Design optimization of hadronic calorimeters for future colliders

Calorimeters are a crucial component in modern particle detectors. They are responsible for providing accurate energy measurements of particles produced in high-energy collisions. The demanding requirements set for next-generation collider experiments impose new challenges on the design of new detectors, and a systematic approach to their optimization is increasingly necessary. The performance of calorimeters is primarily characterized by their energy resolution, parameterized by a stochastic and a constant term, related to sampling fluctuations and non-uniformities respectively. To improve the reconstruction quality of physics objects in the calorimeter, both terms need to be taken into account. Changes in a longitudinally constrained design usually result in a trade-off between these terms, making optimization a non-trivial task. This work focuses on the optimization of a hadronic sampling calorimeter, based on the FCC-ee ALLEGRO detector concept. By controlling the absorber layer thickness in a Geant4 simulation, the impact of the passive to active material proportion on the deposited energy distribution and resolution can be analyzed. Our methodology aims at exploring the design space with practical considerations, paving the way for the development of a closed optimization framework that can evaluate multiple designs against physics performance targets.

💡 Research Summary

This paper presents a systematic investigation into the design optimization of a hadronic sampling calorimeter for future particle colliders, specifically targeting the requirements of the FCC-ee experiment. Calorimeters are essential for measuring particle energies, and their performance is quantified by energy resolution, typically parameterized by stochastic (a/√E), noise (b/E), and constant (c) terms. This work focuses on the intrinsic trade-off between the stochastic term (dominated by sampling fluctuations) and the constant term (arising from non-uniformities and non-compensation), which is a central challenge in calorimeter design.

The study employs a simulation-based approach using the Geant4 toolkit. The model is based on the ALLEGRO detector concept for FCC-ee, approximating a barrel calorimeter with a fixed total depth of 1400 mm. It consists of alternating plates of iron (absorber) and plastic scintillator (active material). The key design variable is the thickness of the iron absorber plates (α), while the scintillator thickness is kept constant at 3 mm. To ensure a fair comparison within the fixed total depth, the number of absorber-scintillator layers is adjusted dynamically as α changes. The single-particle response is simulated for charged pions at eight energies ranging from 1 to 200 GeV.

The core findings reveal a fundamental design constraint: there is no single, universal absorber-to-scintillator ratio that minimizes the energy resolution across all particle energies. Simulation results demonstrate that increasing the absorber thickness (i.e., the sampling ratio) reduces the average energy deposited in the scintillator but also narrows the energy distribution to some extent. The fitted resolution parameters show that a thinner absorber (lower ratio) is beneficial at lower energies (e.g., 10 GeV) where the stochastic term is dominant. Conversely, at higher energies (e.g., above 50 GeV), a thicker absorber (up to an 11:3 ratio of iron to scintillator thickness) becomes advantageous as it improves the constant term, which governs the high-energy resolution. Beyond an 11 mm iron plate thickness, further improvements in the constant term stagnate, indicating a point of diminishing returns for high-energy performance.

The paper concludes that simply tuning a homogeneous absorber thickness is insufficient to achieve dominant performance gains across the broad energy spectrum relevant to a collider experiment like FCC-ee. Instead, the authors propose a promising future direction: longitudinal segmentation and optimization. This involves dividing the calorimeter depth into multiple layers and independently optimizing the absorber-to-scintillator ratio in each layer (p1, p2, … pN). This approach aims to match the varying optimal sampling ratio to the different stages of shower development (initial, peak, tail), thereby accommodating the energy profile of typical hadrons and jets. The authors suggest that implementing such a multi-parameter optimization would benefit from advanced techniques like gradient-based optimization using differentiable surrogate models of the detector response. This work lays the groundwork for a more comprehensive, closed-loop optimization framework that can evaluate complex designs against specific physics performance targets, such as the separation of W and Z boson mass peaks.