Detector performance at SHiP for cascade-produced long-lived particles

This paper evaluates the impact of cascade production on long-lived particle detection at the SHiP experiment, finding that while such processes can enhance event rates for light axion-like particles, the resulting soft kinematics and daughter-level acceptance constraints generally suppress the observable signal for both axion-like particles and heavy neutral leptons, rendering the cascade contribution subdominant except in specific low-mass scenarios.

The Gist

Imagine the SHiP experiment as a giant, high-speed particle factory. A beam of protons (like a stream of tiny, fast bullets) smashes into a thick, heavy wall made of tungsten. This wall is the "target."

Usually, scientists expect to find new, mysterious particles (called Long-Lived Particles or LLPs) right where the first bullet hits the wall. They imagine these particles popping out immediately and flying straight down a long, empty hallway (the decay volume) to be caught by a giant camera at the end.

However, this paper asks a different question: What happens when the bullets don't just hit once, but keep bouncing around inside the wall, creating a chaotic cascade of secondary sparks?

The "Cascading" Effect

Think of the target wall like a dense forest.

• Primary Production: A bullet hits a tree, and a bird (an LLP) flies out immediately. This bird is strong, fast, and flies in a straight line toward the camera.
• Cascade Production: The bullet hits a tree, which hits another tree, which hits a third. Eventually, a bird flies out from deep inside the forest. This bird is weaker, slower, and tired. It doesn't fly straight; it flutters and wanders.

The paper's authors wanted to know: Does this "cascade" of weak, wandering birds actually help us find more new particles, or do they just get lost?

The Two Main Characters

The study looked at two specific types of "birds" (particles) that might be created this way:

1. ALPs (Axion-Like Particles): These are like invisible ghosts that turn into pairs of light (photons). They are often created when the chaotic sparks inside the wall (electromagnetic cascades) interact.
2. HNLs (Heavy Neutral Leptons): These are heavy, invisible cousins of neutrinos. They are often created when secondary particles (like Kaons) decay inside the wall.

The Problem: The "Filter" at the End

The experiment has a very strict set of rules (a "filter") to catch these birds. To count as a successful discovery, the bird must:

1. Fly into the long hallway.
2. Hit the giant camera at the end.
3. The camera must be able to clearly see both pieces of the bird (if it splits into two) and measure exactly where it came from.

Here is the catch: Because the "cascade" birds are weak and slow, they tend to:

• Fly at weird angles: They might hit the side of the hallway instead of the camera.
• Split too wide: If a particle splits into two, the weak ones fly apart so much that the camera sees them as two separate, unrelated events instead of one pair.
• Be too dim: The camera struggles to see the faint, low-energy light from these tired birds.

What the Study Found

The authors ran complex simulations to see how many of these "cascade" birds actually make it through the filter.

1. For the "Ghost" Particles (ALPs):

• Before the filter: There are way more cascade ghosts than primary ones. In fact, for light particles, the cascade could produce 50 times more candidates!
• After the filter: Most of these weak ghosts get lost. They fly off-course or are too dim to be seen.
• The Result: For the lightest particles, the cascade still gives a small boost (maybe 20-30% more events), but for heavier particles, the cascade contribution almost disappears. The "primary" birds are still the main source of discoveries.

2. For the "Heavy" Particles (HNLs):

• Before the filter: The cascade creates a decent number of these particles.
• After the filter: The filter is very strict. Because these particles come from a chaotic mix of secondary decays, they fly in all directions. By the time you apply the rule that they must hit the camera, almost all the cascade HNLs are thrown out.
• The Result: The cascade contribution becomes negligible. The experiment relies almost entirely on the primary production for these particles.

Can We Fix It?

The paper suggests that if the scientists could tweak their "filter," they might catch more of these weak cascade birds.

• Relax the rules: If they allow particles to fly at slightly wider angles or be slightly dimmer, they could catch more.
• Add new sensors: They suggest putting smaller, more sensitive detectors closer to the wall (the target) to catch the birds before they wander off.

The Bottom Line

The paper concludes that while the "cascade" inside the target wall creates a huge number of potential new particles, the current design of the SHI experiment is too strict to catch most of them.

For the lightest particles, the cascade helps a little bit. For the heavier ones, it doesn't help at all. To truly benefit from these cascade events, the experiment would need to be redesigned to be more forgiving of "tired" and "wandering" particles.

In short: The factory makes a lot of extra products in the back room, but the current shipping department (the detector) is too picky to let them out. If they loosen their standards, they might find more treasures.

