⚛️ phenomenology

Nested Disappearing-Track plus Displaced-Vertex Topology at the HL-LHC: A Dual Long-Lived-Particle Signature of the Scotogenic Model

This paper proposes a novel search strategy for the scotogenic model at the High-Luminosity LHC that targets a unique "nested" signature of a disappearing track followed by a displaced vertex, leveraging time-of-flight and spatial correlations to achieve background-free discovery of long-lived particles that simultaneously explain neutrino masses.

Original authors: Renjie Wang

Published 2026-09-24

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Renjie Wang

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 haunted by a single, stubborn question: why do neutrinos have mass? These ghostly particles, which zip through the universe almost without interacting with anything, were long thought to be weightless. Yet, experiments have proven they carry a tiny, non-zero mass, a fact that the standard rules of particle physics cannot explain. One of the most elegant proposed solutions is a framework called the scotogenic model. It suggests that neutrinos gain their mass not through a direct, heavy-handed interaction, but through a subtle, looped process involving new, hidden particles that have never been seen. In this scenario, the universe contains a secret sector of particles that are invisible to our current detectors, yet they hold the key to understanding the fundamental nature of matter. If these hidden particles exist, they should be producible in the world's most powerful particle collider, the Large Hadron Collider, but they would behave in ways that are completely alien to the known laws of physics.

A new study by Renjie Wang at the Institute of High Energy Physics in Beijing proposes a specific way to catch these elusive particles in the act, focusing on a scenario where the hidden particles are surprisingly slow and leave behind a unique, two-part trail. The research simulates what would happen if the Large Hadron Collider were upgraded to its future High-Luminosity version, which will smash protons together with unprecedented intensity. The study focuses on a compressed version of the scotogenic model, where two types of new particles are produced together: a charged scalar and a heavy neutral fermion. In this specific setup, both particles are long-lived, meaning they travel a measurable distance inside the detector before decaying, rather than vanishing instantly. The charged particle leaves a short track that suddenly stops, or "disappears," because it decays into a neutral partner that the detector cannot see. This neutral partner then travels a further distance before decaying itself into a pair of visible leptons, creating a second, displaced point of interaction.

The researchers describe this sequence as a nested topology, a chain of events where one disappearance leads directly to a new appearance. The first particle, the charged scalar, travels a few centimeters to a few tens of centimeters before it decays into a neutral particle and a very soft lepton that is too faint to be detected. To the detector, the charged track simply ends. The neutral particle, which is invisible, then continues on that same path for another distance before it finally decays into two visible leptons, creating a displaced vertex. This creates a distinct signature: a track that vanishes, followed by a gap of empty space, followed by a new cluster of particles appearing further out, all aligned in a straight line. The study simulates millions of these events to see if the upgraded detectors at the High-Luminosity LHC could spot them. The simulation shows that this specific pattern is incredibly rare in the known universe, making it a powerful way to distinguish a new discovery from the background noise of ordinary particle collisions.

What makes this search particularly powerful is the addition of a fourth dimension: time. The two particles involved in this chain are heavy and move slower than the speed of light. This causes a measurable delay in when they arrive at the outer timing detectors compared to particles that travel at light speed. The study calculates that the total time delay for this two-step journey would be between 200 and 800 picoseconds. While this sounds infinitesimally small, the new timing detectors planned for the High-Luminosity LHC are precise enough to measure this difference. By combining the spatial alignment of the two events with this time delay, the researchers can filter out almost all the background noise. The study estimates that the number of false alarms from known physics processes would be vanishingly small, likely less than one event in the entire dataset, while the signal from the new particles would be strong enough to be seen with high confidence.

The paper presents a detailed map of where this signal could be found. The researchers tested a wide range of possible lifetimes for the two particles, varying how far they travel before decaying. They found that their strategy works effectively for charged particles that travel between 15 and 300 millimeters before disappearing, and for the neutral particles that travel between 10 and 1000 millimeters before decaying. This range covers a significant portion of the parameter space that has not been explored by previous searches, which typically looked for only one of these long-lived behaviors in isolation. At a specific benchmark point where the charged particle travels 300 millimeters and the neutral particle travels 189 millimeters, the simulation predicts that the High-Luminosity LHC would detect roughly 1,212 signal events over its full operational lifetime. This is a robust number that would allow for a definitive discovery, even if the background noise were higher than expected.

