Searching for ALP Lepton Flavor Violation via ALP Decays at the LHC

This paper investigates the potential for detecting lepton flavor-violating axion-like particle (ALP) decays into electron-muon pairs at the LHC via gluon fusion production, demonstrating significantly improved sensitivity limits for ALP masses between 5 and 1000 GeV where Standard Model backgrounds are suppressed.

The Gist

Imagine the universe is a giant, high-stakes puzzle. For decades, physicists have been trying to solve it using a rulebook called the Standard Model. This rulebook explains almost everything we see: why apples fall, how stars shine, and what holds atoms together. But there's a problem. The rulebook has some missing pages. It can't explain things like "Dark Matter" (the invisible glue holding galaxies together) or why the universe has more matter than antimatter.

Enter the Axion (or ALP, Axion-Like Particle). Think of the Axion as a "ghost particle" that physicists suspect exists to fill in those missing pages. It's a hypothetical particle that is incredibly light, very shy, and interacts weakly with normal matter.

This paper is like a detective story where the authors (a team from Dalian University of Technology) are trying to catch this ghost particle at the Large Hadron Collider (LHC), the world's biggest particle smasher in Switzerland.

Here is the story of their hunt, broken down simply:

1. The Crime Scene: The LHC

The LHC smashes protons together at nearly the speed of light. It's like firing two handfuls of marbles at each other so hard that they shatter into a billion tiny pieces. Usually, these pieces follow the Standard Model rules. But the physicists are hoping that sometimes, a "ghost" (the Axion) pops out of the wreckage.

2. The Suspect's Signature: Lepton Flavor Violation

In the Standard Model, particles have "flavors," like different types of ice cream. An electron is "chocolate," and a muon is "vanilla." The rulebook says chocolate never turns into vanilla. They are separate families.

However, the Axion is a rebel. If it exists, it might have a special power: Lepton Flavor Violation (LFV). This means the Axion could act like a magical chameleon, turning a "chocolate" electron into a "vanilla" muon (or vice versa) instantly.

The Plan: The team wants to look for a very specific event:

1. Two protons smash together.
2. They create a ghostly Axion.
3. The Axion immediately decays (dies) into one electron and one muon that shouldn't be together.

Finding an electron and a muon born from the same parent particle would be like finding a chocolate chip cookie that suddenly turned into a vanilla cupcake in mid-air. It would be undeniable proof of new physics.

3. The Strategy: How to Catch the Ghost

The Axion is hard to catch because it's so quiet. The team had to figure out the best way to make it appear and how to spot it.

• Making the Ghost: They realized the best way to create an Axion is by smashing gluons (the particles that hold quarks together) together. It's like using a specific type of hammer to knock a specific nail out of a wall. This method produces the most Axions.
• The Filter: The LHC is a noisy place. Every second, billions of "normal" events happen that look similar to what they want. It's like trying to hear a whisper in a rock concert.
  • The Noise: The main background noise comes from "Top Quarks" and "W Bosons" decaying into electrons and muons.
  • The Filter: The team used a computer simulation to set up "security checkpoints." They looked for two specific clues:
    1. Missing Energy: The Axion might leave behind a specific amount of "missing" energy (like a thief leaving a hole in the wall).
    2. The Mass Match: The electron and muon should have a combined weight (mass) that matches the Axion exactly. It's like finding two puzzle pieces that fit together perfectly to form a picture of a specific size, while all the other pieces in the room are random shapes.

4. The Results: A New Map

The team ran their simulation for two scenarios:

• Now: The current power of the LHC.
• Future: The "High-Luminosity" upgrade (a super-charged version of the LHC coming soon).

What they found:

• The Sweet Spot: They found that if the Axion exists and weighs between 5 and 1000 GeV (a specific range of heaviness), their method is incredibly good at finding it.
• Better than Before: Their method is much more sensitive than previous searches for lighter Axions (below 100 GeV) and covers a wider range than other studies.
• The Heavy Limit: If the Axion is very heavy (over 350 GeV), it gets harder to find because it starts decaying into other heavy particles (like top quarks) instead of the electron-muon pair. But for the "middle-weight" range, they have set the tightest rules yet.

