# Deep Learning Study of an Electromagnetic Calorimeter
## 1 Introduction  
An important topic in high-energy physics (HEP) is to identify particles that are the outcome of physical processes under study. To serve this purpose, particle detectors have been designed and built, including calorimeters [1; 2]. Calorimetry in HEP, borrowing the name from thermal physics, is a way to study particles by absorbing them, namely to let incoming particles lose energy during their movement inside the calorimeter by collision until they have stopped moving. Through various interactions, secondary particles may be created during collisions among the particles and the detector elements. Moreover, these secondary particles can also create their own secondary particles. This exponential process is called \"showering\". During the collisions, the total energy of the initial particles is being absorbed by the calorimeter. Depending on the positions and shapes of the showers, the types, amount, and energies of the particles can be deduced. An electromagnetic calorimeter (ECAL) is a detector in HEP based on electromagnetic interactions, including bremsstrahlung and pair creation. Electrons, positrons, and photons can easily create showers inside an ECAL. To obtain a snapshot of the shower, multiple layers of sensitive materials are inserted in an ECAL where the energy of showers is deposited, leading to an image (as in Figure 1) reflecting each event. Monte-Carlo simulations [3] are employed to build these images during the design process. In addition, algorithms for extracting the particle information from the images have to be developed for evaluating the design. It is in this context that we use the deep learning (DL) methodology of a convolutional neural network (CNN) for ECAL information extraction. Neural networks have been used in HEP for decades [4; 5; 6; 7; 8; 9; 10; 11]. Some recent works have also covered shower identification and reconstruction in calorimeters [12; 13; 14]. Most of the neural network studies in HEP are dedicated to the extraction of weak signals from backgrounds, such as in the discovery of the [PERSON] boson [15; 16]. Here we present an example of the design of an ECAL for the proposed _Laser und XFEL Experiment_ (LUXE) [17]. Designed to account for positron identification in LUXE, the ECAL has a three-dimensional (3D) structure of \((110\times 11\times 20=)\) 24,200 elements of detector pads. This detector is exposed to incoming positrons produced by a laser beam colliding with electrons, and creates an image of energy deposition with the 24K pixels. During the experiment, the positrons will be generated periodically. Each batch of positrons is called an \"event\". The energy distribution and multiplicity of positrons hitting the detector depend on a few factors. Apart from statistical and quantum fluctuations, the physical results of the collision will change along with the properties of the laser beam which, in this case, is qualified by a single parameter: the focal radius of the laser beam. In this paper, samples with radii \(\rho=3,5,8\) um are investigated. In the loosely focusing case (\(\rho=8\) um), we find fewer than three positrons per event. A few couples to tens of positrons reach the ECAL when \(\rho=5\) um. The number of positrons dramatically increases above 100 to a few thousands in the tightly focusing scenario (\(\rho=3\) um). Figure 1 sketches an expected shower structure within the detector. The overlapping of showers in a ten-positron event is clearly visible. The challenges for the LUXE ECAL lie in the identification of positrons from the background, as well as its effectiveness in high-multiplicity events. We will provide an algorithm that translates the readings of the 24K variables to the aforementioned positron properties, and covers the different scenarios with largely various numbers of positrons. The difficulties of working within such a data-space may be addressed by a deep neural network.