Deep-Learning based Reconstruction of the Shower Maximum $X_{\mathrm{max}}$ using the Water-Cherenkov Detectors of the Pierre Auger Observatory

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

doi:10.1088/1748-0221/16/07/p07019

Title: Deep-Learning based Reconstruction of the Shower Maximum $$X_{\mathrm{max}}$$ using the Water-Cherenkov Detectors of the Pierre Auger Observatory

Abstract

The atmospheric depth of the air shower maximum X_max is an observable commonly used for the determination of the nuclear mass composition of ultra-high energy cosmic rays. Direct measurements of X_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_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_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_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 g/cm² at energies above 2 × 10¹⁹eV.

Authors:: Aab, A.; Abreu, P.; Aglietta, M.; Albury, J. M.; Allekotte, I.; Almela, A.; Alvarez-Muñiz, J.; Alves Batista, R.; Anastasi, G. A.; Anchordoqui, L.; Andrada, B.; Andringa, S.; Aramo, C.; Araújo Ferreira, P. R.; Arteaga Velázquez, J. C.; Asorey, H.; Assis, P.; Avila, G.; Badescu, A. M.; Bakalova, A. more »« less

Publication Date:: Wed Jul 14 00:00:00 EDT 2021

Research Org.:: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

Contributing Org.:: The Pierre Auger Collaboration

OSTI Identifier:: 1771163

Report Number(s):: FERMILAB-PUB-21-084-AD-AE-SCD-TD; arXiv:2101.02946
Journal ID: ISSN 1748-0221; oai:inspirehep.net:1840067; TRN: US2206891

Grant/Contract Number:: AC02-07CH11359

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Instrumentation

Additional Journal Information:: Journal Volume: 16; Journal Issue: 07; Journal ID: ISSN 1748-0221

Publisher:: Institute of Physics (IOP)

