Reconstruction of the depth of the shower maximum of air showers with the SD-750 surface detector of the Pierre Auger Observatory using neural networks
The Pierre Auger Collaboration,
A. Abdul Halim,
P. Abreu,
M. Aglietta,
I. Allekotte,
K. Almeida Cheminant,
A. Almela, R. Aloisio, J. Alvarez-Muñiz, A. Ambrosone, J. Ammerman Yebra, G.A. Anastasi, L.A. Anchordoqui, B. Andrada, L. Andrade Dourado, S. Andringa, L. Apollonio, C. Aramo, E. Arnone, J.C. Arteaga Velazquez, P. Assis, G. Avila, E. Avocone, A. Bakalova, F. Barbato, A. Bartz Mocellin, J.A. Bellido, C. Berat, M.E. Bertaina, M. Bianciotto, P.L. Biermann, V. Binet, K. Bismark, T. Bister, J. Biteau, J. Blazek, J. Blümer, M. Bohacova, D. Boncioli, C. Bonifazi, L. Bonneau Arbeletche, N. Borodai, J. Brack, P.G. Brichetto Orchera, F.L. Briechle, A. Bueno, S. Buitink, M. Buscemi, M. Büsken, A. Bwembya, K.S. Caballero-Mora, S. Cabana-Freire, L. Caccianiga, F. Campuzano, J. Caraça-Valente, R. Caruso, A. Castellina, F. Catalani, G. Cataldi, L. Cazon, M. Cerda, B. Čermáková, A. Cermenati, J.A. Chinellato, J. Chudoba, L. Chytka, R.W. Clay, A. Cobos Cerutti, R. Colalillo, R. Conceição, G. Consolati, M. Conte, F. Convenga, D. Correia dos Santos, P.J. Costa, C. Covault, M. Cristinziani, C.S. Cruz Sanchez, S. Dasso, K. Daumiller, B.R. Dawson, R.M. de Almeida, E.T. de Boone, B. de Errico, J. de Jesús, S.J. de Jong, J. de Mello Neto, I. De Mitri, J. de Oliveira, D. de Oliveira Franco, F. de Palma, V. de Souza, E. De Vito, A. Del Popolo, O. Deligny, N. Denner, L. Deval, A. di Matteo, C. Dobrigkeit, J.C. D'Olivo, L.M. Domingues Mendes, Q. Dorosti, J. dos Anjos, R.C. dos Anjos, J. Ebr, F.H. Ellwanger, R. Engel, I. Epicoco, M. Erdmann, A. Etchegoyen, C. Evoli, H. Falcke, G.R. Farrar, A. Fauth, T. Fehler, F. Feldbusch, A. Fernandes, M. Fernandez, B. Fick, J.M. Figueira, P. Filip, A. Filipcic, T. Fitoussi, B. Flaggs, T. Fodran, A. Franco, M. Freitas, T. Fujii, A. Fuster, C. Galea, B. Garcia, C. Gaudu, P.L. Ghia, U. Giaccari, F. Gobbi, F. Gollan, G. Golup, M. Gómez Berisso, P.F. Gómez Vitale, J.P. Gongora, J.M. Gonzalez, N.M. Gonzalez, D. Gora, A. Gorgi, M. Gottowik, F. Guarino, G. Guedes, L. Gülzow, S. Hahn*, P. Hamal, M.R. Hampel, P.M. Hansen, V.M. Harvey, A. Haungs, T. Hebbeker, C. Hojvat, J. Hörandel, P. Horvath, M. Hrabovsky, T. Huege, A. Insolia, P.G. Isar, M. Ismaiel, P. Janecek, V. Jilek, K.H. Kampert, B. Keilhauer, A. Khakurdikar, V.V. Kizakke Covilakam, H. Klages, M. Kleifges, J. Köhler, F. Krieger, M. Kubatova, N. Kunka, B.L. Lago, N. Langner, N. Leal, M.A. Leigui de Oliveira, Y. Lema-Capeans, A. Letessier-Selvon, I. Lhenry-Yvon, L. Lopes, J.P. Lundquist, M. Mallamaci, D. Mandat, P. Mantsch, F.M. Mariani, A. Mariazzi, I.C. Maris, G. Marsella, D. Martello, S. Martinelli, M.A. Martins, H.J. Mathes, J. Matthews, G. Matthiae, E.W. Mayotte, S. Mayotte, P. Mazur, G. Medina-Tanco, J. Meinert, D. Melo, A. Menshikov, C. Merx, S. Michal, M.I. Micheletti, L. Miramonti, M. Mogarkar, S. Mollerach, F. Montanet, L. Morejon, K. Mulrey, R. Mussa, W.M. Namasaka, S. Negi, L. Nellen, K. Nguyen, G. Nicora, M. Niechciol, D. Nitz, D. Nosek, A. Novikov, V. Novotný, L. Nozka, A. Nucita, L.A. Nunez, J. Ochoa, C. Oliveira, L. Östman, M. Palatka, J. Pallotta, S. Panja, G. Parente, T. Paulsen, J. Pawlowsky, M. Pech, J. Pękala, R. Pelayo, V. Pelgrims, L.A. Pereira, E.E. Pereira