Long-lived axionlike particles from electromagnetic cascades

This paper demonstrates that considering axionlike particle production from the full electromagnetic shower in beam dump targets, rather than just primary beams or specific meson decays, yields order-of-magnitude enhancements in detectable signals, thereby significantly expanding the sensitivity reach of the SHiP and BDX experiments to previously unexplored regions of ALP parameter space.

The Gist

The Hidden Particle Hunt: Why We Need to Look Deeper into the "Shower"

Imagine you are trying to find a specific, incredibly shy ghost in a massive, crowded stadium. This ghost is called an Axion-Like Particle (ALP). It's a theoretical particle that could explain some of the universe's biggest mysteries, but it barely interacts with anything else. It's so shy that it can pass through walls, and it only reveals itself if it decays (dies) into something we can see, like a flash of light.

For years, scientists have been building "beam dump" experiments to catch these ghosts. The idea is simple:

1. The Cannon: You fire a high-speed beam of protons or electrons (like a cannonball) at a thick block of metal (the target).
2. The Crash: The beam smashes into the metal, creating a chaotic explosion of new particles.
3. The Ghost: Occasionally, one of these new particles is an ALP.
4. The Trap: You place a giant, sensitive detector far away behind a thick wall of shielding. If an ALP is created, it might fly through the wall, travel a long distance, and then decay inside your detector, giving off a flash of light.

The Old Way vs. The New Way

Until now, most scientists calculating how many ghosts they might catch only looked at the first few seconds of the crash. They focused on the "primary" particles created immediately when the beam hit the target.

Think of it like throwing a pebble into a pond. The old method only counted the big splash right where the pebble hit. They assumed that's where all the interesting action happened.

This paper says: "Wait a minute! Look at the ripples!"

When the beam hits the target, it doesn't just make a few particles; it starts a massive electromagnetic cascade (or a "shower"). It's like throwing that pebble in, but instead of just one splash, the water starts churning, creating thousands of smaller splashes, ripples, and droplets that spread out and bounce around for a long time.

The authors, Samuel Patrone, Nikita Blinov, and Ryan Plestid, realized that if you ignore these secondary ripples (the shower), you are missing 99% of the potential ghosts.

The "Shower" Analogy

Imagine the beam dump is a giant, dense forest.

• The Old View: Scientists only looked at the trees that were hit directly by the beam. They thought, "Okay, maybe a bird (the ALP) flew out of that one tree."
• The New View: The authors realized that when the beam hits the first tree, it knocks down a branch, which hits another tree, which knocks down a whole canopy of leaves. This creates a cascade.
  • In the forest, this means thousands of new branches and leaves are flying everywhere.
  • In physics, this means thousands of new photons (light particles), electrons, and positrons are created.
  • Crucially: These "secondary" particles are lower energy, but they are everywhere. Because there are so many of them, they have a much higher chance of accidentally creating an ALP than the few high-energy particles from the initial crash.

The Two Experiments

The paper tests this idea on two specific experiments:

1. SHiP (at CERN, Europe): This uses a proton beam (like a heavy cannonball).
   • The Discovery: When the protons hit the target, they create neutral mesons (particles that decay into photons). These photons start the shower. The authors found that the "ripples" from this shower produce 10 to 10,000 times more ALPs than previously thought, especially for lighter, harder-to-find particles.
2. BDX (at Jefferson Lab, USA): This uses an electron beam (like a fast stream of water).
   • The Discovery: The electron beam creates a massive shower of electrons and positrons. The paper shows that these secondary particles are actually better at making ALPs than the original beam itself.

Why Does This Matter?

The authors updated the "sensitivity maps" for these experiments. Think of a sensitivity map as a fishing net.

• Before: They thought their net could only catch fish in a small, shallow area.
• After: By accounting for the "shower," they realized their net is actually huge and can catch fish in deep, dark waters that were previously thought impossible to reach.

The Result:

• SHiP could now detect ALPs with much weaker interactions (shyer ghosts) than anyone thought possible.
• BDX could explore a completely new region of physics that was previously uncharted.

The "Infrared" Secret

Why does the shower help so much? It comes down to a concept called "infrared sensitivity."

