Impact of Geant4's Electromagnetic Physics Constructors on Accuracy and Performance of Simulations for Rare Event Searches

This paper quantifies the impact of various Geant4 electromagnetic physics constructors on the accuracy of energy deposition and computational performance for rare event searches using CaWO$_4$ and Ge targets, aiming to guide the selection of optimal simulation configurations for background prediction.

The Gist

Imagine you are a detective trying to find a single, tiny whisper in a room full of people shouting. This is exactly what scientists do when they search for "rare events" in physics, like Dark Matter particles or mysterious decays that haven't been seen before. The problem? The "shouting" (background noise from natural radioactivity) is so loud that it can easily hide the whisper.

To solve this, scientists use a super-powerful computer program called Geant4. Think of Geant4 as a virtual reality simulator that builds a digital twin of their experiment. It simulates millions of radioactive particles crashing into their detectors to predict exactly what the "noise" should look like. If the real detector sees something that doesn't match the simulation, that's the whisper (the new discovery)!

The Problem: Too Many Settings

The trouble with Geant4 is that it's like a high-end camera with too many dials. For every type of particle interaction, the software offers different "physics constructors." These are essentially different rulebooks for how the computer calculates what happens when a particle hits something.

• Rulebook A might be super fast but a bit sloppy with the details.
• Rulebook B might be incredibly precise but take forever to run.
• Rulebook C might be a mix of both.

The scientists in this paper asked: "Does it matter which rulebook we use?" If we pick the wrong one, our simulation might be wrong, and we might miss the discovery or, worse, think we found something that isn't there.

The Experiment: The "Taste Test"

To find the best rulebook, the authors set up a massive "taste test" (or in this case, a "simulation test").

1. The Ingredients: They picked common radioactive "contaminants" (like tiny bits of Uranium or Lead) that often sneak into detectors.
2. The Containers: They simulated these particles hitting two different types of detector materials: Germanium (a shiny metal) and CaWO4 (a crystal used in dark matter searches).
3. The Shapes: They tested two sizes:
   • The "Bulky" Target: A thick block (like a brick). Here, almost everything gets absorbed.
   • The "Thin" Target: A wafer-thin slice (like a piece of paper). Here, particles can easily fly right through.
4. The Rulebooks: They ran the simulation 12 different times, using 12 different Geant4 "rulebooks" (physics constructors), and tweaked the settings for each one.

In total, they ran 1,440 different simulations to see which rulebook produced the most consistent results.

The Findings: Speed vs. Accuracy

Here is what they discovered, translated into everyday terms:

1. The "Thin Slice" is the Tricky One
When the target was thick (the brick), most rulebooks gave similar results. But when the target was thin (the paper), the differences became huge.

• Analogy: Imagine throwing a ball at a thick wall vs. a thin sheet of paper. With the wall, it doesn't matter much how you calculate the bounce; it stops either way. With the paper, a tiny difference in your calculation changes whether the ball goes through or bounces back.
• Result: For thin targets, you must use a precise rulebook. If you use a "fast and sloppy" one, your simulation will be wrong.

2. The "Golden Rulebook"
They found one specific rulebook called G4EmLivermorePhysics that was the clear winner.

• It was the most accurate (it matched the "gold standard" simulation almost perfectly).
• It worked well for both thick and thin targets.
• It was also reasonably fast.

3. The "Speedsters" vs. The "Slowpokes"

• The Speedsters: Some rulebooks (like Option 1 and Option 2) were designed to be super fast for huge particle colliders (like the LHC). However, for these tiny, rare-event experiments, they were too sloppy. They missed details, leading to wrong predictions.
• The Slowpokes: Some rulebooks tried to calculate every single tiny bounce of a particle (like counting every grain of sand on a beach). These were incredibly accurate but took 100 times longer to run. They were like using a sledgehammer to crack a nut.

