Probing electroweak pair production of heavy neutral leptons with displaced vertices at the LHC

This paper investigates the sensitivity of LHC displaced vertex searches to electroweak pair-produced heavy neutral leptons within a supersymmetric higgsino decay framework, deriving constraints from ATLAS Run 2 data and projecting discovery potential for the HL-LHC while assessing the generalizability of these results to broader models.

The Gist

Imagine the Large Hadron Collider (LHC) as a giant, high-speed particle smasher. Physicists use it to look for new, heavy particles that might explain why the universe has mass. One of the most elusive suspects in this hunt is the Heavy Neutral Lepton (HNL), often called a "sterile neutrino."

Think of a sterile neutrino as a ghost. It barely interacts with anything. In the standard story, these ghosts are produced so rarely and decay so quickly that they are almost impossible to catch. They are like trying to spot a specific ghost in a crowded stadium by looking for a single, fleeting flash of light.

The New Strategy: The "Double Ghost" Trick

This paper proposes a different way to catch these ghosts. Instead of waiting for them to appear on their own (which is rare), the authors suggest looking for a scenario where two ghosts are produced at the same time as part of a larger, heavier package.

In the specific model they study (a supersymmetric theory), heavy particles called higgsinos are created in collisions. These higgsinos are unstable and immediately decay. Crucially, they don't just vanish; they split apart, releasing a pair of sterile neutrinos along with other particles (like jets of energy).

Here is the clever part:

1. The Production: Because the higgsinos are heavy and created in pairs, the "production" of the sterile neutrinos is guaranteed and happens frequently (like a factory churning out products), rather than being a rare accident.
2. The Decay (The Displaced Vertex): Once created, these sterile neutrinos are still "ghostly." They travel a short distance away from the collision point before they finally decay into visible particles. This creates a "displaced vertex."

The Analogy: Imagine a magician (the higgsino) appearing on stage and immediately throwing two smoke bombs (the sterile neutrinos) into the crowd. The smoke bombs float for a few seconds before popping and revealing a bright flash of light (the decay).

• Standard Search: Looking for a smoke bomb that appears randomly in the crowd and pops instantly. (Hard to see).
• This Search: Looking for the specific pattern of two smoke bombs floating a few feet away from the magician before popping. (Much easier to spot because you know exactly where to look and what the pattern is).

What Did They Do?

The authors took data from the ATLAS detector at the LHC (specifically from 2015–2018, known as "Run 2"). They used a "model-independent" tool provided by the ATLAS team. Think of this tool as a pre-made net with specific hole sizes.

Instead of simulating the entire detector from scratch (which is like building your own camera), they took their theoretical "ghosts" and ran them through ATLAS's existing net to see how many would get caught. They looked for events where:

• There were multiple jets of particles (the debris from the higgsino decay).
• There was a "displaced vertex" (the smoke bomb popping away from the center).

The Results: What Can We Rule Out?

By running their numbers through this net, they found:

1. Run 2 Constraints (Past Data): They can now say with 95% confidence that if these specific sterile neutrinos exist, they cannot have certain combinations of mass and "ghostliness" (mixing).

   • If the neutrino is light (around 20 GeV), it must be extremely "ghostly" (very weak mixing) to have escaped detection so far.
   • If it is heavier (up to 230 GeV), the range of "ghostliness" they can rule out is quite broad.
   • Essentially, they have closed the door on a large chunk of the "middle ground" where these particles might have been hiding.

2. Future Reach (Run 3 and HL-LHC): They projected what will happen when the LHC runs with more energy and more data (Run 3 and the High-Luminosity LHC).

   • Run 3: Will be able to find these particles up to masses of about 250 GeV and detect even "ghostlier" versions (mixing as low as $4 \times 10^{-14}$).
   • HL-LHC (The Future): With massive amounts of data, they could potentially find these particles up to 295 GeV and detect incredibly faint signals (mixing down to $3 \times 10^{-14}$).