The Big Picture Analogy

Imagine you are looking for a specific type of rare bird (the Axion) in a massive forest (the LHC).

• Other scientists have been looking for this bird by listening for its song, but the forest is too noisy.
• This team realized that if you shake a specific type of tree (gluon fusion), this bird is forced to fly out.
• They also realized this bird has a unique feather pattern: it always drops a red feather (electron) and a blue feather (muon) together.
• By setting up cameras that only record when a red and blue feather fall together in a specific spot, they can ignore all the other birds and leaves in the forest.

Conclusion

This paper doesn't say, "We found the Axion." Instead, it says, "We have built the best possible net to catch this Axion if it exists in this specific weight range."

If the Axion is out there, hiding in the 5–1000 GeV range, this study shows that the LHC (especially the future upgraded version) has a very high chance of catching it. If they don't find it, they will have proven that the Axion isn't hiding in that range, forcing physicists to look elsewhere. Either way, it's a win for science!

Technical Summary

Here is a detailed technical summary of the paper "Searching for ALP Lepton Flavor Violation via ALP Decays at the LHC" by Zheng et al.

1. Problem Statement

The Standard Model (SM) strictly conserves lepton flavor, meaning processes where an electron transforms into a muon (or vice versa) without neutrino involvement are forbidden. However, many Beyond Standard Model (BSM) theories, including those involving Axion-Like Particles (ALPs), predict Lepton Flavor Violation (LFV).

The authors aim to search for LFV signatures mediated by ALPs at the Large Hadron Collider (LHC). Specifically, they investigate the production of an ALP ($a$) via gluon fusion ($pp \to a$) followed by its decay into a mixed-flavor lepton pair ($a \to e^\pm \mu^\mp$). The challenge lies in distinguishing this rare signal from significant Standard Model backgrounds (such as $t\bar{t}$ and $WW$ production) and setting competitive exclusion limits on the ALP coupling strength across a wide mass range ($5 \text{ GeV} < m_a < 1000 \text{ GeV}$).

2. Methodology

Theoretical Framework

• Model: The study utilizes an effective Lagrangian describing ALP interactions. Key components include:
  • Gluon Coupling: $L_g \propto a G\tilde{G}$, enabling production via gluon-gluon fusion.
  • LFV Coupling: $L_{e\mu} = \frac{\partial_\mu a}{f_a} \bar{e}\gamma^\mu (C^V_{e\mu} + C^A_{e\mu}\gamma^5)\mu$, describing the decay into electron-muon pairs.
  • Parameters: The ALP mass ($m_a$) and the decay constant ($f_a$) are treated as free parameters. The authors assume $g^V_{e\mu} = g^A_{e\mu}$ to simplify the parameter space.
• Production Mechanism: The authors compare three production channels:
  1. Quark fusion ($q\bar{q} \to a$).
  2. Vector boson fusion/associated production ($pp \to Z/W + a$).
  3. Gluon fusion ($gg \to a$).
  • Decision: Gluon fusion is selected as the dominant channel due to its significantly larger cross-section (scaling as $m_a^3$) and cleaner background environment compared to quark fusion.