• High-energy particles (the primary beam) are like fast cars; they zoom past quickly and don't stick around long enough to decay inside the detector.
• The shower creates slower, lower-energy particles. These are like slow-moving turtles. Because they move slower, they live longer (due to time dilation effects in relativity) and are much more likely to decay inside the detector's trap.

The Bottom Line

This paper is a wake-up call for the physics community. It says: "Stop looking just at the explosion; look at the aftermath."

By using advanced computer simulations (a tool they built called ALPETITE) to track every single particle in the electromagnetic shower, they have shown that our ability to find these hidden particles is orders of magnitude better than we thought.

It's like realizing that while you were looking for a needle in a haystack by only checking the top layer, the haystack was actually full of needles, and you just needed to look deeper into the pile. This discovery opens up a whole new world of possibilities for finding the hidden building blocks of our universe.

Technical Summary

1. Problem Statement

Axion-like particles (ALPs) are well-motivated candidates for physics beyond the Standard Model (BSM), often arising from the spontaneous breaking of global symmetries. Beam dump experiments (where high-energy proton or electron beams strike a thick target) are a primary method for searching for these feebly interacting particles.

The Core Issue:
Existing sensitivity projections for beam dump experiments (specifically SHiP at CERN and BDX at JLab) have historically focused on ALP production mechanisms occurring within the first interaction length of the target. These studies typically consider:

• Primakoff scattering of primary beam particles or real photons from immediate meson decays (e.g., $\pi^0 \to \gamma\gamma$).
• Bremsstrahlung from the primary beam.

These approaches neglect the full electromagnetic cascade (shower) that develops deep within the target. The authors argue that this omission leads to a significant underestimation of ALP production yields, particularly for long-lived particles (LLPs) where the decay length is large. The signal rate for LLPs is infrared (IR) sensitive, meaning it is dominated by lower-energy ALPs produced by the abundant soft photons and electrons in the shower, rather than the high-energy primary beam.

2. Methodology

The authors developed a comprehensive framework to simulate ALP production throughout the entire electromagnetic shower, rather than just the initial interaction.

• Simulation Tool (ALPETITE): They extended the public code PETITE (originally designed for dark photon searches) into a dedicated tool called ALPETITE.

  • Hybrid Approach: The tool combines the computational efficiency of re-weighting simulated Standard Model (SM) shower events with the completeness of dedicated Monte Carlo (MC) samplers for processes unique to axions.
  • Input: It takes SM particle shower information (photons, electrons, positrons) generated by PETITE as direct input.
  • Re-weighting: For processes with analogues in dark photon physics (e.g., bremsstrahlung), it re-weights the dark photon events. For axion-specific processes (e.g., Primakoff), it uses dedicated samplers.

• Production Mechanisms Modeled:
  The study incorporates four dominant electromagnetic production channels within the cascade:

  1. Primakoff Up-scattering: $\gamma Z \to a Z$ (both coherent and incoherent/inelastic scattering on nuclei).
  2. Axion Bremsstrahlung: $e^- Z \to a e^- Z$ (mediated by electron coupling).
  3. Resonant Annihilation: $e^+ e^- \to a (\gamma)$ (positrons from the shower annihilating with atomic electrons).
  4. Compton-like Scattering: $\gamma e^- \to a e^-$.

• Renormalization Group (RG) Running:
  The authors define two benchmark scenarios at the weak scale ($\mu_W = 80$ GeV):

  • $\gamma$-dominated: Coupling to photons ($c_{a\gamma\gamma}$) is non-zero; electron coupling is zero at tree level but induced via loops.
  • $e$-dominated: Coupling to electrons ($c_{aee}$) is non-zero; photon coupling is induced via loops.
    They use RG flow equations to relate couplings at the weak scale to the axion mass scale ($\mu_a = m_a$), ensuring that even "photon-only" models generate necessary electron couplings for processes like bremsstrahlung.

• Experimental Setups:

  • SHiP (CERN): 400 GeV proton beam on a Molybdenum target. Focuses on the Hidden Sector Decay Spectrometer (HSDS).
  • BDX (JLab): 10.6 GeV electron beam on an Aluminum target. Focuses on a downstream calorimeter.