Why Is This Important?

In the "standard" way of looking for these particles, the LHC is limited. It can only find them if they are relatively heavy and interact strongly enough to be seen, or if they are very light. The "naive" theory suggests they should be so weakly interacting that the LHC would never see them.

However, this paper shows that if these particles are produced via the "heavy package" method (higgsino decay), the LHC can actually see them even if they are extremely "ghostly." This opens up a whole new hunting ground that was previously thought to be invisible.

Generalizing the Idea

Finally, the authors asked: "Does this only work for this specific supersymmetric model?"
They concluded that the method works for any model where:

1. A heavy particle is produced in pairs.
2. That heavy particle decays into a sterile neutrino and a standard particle (like a W or Z boson).
3. The sterile neutrino travels a bit before decaying.

If the heavy particles are produced frequently enough (like the higgsinos in their model), the LHC can find the sterile neutrinos. If the heavy particles are very rare to produce, the search becomes much harder, but the logic remains the same.

Summary

The paper is a roadmap for catching elusive "ghost" particles. It shows that by looking for a specific "double-ghost" signature where the ghosts travel a short distance before popping, the LHC can rule out or potentially discover heavy neutral leptons that were previously thought to be undetectable. It turns a needle-in-a-haystack problem into a search for a specific, floating smoke bomb.

Technical Summary

Technical Summary: Probing Electroweak Pair Production of Heavy Neutral Leptons with Displaced Vertices at the LHC

Problem Statement
Heavy neutral leptons (HNLs), or sterile neutrinos, are a generic feature of neutrino mass generation models, such as the type-I seesaw mechanism. In standard scenarios, HNLs are produced via their mixing with active Standard Model (SM) neutrinos (e.g., $pp \to W^\pm \to \ell^\pm N$). This production mechanism is suppressed by the active-sterile mixing angle $|V_{N\alpha}|^2$, which is typically tiny ($\sim m_\nu/m_N$). Consequently, standard searches at the LHC are limited in sensitivity, particularly for masses above the electroweak scale or for mixing angles consistent with the naive seesaw formula. While displaced vertex (DV) searches offer a pathway to probe smaller mixings due to low SM backgrounds, existing projections suggest the High-Luminosity LHC (HL-LHC) will only reach $m_N \lesssim 40$ GeV and $|V_{N\alpha}|^2 \gtrsim 5 \times 10^{-10}$, leaving a significant portion of the parameter space unexplored.

This paper investigates an alternative production scenario where the sterile neutrino is not produced directly via mixing, but rather as a decay product of heavier Beyond-the-Standard-Model (BSM) particles ($\psi$) that are pair-produced with an electroweak-size cross section ($pp \to \psi\bar{\psi} \to N + \text{SM}$). In this framework, the production rate is independent of the active-sterile mixing, allowing for the exploration of much smaller mixing angles while maintaining observable event rates.

Methodology
The authors analyze a specific supersymmetric (SUSY) model with R-parity violation, as proposed in Ref. [34]. In this model:

• The sterile neutrino $N$ is the superpartner of a pseudo-Nambu-Goldstone boson and mixes with higgsinos.
• Higgsinos ($\tilde{\chi}$) are nearly degenerate in mass and are pair-produced via electroweak interactions.
• Higgsinos decay promptly to a sterile neutrino and SM gauge bosons ($W, Z$) with $\approx 100\%$ branching fraction.
• The sterile neutrino subsequently decays into SM particles via its mixing with active neutrinos, resulting in a macroscopic decay length (displaced vertex).

To constrain this model, the authors recast the ATLAS search for displaced vertices with multiple jets (Ref. [35]) using 139 fb$^{-1}$ of Run 2 data ($\sqrt{s} = 13$ TeV).