Technical Summary

Technical Summary: Detector Performance at SHiP for Cascade-Produced Long-Lived Particles

Problem Statement
The SHiP (Search for Hidden Particles) experiment at the CERN SPS is designed to search for GeV-scale long-lived particles (LLPs) via displaced decays. Previous sensitivity studies have largely assumed that LLPs are produced predominantly in the first interaction of the proton beam with the target (primary production). However, recent works have demonstrated that secondary interactions within the thick target generate a significant flux of "cascade-produced" LLPs. While this cascade production can substantially enhance the total number of LLPs—particularly for light masses where the decay probability scales as $1/\gamma$—these secondary particles are typically much softer (lower energy) and more isotropic than primary ones. The central problem addressed by this paper is whether the decay products of these soft, cascade-induced LLPs can survive the geometric acceptance of the downstream detector and be reconstructed with sufficient efficiency to yield an observable signal, or if detector-level effects suppress this potential enhancement.

Methodology
The authors employ a two-step approach to quantify the suppression of cascade signals:

1. Semi-Analytic Event-Rate Calculation: Using the SensCalc tool, the authors calculate the differential fluxes of LLPs produced via primary and cascade mechanisms. They model the production of Axion-Like Particles (ALPs) from electromagnetic cascades (via Primakov scattering and photon fusion) and Heavy Neutral Leptons (HNLs) from the decays of secondary kaons. They apply semi-analytic geometric acceptance cuts at the "daughter level," requiring visible decay products to reach the downstream detector apertures (ECAL for photons, HCAL for hadrons) and satisfying baseline kinematic requirements (momentum $>1$ GeV, vertex compatibility, and impact parameter constraints).
2. Detector-Level Simulation: For the specific case of ALPs decaying into two photons ($a \to \gamma\gamma$), the authors perform a full detector-level simulation using a custom GEANT4 framework. This simulation models the SHiP electromagnetic calorimeter (ECAL) response, including scintillation light collection, SiPM readout, and clustering algorithms. They reconstruct event vertices, invariant masses, and impact parameters to determine the reconstruction efficiency for low-energy cascade events compared to primary events.

Key Contributions

• Quantification of Daughter-Level Suppression: The paper explicitly separates the enhancement of LLP production from the suppression caused by detector acceptance. It demonstrates that the requirement for decay products to remain within the detector aperture (geometric acceptance) is a dominant suppression factor for soft cascade particles due to their large opening angles.
• Reconstruction Efficiency Analysis: By comparing semi-analytic truth-level cuts with full detector simulations, the authors show that low-energy photons suffer from degraded angular resolution and clustering efficiency, further reducing the observable event rate.
• Scenario-Specific Results: The study provides distinct conclusions for two representative scenarios:
  • Photophilic ALPs: Produced in electromagnetic cascades.
  • Heavy Neutral Leptons (HNLs): Produced in decays of secondary kaons.

Results

• ALPs (Photophilic):
  • Before detector effects, cascade production can dominate the flux for light ALPs ($m_a \lesssim 1$ GeV), with event rates potentially 50 times higher than primary production.
  • Imposing geometric acceptance (requiring both photons to hit the ECAL) reduces this cascade-to-primary ratio by a factor of $\sim 4$.
  • Applying baseline selection criteria (energy thresholds, vertexing, impact parameter) and full detector reconstruction further suppresses the signal. For light ALPs ($m_a \approx 50$ MeV), the cascade-to-primary ratio drops from $\sim 70$ (production only) to $\sim 3$ (fully reconstructed).
  • The cascade contribution remains a "moderate enhancement" only for the lightest masses; at higher masses, it becomes subdominant.
• HNLs (from Secondary Kaons):
  • Secondary kaons have broad angular distributions. Consequently, the HNLs produced from their decays inherit this isotropy.
  • The geometric acceptance requirement alone (daughter-level) is sufficient to render the cascade contribution subdominant compared to primary HNL production from charm/beauty meson decays.
  • Given this strong geometric suppression and the complexity of reconstructing charged decay products at low momenta, the authors conclude that a dedicated detector-level study for HNLs is not currently warranted, as the signal is already negligible after geometric cuts.

Significance and Claims
The paper claims that reliable sensitivity estimates for cascade-induced LLP signals at SHiP must include detector effects up to the reconstruction level, as simple production-rate calculations significantly overestimate the observable yield.

• For ALPs: The cascade enhancement is real but heavily mitigated by detector constraints. The authors suggest that the sensitivity to low-energy two-photon signals could be improved by relaxing event-selection criteria (specifically the impact parameter cut, which disproportionately affects cascade events) or by utilizing active subdetectors within the decay volume (e.g., the Surrounding Background Tagger or a potential LAr-based setup) to recover events where decay products fail to reach the main downstream calorimeters.
• For HNLs: The study concludes that the cascade contribution from secondary kaons is likely negligible for the nominal SHiP design once geometric acceptance is imposed.

The authors emphasize that while SHiP is currently in the Technical Design Report (TDR) phase, these findings offer a concrete opportunity to optimize the detector geometry and reconstruction strategies to recover a portion of the cascade-induced event rate, particularly for light ALPs.