Country of Publication:: United States

Language:: English

Subject:: 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY

Citation Formats


                    Aab, A., Abreu, P., Aglietta, M., Albury, J. M., Allekotte, I., Almela, A., Alvarez-Muñiz, J., Alves Batista, R., Anastasi, G. A., Anchordoqui, L., Andrada, B., Andringa, S., Aramo, C., Araújo Ferreira, P. R., Arteaga Velázquez, J. C., Asorey, H., Assis, P., Avila, G., Badescu, A. M., Bakalova, A., Balaceanu, A., Barbato, F., Barreira Luz, R. J., Becker, K. H., Bellido, J. A., Berat, C., Bertaina, M. E., Bertou, X., Biermann, P. L., Bister, T., Biteau, J., Blazek, J., Bleve, C., Boháčová, M., Boncioli, D., Bonifazi, C., Bonneau Arbeletche, L., Borodai, N., Botti, A. M., Brack, J., Bretz, T., Brichetto Orchera, P. G., Briechle, F. L., Buchholz, P., Bueno, A., Buitink, S., Buscemi, M., Caballero-Mora, K. S., Caccianiga, L., Canfora, F., Caracas, I., Carceller, J. M., Caruso, R., Castellina, A., Catalani, F., Cataldi, G., Cazon, L., Cerda, M., Chinellato, J. A., Choi, K., Chudoba, J., Chytka, L., Clay, R. W., Cobos Cerutti, A. C., Colalillo, R., Coleman, A., Coluccia, M. R., Conceição, R., Condorelli, A., Consolati, G., Contreras, F., Convenga, F., Correia dos Santos, D., Covault, C. E., Dasso, S., Daumiller, K., Dawson, B. R., Day, J. A., de Almeida, R. M., de Jesús, J., de Jong, S. J., De Mauro, G., de Mello Neto, J. R.T., De Mitri, I., de Oliveira, J., de Oliveira Franco, D., de Palma, F., de Souza, V., De Vito, E., del Río, M., Deligny, O., Di Matteo, A., Dobrigkeit, C., D'Olivo, J. C., dos Anjos, R. C., Dova, M. T., Ebr, J., Engel, R., Epicoco, I., Erdmann, M., Escobar, C. O., Etchegoyen, A., Falcke, H., Farmer, J., Farrar, G., Fauth, A. C., Fazzini, N., Feldbusch, F., Fenu, F., Fick, B., Figueira, J. M., Filipčič, A., Fodran, T., Freire, M. M., Fujii, T., Fuster, A., Galea, C., Galelli, C., García, B., Garcia Vegas, A. L., Gemmeke, H., Gesualdi, F., Gherghel-Lascu, A., Ghia, P. L., Giaccari, U., Giammarchi, M., Giller, M., Glombitza, J., Gobbi, F., Gollan, F., Golup, G., Gómez Berisso, M., Gómez Vitale, P. F., Gongora, J. P., González, J. M., González, N., Goos, I., Góra, D., Gorgi, A., Gottowik, M., Grubb, T. D., Guarino, F., Guedes, G. P., Guido, E., Hahn, S., Hamal, P., Hampel, M. R., Hansen, P., Harari, D., Harvey, V. M., Haungs, A., Hebbeker, T., Heck, D., Hill, G. C., Hojvat, C., Hörandel, J. R., Horvath, P., Hrabovský, M., Huege, T., Hulsman, J., Insolia, A., Isar, P. G., Janecek, P., Johnsen, J. A., Jurysek, J., Kääpä, A., Kampert, K. H., Keilhauer, B., Kemp, J., Klages, H. O., Kleifges, M., Kleinfeller, J., Köpke, M., Kunka, N., Lago, B. L., Lang, R. G., Langner, N., Leigui de Oliveira, M. A., Lenok, V., Letessier-Selvon, A., Lhenry-Yvon, I., Lo Presti, D., Lopes, L., López, R., Lu, L., Luce, Q., Lucero, A., Lundquist, J. P., Machado