Unexplained bias dip at 60 GeV in CaloFlow calibration

Determine the cause of the dip observed at E_true = 60 GeV in the bias of the CaloFlow-based maximum likelihood energy calibration of single-π+ showers in the ATLAS-like ECAL+HCAL sampling calorimeter dataset, isolating whether it originates from the CaloFlow normalizing flow architecture or training, the likelihood evaluation procedure, the training prior, or genuine features of the Geant4-simulated detector response.

Background

The paper compares direct regression and normalizing-flow (CaloFlow) maximum likelihood calibration of incident pion energies using an ATLAS-like ECAL+HCAL sampling calorimeter dataset. Bias is assessed via the mode of E_pred/E_true as a function of E_true for models trained on uniform and log-uniform energy priors.

While CaloFlow shows prior-independence and smaller overall bias than mean-squared-error regression, the authors note a dip in the bias at E_true = 60 GeV whose origin they could not identify. Understanding this dip is important to ensure the robustness of the normalizing-flow-based calibration and to disentangle potential modeling artifacts from genuine detector-response features.