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Search for long-lived heavy neutral leptons in signatures with one prompt muon and a secondary vertex formed by two non-prompt muons in proton-proton collisions at $\sqrt{s}$ = 13 and 13.6 TeV

This paper presents a search for long-lived heavy neutral leptons in proton-proton collisions at 13 and 13.6 TeV using a signature of one prompt muon and two non-prompt muons forming a secondary vertex, setting 95% confidence level exclusion limits on the mixing parameter for HNL masses between 1 and 5 GeV without observing any excess over the background.

Original authors: CMS Collaboration

Published 2026-11-02

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CC BY 4.0

Original authors: CMS Collaboration

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 known that the universe is missing something. The Standard Model, the theory that describes the fundamental particles and forces making up everything we see, works with stunning precision. Yet, it leaves a glaring gap: it cannot explain why neutrinos, those ghostly particles that stream through the Earth by the trillions every second, have mass. The discovery that these particles can change their identity as they travel proved they are not weightless, but the model offers no reason for this weight. To fix this, scientists have proposed the existence of a hidden partner for the neutrino, a heavy, neutral particle that rarely interacts with anything. If these "heavy neutral leptons" exist, they could explain not only the mass of the neutrinos but also why the universe is made of matter rather than antimatter, and perhaps even what dark matter is. The challenge is that these particles, if they exist, are incredibly elusive, decaying into other particles long after they are created, often far away from the point where they were born.

At the Large Hadron Collider at CERN, a researcher using the CMS detector has taken a fresh look for these elusive particles. They focused on a specific scenario where a heavy neutral lepton is created alongside a standard muon, a heavier cousin of the electron, during high-energy collisions of protons. The theory suggests that the heavy particle would travel a significant distance before decaying into two more muons. Unlike the prompt muon that appears instantly at the collision point, these two new muons would emerge from a "secondary vertex," a point in space noticeably displaced from the center of the machine. The researcher analyzed a massive amount of data, equivalent to 138 units of collision data recorded at an energy of 13 trillion electron volts between 2016 and 2018, plus an additional 34.6 units recorded at a slightly higher energy of 13.6 trillion electron volts in 2022. Their strategy was to ignore the inner tracking systems of the detector, which are designed to catch particles that appear immediately, and instead look only at the outer muon chambers. This allowed them to spot muons that had traveled several meters before being detected, a signature of a particle that lived much longer than the fleeting particles of the Standard Model.

The search was designed to catch these long-lived particles in a very specific way. The researcher looked for events containing exactly three muons: one appearing right at the collision point and two appearing later, far away from the center, forming a distinct pair. They filtered out billions of background events, such as those caused by random noise or common particle decays, by requiring the two distant muons to have no connection to the inner tracking layers and to form a clear, reconstructed point of origin. They also checked that the timing and energy of these particles matched what a heavy neutral lepton would produce. Despite sifting through this enormous dataset with high precision, the researcher found no evidence of these heavy particles. The number of events they observed matched the predictions for known background processes perfectly, with no unexpected excesses that would signal a new discovery.

Because they found no signal, the researcher was able to set strict limits on where these heavy neutral leptons could exist. They calculated that if these particles have a mass between 1 and 5 billion electron volts, their interaction with ordinary neutrinos must be extremely weak, far weaker than previously thought possible in certain ranges. Specifically, they ruled out the existence of these particles for a wide range of masses and mixing strengths, particularly in the region where the particles would live long enough to travel the meters required to reach the outer detectors. This result is significant because it closes the door on a specific window of possibilities that previous experiments had not been able to probe. By looking for particles that decay far from the collision point, this study extended the reach of the search into a region of long lifetimes that had been difficult to access. The findings do not prove that heavy neutral leptons do not exist at all, but they confirm that if they do exist, they are not hiding in the specific mass and lifetime range this experiment was designed to find. The search continues, but this chapter of the story has been written with a clear, negative result that helps guide the next steps in the quest to understand the hidden mass of the universe.