Payeras, A., Mancarella, G., Mandat, D., Manning, B. C., Manshanden, J., Mantsch, P., Marafico, S., Mariazzi, A. G., Mariş, I. C., Marsella, G., Martello, D., Martinez, H., Martínez Bravo, O., Mastrodicasa, M., Mathes, H. J., Matthews, J., Matthiae, G., Mayotte, E., Mazur, P. O., Medina-Tanco, G., Melo, D., Menshikov, A., Merenda, K. -D., Michal, S., Micheletti, M. I., Miramonti, L., Mollerach, S., Montanet, F., Morello, C., Mostafá, M., Müller, A. L., Muller, M. A., Mulrey, K., Mussa, R., Muzio, M., Namasaka, W. M., Nasr-Esfahani, A., Nellen, L., Niculescu-Oglinzanu, M., Niechciol, M., Nitz, D., Nosek, D., Novotny, V., Nožka, L., Nucita, A., Núñez, L. A., Palatka, M., Pallotta, J., Papenbreer, P., Parente, G., Parra, A., Pech, M., Pedreira, F., Pȩkala, J., Pelayo, R., Peña-Rodriguez, J., Pereira Martins, E. E., Perez Armand, J., Pérez Bertolli, C., Perlin, M., Perrone, L., Petrera, S., Pierog, T., Pimenta, M., Pirronello, V., Platino, M., Pont, B., Pothast, M., Privitera, P., Prouza, M., Puyleart, A., Querchfeld, S., Rautenberg, J., Ravignani, D., Reininghaus, M., Ridky, J., Riehn, F., Risse, M., Rizi, V., Rodrigues de Carvalho, W., Rodriguez Rojo, J., Roncoroni, M. J., Roth, M., Roulet, E., Rovero, A. C., Ruehl, P., Saffi, S. J., Saftoiu, A., Salamida, F., Salazar, H., Salina, G., Sanabria Gomez, J. D., Sánchez, F., Santos, E. M., Santos, E., Sarazin, F., Sarmento, R., Sarmiento-Cano, C., Sato, R., Savina, P., Schäfer, C. M., Scherini, V., Schieler, H., Schimassek, M., Schimp, M., Schlüter, F., Schmidt, D., Scholten, O., Schovánek, P., Schröder, F. G., Schröder, S., Schulte, J., Sciutto, S. J., Scornavacche, M., Segreto, A., Sehgal, S., Shellard, R. C., Sigl, G., Silli, G., Sima, O., Šmída, R., Sommers, P., Soriano, J. F., Souchard, J., Squartini, R., Stadelmaier, M., Stanca, D., Stanič, S., Stasielak, J., Stassi, P., Streich, A., Suárez-Durán, M., Sudholz, T., Suomijärvi, T., Supanitsky, A. D., Šupík, J., Szadkowski, Z., Taboada, A., Tapia, A., Taricco, C., Timmermans, C., Tkachenko, O., Tobiska, P., Todero Peixoto, C. J., Tomé, B., Travaini, A., Travnicek, P., Trimarelli, C., Trini, M., Tueros, M., Ulrich, R., Unger, M., Vaclavek, L., Vacula, M., Valdés Galicia, J. F., Valore, L., Varela, E., Varma K.C., V., Vásquez-Ramírez, A., Veberič, D., Ventura, C., Vergara Quispe, I. D., Verzi, V., Vicha, J., Vink, J., Vorobiov, S., Wahlberg, H., Watanabe, C., Watson, A. A., Weber, M., Weindl, A., Wiencke, L., Wilczyński, H., Winchen, T., Wirtz, M., Wittkowski, D., Wundheiler, B., Yushkov, A., Zapparrata, O., Zas, E., Zavrtanik, D., Zavrtanik, M., Zehrer, L., and Zepeda, A. Deep-Learning based Reconstruction of the Shower Maximum $X_{\mathrm{max}}$ using the Water-Cherenkov Detectors of the Pierre Auger Observatory.  United States: N. p., 2021. 
Web.  doi:10.1088/1748-0221/16/07/p07019.