Simulation and Analysis Strategy

• Event Generation:
  • Signal: Generated using MadGraph5_aMC@NLO with a custom UFO model file derived from FeynRules.
  • Backgrounds: Six major SM background processes were simulated:
    1. $t\bar{t}$ (dileptonic decay).
    2. $tW$ (single top + W).
    3. $tW + \text{jet}$.
    4. $W^+W^-$ (dileptonic).
    5. $W^+W^- + \text{jet}$.
    6. $WZ$ (where one lepton is missed/misidentified).
• Detector Simulation:
  • Parton showers were handled by Pythia 8.
  • Detector effects (resolution, efficiency) were simulated using Delphes 3 with a standard LHC configuration card.
• Kinematic Selection:
  • Missing Transverse Energy ($E_T^{miss}$): A strict cut of $E_T^{miss} < 20 \text{ GeV}$ was applied. Since signal events ($a \to e\mu$) do not involve neutrinos (unlike $W/Z$ decays in backgrounds), this effectively suppresses backgrounds with genuine missing energy.
  • Invariant Mass ($m_{e\mu}$): A mass window cut ($320 \text{ GeV} < m_{e\mu} < 360 \text{ GeV}$for the benchmark$m_a=350 \text{ GeV}$) was applied to isolate the resonant peak of the ALP decay from the smooth continuum of SM backgrounds.
• Luminosity Scenarios: Analysis was performed for:
  • Low Luminosity (Run 3): $L = 300 \text{ fb}^{-1}$.
  • High Luminosity (HL-LHC): $L = 3000 \text{ fb}^{-1}$.

3. Key Contributions

• Comprehensive Mass Range: The study covers a broad ALP mass spectrum from 5 GeV to 1000 GeV, a range where previous studies often had gaps or limited sensitivity.
• Optimized Background Suppression: By leveraging the unique kinematic features of the $gg \to a \to e\mu$ process (specifically the lack of neutrinos and the resonant mass peak), the authors developed a selection strategy that drastically reduces SM backgrounds while maintaining high signal efficiency.
• Complementarity: The work explicitly demonstrates how LHC constraints complement existing low-energy constraints (e.g., Muonium-Antimuonium conversion) and other collider searches (e.g., $\mu$TRISTAN), filling the "mass window" gap.

4. Results

• Sensitivity Limits: The authors derived exclusion limits on the LFV coupling coefficient ($g_{e\mu}$) for both luminosity scenarios.
  • **Low Mass Region ($5 - 100 \text{ GeV}$):** The analysis yields significantly tighter constraints than previous studies at$\sqrt{s} = 110 \text{ GeV}$.
  • **Intermediate Mass ($110 - 300 \text{ GeV}$):** The study provides stronger limits than previous$\sqrt{s} = 346 \text{ GeV}$ studies, extending the reach up to 300 GeV.
  • High Mass Region ($350 - 1000 \text{ GeV}$): Sensitivity decreases in this region. This is attributed to two factors:
    1. The opening of the $a \to t\bar{t}$ decay channel, which competes with and suppresses the $a \to e\mu$ branching ratio.
    2. Reduced production cross-sections at higher masses.
• Event Yields: Table 2 in the paper details the surviving event counts. For example, at $m_a = 350 \text{ GeV}$ and $L=3000 \text{ fb}^{-1}$, the background is reduced to negligible levels (mostly 0 events after cuts) while retaining a significant number of signal events, allowing for a $Z \approx 2$ (95% CL) exclusion.
• Comparison: Figure 3 shows that the derived limits (green and purple curves) surpass existing experimental constraints (blue shaded region) and previous collider limits (red/orange lines) in the 5–300 GeV range.

5. Significance

This research establishes the LHC as a powerful probe for ALP-mediated Lepton Flavor Violation.

• New Physics Potential: It demonstrates that the clean signature of $e\mu$ final states from gluon-fusion-produced ALPs is a viable channel for discovering new physics, provided the coupling is within the projected sensitivity.
• Guidance for Future Experiments: The results provide critical benchmarks for the High-Luminosity LHC (HL-LHC) program, suggesting that with $3000 \text{ fb}^{-1}$, the LHC can probe ALP couplings down to the$10^{-5}$ level in the 5–300 GeV mass range.
• Theoretical Consistency: The work bridges the gap between low-energy precision experiments and high-energy collider searches, offering a unified view of ALP phenomenology across different energy scales.

In conclusion, the paper confirms that the $pp \to a \to e^\pm \mu^\mp$ channel is a highly sensitive probe for LFV ALPs, offering improved exclusion limits over a wide mass range compared to existing literature, particularly in the 5–300 GeV window.