Technical Summary: Search for Long-Lived Heavy Neutral Leptons in Signatures with One Prompt Muon and a Secondary Vertex Formed by Two Non-Prompt Muons

Problem and Motivation
The discovery of neutrino oscillations confirms that neutrinos possess non-zero masses, suggesting physics beyond the Standard Model (SM). Heavy Neutral Leptons (HNLs), introduced as massive right-handed counterparts to SM neutrinos, offer a theoretical framework to explain these masses via the seesaw mechanism and potentially address cosmological puzzles such as dark matter and matter-antimatter asymmetry. While HNLs are singlets under the SM gauge group, they can be produced in proton-proton (pp) collisions via mixing with SM neutrinos.

This analysis targets HNLs produced in the decay of W bosons ( $W \to \ell N$ ), followed by the decay of the HNL into two charged leptons and a neutrino ( $N \to \ell' \ell'' \nu$ ). The specific focus is on the final state containing three muons: one prompt muon from the primary W decay and two highly displaced (non-prompt) muons originating from a secondary vertex (SV) formed by the HNL decay. This search is particularly motivated by the "long-lifetime" region of the HNL parameter space, corresponding to low masses ( $m_N \lesssim 5$ GeV) and small mixing parameters ( $|V_{N\mu}|^2 \sim 10^{-6}–10^{-5}$ ). In this regime, HNLs travel macroscopic distances before decaying, often outside the inner silicon tracker. Traditional tracker-based searches have limited acceptance for transverse decay lengths ( $L_{xy}$ ) exceeding $\sim 1$ m. This analysis aims to extend sensitivity to decay lengths of approximately 50–400 cm by reconstructing muons using only the outer CMS muon system.

Methodology

Data Sets: The analysis utilizes proton-proton collision data collected by the CMS experiment at the LHC. This includes an integrated luminosity of 138 fb $^{-1}$ recorded at $\sqrt{s} = 13$ TeV (2016–2018) and, for the first time in an HNL search at the LHC, 34.6 fb $^{-1}$ recorded at $\sqrt{s} = 13.6$ TeV (2022).
Signal Model: Signal events are simulated using MADGRAPH5_aMC@NLO at leading order, with parton showering via PYTHIA. The simulation assumes a Majorana HNL coupling exclusively to the muon neutrino flavor ( $|V_{Ne}|=|V_{N\tau}|=0$ ). Samples are generated for $m_N$ in the range 1–6 GeV. To account for the dependence of the HNL lifetime on mass and mixing strength, per-event reweighting is applied to match the proper lifetime distribution for specific target mixing parameters.
Event Reconstruction and Selection:
- Trigger: Events are selected via single-muon triggers requiring an isolated muon with $p_T > 27$ (24) GeV.
- Prompt Muon ( $\mu_0$ ): Exactly one prompt muon is required, satisfying tight identification and isolation criteria ( $I_{rel} < 0.15$ ) and originating from the primary vertex (PV).
- Displaced Muons ( $\mu_1, \mu_2$ ): The core of the analysis relies on "displaced standalone" (DSA) muons. These are reconstructed using only hits in the muon system (drift tubes, cathode strip chambers, resistive plate chambers) without requiring matching tracks in the inner silicon tracker. This technique allows reconstruction of muons decaying in the outer tracker layers or beyond.
- Secondary Vertex: The two DSA muons must form a converging secondary vertex with a fit $p$ -value $> 0.001$ . Crucially, these muons must not match any track in the tracker system, ensuring orthogonality to previous tracker-based searches and suppressing prompt backgrounds.
- Kinematic Cuts: Selection criteria exploit the signal topology, including the large boost of the HNL. Requirements include:
  - Dimuon transverse momentum $p_T^{pair} > 10$ GeV.
  - Angular separation $\Delta R(\mu_1, \mu_2) < 1.0$ and $\cos \theta(\mu_1, \mu_2) > 0.9$ .
  - Invariant mass of the three muons $40 < m(\mu_0, \mu_1, \mu_2) < 90$ GeV.
  - Azimuthal separation $\Delta \phi(\mu_0, \mu_{1/2}) > 1.5$ .
  - Veto on b-tagged jets and Z boson candidates ( $m(\mu_0, \mu') < 80$ GeV).
Signal Regions (SR): The SR is divided into four bins based on two discriminating variables: the dimuon transverse momentum ( $p_T^{pair}$ ) and the significance of the secondary vertex displacement ( $L_{xy}/\sigma_{L_{xy}}$ ). The optimal binning thresholds are $p_T^{pair} > 22$ GeV and $L_{xy}/\sigma_{L_{xy}} > 4$ .
Background Estimation: The dominant backgrounds arise from misreconstructed prompt or mildly displaced muon pairs (e.g., from pileup $J/\psi$ decays or semileptonic b-hadron decays). Since Monte Carlo simulation cannot reliably model instrumental inefficiencies causing such misreconstruction, a data-driven "ABCD method" is employed. Two statistically independent conditions define four regions: a tracker veto on $\mu_1$ and a reduced signal selection. The background yield in the SR (Region A) is estimated as $n_A = n_B \times (n_C / n_D)$ , where $n_B, n_C, n_D$ are yields in control regions. Validation regions (VRs) confirm the method's robustness, with observed non-closure in low- $p_T$ sidebands attributed to photon conversions, a contribution deemed negligible in the high- $p_T$ SR.