3. Key Contributions

1. Inclusion of Full Electromagnetic Cascades: The paper provides the first systematic inclusion of shower-induced production for ALPs in beam dump sensitivity projections, moving beyond the "first interaction length" approximation.
2. Development of ALPETITE: A new, open-source tool that allows for the efficient calculation of ALP fluxes from electromagnetic cascades for arbitrary beam dump configurations.
3. Quantification of IR Sensitivity: The authors demonstrate that the event rate for long-lived ALPs scales with the integral of the production spectrum weighted by $m_a/\omega_a$. Since the electromagnetic cascade produces a vast number of low-energy particles, the integrated yield is orders of magnitude higher than primary-beam-only estimates.
4. Inelastic Primakoff Scattering: The study includes inelastic nuclear form factors for Primakoff scattering, showing they provide an $\mathcal{O}(1)$ enhancement, particularly at higher masses.

4. Key Results

The inclusion of electromagnetic cascades leads to order-of-magnitude enhancements in the predicted number of detectable ALP events across a wide range of masses.

• Flux Enhancement:

  • For SHiP, the electromagnetic cascade enhances the ALP flux by up to $10^3$ (photon-dominated) and $10^4$ (electron-dominated) compared to primary-only estimates at low masses ($m_a \sim 3$ MeV).
  • For BDX, the enhancement is at least $10^2$ across all masses.
  • This translates to a sensitivity improvement (in terms of coupling $1/f$) of roughly one order of magnitude.

• Dominant Channels by Scenario:

  • Photon-Dominated (SHiP): Primakoff scattering from secondary shower photons dominates. The cascade generates a massive flux of lower-energy photons that efficiently produce ALPs via Primakoff scattering.
  • Electron-Dominated (SHiP & BDX):
    • At low masses ($m_a \lesssim 100$ MeV), resonant annihilation ($e^+ e^- \to a$) and bremsstrahlung from shower electrons/positrons become the dominant production mechanisms.
    • In the electron-dominated scenario for SHiP, shower-induced channels completely dominate the sensitivity for $m_a \le 100$ MeV, extending the reach in $1/f$ by $>10\times$.
  • BDX Specifics: For BDX, photon fusion (from the primary beam) competes with bremsstrahlung. However, the shower-induced bremsstrahlung and annihilation channels provide the dominant sensitivity for lighter masses, while Primakoff from shower photons dominates at higher masses ($m_a \gtrsim 100$ MeV).

• Sensitivity Projections:

  • SHiP: The updated sensitivity curve covers significantly more parameter space than previous literature (e.g., PBC, ALPINIST), particularly at lower couplings and lighter masses.
  • BDX: The paper provides the first comprehensive sensitivity projection for BDX regarding ALPs, showing it can probe currently unexplored regions up to $m_a \sim 1$ GeV.
  • Energy Thresholds: The authors show that lowering energy thresholds (e.g., from 1 GeV to 200–300 MeV) is crucial for capturing the enhanced yield from the cascade, as the signal is dominated by softer particles.

5. Significance

• Re-evaluation of Past Experiments: The results suggest that the sensitivity of past experiments (like CHARM and NuCal) may have been underestimated because they did not fully account for shower effects, although their high energy cuts limited the impact of this enhancement.
• Design of Future Experiments: For upcoming experiments like SHiP and BDX, this work implies that lowering analysis thresholds (accepting lower energy decay products) is essential to fully exploit the electromagnetic cascade. Ignoring the shower leads to a false sense of security regarding exclusion limits or a missed opportunity for discovery.
• Hadrophobic ALPs: The study confirms that for ALPs that couple primarily to leptons or photons (and weakly to hadrons), electromagnetic cascades are not a minor correction but the dominant production mechanism. Even if gluon couplings are only slightly smaller than photon couplings, the shower enhancement can make electromagnetic production competitive with hadronic production.
• Methodological Shift: The paper establishes that accurate sensitivity projections for beam dumps require full 3D simulation of the electromagnetic cascade (including transverse dynamics and multiple scattering) rather than simple 1D approximations, a lesson previously learned for dark photon searches but often overlooked for ALPs.

In conclusion, this work fundamentally updates the expected reach of beam dump experiments for ALPs, demonstrating that electromagnetic cascades are an essential component for accurate sensitivity estimates, potentially opening up new discovery windows for long-lived particles.