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                    Aab, A., Abreu, P., Aglietta, M., Albury, J. M., Allekotte, I., Almela, A., Alvarez-Muñiz, J., Alves Batista, R., Anastasi, G. A., Anchordoqui, L., Andrada, B., Andringa, S., Aramo, C., Araújo Ferreira, P. R., Arteaga Velázquez, J. C., Asorey, H., Assis, P., Avila, G., Badescu, A. M., Bakalova, A., Balaceanu, A., Barbato, F., Barreira Luz, R. J., Becker, K. H., Bellido, J. A., Berat, C., Bertaina, M. E., Bertou, X., Biermann, P. L., Bister, T., Biteau, J., Blazek, J., Bleve, C., Boháčová, M., Boncioli, D., Bonifazi, C., Bonneau Arbeletche, L., Borodai, N., Botti, A. M., Brack, J., Bretz, T., Brichetto Orchera, P. G., Briechle, F. L., Buchholz, P., Bueno, A., Buitink, S., Buscemi, M., Caballero-Mora, K. S., Caccianiga, L., Canfora, F., Caracas, I., Carceller, J. M., Caruso, R., Castellina, A., Catalani, F., Cataldi, G., Cazon, L., Cerda, M., Chinellato, J. A., Choi, K., Chudoba, J., Chytka, L., Clay, R. W., Cobos Cerutti, A. C., Colalillo, R., Coleman, A., Coluccia, M. R., Conceição, R., Condorelli, A., Consolati, G., Contreras, F., Convenga, F., Correia dos Santos, D., Covault, C. E., Dasso, S., Daumiller, K., Dawson, B. R., Day, J. A., de Almeida, R. M., de Jesús, J., de Jong, S. J., De Mauro, G., de Mello Neto, J. R.T., De Mitri, I., de Oliveira, J., de Oliveira Franco, D., de Palma, F., de Souza, V., De Vito, E., del Río, M., Deligny, O., Di Matteo, A., Dobrigkeit, C., D'Olivo, J. C., dos Anjos, R. C., Dova, M. T., Ebr, J., Engel, R., Epicoco, I., Erdmann, M., Escobar, C. O., Etchegoyen, A., Falcke, H., Farmer, J., Farrar, G., Fauth, A. C., Fazzini, N., Feldbusch, F., Fenu, F., Fick, B., Figueira, J. M., Filipčič, A., Fodran, T., Freire, M. M., Fujii, T., Fuster, A., Galea, C., Galelli, C., García, B., Garcia Vegas, A. L., Gemmeke, H., Gesualdi, F., Gherghel-Lascu, A., Ghia, P. L., Giaccari, U., Giammarchi, M., Giller, M., Glombitza, J., Gobbi, F., Gollan, F., Golup, G., Gómez Berisso, M., Gómez Vitale, P. F., Gongora, J. P., González, J. M., González, N., Goos, I., Góra, D., Gorgi, A., Gottowik, M., Grubb, T. D., Guarino, F., Guedes, G. P., Guido, E., Hahn, S., Hamal, P., Hampel, M. R., Hansen, P., Harari, D., Harvey, V. M., Haungs, A., Hebbeker, T., Heck, D., Hill, G. C., Hojvat, C., Hörandel, J. R., Horvath, P., Hrabovský, M., Huege, T., Hulsman, J., Insolia, A., Isar, P. G., Janecek, P., Johnsen, J. A., Jurysek, J., Kääpä, A., Kampert, K. H., Keilhauer, B., Kemp, J., Klages, H. O., Kleifges, M., Kleinfeller, J., Köpke, M., Kunka, N., Lago, B. L., Lang, R. G., Langner, N., Leigui de Oliveira, M. A., Lenok, V., Letessier-Selvon, A., Lhenry-Yvon, I., Lo Presti, D., Lopes, L., López, R., Lu, L., Luce, Q., Lucero, A., Lundquist, J. P., Machado Payeras, A., Mancarella, G., Mandat, D., Manning, B. C., Manshanden, J., Mantsch, P., Marafico, S., Mariazzi, A. G., Mariş, I. C., Marsella, G., Martello, D., Martinez, H., Martínez Bravo, O., Mastrodicasa, M., Mathes, H. J., Matthews, J., Matthiae, G., Mayotte, E., Mazur, P. O., Medina-Tanco, G., Melo, D., Menshikov, A., Merenda, K. -D., Michal, S., Micheletti, M. I., Miramonti, L., Mollerach, S., Montanet, F., Morello, C., Mostafá, M., Müller, A. L., Muller, M. A., Mulrey, K., Mussa, R., Muzio, M., Namasaka, W. M., Nasr-Esfahani, A., Nellen, L., Niculescu-Oglinzanu, M., Niechciol, M., Nitz, D., Nosek, D., Novotny, V., Nožka, L., Nucita, A., Núñez, L. A., Palatka, M., Pallotta, J., Papenbreer, P., Parente, G., Parra, A., Pech, M., Pedreira, F., Pȩkala, J., Pelayo, R., Peña-Rodriguez, J., Pereira Martins, E. E., Perez Armand, J., Pérez Bertolli, C., Perlin, M., Perrone, L., Petrera, S., Pierog, T., Pimenta, M., Pirronello, V., Platino, M., Pont, B., Pothast, M., Privitera, P., Prouza, M., Puyleart, A., Querchfeld, S., Rautenberg, J., Ravignani, D., Reininghaus, M., Ridky, J., Riehn, F., Risse, M., Rizi, V., Rodrigues de Carvalho, W., Rodriguez Rojo, J., Roncoroni, M. J., Roth, M., Roulet, E., Rovero, A. C., Ruehl, P., Saffi, S. J., Saftoiu, A., Salamida, F., Salazar, H., Salina, G., Sanabria Gomez, J. D., Sánchez, F., Santos, E. M., Santos, E., Sarazin, F., Sarmento, R., Sarmiento-Cano, C., Sato, R., Savina, P., Schäfer, C. M., Scherini, V., Schieler, H., Schimassek, M., Schimp, M., Schlüter, F., Schmidt, D., Scholten, O., Schovánek, P., Schröder, F. G., Schröder, S., Schulte, J., Sciutto, S. J., Scornavacche, M., Segreto, A., Sehgal, S., Shellard, R. C., Sigl, G., Silli, G., Sima, O., Šmída, R., Sommers, P., Soriano, J. F., Souchard, J., Squartini, R., Stadelmaier, M., Stanca, D., Stanič, S., Stasielak, J., Stassi, P., Streich, A., Suárez-Durán, M., Sudholz, T., Suomijärvi, T., Supanitsky, A. D., Šupík, J., Szadkowski, Z., Taboada, A., Tapia, A., Taricco, C., Timmermans, C., Tkachenko, O., Tobiska, P., Todero Peixoto, C. J., Tomé, B., Travaini, A., Travnicek, P., Trimarelli, C., Trini, M., Tueros, M., Ulrich, R., Unger, M., Vaclavek, L., Vacula, M., Valdés Galicia, J. F., Valore, L., Varela, E., Varma K.C., V., Vásquez-Ramírez, A., Veberič, D., Ventura, C., Vergara Quispe, I. D., Verzi, V., Vicha, J., Vink, J., Vorobiov, S., Wahlberg, H., Watanabe, C., Watson, A. A., Weber, M., Weindl, A., Wiencke, L., Wilczyński, H., Winchen, T., Wirtz, M., Wittkowski, D., Wundheiler, B., Yushkov, A., Zapparrata, O., Zas, E., Zavrtanik, D., Zavrtanik, M., Zehrer, L., & Zepeda, A. Deep-Learning based Reconstruction of the Shower Maximum $X_{\mathrm{max}}$ using the Water-Cherenkov Detectors of the Pierre Auger Observatory.  United States.  https://doi.org/10.1088/1748-0221/16/07/p07019

