Deep-Learning based Reconstruction of the Shower Maximum $X_{\mathrm{max}}$ using the Water-Cherenkov Detectors of the Pierre Auger Observatory
Creators: name: The Pierre Auger Collaboration
name: Aab, A.
name: Abreu, P.
name: Aglietta, M.
name: Albury, J. M.
name: Allekotte, I.
name: Almela, A.
name: Alvarez-Muñiz, J.
name: Batista, R. Alves
name: Anastasi, G. A.
name: Anchordoqui, L.
name: Andrada, B.
name: Andringa, S.
name: Aramo, C.
name: Ferreira, P. R. Araújo
name: Velázquez, J. C. Arteaga
name: Asorey, H.
name: Assis, P.
name: Avila, G.
name: Badescu, A. M.
name: Bakalova, A.
name: Balaceanu, A.
name: Barbato, F.
name: Luz, R. J. Barreira
name: Becker, K. H.
name: Bellido, J. A.
name: Berat, C.
name: Bertaina, M. E.
name: Bertou, X.
name: Biermann, P. L.
name: Bister, T.
name: Biteau, J.
name: Blazek, J.
name: Bleve, C.
name: Boháčová, M.
name: Boncioli, D.
name: Bonifazi, C.
name: Arbeletche, L. Bonneau
name: Borodai, N.
name: Botti, A. M.
name: Brack, J.
name: Bretz, T.
name: Orchera, P. G. Brichetto
name: Briechle, F. L.
name: Buchholz, P.
name: Bueno, A.
name: Buitink, S.
name: Buscemi, M.
name: Caballero-Mora, K. S.
name: Caccianiga, L.
name: Canfora, F.
name: Caracas, I.
name: Carceller, J. M.
name: Caruso, R.
name: Castellina, A.
name: Catalani, F.
name: Cataldi, G.
name: Cazon, L.
name: Cerda, M.
name: Chinellato, J. A.
name: Choi, K.
name: Chudoba, J.
name: Chytka, L.
name: Clay, R. W.
name: Cerutti, A. C. Cobos
name: Colalillo, R.
name: Coleman, A.
name: Coluccia, M. R.
name: Conceição, R.
name: Condorelli, A.
name: Consolati, G.
name: Contreras, F.
name: Convenga, F.
name: Santos, D. Correia dos
name: Covault, C. E.
name: Dasso, S.
name: Daumiller, K.
name: Dawson, B. R.
name: Day, J. A.
name: de Almeida, R. M.
name: de Jesús, J.
name: de Jong, S. J.
name: De Mauro, G.
name: Neto, J. R. T. de Mello
name: De Mitri, I.
name: de Oliveira, J.
name: Franco, D. de Oliveira
name: de Palma, F.
name: de Souza, V.
name: De Vito, E.
name: del Río, M.
name: Deligny, O.
name: Di Matteo, A.
name: Dobrigkeit, C.
name: D'Olivo, J. C.
name: Anjos, R. C. dos
name: Dova, M. T.
name: Ebr, J.
name: Engel, R.
name: Epicoco, I.
name: Erdmann, M.
name: Escobar, C. O.
name: Etchegoyen, A.
name: Falcke, H.
name: Farmer, J.
name: Farrar, G.
name: Fauth, A. C.
name: Fazzini, N.
name: Feldbusch, F.
name: Fenu, F.
name: Fick, B.
name: Figueira, J. M.
name: Filipčič, A.
name: Fodran, T.
name: Freire, M. M.
name: Fujii, T.
name: Fuster, A.
name: Galea, C.
name: Galelli, C.
name: García, B.
name: Vegas, A. L. Garcia
name: Gemmeke, H.
name: Gesualdi, F.
name: Gherghel-Lascu, A.
name: Ghia, P. L.
name: Giaccari, U.
name: Giammarchi, M.
name: Giller, M.
name: Glombitza, J.
name: Gobbi, F.
name: Gollan, F.
name: Golup, G.
name: Berisso, M. Gómez
name: Vitale, P. F. Gómez
name: Gongora, J. P.
name: González, J. M.
name: González, N.
name: Goos, I.
name: Góra, D.
name: Gorgi, A.
name: Gottowik, M.
name: Grubb, T. D.
name: Guarino, F.
name: Guedes, G. P.
name: Guido, E.
name: Hahn, S.
name: Hamal, P.
name: Hampel, M. R.
name: Hansen, P.
name: Harari, D.
name: Harvey, V. M.
name: Haungs, A.
name: Hebbeker, T.
name: Heck, D.
name: Hill, G. C.
name: Hojvat, C.
name: Hörandel, J. R.
name: Horvath, P.
name: Hrabovský, M.
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name: Hulsman, J.
name: Insolia, A.
name: Isar, P. G.
name: Janecek, P.
name: Johnsen, J. A.
name: Jurysek, J.
name: Kääpä, A.
name: Kampert, K. H.
name: Keilhauer, B.
name: Kemp, J.
name: Klages, H. O.
name: Kleifges, M.
name: Kleinfeller, J.
name: Köpke, M.
name: Kunka, N.
name: Lago, B. L.
name: Lang, R. G.
name: Langner, N.
name: de Oliveira, M. A. Leigui
name: Lenok, V.
name: Letessier-Selvon, A.
name: Lhenry-Yvon, I.
name: Presti, D. Lo
name: Lopes, L.
name: López, R.
name: Lu, L.
name: Luce, Q.
name: Lucero, A.
name: Lundquist, J. P.
name: Payeras, A. Machado
name: Mancarella, G.
name: Mandat, D.
name: Manning, B. C.
name: Manshanden, J.
name: Mantsch, P.
name: Marafico, S.
name: Mariazzi, A. G.
name: Mariş, I. C.
name: Marsella, G.
name: Martello, D.
name: Martinez, H.
name: Bravo, O. Martínez
name: Mastrodicasa, M.
name: Mathes, H. J.
name: Matthews, J.
name: Matthiae, G.
name: Mayotte, E.
name: Mazur, P. O.
name: Medina-Tanco, G.
name: Melo, D.
name: Menshikov, A.
name: Merenda, K. -D.
name: Michal, S.
name: Micheletti, M. I.
name: Miramonti, L.
name: Mollerach, S.
name: Montanet, F.
name: Morello, C.
name: Mostafá, M.
name: Müller, A. L.
name: Muller, M. A.
