Updated sensitivities to heavy neutral leptons at the LHC far detectors and SHiP

This paper updates the sensitivity projections for minimal heavy neutral leptons at LHC far detectors and SHiP by incorporating the latest experimental designs, including revised geometries, background estimates, and operational durations, into the Displaced Decay Counter tool.

The Gist

The Great Particle Hunt: A New Map for the Future

Imagine the Large Hadron Collider (LHC) at CERN as a massive, high-speed particle racetrack. Scientists smash protons together at incredible speeds, hoping to find new, exotic particles that could explain the mysteries of our universe. For years, they've been looking for "Heavy Neutral Leptons" (HNLs)—ghostly, heavy cousins of the neutrino that might hold the key to why the universe has mass.

The problem? These HNLs are shy. They don't just appear and vanish instantly. Instead, they are Long-Lived Particles (LLPs). Think of them like a ghost that doesn't disappear immediately after a crash; it wanders off, travels a long distance, and then fades away.

Because they travel far, the main detectors at the racetrack (like ATLAS and CMS) often miss them. They need special "far detectors" placed miles away from the crash site to catch these ghosts before they vanish.

This paper is essentially a major update to the "Hunt Map." The researchers, Zeren Simon Wang and Yu Zhang, have looked at the blueprints for several of these special detectors and realized that the plans have changed significantly. They recalculated how good these new designs will be at catching the ghosts.

Here is the breakdown of their findings using some everyday analogies:

1. The "Ghost" We Are Hunting

The target is the Heavy Neutral Lepton (HNL).

• The Analogy: Imagine a heavy, invisible ball rolling out of a factory. It travels a long way down a hallway before it finally stops and turns into a pile of visible trash (decay products) that we can see.
• The Goal: We want to know how small the ball can be (its mass) and how "slippery" it is (how rarely it interacts with normal matter) before we can no longer find it.

2. The Detectors: The "Net" and the "Bucket"

The paper focuses on three main types of detectors, and their designs have been tweaked:

• MATHUSLA (The Giant Net):

  • Original Plan: A massive, 200-meter-wide net hanging high above the racetrack.
  • The Update: Due to budget cuts, the net has been shrunk. First to a medium size (100m), and now to a smaller, more compact version (40m).
  • The Result: A smaller net catches fewer ghosts. The authors found that the new, smaller MATHUSLA is about 5 times less sensitive than the original giant plan. It's like trying to catch rain with a bucket instead of a tarp; you'll still catch some, but you'll miss a lot more.

• ANUBIS (The Service Shaft vs. The Ceiling):

  • Original Plan: A cylindrical tube placed in a narrow service shaft far from the crash site.
  • The Update: They moved the detector to the ceiling of the main cavern, much closer to the crash site.
  • The Result: Being closer is a double-edged sword.
    • Good: It's closer to the action, so it catches more ghosts (better "acceptance").
    • Bad: It's also closer to the noise and debris of the crash, meaning more "background noise" (false alarms).
  • The Verdict: Despite the noise, the new ceiling location is actually twice as good at finding the ghosts as the old shaft location because the proximity wins out.

• SHiP (The Beam Dump):

  • The Setup: This isn't a detector at the racetrack; it's a "beam dump" experiment. Imagine shooting a cannonball into a thick wall of lead. The wall stops the cannonball, but the ghost particles (HNLs) pass right through. We wait for them to decay in a long tunnel behind the wall.
  • The Update: The physical tunnel hasn't changed much, but the time has. They are now planning to run the experiment for 15 years instead of 5.
  • The Result: Running the experiment three times longer means they get three times more data. This makes SHiP the champion for finding these particles, especially for lighter masses. It can now find ghosts that are twice as "slippery" (harder to detect) as the old plan could.

3. The "Noise" Problem

In the past, scientists assumed these far detectors would be perfectly quiet (zero background noise).

• The Reality Check: The new ANUBIS design is closer to the main action, so it's noisier. The authors had to do the math to account for this "static." Even with the noise, the new design is still a winner, but it requires smarter filtering to ignore the false alarms.

