Dark sector searches with high-intensity positron beams in the CERN North Area

This paper proposes utilizing high-intensity positron beams at CERN's NA62 experiment to search for dark sector particles in both visible and invisible decay channels while enabling precision measurements of Standard Model observables and the potential discovery of True Muonium.

The Gist

Imagine the CERN laboratory in Switzerland as a massive, high-speed train station. Usually, this station sends out heavy, powerful trains made of protons (the "primary" particles) to smash into targets and look for new physics.

This paper proposes a new, specialized project called NA62e+. Instead of just using the heavy proton trains, they want to build a high-speed positron (anti-electron) express line right next to the existing tracks. They plan to use the giant, sensitive detector already sitting at the station (the NA62 experiment) to catch these positrons as they crash into a target.

Here is the breakdown of their plan, using simple analogies:

1. The Goal: Hunting the "Invisible"

Physicists believe there is a "Dark Sector" of the universe—a hidden world of particles that don't interact with light or normal matter. We can't see them, but we think they exist.

• The Analogy: Imagine trying to find a ghost in a room. You can't see the ghost, but if you throw a ball (a positron) at a wall and the ball suddenly bounces back with less energy or changes direction in a weird way, you know something invisible was there.
• The Strategy: By smashing high-energy positrons into a target, they hope to create these dark particles. If the dark particles are invisible, the detector will see "missing energy." If they are visible, the detector will see them decay into normal particles (like electrons or muons) in a specific pattern.

2. Why Positrons? (The "Key" to the Lock)

Why not just use electrons or protons?

• The Analogy: Think of the dark particles as a specific type of lock. Protons are like a sledgehammer; they can break many things, but they might not fit the specific keyhole needed for these dark particles. Electrons are like a standard key. Positrons, however, are the "master key" for a specific type of lock called Resonant Annihilation.
• The Benefit: When a positron hits an electron in the target, they can annihilate each other perfectly to create a dark particle. This happens much more efficiently with positrons than with electrons, especially for particles with a specific mass (around 277 MeV). It's like hitting a bell: if you hit it with the right hammer (positron), it rings loud and clear. If you use the wrong hammer, it just makes a dull thud.

3. The Three Ways to Look for Dark Matter

The paper outlines three different "search techniques" using the NA62 detector:

• The "Missing Mass" Search (The Single Photon):

  • How it works: A positron hits an electron, creating a dark particle and a single flash of light (a photon). The detector catches the photon. Since we know exactly how much energy went in, and we see the photon, we can calculate what's "missing."
  • The Metaphor: You order a pizza for $20. You get the receipt showing the pizza cost $15. You know $5 is missing. You don't see the $5, but you know it's gone. That missing $5 is the dark particle.

• The "Missing Momentum" Search (The Recoil):

  • How it works: A positron hits a nucleus and bounces off, but it loses a chunk of its speed because it created a dark particle. The detector measures the speed of the incoming positron and the outgoing positron. If the outgoing one is slower than expected, the difference is the dark particle.
  • The Metaphor: A bowling ball rolls down a lane. If it hits a pin and slows down significantly, you know it transferred energy to that pin. If the pin is invisible, you still know it was there because the ball slowed down.

• The "Dump" Mode (The Heavy Hitter):

  • How it works: Instead of a thin target, they use a thick block of metal (like a lead wall). The positrons crash in, creating a shower of particles. If a dark particle is made, it might be long-lived and escape the block, decaying later into visible particles.
  • The Metaphor: Throwing a handful of confetti into a dense forest. Most of it gets stuck in the trees, but if a special, magical piece of confetti (the dark particle) is made, it might fly out of the forest and land in a clear field where we can see it.

4. Bonus: Solving a Mystery and Finding a New Atom

While hunting for dark matter, this experiment will also do two other cool things:

• Fixing the "Muon Mystery": There is a famous discrepancy in physics regarding the "g-2" of the muon (a heavy cousin of the electron). The math doesn't quite match the experiment. This experiment will measure how positrons turn into pions (a type of particle) with extreme precision. This data will help fix the math and solve the mystery.

  • Analogy: It's like re-measuring a famous landmark with a laser ruler to see if the old map was slightly wrong.