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name: Mussa, R.
name: Muzio, M.
name: Namasaka, W. M.
name: Nasr-Esfahani, A.
name: Nellen, L.
name: Niculescu-Oglinzanu, M.
name: Niechciol, M.
name: Nitz, D.
name: Nosek, D.
name: Novotny, V.
name: Nožka, L.
name: Nucita, A
name: Núñez, L. A.
name: Palatka, M.
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name: Parente, G.
name: Parra, A.
name: Pech, M.
name: Pedreira, F.
name: Pękala, J.
name: Pelayo, R.
name: Peña-Rodriguez, J.
name: Martins, E. E. Pereira
name: Armand, J. Perez
name: Bertolli, C. Pérez
name: Perlin, M.
name: Perrone, L.
name: Petrera, S.
name: Pierog, T.
name: Pimenta, M.
name: Pirronello, V.
name: Platino, M.
name: Pont, B.
name: Pothast, M.
name: Privitera, P.
name: Prouza, M.
name: Puyleart, A.
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name: Rautenberg, J.
name: Ravignani, D.
name: Reininghaus, M.
name: Ridky, J.
name: Riehn, F.
name: Risse, M.
name: Rizi, V.
name: de Carvalho, W. Rodrigues
name: Rojo, J. Rodriguez
name: Roncoroni, M. J.
name: Roth, M.
name: Roulet, E.
name: Rovero, A. C.
name: Ruehl, P.
name: Saffi, S. J.
name: Saftoiu, A.
name: Salamida, F.
name: Salazar, H.
name: Salina, G.
name: Gomez, J. D. Sanabria
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name: Santos, E. M.
name: Santos, E.
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name: Schieler, H.
name: Schimassek, M.
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name: Schlüter, F.
name: Schmidt, D.
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name: Schovánek, P.
name: Schröder, F. G.
name: Schröder, S.
name: Schulte, J.
name: Sciutto, S. J.
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name: Suárez-Durán, M.
name: Sudholz, T.
name: Suomijärvi, T.
name: Supanitsky, A. D.
name: Šupík, J.
name: Szadkowski, Z.
name: Taboada, A.
name: Tapia, A.
name: Taricco, C.
name: Timmermans, C.
name: Tkachenko, O.
name: Tobiska, P.
name: Peixoto, C. J. Todero
name: Tomé, B.
name: Travaini, A.
name: Travnicek, P.
name: Trimarelli, C.
name: Trini, M.
name: Tueros, M.
name: Ulrich, R.
name: Unger, M.
name: Vaclavek, L.
name: Vacula, M.
name: Galicia, J. F. Valdés
name: Valore, L.
name: Varela, E.
name: C., V. Varma K.
name: Vásquez-Ramírez, A.
name: Veberič, D.
name: Ventura, C.
name: Quispe, I. D. Vergara
name: Verzi, V.
name: Vicha, J.
name: Vink, J.
name: Vorobiov, S.
name: Wahlberg, H.
name: Watanabe, C.
name: Watson, A. A.
name: Weber, M.
name: Weindl, A.
name: Wiencke, L.
name: Wilczyński, H.
name: Winchen, T.
name: Wirtz, M.
name: Wittkowski, D.
name: Wundheiler, B.
name: Yushkov, A.
name: Zapparrata, O.
name: Zas, E.
name: Zavrtanik, D.
name: Zavrtanik, M.
name: Zehrer, L.
name: Zepeda, A.
Publisher: name: arXiv
Year: 2021
Subjects: subject: Instrumentation and Methods for Astrophysics (astro-ph.IM)
subject: High Energy Astrophysical Phenomena (astro-ph.HE)
subject: High Energy Physics - Experiment (hep-ex)
subject: FOS: Physical sciences
subject: FOS: Physical sciences

description: The atmospheric depth of the air shower maximum $X_{\mathrm{max}}$ is an observable commonly used for the determination of the nuclear mass composition of ultra-high energy cosmic rays. Direct measurements of $X_{\mathrm{max}}$ are performed using observations of the longitudinal shower development with fluorescence telescopes. At the same time, several methods have been proposed for an indirect estimation of $X_{\mathrm{max}}$ from the characteristics of the shower particles registered with surface detector arrays. In this paper, we present a deep neural network (DNN) for the estimation of $X_{\mathrm{max}}$. The reconstruction relies on the signals induced by shower particles in the ground based water-Cherenkov detectors of the Pierre Auger Observatory. The network architecture features recurrent long short-term memory layers to process the temporal structure of signals and hexagonal convolutions to exploit the symmetry of the surface detector array. We evaluate the performance of the network using air showers simulated with three different hadronic interaction models. Thereafter, we account for long-term detector effects and calibrate the reconstructed $X_{\mathrm{max}}$ using fluorescence measurements. Finally, we show that the event-by-event resolution in the reconstruction of the shower maximum improves with increasing shower energy and reaches less than $25~\mathrm{g/cm^{2}}$ at energies above $2\times 10^{19}~\mathrm{eV}$.
description: Published version, 29 pages, 12 figures