Gammahadron discrimination in groundbased gammaray observatories at the GeV energy range is challenging as traditional muonbased methods become less effective at lower energies. This work explores a novel gammahadron discrimination method for Extensive Air Shower arrays that analyzes the shower signal footprint patterns using advanced Vision Transformer ViT models. The robustness of this method against noise including atmospheric muons and lowenergy proton showers demonstrates its potential for application in future gammaray observatories.
['High Energy Physics - Experiment', 'Astrophysics - High Energy Astrophysical Phenomena']
Gammahadron discrimination through the analysis of the shower footprint at low energies
{'Gamma/hadron discrimination through the analysis of the shower footprint at low energies': "R. Concei¸c˜ao, 1 A. Guill'en, 2 B. S. Gonz'alez, 1, ∗ M. Pimenta, 1 and B. Tom'e 1  \n1 Laborat'orio de Instrumenta¸c˜ao e F'ısica Experimental de Part'ıculas - LIP and Instituto Superior T'ecnico - IST, Universidade de Lisboa - UL, Lisboa, Portugal 2 Computer Engineering, Automatics and Robotics Department, University of Granada, Granada, Spain (Dated: September 18, 2024)  \nGamma/hadron discrimination in ground-based gamma-ray observatories at the GeV energy range is challenging as traditional muon-based methods become less effective at lower energies. This work explores a novel gamma/hadron discrimination method for Extensive Air Shower arrays that analyzes the shower signal footprint patterns using advanced Vision Transformer (ViT) models. The robustness of this method against noise, including atmospheric muons and low-energy proton showers, demonstrates its potential for application in future gamma-ray observatories.", 'I. INTRODUCTION': "The study of gamma rays is crucial for understanding extreme astrophysical events and probing fundamental physics. Gamma-rays in the sub-TeV to TeV range can provide insights into Active Galactic Nuclei (AGNs), Gamma Ray Bursts (GRBs), and potential new physics beyond the standard model, including dark matter research [1, 2].  \nTheir detection above a few hundred of GeV is possible using ground-based detectors as satellite detection is limited by low fluxes [3]. These experiments indirectly detect gamma rays at very high altitudes by using Extensive Air Showers (EAS), which are a cascade of secondary shower particles produced in the atmosphere due to the interaction of the gamma-ray with it. Then, the characteristics of the primary particle such as energy and direction are inferred from the secondary particles detected at the ground. This method enables surveying large portions of the sky and is sensitive to transient phenomena. However, gamma rays must be distinguished from the dominant hadronic background [4-6].  \nMuon identification remains one of the main methods for gamma/hadron separation at TeV energies [710]. However, the muon content of hadronic showers is scarce at sub-TeV energies. Alternatively, one may analyze the shower footprint patterns on the ground to infer features of the shower development [11-14]. Hadroninduced showers, unlike pure electromagnetic showers, generate particles with high transverse momentum, causing the shower to spread more laterally and form clusters. Initial studies have shown great potential in using these ground patterns for gamma/hadron discrimination, but further work is needed to fully understand and optimize their effectiveness against noise [15].  \nThis study demonstrates the potential of employing advanced Vision Transformer (ViT) models [16, 17] to accurately discriminate between gamma and hadroninduced air showers. The footprint image, created from  \nsignals detected by the individual Water Cherenkov Detectors (WCDs) in the detector array, is used as input for the model. The method's robustness against noise, including atmospheric muons and low-energy proton showers, is also assessed.  \nThe paper is structured as follows: Section II describes the set of simulations used and the detector configuration. Section III details the analysis of shower footprint patterns. Section IV evaluates the method's performance and resilience to various noise sources. Finally, the conclusions are presented in Section V.", 'II. SET OF SIMULATIONS': 'The Extensive Air Showers were simulated with CORSIKA (version 7.5600) [18], taking FLUKA [19, 20] and QGSJet-II.04 [21] as the low- and high-energy hadronic interaction model, respectively. The detector response was emulated by summing the expected signals from particles hitting the station. These signals were derived using specific parameterizations based on the energy of protons, muons, and electrons/gammas, created by injecting uniformly sampled vertical particles onto a small water Cherenkov detector (WCD) station with three PMTs at the bottom [22]. These parameterizations included both the mean signal and its standard deviation, allowing us to simulate fluctuations in the WCD signal response due to particle interactions and light collection. Additional fluctuations for muons, taking into account the variations in the tracklength caused by trajectory changes, were included using muon distribution data from proton-induced shower simulations with Geant4 (version 4.10.05.p01) [23-25].  \nThe experimental observation level was set at 5 200 m above sea level [26]. The detector array comprises 5 720 Mercedes WCDs [22], covering an area of 80 000 m 2 with a fill factor of approximately 85%.  \nThe CORSIKA simulations were generated using an E -1 spectrum to balance computational time with statistical accuracy. During the analysis, weights of E -1 0 and E -2 0 were applied to gammas and protons respec-  \ntively to ensure a realistic power-law energy spectrum. The showers are nearly vertical, with simulated zenith angles of θ 0 = 10 · and θ 0 ∈ [5 · ; 10 · ] for gammas and protons, respectively.  \nEach CORSIKA shower was simulated six times with different core positions to enhance statistical reliability. The simulated cores where distributed uniformly over the array, and its impact on the gamma/hadron discrimination power is assessed in section IV B. The event was simulated in four conditions: without noise, with noise from atmospheric muons, noise from low-energy proton showers, and noise from both sources. The dataset is split such that a given CORSIKA shower appears in only one dataset, regardless of its core position or contamination. This approach ensures realistic results, preventing data leakage, where the model could learn a specific CORSIKA shower in training and test it correctly in other sets. It also helps the network learn that the CORSIKA shower corresponds to a given primary particle, independent of contamination or core position.  \nThree energy bins were selected to evaluate this method, corresponding to reconstructed energies of approximately 200 GeV, 500 GeV, and 1 TeV. A calibration was performed using the total signal at the ground to emulate the typical energy reconstruction in groundbased observatories, as shown in Figure 1. The energy bins were chosen according to the energy resolution of the selected bin (see Figure 2), which is of about a 50% at 500 GeV. Thus, the analysis bins are defined as E r ∈ [200 , 500] GeV, E r ∈ [500 , 900] GeV, and E r ∈ [1 000 , 1 600] GeV.  \nThe number of events generated after having simulated six core positions for each CORSIKA shower and added the above-mentioned contamination sources are detailed for each energy bin in Table I.  \nTABLE I. Number of EAS events in each data set.', 'III. ANALYSIS STRATEGY: VISION TRANSFORMERS': "ViTs [16, 17] are emerging in the field of computer vision. Unlike traditional Convolutional Neural Networks (CNNs) [27], which rely on convolutional and fully connected layers, ViTs depend on self-attention mechanisms, enabling them to capture long-range dependencies and  \n)  \n.  \ne  \n.  \np  \n/  \nS  \n(  \ng  \no  \nl  \nFIG. 1. Energy calibration using gamma-induced showers. The black line represents the calibration and the red points the mean signal for each energy bin.  \n<!-- image -->  \nNumber of events  \n0.5  \nFIG. 2. Bias and resolution of the energy calibration. The grey area highlights the region with a bias of ≤ 5%. The resolution is fitted with the formula: y = √ a/ √ x + b .  \n<!-- image -->  \ncontext within images. To do this, the image is divided into fixed-size patches, each of which is linearly embedded, followed by the addition of position embeddings. Subsequently, the resulting sequence of vectors is fed into a standard Transformer encoder, where extra learnable classification tokens are added for classification [17]. This innovation enables these models to capture intricate longrange dependencies and contextual information within images, leading to enhanced capabilities in various applications.  \nThe pre-trained ViT model ' google/vit-base-patch16224-in21k ' [17, 28] has been employed in this study. This  \n(a) Gamma-induced shower event.  \n<!-- image -->  \n(b) Proton-induced shower event.  \nis a transformer encoder model (BERT-like) pre-trained on a large data set called ImageNet-21k [29], which is composed of 14 million images at a resolution of 224x224 pixels and has 21 843 classes. Afterwards, a linear layer was placed on top of the final hidden state of the [CLS] token and trained with our problem's data for 30 additional epochs with a batch size of 32, the default learning rate of 5 · 10 -5 and warm-up ratio of 10%. This pipeline was done with the Hugging Face Transformers open-source library [30], which provides APIs and tools to download and train state-of-the-art pre-trained models.  \nThe input of the model is an image created by mapping the positions of the WCDs and assigning colours based on the total signal in each tank. To emphasize signal structures within the footprint and group stations with similar signals, a linear contour plot with 5 levels and a grid with cells of similar size to the stations is overlaid. A logarithmic scale is applied to prevent saturation of the colour scale due to the high signals in stations near the shower core. To reduce noise from background or late-arriving particles, the shower plane is fitted using the positions of all active stations, with the time of the first particle arrival at each station as the Z coordinate [31]. It was found that with an average background of 23 stations, the plane fit successfully converges when at least 30 stations are present in the event. Therefore, only events with more than 30 active stations (signal + background) were considered for analysis. Following this procedure, only stations with a temporal offset of less than 50 ns from the fitted shower plane were selected.  \nThe outcome of this preprocessing pipeline is illustrated in Figure 3 for proton and gamma-ray shower events, each with a reconstructed energy of 1 TeV. Certain distinguishing features of each class can be discerned from these examples. The gamma-ray event displays a well-defined shower core with a uniform signal, charac-  \nteristic of a purely electromagnetic shower. In contrast, the proton event shows a more irregular and complex footprint, with clusters of signal appearing far from the shower core, resulting from particles with high transverse momentum generated in hadronic interactions.  \nFinally, the objective function of the method is defined as the classification probability, denoted as P ∈ [0; 1], that a proton has induced the analyzed shower.", 'IV. RESULTS': 'In this section, the gamma/hadron separation capability of the method is evaluated. The background rejection factor is computed for a selection efficiency of roughly 75% and compared with the results achieved by the LATTES [32], HAWC [33], and LHAASO-WCDA [34, 35] experiments. The background rejection factor for a gamma efficiency selected to achieve the optimal Q-factor is also presented in Appendix V A. A single model is trained for each energy bin and assessed under various noise conditions.', 'A. Resilience to Noise from Atmospheric Muons and Low-Energy Proton Showers': 'For an EAS array with the given characteristics, the number of stations triggered by atmospheric muons within a 200 ns time window is expected to follow a Poisson distribution with a mean of 23 stations [31]. To assess the resilience of the method against noise from atmospheric muons, each shower event is contaminated with a random number of stations based on this distribution. The muonic signal added to the contaminated tanks is randomly selected using a probability function derived  \nFIG. 3. Shower events with similar reconstructed energy ( E r ∼ 1 TeV) and shower core position. The station color scale ranges from 0 p . e . (black) to 10 5 p . e . (brightest color). The contour groups the stations into five color levels, from the lowest (darkest) to the highest (brightest) signals.  \n<!-- image -->  \nFIG. 6. Dependence of the efficiency on the shower core position at different energy bins for noise-free showers.  \n<!-- image -->  \n<!-- image -->  \n<!-- image -->  \n(a) Noise free.  \n(b) Contamination by atmospheric muons with 29 triggered stations and a total signal of 6 600 p.e.  \n(c) Contamination with a 126 GeV proton-induced shower with 68 triggered stations and a total signal of 2 300 p.e.  \nFIG. 4. Example of contamination for a photon-induced shower event with a reconstructed energy of 550 GeV.  \n1.0  \nFIG. 5. Proton rejection efficiency at different energies and noise sources.  \n<!-- image -->  \nfrom the signal distribution of approximately 150 000 single muon events from proton showers in the ∼ 1 TeV energy bin.  \nAdditionally, to evaluate the resilience against background showers, the events were contaminated with a single low-energy proton shower with E 0 ∈ [10 , 160] GeV.  \n1.0  \n<!-- image -->  \np  \nThe background event is selected based on a probability function that follows the proton energy spectrum. The shower is then injected at a random position within the array area, and the signals from both showers are combined.  \nAn example of these two sources of background is depicted in Figure 4. It can be seen that atmospheric muons generate a uniform noise with a characteristic  \nsignal across the entire footprint, while the low-energy background shower triggers stations within a small and concentrated portion of the array. Even though these background footprints may seem small, they could be potentially problematic since they can mimic the clusters and muons found in hadronic showers.  \nFor each of the selected reconstructed energy bins, a ViT model is trained and tested using the original shower-derived images and their two extra images with contamination. The results for the test data set are shown in Figure 5. The results show a minimal impact of adding noise from low-energy proton showers on the gamma/hadron separation method, with negligible differences observed across energy bins. However, the noise from atmospheric muons does have a more noticeable effect as the energy increases. This trend is expected to be related to the fact that low-energy showers rarely contain muons, leading the model to rely less on those features for classification. The same behaviour was found for the worst-case scenario in which both noise sources are superimposed in the shower footprints. The developed model was able to outperform LATTES, HAWC and LHAASO across all tested conditions.', 'B. Dependence on the position of the shower core': 'To assess the model performance dependence on the position of the shower core, two subsets of noise-free shower events were created according on their true core position: r core ∈ [0 , 50] m and r core ∈ [100 , 150] m. The same models used in the previous subsection were employed for this analysis.  \nThe results, shown in Figure 6, indicate that although there is a slight degradation in performance, particularly at low energies where the shower footprint is smaller, the difference is minimal between events with simulated shower cores near the array center and those farther away. Thus, a limited dependence on the shower core position has been observed.', 'C. Dependence on the muon content of the shower': "As previously noted, muon detection is one of the most effective methods for gamma/hadron separation at TeV energies, given that muons are primarily produced in hadronic interactions. To determine if the model relies on features beyond the muon content of the shower for classification, Figure 7 shows the output probability as a function of the number of stations with muons for events in the intermediate energy bin, with E r ∼ 500 GeV.  \nThe results indicate that the probability of protoninduced showers increases with the number of stations containing muons, as expected for events with a dominant hadronic component. However, significant probabilities are still observed for events with few muons, confirming that the model utilizes additional footprint features.  \nFor gamma-induced showers, a constant behaviour is observed, with most events, as expected, having no stations with muons.  \nP  \nFIG. 7. 2D histogram showing the method's probability as a function of the number of muons in stations for proton showers with E r ∼ 500 GeV. Mean values are shown with error bars representing the standard deviation for both proton (red) and gamma (blue) showers in this reconstructed energy bin.  \n<!-- image -->  \nNumber of events", 'V. CONCLUSIONS': 'In this study, the gamma/hadron separation capability of a footprint-based method across various conditions, including the presence of atmospheric muons, low-energy proton shower noise, and differing shower core positions was evaluated.  \nThe method demonstrates strong resilience against noise from low-energy proton showers and atmospheric muons, with negligible impact on the separation efficiency across the energy bins tested. The method consistently outperformed the HAWC and LHAASO experiments across all tested conditions.  \nIt was observed that the performance shows minimal dependence on the position of the shower core, with only a slight degradation noted between events closer to and farther from the center of the array at the lowest reconstructed energy bin, where shower footprints are smaller. This suggests that the classification performance remains robust across different core positions.  \nFinally, although the presence of muons enhances the performance, it is still effective even in their absence. This demonstrates that the model is not solely dependent on muons but also leverages other footprint features for gamma/hadron separation.  \nOverall, the ViT-based approach shows promise in achieving efficient gamma/hadron separation under realistic conditions, making it a viable candidate for use in current and future gamma-ray observatories.', 'ACKNOWLEDGMENTS': "We would like to express our gratitude to Antonio Bueno for his valuable discussions during the early stages of this work. 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Optimal gamma selection efficiency': 'Figure 8 presents the background rejection factor for a gamma efficiency selected to achieve the optimal Qfactor, as defined in Equation 1.  \nQ = ε γ √ ε p (1)  \n1.0  \nFIG. 8. Proton rejection efficiency at different energies and noise sources, with the gamma selection efficiency set to achieve the optimal Q-factor.  \n<!-- image -->'}