• Finding "True Muonium": This is a proposed atom made of a muon and an anti-muon orbiting each other. It has never been seen before.

  • Analogy: We know what a hydrogen atom looks like (proton + electron). We know what positronium looks like (electron + anti-electron). "True Muonium" is like a heavy, exotic cousin of these atoms. Finding it would be like discovering a new species of bird that scientists have only heard about in theory.

5. Why This is a Big Deal

• It's Cheap and Fast: They don't need to build a brand-new giant machine. They are using the existing NA62 detector and just tweaking the beam line to send positrons instead of protons.
• It's Powerful: They expect to send about 200 trillion positrons per year. That's a lot of "bullets" to fire at the dark sector.
• It Complements Others: While another big experiment at CERN (SHiP) is looking for dark matter using protons, NA62e+ uses positrons. This covers different types of dark matter models, ensuring that if dark matter exists, we have a better chance of finding it.

In Summary:
This paper proposes turning a particle detector into a "Dark Matter Trap" by firing a specialized beam of anti-electrons (positrons) at a target. It's a clever, cost-effective way to hunt for invisible particles, solve a 10-year-old physics mystery, and potentially discover a brand-new type of atom, all using the existing infrastructure at CERN.

Technical Summary

1. Problem Statement

Dark sector models, which propose new particles interacting feebly with the Standard Model (SM), require high-intensity beams and precision detectors for thorough exploration. While the CERN NA62 experiment has successfully constrained dark sector models using proton beam dumps and meson decays, there is a significant gap in exploring positron-on-target interactions.

• Limitations of Current Facilities: Accelerating primary positrons to hundreds of GeV is prohibitively expensive. Secondary positron beams produced from proton collisions exist but have historically been limited by low intensity and purity (high hadron contamination).
• Physics Motivation: Positron beams offer unique advantages over electron beams, including resonant annihilation ($e^+e^- \to A'$) and associated production mechanisms that are enhanced in specific mass ranges. Furthermore, positron beams are essential for probing lepto-philic dark sector models and measuring precise SM cross-sections (e.g., for the $(g-2)_\mu$ anomaly) that are difficult to access with circular colliders due to systematic uncertainties.

2. Methodology

The paper proposes the NA62e+ experiment, a new physics program utilizing the existing NA62 detector at CERN's North Area (NA) coupled with a newly developed high-intensity positron beamline.

• Beam Production Strategy:

  • Source: Utilizes the SPS 400 GeV proton beam extracted to the North Area.
  • Target: A dedicated production target (e.g., 500 mm Beryllium) similar to those used in the NA64 experiment.
  • Beamline: Leverages the existing K12 beamline (designed for 75 GeV kaons) or a modified version to deliver secondary positrons.
  • Intensity & Energy: The proposal estimates a deliverable flux of $\sim 2 \times 10^{14}$ positrons on target (e+OT) per year with energies ranging from 40 GeV to 150 GeV (optimally 75 GeV).
  • Purity: Two configurations are considered:
    1. Unseparated (Focused): High intensity ($\sim 2 \times 10^{14}$) with $\sim 30\%$ positron purity at 50 GeV, reduced to $<1\%$ hadron contamination via collimation.
    2. Separated: Lower intensity ($\sim 2 \times 10^{13}$) but higher purity, utilizing synchrotron radiation separation (effective above 120 GeV).

• Detector Configuration:

  • The NA62 detector is repurposed with its high-precision tracking (GigaTracker, Straw Tracker), calorimetry (LKr), and extensive veto systems (photon and charged particle vetos).
  • Target Modes:
    • Thin Target: Active targets (Silicon or Tungsten) for precision measurements and "bump-hunt" searches.
    • Thick Target (Dump Mode): A 35–50 cm absorber to stop the beam, searching for long-lived particles decaying downstream.

