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

Eur. Phys. J. C (2022) 82:92 https://doi.org/10.1140/epjc/s10052-022-10031-7 Regular Article - Experimental Physics Optimising longitudinal and lateral calorimeter granularity for software compensation in hadronic showers using deep neural networks Coralie Neubüser1,a , Jan Kieseler2,b , Paul Lujan3,c 1 INFN TIFPA, Via Sommarive 14, 38123 Trento, Italy 2 CERN, 1211 Genève 23, Switzerland 3 University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand Received: 21 January 2021 / Accepted: 17 January 2022 © The Author(s) 2022 Abstract 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%/ E for pion showers is observed. 1 Introduction Both existing high-energy physics experiments, such as those at the CERN LHC, and future experiments at future colliders, like the Future Circular Collider (FCC), rely heavily on the performance of hadron calorimeters and their particle flow capabilities for measuring jet and missing transverse momentum ( pT ) [1–9]. Hadron calorimeters are currently characterized not only in terms of their intrinsic energy resolution, but by their imaging capabilities, which allow for a e-mail: (corresponding author) b e-mail: c e-mail: 0123456789().: V,-vol offline corrections using smart algorithms. Due to the diverse composition of hadronic showers and the differences in the calorimeter response, a correct energy measurement becomes challenging. In general, the components of hadronic showers can be divided into electromagnetic (EM) and hadronic parts. The hadronic part of the shower consists of particles such as neutrinos and neutrons which are partially invisible to the detector. This can be affected by the chosen active detector material, where, e.g., plastic scintillators allow for neutron detection via strong interaction with the atomic nucleus. The undetectable particles in the hadronic shower result in an unequal detector response; that is, e/ h = 1, where e and h are the calorimeter response to electromagnetic and hadronic shower fractions, respectively. Many hadronic calorimeters currently in use and planned for future experiments are sampling calorimeters, which consist of alternating active and passive absorber layers [10–13]. The sampling of the hadronic shower allows for tuning of the hadronic and electromagnetic shower responses. In the past, the e/ h ratio has been adjusted closer to 1 by either suppressing the electromagnetic response, e.g., by using highZ absorbers, or by enhancing the hadronic response, using neutron-sensitive active materials. Calorimeters that have a ratio e/ h ∼ 1 are called “compensating” calorimeters. These optimizations in the active and passive materials often require a decreased sampling fraction (ratio of active/passive material), which itself degrades the calorimeter energy resolution by increasing the stochastic term α of α σE = √ ⊕ c. E E (1) The stochastic term is dominated by the sampling fraction (per layer) and the frequency (the number of layers) for sampling calorimeters, and expresses the dependence of the 123 92 Page 2 of 9 calorimeter resolution on the fluctuations of the number of particles within the hadronic shower (following a Poisson distribution). The constant term c expresses linearly energydependent uncertainties, such as energy losses due to particles escaping the detector, caused by limited calorimeter sizes. The fluctuations on the EM-to-hadronic shower fraction increase logarithmically with energy and can thus contribute to both terms. This contribution can be removed either by intrinsic compensation, or by an event-by-event measurement of the EM fraction, which is called software compensation. Due to the cost and mechanical stability benefits, absorbers made of steel or lead are widely in use. These materials have been found to require very small sampling fractions in, e.g., scintillator-steel calorimeters in order to achieve compensating behavior. Since such low sampling fractions would degrade the performance, especially for particles at low energies (< 50 GeV), the solution to correct for fluctuations in the electromagnetic shower fraction is to use software compensation techniques. In order to allow algorithms to distinguish between the dense electromagnetic shower core and other shower parts, e.g., disappearing tracks, the granularity of the calorimeter plays a key role. The first attempt in so-called imaging calorimetry has been made by the CALICE collaboration, which started a R&D program of calorimeters for a future e− e+ linear collider [14,15], where the calorimeter designs have been optimised for particle flow algorithms [5]. These algorithms allow for jet energy measurements using the best suited sub-detector to reconstruct each jet particle. The prototypes of these calorimeters have been realised with active layers made of silicon for the EM shower part and scintillator or resistive plate chambers for the measurement of hadronic showers. The active layers were tested and interleaved within both steel and tungsten absorber stacks [16,17] and achieved such good results in test beams [18] that the CMS Collaboration decided to adopt this concept in a full silicontungsten/scintillator-steel endcap calorimeter [12,19]. The developments in, e.g., silicon photomultiplier (SiPM) technologies have been key to measuring the scintillation light produced in calorimeter cell sizes of 3 × 3 × 0.5 cm3 [20]. The impact of software compensation techniques on the performance of particle flow algorithms has been studied in a specific detector design [9], and proven to provide a significant improvement to the jet energy measurement by using a corrected calorimeter cluster which is matched to tracks in the tracking system. The next step towards a calorimeter design optimized for the use of software compensation techniques is to study the necessary granularity that allows an algorithm to determine most accurately the hadronic shower energy. In this paper, we will discuss the performance of a software (...truncated)