Optimising longitudinal and lateral calorimeter granularity for software compensation in hadronic showers using deep neural networks

We investigate the effect of longitudinal and transverse calorimeter segmentation on event-by-event software compensation for hadronic showers. To factorize out sampling and detector effects, events are simulated in which a single charged pion is shot at a homogenous lead glass calorimeter, split into longitudinal and transverse segments of varying size, and the total energy loss within each segment is used as the signal. As an approximation of an optimal reconstruction, a neural network-based energy regression is trained based on these signals. The architecture is based on blocks of convolutional kernels customized for shower energy regression using local energy densities; biases at the edges of the training dataset are mitigated using a histogram technique. With this approximation, we find that a longitudinal and transverse segment size less than or equal to 0.5 and 1.3 nuclear interaction lengths, respectively, is necessary to achieve an optimal energy measurement. In addition, an intrinsic energy resolution of $8\%/\sqrt{E}$ for pion showers is observed.