• Search Techniques:

  • Invisible Decays:
    • Missing Mass: $e^+e^- \to \gamma X$ (Mono-photon).
    • Missing Momentum: $e^+N \to e^+NX$ (Recoil positron momentum loss).
    • Missing Energy: $e^+Z \to e^+Z X$ (Total energy deposition deficit in a dump).
  • Visible Decays:
    • Bump Hunt: Resonant production $e^+e^- \to X \to \ell^+\ell^-$.
    • Displaced Vertex: Searching for long-lived particles decaying meters away from the target.
    • Dump Mode: Long-lived particles decaying after passing through an absorber.

3. Key Contributions

• Feasibility Study: Provides a concrete estimate of positron flux achievable in the CERN North Area post-LS3 (Long Shutdown 3), demonstrating that NA62e+ can operate concurrently with the Beam Dump Facility (BDF/SHiP).
• Production Mechanism Analysis: Detailed calculation of Dark Photon ($A'$) and Axion-Like Particle (ALP) production rates, highlighting the unique advantage of resonant annihilation ($e^+e^- \to A'$) and the enhancement of production rates due to the motion of atomic electrons in high-Z targets (surpassing the $\sqrt{2m_e E_{beam}}$ kinematic limit).
• Sensitivity Projections: Comprehensive sensitivity projections for both visible and invisible decay channels across a wide mass range (MeV to GeV), comparing them against existing limits from NA64, BaBar, and LHCb.
• Standard Model Precision: Proposes high-precision measurements of $e^+e^- \to \pi^+\pi^-$ and $e^+e^- \to \mu^+\mu^-$ cross-sections, crucial for resolving the $(g-2)_\mu$ anomaly and validating QED at low energies.
• True Muonium Discovery: Outlines a specific strategy to observe True Muonium ($\mu^+\mu^-$ bound state) for the first time using a multi-target lithium setup and displaced vertex reconstruction.

4. Results

• Dark Sector Sensitivity:
  • Invisible Decays: NA62e+ is projected to improve limits on Dark Photon and ALP couplings by 1–2 orders of magnitude in the 150–277 MeV mass range compared to NA64. In dump mode, it can probe masses up to 1 GeV, surpassing electron-beam limits.
  • Visible Decays: The experiment can access unexplored regions of the Dark Photon parameter space, particularly for masses near the resonant energy ($\sim 277$ MeV) and in the 100–200 MeV range using displaced vertex techniques.
  • Non-Minimal Models: The setup is sensitive to extended models, such as those involving a Dark Higgs, potentially reaching couplings ($\epsilon \alpha_D$) as low as $10^{-8}$.
• Standard Model Measurements:
  • $(g-2)_\mu$ Input: With $\sim 2 \times 10^{14}$ e+OT, NA62e+ can scan the di-pion threshold with unprecedented precision, reducing theoretical uncertainties in the hadronic vacuum polarization contribution.
  • Di-muon Cross Section: A per-mille level precision measurement of $\sigma(e^+e^- \to \mu^+\mu^-)$ is achievable, validating QED predictions and muon collider production schemes.
• True Muonium:
  • A dedicated run at 43.7 GeV (di-muon threshold) with a multi-target lithium setup could achieve a $16.8\sigma$ discovery significance in just one month, or $7.2\sigma$ in a parasitic 3-month run, with negligible background.

5. Significance

• Complementarity: NA62e+ fills a critical gap in the dark sector search landscape by utilizing positron beams, which are complementary to the proton-based SHiP experiment and electron-based NA64/LDMX. It covers lepto-philic models and specific mass-coupling regions inaccessible to other facilities.
• Technological Innovation: It demonstrates the potential of reusing existing, high-performance detectors (NA62) for new physics frontiers, offering a cost-effective path to world-leading sensitivity.
• Fundamental Physics: Beyond dark matter, the program addresses long-standing discrepancies in the Standard Model, specifically the muon anomalous magnetic moment, and aims for the first observation of True Muonium, a purely leptonic bound state.
• Future Foundation: The techniques developed (high-intensity positron beams, precision vertexing in positron environments) lay the groundwork for future experiments at the FCC-ee and other high-luminosity lepton facilities.

In conclusion, the paper establishes that a high-intensity positron beam at CERN, coupled with the NA62 detector, offers a unique and powerful opportunity to explore the dark sector with leading sensitivity while simultaneously performing critical precision tests of the Standard Model.