful, predicting the behavior of matter and energy with precision. Yet, it leaves a glaring hole: it cannot explain why neutrinos, the ghostly particles that stream through everything, have mass. The discovery that these particles possess even a tiny weight suggests that the Standard Model is incomplete, hinting at a hidden layer of physics. One leading idea to fill this gap involves "heavy neutral leptons," massive cousins of the known neutrinos that might hold the key to why the universe contains more matter than antimatter. If these heavy particles exist, they would interact very weakly with ordinary matter, making them incredibly difficult to catch. They are the missing pieces that could explain the origin of mass and the balance of the cosmos, but finding them requires looking in places where the noise of the universe is quietest.

Researchers have proposed a new way to hunt for these elusive particles using a future machine called a same-sign muon collider, specifically a concept known as µTRISTAN. Unlike the massive colliders currently in operation that smash protons together, creating a chaotic spray of debris, this proposed facility would collide two beams of positively charged muons. Muons are unstable particles similar to electrons but much heavier. Because they are charged, they can be accelerated to incredible speeds, and because they are heavier than electrons, they do not lose as much energy when circling in a ring, allowing for a compact, high-energy machine. The unique feature of this setup is that both beams carry the same electric charge. This creates a rare initial state where the total "lepton number"—a property that usually stays constant in particle interactions—is positive. This specific condition acts as a filter, suppressing the usual background noise that drowns out rare events in other experiments, and opens a window to see processes that are otherwise impossible to observe.

In a new study, a team of physicists simulated what would happen if this machine were built and operated at an energy level of 10 trillion electron volts. They focused on two specific ways the heavy neutral leptons might reveal themselves. The first scenario involves a process where the collision produces a W boson, a heavy carrier of the weak force, and a tau particle, a heavy cousin of the electron, while changing the "flavor" of the neutrinos involved. This event would break the rule that lepton flavors must stay the same, signaling that the heavy neutral leptons are mixing with the known neutrinos. The second scenario is even more profound: a collision that produces two W bosons, both carrying a positive charge. This event would violate the conservation of lepton number by two units, a phenomenon that can only happen if the neutrinos are their own antiparticles, a type of matter known as a Majorana particle. Observing this would be a direct confirmation that neutrinos have this unique, self-identical nature.

The researchers ran detailed computer simulations to see if these signals could be distinguished from the background noise of the machine. They found that by carefully selecting the energy and direction of the particles produced in the collision, they could isolate the heavy neutral lepton signals with high confidence. For the flavor-changing signal, the best method was to look for a specific pattern where a tau particle decays into a jet of particles, accompanied by another jet of particles that is not a tau. For the lepton-number-violating signal, the most effective approach was to look for two jets of particles that behave like two W bosons. The simulations showed that with a year of data collection, the machine could detect these events even if the heavy neutral leptons were extremely massive, far heavier than anything currently known.

The results of these simulations indicate that this proposed collider would be far more sensitive than current experiments. Existing limits on these particles come from precise measurements of how the W and Z bosons behave, but those measurements are indirect. The new study shows that the muon collider could improve the search limits by a factor of ten for particles with masses between 5 and 10 trillion electron volts. This range is crucial because it covers the mass scale where these particles might naturally explain the small masses of the neutrinos we observe today. The study also highlights that the two different signals provide complementary information: one tells us about how the different types of neutrinos mix, while the other tells us about the fundamental nature of the neutrino itself.

While the machine described in the paper does not yet exist, the study provides a clear roadmap for what to look for if it is built. The researchers emphasize that the unique environment of a same-sign muon collider offers a clean stage where these rare events can be seen without the interference that plagues other experiments. If such a facility were constructed, it would not only search for these heavy particles but also test the very nature of matter and antimatter. The ability to see if neutrinos are their own antiparticles would be a monumental step in understanding the universe, potentially solving the mystery of why we exist at all. The work confirms that with the right tools, the heavy neutral leptons, long hidden in the shadows of theoretical physics, could finally be brought into the light.

Technical Summary: Heavy Neutral Lepton at Same-Sign Muon Collider

Problem and Motivation
The Standard Model (SM) remains incomplete, failing to explain neutrino masses, dark matter, and matter-antimatter asymmetry. Heavy Neutral Leptons (HNLs), or sterile neutrinos, are well-motivated extensions of the SM that address the origin of neutrino masses via seesaw mechanisms (e.g., Type-I, linear, and inverse seesaw). While the Large Hadron Collider (LHC) has searched for HNLs, its hadronic environment limits sensitivity to rare Lepton Number Violating (LNV) processes. Furthermore, current constraints on HNL mixing parameters are primarily derived from Electroweak Precision Observables (EWPOs) and charged lepton flavor violation (cLFV) measurements, which are indirect.

The paper investigates the discovery potential of HNLs at the proposed $\mu$ TRISTAN, a high-energy same-sign muon collider ( $\mu^+\mu^+$ ). Unlike conventional colliders, the $\mu^+\mu^+$ initial state possesses a non-vanishing lepton number, offering a unique environment to probe LNV and Lepton Flavor Violating (LFV) processes with suppressed SM backgrounds.