The significance of this work lies in its ability to connect a collider signature directly to the origin of neutrino mass. In the scotogenic model, the same tiny forces that give neutrinos their mass also determine how long these new particles live. By measuring the distance these particles travel before decaying, physicists would not just be finding a new particle; they would be measuring the very interaction responsible for the mass of the neutrino. The study concludes that this nested disappearing-track plus displaced-vertex signature is a unique and powerful tool. It offers a clear path to testing a fundamental theory of the universe using the next generation of collider technology, turning the High-Luminosity LHC into a direct probe of the mechanism that gives neutrinos their weight. The research provides a concrete roadmap for experimentalists to follow, defining exactly what to look for and how to distinguish it from the rest of the chaotic particle zoo.

Technical Summary: Nested Disappearing-Track plus Displaced-Vertex Topology at the HL-LHC

Problem and Motivation
The origin of neutrino mass remains a primary open question in particle physics. The scotogenic model offers a radiative solution by extending the Standard Model (SM) with an inert scalar doublet ( $\tilde{\eta}$ ) and right-handed Majorana fermions ( $N_k$ ), stabilized by a $Z_2$ symmetry. In the "open-spectrum" regime, the heavy neutral fermion $N_2$ is long-lived due to small Yukawa couplings ( $y \sim \mathcal{O}(10^{-3})$ ) required for sub-eV neutrino masses, while the charged scalar $\tilde{\eta}^\pm$ decays promptly. However, in the "compressed-spectrum" regime ( $\Delta M_{\text{comp}} = m_{\tilde{\eta}^\pm} - m_{N_2} \simeq 200$ MeV), a distinct phenomenology arises. Here, a separate, even smaller Yukawa entry ( $y_2 \sim \mathcal{O}(10^{-6})$ ) renders $\tilde{\eta}^\pm$ long-lived as well. This creates a "nested" cascade where $\tilde{\eta}^\pm$ produces a disappearing track (DT) before decaying into a long-lived $N_2$ , which subsequently decays into a displaced vertex (DV). Existing searches typically target either DT or DV signatures in isolation, leaving the correlated, simultaneous long-lived particle (LLP) topology unexplored.

Methodology
The study investigates the two-inert-doublet, three-right-handed-neutrino extension of the scotogenic model (2IDM3N) at the High-Luminosity LHC (HL-LHC) with $\sqrt{s} = 14$ TeV and an integrated luminosity of $3000 \text{ fb}^{-1}$ .

Signal Topology: The dominant production channel is electroweak pair production ( $pp \to \tilde{\eta}^\pm \tilde{\eta}^0 + \text{ISR}$ $pp \to \tilde{η}^{\pm} \tilde{η}^{0} + ISR$ ). The signal unfolds in four dimensions:
1. A high- $p_T$ charged track ( $\tilde{\eta}^\pm$ ) travels macroscopically ( $R_{\text{DT}} \sim 160\text{--}300$ mm) and disappears, decaying into a soft lepton ( $p_\ell \lesssim 0.2$ GeV, unreconstructed) and a neutral $N_2$ .
2. The neutral $N_2$ travels invisibly to a second macroscopic displacement ( $R_{\text{DV}} > R_{\text{DT}} + 20$ mm) and decays via $N_2 \to N_1 \ell^+ \ell^-$ .
3. The displaced dilepton pair arrives at the CMS MIP Timing Detector (MTD) with a time-of-flight delay ( $\Delta t$ ) relative to the primary vertex.
Analysis Strategy: The analysis employs a logical OR of two Level-1 triggers: an ISR jet plus missing transverse energy ( $E_T^{\text{miss}}$ $E_{T}^{miss}$ ) or a displaced muon. The signal region (SR-DT4DV) is defined by reconstruction-level cuts:
- Disappearing Track: $p_T > 50$ GeV, $160 \leq L_{\text{track}} \leq 300$ mm, no calorimeter deposits beyond the endpoint.
- Displaced Vertex: Reconstructed $\ell^+\ell^-$ pair with $p_T > 5$ GeV, $R_{\text{DV}} \in [180, 700]$ mm, and $m_{\ell\ell} < 48$ GeV.
- 4D Timing: Mean arrival-time delay $\Delta t > 200$ ps.
- Spatial Pointing: The displacement vector from the DT endpoint to the DV must align with the DT direction ( $\Delta \phi, \Delta \theta < 0.1$ rad).
Simulation: Events were generated using MadGraph5 aMC@NLO and Pythia 8, with detector simulation via Delphes 3 (CMS Phase-II card). The study scans a grid of 56 benchmark points varying the proper decay lengths $c\tau_{\tilde{\eta}^\pm}$ and $c\tau_{N_2}$ .

