Long-Lived HNLs via ALP Portal at the LHC

This paper investigates the prospects for detecting long-lived heavy neutral leptons (HNLs) at the high-luminosity LHC via an axion-like particle (ALP) portal, utilizing simulations for both far detectors and ATLAS while also evaluating sensitivities from dimension-8 operators in the limit of heavy ALP masses.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle smasher. It's like a giant, high-speed collision course where scientists smash protons together to see what tiny fragments fly out. Usually, they are looking for heavy, short-lived particles that vanish instantly. But this paper is about hunting for something much sneakier: ghostly particles that don't die immediately but travel a long way before disappearing.

Here is the story of the paper, broken down into simple concepts and analogies.

1. The Mystery Guests: HNLs and ALPs

The paper focuses on two theoretical "ghosts" that might be hiding in the universe:

• HNLs (Heavy Neutral Leptons): Think of these as the "missing cousins" of the neutrino. Neutrinos are tiny, ghostly particles that pass through everything. HNLs are like their heavier, heavier-weight versions. They are so shy that they barely interact with normal matter, which is why we haven't found them yet.
• ALPs (Axion-Like Particles): Imagine these as "invisible messengers." They are light, wavy particles that could explain some of the universe's biggest mysteries (like dark matter).

2. The Secret Tunnel: The "ALP Portal"

The big question is: How do we catch these shy HNLs?
Usually, HNLs are hard to make because they don't like to interact with the proton beams. But the authors propose a clever shortcut: The ALP Portal.

• The Analogy: Imagine you want to catch a shy fish (the HNL) in a lake. It's hard to catch directly. But, imagine there is a magical worm (the ALP) that the fish loves to eat. If you throw a lot of that magical worm into the lake, the fish will swarm to eat it.
• How it works at the LHC: The LHC smashes protons together. These protons are full of gluons (the "glue" holding the proton together). The paper suggests that if we have enough ALPs, they can be created easily from these gluons. Once created, the ALP acts like a delivery truck. It drives to a spot, drops off two HNLs, and then vanishes.
• The Result: Because the ALP is so easy to make from gluons, it can produce lots of HNLs, giving us a much better chance to spot them.

3. The Long-Lived Mystery

The HNLs produced by this method are special because they are Long-Lived Particles (LLPs).

• The Analogy: Most particles created in the collider are like firecrackers—they explode instantly. These HNLs are like fireflies. They are created, but instead of vanishing immediately, they fly around for a while before dying.
• The Hunt: Because they fly for a while, they might escape the main detectors (like ATLAS) and travel into the empty space around the collider.
  • ATLAS: This is the main detector, like a giant net right next to the collision point. It catches the fireflies that don't fly very far.
  • Far Detectors (MATHUSLA, ANUBIS, CODEX-b): These are like satellite observation towers built far away from the collision point. They are waiting to catch the fireflies that managed to fly a long distance before they "blink out" (decay).

4. The Heavyweights: When the Messenger is Too Heavy

The paper also looks at a scenario where the "magical worm" (the ALP) is extremely heavy (heavier than a TeV scale).

• The Analogy: If the worm is too heavy to be created as a real particle, it's like trying to throw a bowling ball. You can't throw it, but you can still feel its "push" or "influence" from a distance.
• The Physics: In this case, the ALP disappears from the equation, and we are left with a direct "push" from the gluons to the HNLs. The paper calculates how well we can still find the HNLs using this indirect push, even without the ALP being physically present.

5. The Results: What Can We Find?

The authors ran simulations to see what the LHC could find in the future (specifically the High-Luminosity LHC, which will run for many more years).

• The Good News: This "ALP Portal" method is incredibly powerful. It could allow us to find HNLs that are much harder to catch than before. We might detect them even if they are incredibly shy (have very tiny mixing angles).
• The Reach: They found that the "Far Detectors" (like MATHUSLA and ANUBIS) are the best at catching these long-lived ghosts, especially if the HNLs travel far. However, the main ATLAS detector is still very good at catching them if they don't travel as far.
• The Scale: They calculated that this method could probe energy scales up to 300 TeV. To put that in perspective, that's like being able to see details of a coin from 300 kilometers away.

Summary

This paper is a roadmap for a new treasure hunt.