Methodology
The authors analyze two complementary HNL-mediated processes at a center-of-mass energy $\sqrt{s} = 10$ TeV with an integrated luminosity of $1 \text{ ab}^{-1}$ :

LFV Channel: $\mu^+\mu^+ \to W^+\tau^+\bar{\nu}_\mu$ . This process violates lepton flavor but conserves lepton number. It probes the mixing combination $|\sum U_{\mu I} U^*_{\tau I}|$ and does not rely on the Majorana nature of neutrinos.
LNV Channel: $\mu^+\mu^+ \to W^+W^+$ . This process violates lepton number by two units, serving as the muon-sector analogue of inverse neutrinoless double beta decay. It probes the mixing combination $|\sum U_{\mu I}^2|$ and is sensitive to the Majorana mass term.

Simulation and Analysis:

Event Generation: Signal and background events were generated using MadGraph5_aMC@NLO interfaced with the SM HeavyN NLO model. Unstable particle decays, parton showering, and hadronization were simulated with Pythia8, and detector effects were modeled using Delphes with a Muon Collider card.
Backgrounds: Major SM backgrounds include $\mu^+\mu^+ \to \mu^+\mu^+Z$ , $\mu^+\mu^+ \to \mu^+\mu^+ZZ$ , $\mu^+\mu^+ \to \mu^+\mu^-W^+W^-$ , and processes involving $Z\tau^+\tau^-$ . A specific challenge addressed was the collinear divergence in processes with final-state muons; the authors employed a method splitting phase space into low- and high- $p_T$ regions, using the Effective Photon Approximation (EPA) for the former and MadGraph for the latter.
Selection Strategy:
- For the LFV process, the most sensitive topology was identified as one $\tau$ -jet plus one non- $\tau$ jet. Optimized cuts included high transverse momentum ( $p_T$ ) requirements for the jets ( $p_T^{\tau\text{-jet}} \gtrsim 0.5\text{--}0.8$ TeV, $p_T^{\text{non-}\tau\text{-jet}} \sim 3.0\text{--}3.2$ TeV) and a total invariant mass cut ( $M_{\text{tot}} \gtrsim 2.7\text{--}3.2$ TeV).
- For the LNV process, the fully hadronic two-jet topology was selected. Cuts required $p_T^{j1} > 4.2$ TeV, $p_T^{j2} > 1.9$ TeV, and $M_{\text{tot}} > 6.45\text{--}6.75$ TeV.
Statistical Treatment: 95% Confidence Level (CL) upper limits on the mixing parameters were derived assuming the background-only hypothesis, utilizing the exact two-sided Poisson interval.

Key Contributions and Results
The study provides projected sensitivity curves for HNL mass ( $M_N$ ) versus mixing parameters, comparing them against current EWPO bounds.

LFV Sensitivity: The analysis demonstrates that $\mu$ TRISTAN can probe the mixing parameter $|\sum U_{\mu I} U^*_{\tau I}|$ more strictly than current EWPO constraints for $M_N \lesssim 3$ TeV.
LNV Sensitivity: The LNV channel offers a significant improvement in sensitivity for the parameter $|\sum U_{\mu I}^2|$ . Specifically, for HNL masses in the range of 5–10 TeV, the projected collider bound improves upon current limits by approximately one order of magnitude.
Cross-Section Behavior: The paper highlights distinct scaling behaviors for the two processes. The LNV cross-section ( $\sigma_{W^+W^+}$ ) scales as $M_N^2$ at high energies (peaking near $M_N \approx 0.74\sqrt{s}$ ) due to the Majorana nature of the propagator, whereas the LFV cross-section scales differently, lacking the $M_N$ insertion required for LNV.
Event Yields: At benchmark mixing values close to current precision limits ( $|\sum U_{\mu I} U^*_{\tau I}| \simeq 7.1 \times 10^{-4}$ and $|\sum U_{\mu I}^2| \simeq 2.8 \times 10^{-4}$ ), the paper estimates a cross-section of $\sigma_{W^+\tau^+\bar{\nu}_\mu} \simeq 0.06$ fb for the LFV process and $\sigma_{W^+W^+} \simeq 0.3 \text{ fb} (M_N/\text{TeV})^2$ for the LNV process (in the limit $\sqrt{s} \gg M_N$ ). Consequently, for the LNV process, 300 or more signal events are expected at $\sqrt{s} = 10$ TeV with $1 \text{ ab}^{-1}$ luminosity, whereas the LFV process yields a significantly smaller event count under these specific benchmark conditions.

Significance and Claims
The paper claims that the $\mu$ TRISTAN facility offers a decisive test for HNLs in a mass range (up to $\mathcal{O}(10)$ TeV) that is difficult to access via current or near-future $e^+e^-$ colliders or the HL-LHC.

Complementarity: The two channels probe distinct aspects of the HNL sector: the LFV channel tests the flavor structure of active-sterile mixing independently of the Majorana nature, while the LNV channel directly tests lepton number violation and the Majorana nature of neutrinos.
Majorana Evidence: Observation of the $\mu^+\mu^+ \to W^+W^+$ process would provide strong evidence for Majorana neutrinos, analogous to the observation of neutrinoless double beta decay but in the muon sector.
Future Outlook: The authors note that their results are based on cut-based selections. They suggest that future work employing machine-learning-based multivariate analyses could further enhance sensitivity. Additionally, they note that if beam polarization is available, the helicity dependence of the signal (requiring right-handed $\mu^+$ ) could serve as a powerful tool to distinguish signal from background and discriminate between underlying models.

The study concludes that $\mu$ TRISTAN would significantly extend experimental sensitivity to HNLs, providing a nontrivial consistency check on neutrino mass generation scenarios and potentially confirming the Majorana nature of neutrinos.

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