Key Contributions

Novel Topology: This work presents the first study of the nested DT+DV topology in the scotogenic model, exploiting the simultaneous macroscopic lifetimes of both $\tilde{\eta}^\pm$ and $N_2$ .
Dual Handles for Background Suppression: The strategy utilizes two unique discriminants:
- Spatial Correlation: The requirement that the DV back-points to the DT endpoint with no SM analogue.
- 4D Timing: The double-delay signature ( $\Delta t \sim 200\text{--}800$ ps) from the sequential slow flights of $\tilde{\eta}^\pm$ and $N_2$ , which suppresses prompt backgrounds (e.g., photon conversions) and instrumental noise.
Parameter Space Coverage: The analysis targets a region in the $(c\tau_{\tilde{\eta}^\pm}, c\tau_{N_2})$ plane ( $15 \text{ mm} \lesssim c\tau_{\tilde{\eta}^\pm} \lesssim 300 \text{ mm}$ , $10 \text{ mm} \lesssim c\tau_{N_2} \lesssim 1000 \text{ mm}$ ) that is not simultaneously covered by existing standalone DT or DV searches.

Results

Signal Yield: At the benchmark point ( $m_{N_2} = 150$ GeV, $c\tau_{\tilde{\eta}^\pm} = 300$ mm, $c\tau_{N_2} = 189$ mm), the total efficiency is $\epsilon \approx 1.18\%$ , yielding approximately $N_s \approx 1212$ signal events at $3000 \text{ fb}^{-1}$ . Peak sensitivity occurs at $(c\tau_{\tilde{\eta}^\pm}, c\tau_{N_2}) = (150 \text{ mm}, 60 \text{ mm})$ with $N_s \approx 1635$ .
Background Estimation: The dominant background is estimated to be pileup combinatorics, with an analytic upper bound of $B \sim 10^{-5} \text{--} 10^{-3}$ events. Prompt SM backgrounds are effectively eliminated by the $\Delta t > 200$ ps cut and material vetoes.
Discovery Reach: The analysis demonstrates a $5\sigma$ discovery potential for any background level up to $B \sim 10$ events. For the expected background ( $B \lesssim 10^{-3}$ ), the benchmark point yields a significance of $\gtrsim 96\sigma$ . The $5\sigma$ discovery contour and $95\%$ CL exclusion limits nearly coincide across the scanned parameter space, covering the central region where both particles are long-lived.

Significance
The paper claims that this nested strategy transforms the HL-LHC into a direct probe of the interaction responsible for neutrino mass generation. Since the $N_2$ decay length is governed by the same Yukawa couplings ( $y_1 \sim \mathcal{O}(10^{-3})$ ) that generate sub-eV neutrino masses, mapping this cascade directly tests the neutrino-mass-generating sector. The study provides a concrete roadmap for the HL-LHC Run 4 search programme, identifying a correlated LLP signature that is unique in the SM and robust against background uncertainties.

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