3D software compensation of hadronic showers in the CRILIN crystal calorimeter
Future electron-positron Higgs factories require excellent jet energy resolution to perform precision measurements of Higgs boson couplings to quarks and gluons. Although homogeneous crystal calorimeters provide remarkable electromagnetic energy resolution, their highly non-compensating response makes hadronic energy reconstruction particularly challenging. In this work, software compensation techniques are investigated for CRILIN, a longitudinally segmented Cherenkov crystal electromagnetic calorimeter based on PbF$_2$ crystals. Using Geant4 simulations of pion showers, it is shown that shower-shape observables are strongly correlated with the fraction of deposited energy reconstructed in a CRILIN module. Simple event-by-event corrections based on the shower transverse RMS and longitudinal center-of-gravity already yield a substantial improvement in hadronic energy reconstruction. A ParticleNet Graph Neural Network exploiting the full three-dimensional shower topology achieves significantly improved performance with respect to simple energy sum reconstruction. Under several different assumptions for the downstream hadronic calorimeter resolution, the GNN-based reconstruction significantly reduces the effective CRILIN contribution to the combined calorimetric resolution, therefore preserving an excellent combined ECAL+HCAL performance. The dependence of the result on the assumed HCAL resolution is also studied and found to be limited within the range considered. These results demonstrate that highly granular crystal calorimeters can recover a large fraction of the information lost because of their intrinsically non-compensating response through software-based compensation techniques, enabling excellent hadronic energy resolution in a combined ECAL+HCAL system and making such detectors promising candidates for future collider experiments.