Key Contributions

Extended Decay Length Sensitivity: By utilizing DSA muons reconstructed solely from the muon system, this analysis significantly extends the search reach for HNLs with transverse decay lengths up to $\sim 400$ cm, a regime inaccessible to standard tracker-based analyses.
First Use of 13.6 TeV Data: This is the first HNL search at the LHC to incorporate data from the 2022 run at $\sqrt{s} = 13.6$ TeV.
Orthogonality to Previous Searches: The requirement that displaced muons have no associated tracker information makes this search complementary to the CMS search reported in Ref. [40], which relied on displaced tracks within the silicon tracker.
Comprehensive Background Control: The application of the ABCD method with rigorous validation in low- $p_T$ and inverted tracker veto regions provides a robust estimate of the residual SM background.

Results
No significant excess of events over the predicted background was observed in any of the four signal bins for either the 13 TeV or 13.6 TeV data sets. The observed yields are consistent with the background-only hypothesis within statistical and systematic uncertainties.

Under the assumption of the Majorana HNL hypothesis, 95% confidence level (CL) exclusion limits were set on the mixing parameter $|V_{N\mu}|^2$ as a function of the HNL mass $m_N$ in the range 1–5 GeV.

The analysis excludes mixing parameters in the range of $10^{-6}$ to $10^{-5}$ for masses between 2 and 4 GeV.
The sensitivity drops for $m_N \gtrsim 4.5$ GeV due to the rapid decrease in HNL lifetime (scaling as $m_N^{-5}$ ), causing heavier HNLs to decay before reaching the sensitive decay volume.
When compared to previous CMS analyses targeting similar mass ranges (including prompt, displaced tracker, and B-meson decay searches), this analysis improves the expected sensitivity for masses between 2.5 and 4.2 GeV, specifically probing the long-lifetime, low-mixing region.

Significance
The paper claims that this analysis surpasses previous experimental results in sensitivity to HNLs with masses between 2.5 and 4.2 GeV. By targeting highly displaced vertices reconstructed exclusively in the muon system, the search probes a specific region of the HNL parameter space (low mass, small mixing, long lifetime) that was previously less constrained. The null result further tightens the constraints on the existence of Majorana HNLs in this mass range, ruling out specific mixing scenarios that could have explained neutrino mass generation or dark matter candidates within this kinematic window. The successful integration of 13.6 TeV data demonstrates the capability of the CMS experiment to utilize higher-energy datasets for rare process searches.

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