The k4Clue package: Empowering future collider experiments with the CLUE algorithm

High granularity calorimeters have become increasingly crucial in modern particle physics experiments, and their importance is set to grow even further in the future. The CLUstering of Energy (CLUE) algorithm has shown excellent performance in clustering calorimeter hits in the High Granularity Calorimeter (HGCAL) developed for the Phase-2 upgrade of the CMS experiment. In this paper, the suitability of the CLUE algorithm for future collider experiments has been investigated and its capabilities tested outside the HGCAL reconstruction software. To this end, a new package, k4Clue, was developed which is now fully integrated into the Gaudi software framework and supports the EDM4hep data format for inputs and outputs. The performance of CLUE was demonstrated in three detectors for future colliders: CLICdet for the CLIC accelerator, CLD for the FCC-ee collider and a second calorimeter based on Noble Liquid technology also proposed for FCC-ee. Excellent reconstruction performance was observed for single photon events, even in the presence of noise, and the results are compatible with the performance of the algorithms used currently as the baseline for shower reconstruction in future e(+)e(-)-colliders. Moreover, CLUE demonstrates impressive timing capabilities, outperforming the current baseline algorithms and this advantage remains consistent regardless of the number of input hits. This work highlights the adaptability and versatility of the CLUE algorithm for a wide range of experiments and detectors and the algorithm's potential for future high-energy physics experiments beyond CMS.