4. The Big Picture: Who Wins?

The authors created a new "Sensitivity Map" (Figure 1 in the paper) that shows which detector is best for which type of ghost:

• For Light Ghosts: The SHiP experiment (the beam dump) is the undisputed king. Its long runtime and massive data collection make it the best at finding lighter particles.
• For Medium-Weight Ghosts: The MATHUSLA100 (the medium-sized net) is the strongest contender.
• For Heavy Ghosts: The ANUBIS-ceiling and SHiP take the lead.

Why Does This Matter?

This paper is like a GPS update for future explorers.

• Before, scientists were planning their expeditions based on old maps that said, "We'll build a giant net here."
• Now, the map says, "Actually, we're building a smaller net, and we're moving the telescope to the ceiling."
• Without this update, scientists might have overestimated their chances of success or planned their resources incorrectly.

By using the latest blueprints and realistic noise estimates, Wang and Zhang have given the physics community a clear, honest picture of what we can actually expect to find in the next decade. They've shown that while some plans got smaller (MATHUSLA), others got smarter and longer-running (SHiP and ANUBIS), and together, they still have a very good shot at finally catching these elusive "ghosts" of the universe.

Technical Summary

1. Problem Statement

The search for physics Beyond the Standard Model (BSM) has shifted focus toward Long-Lived Particles (LLPs) as heavy, promptly decaying states have not been observed. A primary candidate for LLPs is the Heavy Neutral Lepton (HNL), also known as a sterile neutrino.

While sensitivity projections for various LLP experiments (such as MATHUSLA, ANUBIS, FASER, and SHiP) have been extensively studied, several critical experimental designs have recently undergone significant revisions:

• MATHUSLA: The fiducial volume was substantially reduced due to cost constraints.
• ANUBIS: The detector location was moved from a service shaft to the cavern ceiling above the ATLAS detector, drastically altering background conditions and acceptance.
• SHiP: The projected operational duration was extended from 5 to 15 years.

Existing sensitivity studies often rely on outdated geometrical configurations or optimistic background assumptions (zero background). There is a need for a timely re-evaluation of the discovery potential for minimal HNLs using the latest experimental designs and updated background estimates.

2. Methodology

The authors employed a computational approach using the public tool Displaced Decay Counter (DDC) to simulate signal acceptances and event yields.

• Physics Model:

  • Scenario: Minimal HNL scenario where a single HNL ($N$) mixes exclusively with the electron neutrino ($\nu_e$).
  • Nature: $N$ is assumed to be a Majorana fermion.
  • Production: HNLs are produced via rare decays of charm ($D$) and bottom ($B$) mesons ($D^0, D^\pm, D_s^\pm, B^0, B^\pm, B_s$) at the LHC and SHiP.
  • Decay: HNLs decay into visible Standard Model particles via charged and neutral currents.
  • Parameters: The study scans the mass ($m_N$) range from 0.1 GeV to the $B$-meson threshold and the mixing parameter $|V_{eN}|^2$.

• Simulation & Calculation:

  • Event Generation: Used Pythia8 to simulate hard QCD $c\bar{c}$ and $b\bar{b}$ events, followed by showering and hadronization.
  • Acceptance Calculation: The DDC tool calculates the probability ($\epsilon$) of an HNL decaying within the detector's fiducial volume using the exponential decay formula:
    $$\epsilon_i = \frac{\delta\phi}{2\pi} e^{-\frac{D}{\beta_i \gamma_i c \tau_N}} \left( 1 - e^{-\frac{L}{\beta_i \gamma_i c \tau_N}} \right)$$
    Where $D$ is the distance to the detector, $L$ is the path length inside, and $\beta, \gamma$ are kinematic factors.
  • Signal Yield: Calculated by summing contributions from $D$ and $B$ meson decays, weighted by production rates, branching ratios, and acceptance.

• Background Handling:

  • Zero-Background Assumption: Applied to most experiments (FASER, CODEX-b, MATHUSLA, etc.), setting the 95% Confidence Level (C.L.) exclusion limit at 3 signal events.
  • ANUBIS Specifics: Unlike previous optimistic studies, the authors incorporated updated background estimates from Ref. [34].
    • ANUBIS-shaft: $\sim 64$ background events.
    • ANUBIS-ceiling: $\sim 195$ background events.
    • The 95% C.L. exclusion limits were adjusted to $\sim 17$ and $\sim 28$ signal events, respectively.