Martins, C. Pérez Bertolli, L. Perrone, S. Petrera, C. Petrucci, T. Pierog, M. Pimenta, M. Platino, B. Pont, M. Pourmohammad Shahvar, P. Privitera, C. Priyadarshi, M. Prouza, K. Pytel, S. Querchfeld, J. Rautenberg, D. Ravignani, J.V. Reginatto Akim, A. Reuzki, J. Ridky, F. Riehn, M. Risse, V. Rizi, E. Rodriguez, G. Rodriguez Fernandez, J.R. Rodriguez Rojo, S. Rossoni, M. Roth, E. Roulet, A. Rovero, A. Saftoiu, M. Saharan, F. Salamida, H.I. Salazar, G. Salina, P. Sampathkumar, N. San Martin, J. Sanabria Gomez, F.A. Sánchez, E.M. Santos, E. Santos, F. Sarazin, R. Sarmento, R. Sato, P. Savina, V. Scherini, H. Schieler, M. Schimassek, M. Schimp, D. Schmidt, O. Scholten, H. Schoorlemmer, P. Schovanek, F.G. Schröder, J. Schulte, T. Schulz, S.J. Sciutto, M. Scornavacche, A. Sedoski, A. Segreto, S. Sehgal, S.U. Shivashankara, G. Sigl, K. Simkova, F. Simon, R. Smida, P. Sommers, R. Squartini, M. Stadelmaier, S. Stanič, J. Stasielak, P. Stassi, S. Strähnz, M. Straub, T. Suomijarvi, A.D. Supanitsky, Z. Svozilikova, K. Syrokvas, Z. Szadkowski, F. Tairli, M. Tambone, A. Tapia, C. Taricco, C. Timmermans, O. Tkachenko, P. Tobiska, C.J. Todero Peixoto, B. Tomé, A. Travaini, P. Travnicek, M.J. Tueros, M. Unger, R. Uzeiroska, L. Vaclavek, M. Vacula, I. Vaiman, J.F. Valdés Galicia, L. Valore, P. van Dillen, E. Varela, V. Vašíčková, A. Vásquez-Ramírez, D. Veberic, I.D. Vergara Quispe, S. Verpoest, V. Verzi, J. Vicha, J. Vink, S. Vorobiov, J.B. Vuta, C.K.O. Watanabe, A. Watson, A. Weindl, M. Weitz, L. Wiencke, H. Wilczyński, B. Wundheiler, B. Yue, A. Yushkov, E. Zas, D. Zavrtanik and M. Zavrtaniket al. (click to show)*: corresponding author
Pre-published on:
September 23, 2025
Published on:
December 30, 2025
Abstract
The origin of ultra-high-energy cosmic rays (UHECRs) is one of the intriguing mysteries in astroparticle physics.
In order to identify their sources, we need precise knowledge of the mass composition of UHECRs.
The direct detection of UHECRs is not feasible at energies above 0.1 PeV, necessitating the use of mass-sensitive observables of extended air showers induced by UHECRs interacting with the atmosphere.
One way to achieve high statistics for these mass-sensitive observables is to use ground-based detector arrays, such as the Surface Detector (SD) of the Pierre Auger Observatory.
The SD consists of three sub-arrays of independent detector stations arranged in triangular grids with different spacings.
Recently, it has been shown that neural networks (NNs) can extract mass-sensitive observables from data taken by the SD-1500, the largest sub-detector of the SD.
In this contribution, we demonstrate the feasibility of using NNs to reconstruct a high-level shower observable, the depth of the shower maximum, from data simulated for and observed by the SD-750, the second-largest detector array nested within the SD-1500.
A simulation study shows that the SD-750 NN exhibits behavior similar to that of an SD-1500 NN and outperforms the latter in the energy range [1, 10) EeV.
Moreover, we show that, after performing a correction and calibration procedure, the predictions of the SD-750 NN are consistent with the measurement of the depth of the shower maximum obtained by the Fluorescence Detector of the Pierre Auger Observatory.
DOI: https://doi.org/10.22323/1.501.0284
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