1. The Treasure: Heavy Neutral Leptons (HNLs), which could explain why the universe has more matter than antimatter.
2. The Map: Use Axion-Like Particles (ALPs) as a bridge to create them easily from the gluons in the proton beam.
3. The Strategy: Look for these particles not just in the main explosion, but in the quiet, empty spaces far away from the collision, where they might be flying before they vanish.

The authors are essentially saying: "If we look in the right places using this specific 'portal' trick, we might finally catch these elusive particles that have been hiding from us for decades."

Technical Summary

1. Problem Statement and Motivation

Heavy Neutral Leptons (HNLs) and Axion-Like Particles (ALPs) are prominent candidates for Beyond the Standard Model (BSM) physics. While HNLs are often searched for via their mixing with active neutrinos, their production cross-sections at the Large Hadron Collider (LHC) are typically suppressed by small mixing angles ($|V_{\ell N}|^2$).

The paper addresses the following gaps in existing literature:

• Production Mechanism: Previous studies (e.g., [50, 51]) focused on ALP-mediated HNL production but assumed light ALPs ($m_a \approx 2$ GeV) and prompt HNL decays.
• Mass Range: There was a lack of exploration for heavier ALPs ($m_a > 10$ GeV) and the transition to effective field theory (EFT) regimes where the ALP is too heavy to be produced on-shell.
• Long-Lived Signatures: Existing studies did not comprehensively simulate long-lived HNL decays in both main detectors (ATLAS) and proposed "far detectors" (MATHUSLA, ANUBIS, CODEX-b, MAPP).
• Direct Couplings: The potential for HNLs to couple directly to gluons via higher-dimensional operators (dimension-7 and dimension-8) without an explicit light ALP mediator needed investigation.

2. Theoretical Framework

The authors analyze two primary theoretical setups:

A. The ALP Portal Model

• Lagrangian: Includes an ALP ($a$) with couplings to gluons ($c_{G\tilde{G}a}$) and HNLs ($c_{NNa}$).
• Production: At the LHC, ALPs are produced via gluon fusion ($gg \to a$).
• Decay: The ALP decays into HNL pairs ($a \to NN$).
• Kinematic Regimes:
  1. On-shell ALP ($2m_N \le m_a \lesssim 1$ TeV): Resonant production enhances the cross-section.
  2. Off-shell ALP ($m_a \le 2m_N$): Suppressed cross-section.
  3. Heavy ALP / EFT Limit ($m_a \gtrsim 1-2$ TeV): The ALP is integrated out, resulting in an effective dimension-8 operator connecting HNL pairs directly to gluons ($G\tilde{G}NN$).

B. Direct EFT Couplings (NRSMEFT)

• Dimension-7 Operators: The authors include operators of the form $O_{d=7} \sim \frac{1}{\Lambda^3} G_{\mu\nu}G^{\mu\nu} N_R N_R$ (and the dual version). These violate lepton number by two units and allow direct HNL production from gluons.
• Dimension-8 Operators: Arise naturally when integrating out a heavy ALP in the portal model.

UV Completions

The paper discusses UV-complete models that could realize these couplings, including:

• Majoron models with color-charged fermions.
• Vector-like quarks and singlet HNLs charged under a global $U(1)$ symmetry.
• Mirror SM scenarios proposed to solve the axion quality problem, which can naturally yield TeV-scale ALPs with large gluon couplings.

3. Methodology

• Simulation Tools:
  • FeynRules: Used to generate UFO models for the Lagrangians.
  • MadGraph5_aMC@NLO: Used to calculate production cross-sections ($pp \to a^* \to NN$ and $pp \to NN$ via EFT).
  • Displaced Decay Counter (DDC): Used to simulate decays in far detectors (MATHUSLA, ANUBIS, CODEX-b, MAPP).
  • Custom Code: Used for ATLAS displaced vertex (DV) reconstruction simulations.
• Experimental Scenarios:
  • Luminosity: High-Luminosity LHC (HL-LHC) with $\mathcal{L} = 3 \text{ ab}^{-1}$ (except CODEX-b/MAPP2 at $300 \text{ fb}^{-1}$).
  • Detectors:
    • ATLAS: Focus on displaced vertices ($N \to e jj$) within the inner tracker ($4 \text{ mm} < r_{DV} < 300 \text{ mm}$).
    • Far Detectors: MATHUSLA-40 (updated dimensions $40\times40\times16 \text{ m}^3$), ANUBIS-C (ceiling installation), CODEX-b, and MAPP2.
  • Backgrounds: Assumed background-free for most far detectors, but ANUBIS-C includes a realistic background estimate ($\sim 182$ events), leading to sensitivity contours based on 28 events ($\approx 2\sigma$ above background) and 195 events.
• Parameters:
  • HNL mass ($m_N$): $10 - 1000$ GeV.
  • ALP mass ($m_a$): Scenarios at 5 GeV, 500 GeV, and 5 TeV.
  • Mixing: $|V_{eN}|^2$ scanned from $10^{-7}$ to $10^{-25}$.
  • Scale: $\Lambda = 10$ TeV (unless varied in sensitivity plots).

