Design and Expected Performance for an hKLM at the EIC

TL;DR

The paper presents the design and expected performance of hKLM, an iron–scintillator sampling calorimeter for the Electron Ion Collider that fuses fast timing and fine segmentation with ML-driven optimization. The detector aims to provide muon identification down to $p_T\approx$1 GeV/$c$ and neutral-hadron calorimetry (neutrons and $K_L$) using time-of-flight at low momenta and calorimetric energy reconstruction at higher momenta, all within a cost-effective, compact barrel integrated into the magnet flux return. A fast parametric optical-photon model based on Normalizing Flows accelerates simulations by ~20×, enabling multi-objective Bayesian optimization (MOBO) over steel-to-scintillator ratios, layer counts, and pre-shower configurations. Key results include a neutron $E$-resolution scaling as $\sim 33\%/\sqrt{E}$, MuID AUC approaching $0.99$ with a Graph Neural Network, and a timing target near $100$ ps that supports precise shower localization and ToF-based energy estimates. These advances, together with ML-assisted reconstruction and optimization, suggest hKLM can outperform comparable HCAL/MuID systems and inform co-design with other EIC subsystems for robust jet and event-level physics.

Abstract

We describe the design concept and estimated performance of an iron-scintillator sampling calorimeter for the future Electron Ion Collider. The novel aspect of this detector is a multi-dimensional readout coupled with foreseen excellent timing resolution, enabling time-of-flight capabilities as well as a more compact overall assembly. Machine learning has been integrated into the detector design process from the ground up. Detector design objectives are defined using Machine Learning based reconstruction and Machine Learning is used to optimize the detector design. The highly segmented readout is implemented with Machine Learning algorithms in mind to reach performance levels usually reserved for much more expensive detector systems. The primary physics objective is to serve as a muon detector/ID system and a neutron hadron calorimeter. In EIC kinematics, charged particles are best measured through tracking rather than calorimetry, but the hKLM can identify and measure the momentum of neutral hadrons. The latter are mainly $K_L$'s and neutrons: for lower energies, excellent relative momentum measurements of a few 10\% are achieved using time of flight, while for higher particle momenta, the energy can be measured calorimetrically with a resolution significantly better than that demonstrated for similar calorimeters read out with less granularity.

Figures (13)

• Figure 1: Octagonal arrangement of sectors around the beampipe (left) and iron/scintillator sandwich structure of one sector (right).
• Figure 2: Comparison of arrival time distributions of the first photon in the full simulation and the parametrization with normalizing flows.
• Figure 3: ROC curves for MuID performance with baseline design using the conventional ID method for 1-GeV/$c$ muons (left) and 5-GeV/$c$ muons (second from left). The next-to-last and the last plots on the right show the performance using a GNN for 1-GeV/$c$ and 5-GeV/$c$ muons, respectively.
• Figure 4: Top: GNN Architecture including input and graph features used by the GNN. Middle: Graph Operation, Bottom: Example of the graph structure used by the GNN in a specific event. The graph has edges between the five nearest hits in the detector.
• Figure 5: Energy resolution for neutrons for the baseline design. Left: total error. Middle: relative error. A fit to the functional form $A/\sqrt{E}$ indicating a relative error of 33%/$\sqrt{E}$. Right: True and predicted particle energy energy.