🔬 applied physics

Exploring the limits of high-energy proton-pion separation in granular calorimeters

This study demonstrates that Deep Sets models applied to Geant4 simulations of a highly granular lead-tungstate calorimeter can effectively distinguish protons from charged pions across a 10–100 GeV energy range, with performance heavily dependent on detector segmentation and enhanced by the combined use of shower topology, energy deposition, and timing information.

Original authors: Andrea De Vita, Abhishek, Tommaso Dorigo, Pietro Vischia

Published 2026-08-20

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Andrea De Vita, Abhishek, Tommaso Dorigo, Pietro Vischia

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the high-energy world of particle physics, scientists smash protons and other particles together at incredible speeds to uncover the fundamental building blocks of the universe. When these particles collide, they create sprays of new particles called showers that crash into massive detectors. For decades, the primary job of these detectors, known as calorimeters, has been to measure the total energy of these showers, much like a scale weighs a package. However, a newer generation of detectors is being built with a much finer grid, capable of seeing the individual drops of energy within the spray rather than just the total weight. This shift allows physicists to look at the shape and timing of the shower itself, hoping to identify exactly what kind of particle started the cascade. Knowing whether a shower began as a proton or a pion is crucial because these particles behave differently, and distinguishing them helps scientists reconstruct the original collision with greater precision.

A team of researchers recently set out to test the limits of this new approach, asking a simple but difficult question: how well can a highly detailed detector tell the difference between a proton and a positively charged pion using only the information from the shower it creates? To find the answer, they did not use a physical machine but instead created a sophisticated computer simulation of a detector made of lead tungstate, a dense crystal material. They simulated beams of protons and pions with energies ranging from 10 to 100 billion electron volts, a scale typical of modern particle accelerators. The virtual detector was divided into tiny cubes, each measuring 3 by 3 by 6 millimeters, creating a grid of over two million cells. As the simulated particles struck the detector, the software recorded exactly where energy was deposited, how much energy was released, and the precise moment each hit occurred.

The researchers then fed this data into two different types of computer learning systems to see which could best identify the particle type. One system relied on traditional methods, where human experts first summarize the complex data into a list of specific numbers, such as the total energy or the width of the shower, before the computer makes a guess. The other system, called Deep Sets, was given the raw data directly—the exact position, energy, and time of every single hit—allowing it to find patterns without human guidance. The results showed that the system working with the raw, detailed data significantly outperformed the traditional method. At the lowest energy level of 10 billion electron volts, the advanced system correctly identified the particle 93.8 percent of the time. However, as the energy increased to 100 billion electron volts, the accuracy dropped to 67.2 percent, reflecting the fact that higher-energy showers become more chaotic and harder to distinguish.

A key discovery in the study was that not all parts of the detector grid are equally important for identification. The researchers found that the ability to tell protons from pions depends much more heavily on how finely the detector is sliced along the direction the particle is traveling, rather than how finely it is sliced side-to-side. If the cells were made longer in the direction of the particle's path, the computer's ability to identify the particle dropped sharply. In contrast, making the cells wider or narrower had a much smaller effect. This suggests that the most critical clues about a particle's identity are hidden in the sequence of interactions as the shower moves deeper into the material, rather than in how wide the spray spreads out.

The study also broke down which pieces of information were most valuable. The shape of the shower alone provided a good starting point for identification, but adding the amount of energy deposited gave the biggest boost to accuracy. The timing of the hits provided extra, helpful details, though it was not the main factor. The researchers noted that their results are based on simulations of isolated particles in a perfect environment, without the noise and overlapping signals that would occur in a real, busy collider. Therefore, the high accuracy numbers represent an optimistic benchmark of what is theoretically possible with such fine-grained detectors.

These findings offer a clear guide for the design of future particle detectors. They suggest that to get the best particle identification, engineers should prioritize making the detector layers very thin along the path of the particle, even if that means the side-to-side grid can be slightly coarser. This approach could allow future experiments to identify particles more effectively without needing to build impossibly large or expensive machines. By proving that the detailed structure of a particle shower holds a unique fingerprint for protons and pions, the study encourages the inclusion of particle identification as a primary goal in the design of the next generation of high-energy physics instruments.

Technical Summary: Exploring the Limits of High-Energy Proton-Pion Separation in Granular Calorimeters

Problem Statement
Historically, calorimeters in collider experiments have been designed primarily for energy measurement. While Particle Flow (PF) algorithms and boosted-object reconstruction have increased the demand for resolving internal shower structures, identifying charged-hadron species (specifically protons vs. pions) using calorimeter information alone remains a significant challenge. Hadronic showers exhibit large event-by-event fluctuations, and the physical differences between protons and pions—such as longitudinal development, transverse spread, electromagnetic fraction, and timing—are often subtle. The paper addresses the need to quantify how much discrimination power is retained in highly granular calorimeters and how this performance depends on detector segmentation (longitudinal vs. transverse) and incident particle energy.