4. Key Results

Production Cross-Sections

• Resonance Enhancement: For $m_a \approx 2m_N$, the cross-section is enhanced by the narrow width of the ALP, reaching $\mathcal{O}(\text{nb})$ despite large $\Lambda$.
• EFT Suppression: For $m_a \gg 1$ TeV, the cross-section scales as $\sigma \propto 1/(m_a \Lambda)^4$, behaving like a dimension-8 operator.
• Direct D=7 Operators: These provide significant cross-sections even without a light ALP, though generally lower than the resonant ALP case.

Sensitivity Projections

• Mixing Reach: The ALP portal allows probing mixing angles as small as $|V_{eN}|^2 \sim 10^{-24}$, significantly below the "seesaw line" ($|V|^2 \sim m_\nu/m_N$) for many mass ranges.
• Detector Performance:
  • Far Detectors: Generally probe smaller mixings than ATLAS due to larger decay volumes and distances from the interaction point (IP).
  • ANUBIS-C: Shows the best sensitivity among far detectors, reaching $|V_{eN}|^2 \sim 10^{-23}$ even with non-zero backgrounds.
  • ATLAS: Competitive for prompt or short-lived decays and offers the best reach for the effective scale $\Lambda$ in certain regimes.
• Scale Reach ($\Lambda$):
  • For the ALP portal (light ALP), ATLAS can probe $\Lambda$ up to $\sim 300$ TeV.
  • For the dimension-7 operator, sensitivity drops to $\Lambda \sim 20-50$ TeV.
• Mass Dependence:
  • Light ALP ($m_a = 5$ GeV): Sensitive to a wide range of $m_N$.
  • Heavy ALP ($m_a = 5$ TeV): Sensitivity is restricted to large $m_N$ because the branching ratio $Br(a \to NN) \propto m_N^2$.

Impact of Design Updates

• MATHUSLA-40: The reduction in detector size (from $200^3$ to $40^3$ m) results in a sensitivity loss equivalent to roughly a factor of 20 in event counts (e.g., the 3-event line of MATHUSLA-40 matches the 60-event line of the original design).
• ANUBIS-C: Moving the detector to the ATLAS cavern ceiling (closer to the IP) increases the solid angle and sensitivity to shorter decay lengths, compensating for the background estimates.

5. Significance and Conclusions

• Unprecedented Sensitivity: The study demonstrates that the ALP portal is a highly efficient mechanism for producing long-lived HNLs, offering sensitivity to mixing parameters orders of magnitude better than standard minimal HNL searches.
• Complementarity: The combination of main detectors (ATLAS) and far detectors covers a vast parameter space in $(m_N, |V_{eN}|^2)$ and the effective scale $\Lambda$.
• EFT Validity: The work bridges the gap between explicit ALP models and EFT descriptions, showing that even for heavy ALPs, the LHC can probe the underlying new physics scale up to hundreds of TeV.
• Future Outlook: The results highlight the critical role of proposed far detectors (especially ANUBIS-C and MATHUSLA) in discovering BSM physics that is inaccessible to standard prompt searches. The authors also note that while they focused on gluon couplings, similar searches could be conducted via vector boson fusion (couplings to $W/B$ fields), albeit with lower cross-sections.

In summary, this paper provides a comprehensive roadmap for searching for long-lived HNLs at the HL-LHC, establishing that the ALP portal offers a robust and highly sensitive window into BSM physics, potentially revealing HNLs with mixing angles far below the canonical seesaw expectation.