4. The "Cut" Setting
There was also a setting called the "production cut." Think of this as the resolution of your simulation.

• High Resolution (Small cut): The computer tracks every tiny particle. Accurate, but slow.
• Low Resolution (Large cut): The computer ignores tiny particles and just guesses their energy. Fast, but risky.
• The Finding: For thin targets, you must turn the resolution up (use a small cut). If you leave it low, particles "leak" out of the simulation, and your math breaks.

The Bottom Line

If you are a scientist building a detector to find Dark Matter or rare decays:

1. Don't just pick the default settings. The "default" might be too fast and not accurate enough for your specific experiment.
2. Use the "Livermore" rulebook. It's the best balance of accuracy and speed for these types of experiments.
3. Watch your target size. If your detector is thin, you need high-precision settings, or your background predictions will be garbage.

The Takeaway: This paper is like a user manual for scientists, telling them, "Don't just guess which setting to use. Here is the one that works best so you don't waste years of your life on a simulation that gets the math wrong."

Technical Summary

1. Problem Statement

Rare event searches (e.g., Dark Matter detection, neutrinoless double beta decay) rely heavily on accurate Monte Carlo simulations to predict and subtract background noise. The Geant4 toolkit is the standard for these simulations, offering users various "physics constructors" (pre-defined sets of physics models and parameters) to handle electromagnetic (EM) interactions.

However, the choice of a specific physics constructor and its associated parameters (specifically the production cut, which determines when secondary particles are tracked vs. locally absorbed) can significantly alter the simulated total energy deposition.

• The Gap: While validation studies exist for specific interactions (e.g., electron backscattering), there was no comprehensive study quantifying how different EM physics constructors affect the total energy deposition in the specific context of rare event search targets (CaWO$_4$ and Ge) across varying geometries (thin vs. bulky).
• The Risk: Extrapolating results from one use case (e.g., thin targets) to another (e.g., thick targets) is precarious. An inaccurate constructor choice introduces systematic uncertainties in background prediction, potentially masking rare signals or creating false positives.

2. Methodology

The authors conducted a systematic study using Geant4 version 10.6.3 to evaluate the compatibility of different physics configurations against a reference standard.

A. Test Cases

The study simulated 24 distinct test cases defined by:

• Target Materials: Calcium Tungstate (CaWO$_4$) and Germanium (Ge).
• Geometries:
  • Bulky: 64 mm thickness (representing absorber crystals).
  • Thin: 100 $\mu$m thickness (representing bond wires).
• Radioactive Contaminants: Six common nuclides covering $\alpha$, $\beta$, and $\gamma$ decays with varying Q-values:
  • Low Q-value $\beta$: $^{228}$Ra, $^{210}$Pb.
  • High Q-value $\beta$: $^{208}$Tl, $^{210}$Tl.
  • $\alpha$ emitters: $^{211}$Bi, $^{234}$U.

B. Physics Configurations

The study evaluated 60 unique physics configurations formed by:

• 12 Electromagnetic Physics Constructors: Including standard options (1–4), Livermore, Penelope, LowEP, and specialized scattering models (SS, WVI, GS).
• 5 Production Cut Values: 100 nm, 1 $\mu$m, 1 mm, 1 cm, and 10 cm.
• Reference Configuration ($\pi_{ref}$): G4EmStandardPhysics option4 with a 1 mm production cut (regarded as the most accurate standard).

C. Statistical Analysis

To determine compatibility, the authors employed a two-stage statistical approach comparing simulated energy spectra:

1. Goodness-of-Fit (GoF) Tests: Three independent tests were used to compare test spectra against the reference spectrum:
   • Kolmogorov-Smirnov (KS)
   • $\chi^2$ test
   • Anderson-Darling (AD)
   • Metric: Efficiency ($\xi$) defined as the fraction of test cases where the null hypothesis (spectra are compatible) was accepted ($p > 0.05$).
2. Categorical Tests: To determine if differences between configurations were statistically significant:
   • McNemar's test for paired data (same constructor, different cuts).
   • Pearson's $\chi^2$ and Fisher's exact tests for unpaired data (different constructors).