Methodology
The study utilizes Geant4 simulations of isolated protons and positively charged pions ( $\pi^+$ ) with energies ranging from 10 GeV to 100 GeV. The detector is modeled as a homogeneous lead-tungstate (PbWO $_4$ ) calorimeter, initially segmented into $100 \times 100 \times 200$ cells ( $3 \times 3 \times 6$ mm $^3$ ).

Two distinct data representations and machine learning strategies are employed:

High-Level Features (HLFs): A set of engineered observables (e.g., shower radius, energy variance, vertex position) is extracted. These are classified using a Boosted Decision Tree (BDT) implemented via XGBoost. This approach serves as a baseline and offers interpretability through feature importance metrics.
Point Clouds (Low-Level Features): The raw calorimeter response is represented as an enriched point cloud, where each active cell is a point defined by its spatial coordinates $(x, y, z)$ , deposited energy ( $E$ ), and characteristic time ( $t$ ). This representation is processed using a Deep Sets architecture, which is permutation-invariant and designed for unordered sets of variable cardinality.

The study systematically varies detector granularity by merging adjacent cells to simulate coarser longitudinal and transverse segmentation. Data preprocessing includes an energy threshold ( $E_{cell} > 5$ MeV) to suppress low-energy noise and enhance topological visibility. For the point-cloud analysis, timing information is treated with two approaches: smeared with a Gaussian resolution ( $\sigma = 30$ ps) for HLFs, and unsmeared (idealized) for the Deep Sets analysis to establish an upper bound on timing utility.

Key Contributions

Architecture Comparison: The paper demonstrates that a Deep Sets model operating directly on point clouds outperforms a BDT based on reconstructed high-level observables, particularly in segmented configurations. This suggests that cell-level representations retain information lost when compressing showers into global observables.
Granularity Sensitivity: A critical finding is the asymmetric dependence of classification performance on segmentation. The study quantifies that performance is significantly more sensitive to longitudinal segmentation than to transverse segmentation. Reducing longitudinal granularity causes a steeper drop in accuracy than a comparable reduction in transverse granularity.
Feature Decomposition: Through restricted-feature evaluation, the authors isolate the contributions of different observables. Shower topology alone provides substantial discrimination (74.6% accuracy at 10 GeV). Deposited energy provides the largest additional gain, while timing offers complementary information.
Energy Dependence: The work characterizes the degradation of PID performance as particle energy increases, attributing this to the increasing complexity of hadronic cascades which average out the distinguishing features of primary interactions.

Results

Performance at 10 GeV: With the finest segmentation ( $3 \times 3 \times 6$ mm $^3$ ), the Deep Sets model achieves an accuracy of 93.8%. This decreases to 67.2% at 100 GeV.
Segmentation Impact: At 10 GeV, varying the transverse cell size while keeping the longitudinal size fixed results in only minor accuracy changes. Conversely, increasing the longitudinal cell size (coarsening the $z$ -axis) leads to significant accuracy losses. For example, at 10 GeV, accuracy drops from ~93% to ~80% when the longitudinal cell size is increased from 6 mm to 48 mm, even if transverse segmentation remains fine.
Baseline Comparison: At 100 GeV, the Deep Sets model with maximum granularity outperforms the BDT baseline (67.2% vs. ~61.4%). However, the "no-segmentation" (homogeneous) performance of Deep Sets is lower than the BDT, likely due to the absence of time-of-flight (ToF) information in the point-cloud input for the homogeneous case.
Feature Importance: The BDT analysis confirms that total deposited energy and shower radius are the most discriminating features. The Deep Sets ablation study confirms that while topology is informative, energy is the dominant driver of separation power, with timing providing a smaller but distinct contribution.

Significance and Claims
The paper claims that highly granular calorimeters encode significantly richer information about particle identity than traditionally exploited in event reconstruction. The results serve as an encouraging benchmark for calorimeter-based hadron identification, suggesting that PID can be a complementary system to dedicated detectors (like Cherenkov or ToF systems).

The authors modestly note that the reported accuracies are optimistic benchmarks based on idealized simulations (perfect timing, no pileup, no electronic noise). They do not claim these numbers are directly attainable in a realistic detector without further optimization. However, the qualitative conclusions regarding the importance of longitudinal granularity and the viability of cell-level machine learning are robust.

The primary significance lies in providing guidance for the optimization of future detector designs. The authors argue that PID sensitivity should be included as an objective in the multi-objective optimization of future calorimeters (alongside energy resolution and cost), and that allocating segmentation preferentially along the longitudinal direction may offer a favorable balance between information content and channel count for isolated particle identification.

Technical Summary: Exploring the Limits of High-Energy Proton-Pion Separation in Granular Calorimeters

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