Design optimization of hadronic calorimeters for future colliders

TL;DR

This work addresses the design optimization of hadronic calorimeters for future colliders by examining how the absorber-to-scintillator proportion affects energy resolution in a Geant4-based model of a FCC-ee ALLEGRO-like calorimeter. The authors quantify the stochastic and constant components of the resolution via $\sigma_E/E = a/\sqrt{E} \oplus c$ (with $b=0$) and reveal an energy-dependent optimum for absorber thickness, finding that no single design minimizes the metric across all energies. They demonstrate that thicker absorbers can reduce sampling fluctuations but also lower the deposited energy, leading to trade-offs that vary with energy (e.g., $p=11/3$ showing diminishing returns above 50 GeV). The study proposes a path toward a closed optimization framework, including layer-wise optimization of longitudinal profiles and gradient-based methods with differentiable surrogate models to efficiently navigate design space and target physics performance targets.

Abstract

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.

Figures (5)

• Figure 1: Impact of jet energy resolution on the separation of $W/Z$ invariant mass peaks. Image from seminar.
• Figure 2: Schematic representation of the simulated calorimeter. The charged pions are shot in the longitudinal direction and hit the center of the square face of the calorimeter perpendicularly. The absorber plates are made of iron (Fe) and their thickness ($\alpha$) is variable. The plastic scintillator plates are composed of Polyvinyl toluene, with a thickness of 3 mm. The total depth of the calorimeter is fixed at 1400 mm.
• Figure 3: Energy deposited in the scintillator by 10 GeV $\pi^+$ for different absorber thicknesses. The histogram bins are shown in the expanded plot for a 9 mm thick absorber, along with a kernel density estimation (KDE) curve. For visual clarity, only estimates above $10^{-5}$ density are shown on the plot. The non-Gaussian shape of the distributions is an indicator of a non-compensating calorimeter. The small low energy peaks are excluded with sigma clipping and therefore don't directly impact this calculation of the resolution.
• Figure 4: Left: Resolution curves for different absorber proportions. The response to charged pions ($\pi^+$) at the simulated energies is used to estimate the stochastic and constant parameters of the energy resolution by fitting Eq. \ref{['eq:enery_res']} to the points. Four selected proportions are shown. Right: Energy resolution as a function of absorber proportion for $\pi^+$ with three different energies. The best resolution is achieved with different proportions at different energies.
• Figure 5: Stochastic and constant components of the energy resolution for different absorber proportions at four energies. The distance to the origin is the resolution, since the components are added in quadrature. The dashed lines are constant in resolution and are used to compare different proportions at a given energy.