• Simulation: Event generation was performed using MadGraph 5, with parton showering and hadronization via Pythia 8. Jet clustering was done with FastJet.
• Recasting: Instead of full detector simulation, the authors applied model-independent reconstruction efficiencies and acceptance requirements provided by ATLAS. These include event-level cuts (jet multiplicity and $p_T$ thresholds) and vertex-level cuts (decay position within the fiducial volume, transverse impact parameter, number of tracks, and invariant mass).
• Parameter Space: The study varies the higgsino mass parameter $\mu$ (500 GeV – 2 TeV), the sterile neutrino mass $m_N$ (10 – 300 GeV), and the complex mixing parameter $z$. The analysis considers two limiting cases for the active-sterile mixing: "minimal mixing" ($z=\pi/2$) and "maximal real mixing" ($z=0$), as well as intermediate values.
• Projections: Discovery reach for LHC Run 3 ($\sqrt{s}=13.6$ TeV, $L=300$ fb$^{-1}$) and the HL-LHC ($\sqrt{s}=14$ TeV, $L=3000$ fb$^{-1}$) is estimated by extrapolating the Run 2 results, assuming negligible SM background and constant reconstruction efficiencies.

Key Results

1. Run 2 Constraints: Using the ATLAS multijet DV search, the authors exclude regions of the $(m_N, \mu)$ and $(m_N, V_N^2)$ parameter spaces.

   • For $\mu \le 800$ GeV, sterile neutrino masses between 20 GeV and 230 GeV are excluded.
   • Correspondingly, active-sterile mixing values in the range $4 \times 10^{-14} \lesssim V_N^2 \lesssim 3 \times 10^{-10}$ are excluded, depending on $m_N$.
   • The exclusion limits are driven by the "Trackless jet" signal region for lower $\mu$ and the "High-$p_T$" region for higher $\mu$.

2. Run 3 and HL-LHC Reach:

   • Run 3: Sensitivity extends to $\mu \approx 1.35$ TeV (Trackless jet) and $\mu \approx 1.5$ TeV (High-$p_T$). The mixing reach improves to $V_N^2 \approx 4 \times 10^{-14}$ for $m_N \approx 245$ GeV.
   • HL-LHC: The discovery reach significantly expands. Sterile neutrino masses up to 295 GeV can be probed. The mixing sensitivity reaches down to $V_N^2 \approx 3 \times 10^{-14}$.
   • The authors note that for $m_N \approx 100$ GeV, higgsino masses up to $\mu \approx 2$ TeV could be accessible at the HL-LHC.

3. Generalization: The paper investigates the applicability of these results to a broader class of models where a generic heavy particle $\psi$ decays to $N + V$.

   • The discovery reach is largely insensitive to the specific production cross-section $\sigma(pp \to \psi\psi)$ as long as the cross-section is of the order of the higgsino pair production cross-section (tens of fb).
   • However, for smaller cross-sections ($\sigma \lesssim 1$ fb), the sensitivity to $V_N^2$ and $m_N$ degrades significantly.

Significance and Claims
The paper claims that the proposed production mechanism (pair production of heavy BSM particles decaying to HNLs) offers a distinct advantage over standard HNL searches. By decoupling the production cross-section from the active-sterile mixing angle, this scenario allows the LHC to probe mixing values consistent with the naive seesaw formula ($V_N^2 \sim m_\nu/m_N$) and even smaller values, which are otherwise inaccessible.

Specifically, the authors highlight that while standard DV searches at the HL-LHC are limited to $m_N \lesssim 40$ GeV and $V_N^2 \gtrsim 5 \times 10^{-10}$, their proposed scenario extends the reach to $m_N \approx 295$ GeV and $V_N^2 \approx 3 \times 10^{-14}$. This effectively covers the parameter space suggested by the inverse seesaw mechanism and other low-scale models, providing a robust target for current and future LHC searches using displaced vertex signatures. The study emphasizes the importance of using model-independent recasting tools to constrain specific BSM realizations without assuming 100% reconstruction efficiency, a common but unrealistic assumption in phenomenological studies.