• Experimental Configurations Updated:

  • MATHUSLA: Compared the original 200m design, the intermediate "MATHUSLA100" ($100\times100\times25$ m), and the latest "MATHUSLA40" ($40\times40\times11$ m).
  • ANUBIS: Compared the shaft design (ANUBIS-shaft) with the new ceiling design (ANUBIS-ceiling).
  • SHiP: Updated the operational duration to 15 years ($6 \times 10^{20}$ Protons on Target).

3. Key Contributions

1. Implementation of Latest Designs: The first comprehensive study to implement the MATHUSLA40, ANUBIS-ceiling, and SHiP (15-year) configurations into the DDC framework.
2. Realistic Background Modeling: Moving beyond the "zero-background" assumption for ANUBIS by utilizing the latest, more conservative background estimates, which significantly impacts sensitivity projections.
3. Comparative Analysis: Provided a direct comparison between the sensitivity of updated vs. outdated designs, quantifying the performance loss or gain resulting from design changes.
4. Benchmarking: Established a new reference for the constraining power of LHC far detectors and SHiP on minimal HNLs mixing with electron neutrinos.

4. Key Results

The sensitivity reach is presented in the $(m_N, |V_{eN}|^2)$ plane (Figure 1):

• MATHUSLA Impact:

  • The reduction from MATHUSLA100 to MATHUSLA40 results in a factor of $\sim 5$ degradation in sensitivity to $|V_{eN}|^2$.
  • MATHUSLA40's exclusion limits are comparable to the older ANUBIS-shaft design, except at high masses ($m_N \gtrsim 2.8$ GeV) where ANUBIS-shaft performs better due to its transverse geometry.

• ANUBIS Impact:

  • ANUBIS-ceiling (closer to the Interaction Point) offers $\sim 2\times$ better sensitivity to $|V_{eN}|^2$ than ANUBIS-shaft.
  • This improvement is driven by higher acceptance rates, which outweigh the penalty of significantly higher background levels.

• SHiP Impact:

  • The extension of the operational period to 15 years (tripling the Protons on Target) improves SHiP's sensitivity to $|V_{eN}|^2$ by a factor of $\sim 2$ compared to the previous 5-year plan.
  • SHiP dominates the sensitivity for low masses ($m_N \lesssim m_D$) and in the mass window $3.8 \text{ GeV} \lesssim m_N \lesssim 5.2 \text{ GeV}$.

• Overall Landscape:

  • Low Mass ($m_N \lesssim m_D$): Dominated by SHiP, followed by MATHUSLA100 and ANUBIS-ceiling.
  • Intermediate Mass: MATHUSLA100 provides the strongest reach.
  • FASER: Due to its small volume and limited dataset (150 fb$^{-1}$), it cannot probe any currently unexcluded parameter regions.
  • Type-I Seesaw: Most experiments can probe parameter regions beyond current bounds, potentially reaching the region targeted by the Type-I seesaw mechanism for active neutrino masses ($0.05 - 0.12$ eV).

5. Significance

This paper provides a critical, up-to-date reference for the LLP community. It demonstrates that design revisions have non-trivial consequences:

• Cost vs. Sensitivity: The downsizing of MATHUSLA significantly reduces its physics reach, highlighting the trade-off between feasibility and discovery potential.
• Location Matters: The relocation of ANUBIS to the cavern ceiling, despite higher backgrounds, proves to be a superior configuration for sensitivity.
• Operational Time: The extended timeline for SHiP is a major driver for its enhanced sensitivity, emphasizing the importance of long-term data-taking plans.

The study confirms that while some experiments (like FASER) may have limited reach for minimal HNLs, the combination of updated far detectors and the SHiP beam-dump experiment offers robust coverage of the minimal HNL parameter space, particularly in the low-mass and intermediate-mass regimes. The methodology is also noted as applicable to non-minimal HNL scenarios and other LLP models.