D. Performance Metrics

Computing performance was measured via CPU time on two clusters (MPCDF and CLIP), normalized against the reference configuration.

3. Key Contributions

• Systematic Quantification: First dedicated study quantifying the systematic uncertainty introduced by the choice of EM physics constructors specifically for total energy deposition in CaWO$_4$ and Ge targets.
• Methodological Framework: Established a robust, multi-test statistical framework (using KS, $\chi^2$, and AD) to objectively assess simulation compatibility, avoiding biases inherent in single-test approaches.
• Performance-Accuracy Trade-off Analysis: Provided data on the computational cost of high-precision models versus simplified ones, specifically for low-energy radioactive backgrounds.
• Guidance for Experimentalists: Offered concrete recommendations for selecting physics constructors to minimize systematic errors in rare event searches.

4. Key Results

A. Compatibility and Efficiency

• Best Performer: G4EmLivermorePhysics achieved the highest efficiency (100% compatibility in $\chi^2$ tests) across all test cases and production cuts.
• Worst Performers: G4EmStandardPhysics option1 and option2 showed the poorest compatibility (efficiencies $\le$ 67%). These are optimized for high-energy physics (LHC) and large volumes, making them unsuitable for the small volumes and low energies of rare event searches.
• Reference Consistency: The reference constructor (option4) showed strong dependence on the production cut value, whereas G4EmLivermore remained stable across different cut values.

B. Impact of Geometry and Cuts

• Thin vs. Bulky: Simulations for thin targets (100 $\mu$m) were significantly more sensitive to the choice of physics constructor and production cut than bulky targets. In thin targets, leakage of decay products makes the simulation highly dependent on the precise modeling of individual particle interactions.
• Production Cut:
  • Generally, lower production cuts (e.g., 100 nm) improved compatibility, especially for thin targets.
  • However, a smaller cut does not always guarantee better results; in some cases, a cut larger than the target thickness still yielded compatible spectra.
  • G4EmStandardPhysics option1 was uniquely sensitive to production cut changes because it applies the cut to all EM interactions, unlike others that apply it only to ionization/bremsstrahlung.

C. Computing Performance

• Scattering Models: The choice of Coulomb scattering model had the most drastic impact on speed.
  • Single-scattering/Hybrid models (e.g., G4EmStandardSS, G4EmStandardWVI) were ~100 times slower than multiple-scattering models.
  • Multiple-scattering models showed performance variations within the noise of the hardware uncertainty.
• Production Cut: Performance remained stable for cuts $\ge$ 1 $\mu$m but degraded by a factor of ~10 when the cut dropped below 1 $\mu$m.
• Optimal Choice: G4EmLivermore offered the best balance, providing high accuracy with reasonable computational cost (similar to standard multiple-scattering models).

5. Significance and Conclusion

The paper concludes that the choice of physics constructor is a critical source of systematic uncertainty in rare event background simulations.

• Recommendation: For experiments using CaWO$_4$ or Ge targets, G4EmLivermorePhysics is recommended as the optimal choice, offering the highest statistical compatibility with the reference standard and robust performance across different production cuts.
• Avoidance: Constructors designed for high-energy physics (e.g., option1, option2) should be avoided for low-energy, small-volume rare event searches.
• Future Workflow: Since G4EmLivermore, G4EmPenelope, G4EmStandardPhysics option4, and G4EmWenzelWVI (excluding the slow WVI) form a set of statistically compatible configurations, future experimental validation efforts need only verify one of these to establish the accuracy of the entire set, significantly reducing the validation burden.

This work provides a vital roadmap for the low-background physics community to optimize their Geant4 simulations, ensuring that background predictions are as reliable as possible for the detection of new physics.