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                    Aab, A., Abreu, P., Aglietta, M., Albury, J. M., Allekotte, I., Almela, A., Alvarez-Muñiz, J., Alves Batista, R., Anastasi, G. A., Anchordoqui, L., Andrada, B., Andringa, S., Aramo, C., Araújo Ferreira, P. R., Arteaga Velázquez, J. C., Asorey, H., Assis, P., Avila, G., Badescu, A. M., Bakalova, A., Balaceanu, A., Barbato, F., Barreira Luz, R. J., Becker, K. H., Bellido, J. A., Berat, C., Bertaina, M. E., Bertou, X., Biermann, P. L., Bister, T., Biteau, J., Blazek, J., Bleve, C., Boháčová, M., Boncioli, D., Bonifazi, C., Bonneau Arbeletche, L., Borodai, N., Botti, A. M., Brack, J., Bretz, T., Brichetto Orchera, P. G., Briechle, F. L., Buchholz, P., Bueno, A., Buitink, S., Buscemi, M., Caballero-Mora, K. S., Caccianiga, L., Canfora, F., Caracas, I., Carceller, J. M., Caruso, R., Castellina, A., Catalani, F., Cataldi, G., Cazon, L., Cerda, M., Chinellato, J. A., Choi, K., Chudoba, J., Chytka, L., Clay, R. W., Cobos Cerutti, A. C., Colalillo, R., Coleman, A., Coluccia, M. R., Conceição, R., Condorelli, A., Consolati, G., Contreras, F., Convenga, F., Correia dos Santos, D., Covault, C. E., Dasso, S., Daumiller, K., Dawson, B. R., Day, J. A., de Almeida, R. M., de Jesús, J., de Jong, S. J., De Mauro, G., de Mello Neto, J. R.T., De Mitri, I., de Oliveira, J., de Oliveira Franco, D., de Palma, F., de Souza, V., De Vito, E., del Río, M., Deligny, O., Di Matteo, A., Dobrigkeit, C., D'Olivo, J. C., dos Anjos, R. C., Dova, M. T., Ebr, J., Engel, R., Epicoco, I., Erdmann, M., Escobar, C. O., Etchegoyen, A., Falcke, H., Farmer, J., Farrar, G., Fauth, A. C., Fazzini, N., Feldbusch, F., Fenu, F., Fick, B., Figueira, J. M., Filipčič, A., Fodran, T., Freire, M. M., Fujii, T., Fuster, A., Galea, C., Galelli, C., García, B., Garcia Vegas, A. L., Gemmeke, H., Gesualdi, F., Gherghel-Lascu, A., Ghia, P. L., Giaccari, U., Giammarchi, M., Giller, M., Glombitza, J., Gobbi, F., Gollan, F., Golup, G., Gómez Berisso, M., Gómez Vitale, P. F., Gongora, J. P., González, J. M., González, N., Goos, I., Góra, D., Gorgi, A., Gottowik, M., Grubb, T. D., Guarino, F., Guedes, G. P., Guido, E., Hahn, S., Hamal, P., Hampel, M. R., Hansen, P., Harari, D., Harvey, V. M., Haungs, A., Hebbeker, T., Heck, D., Hill, G. C., Hojvat, C., Hörandel, J. R., Horvath, P., Hrabovský, M., Huege, T., Hulsman, J., Insolia, A., Isar, P. G., Janecek, P., Johnsen, J. A., Jurysek, J., Kääpä, A., Kampert, K. H., Keilhauer, B., Kemp, J., Klages, H. O., Kleifges, M., Kleinfeller, J., Köpke, M., Kunka, N., Lago, B. L., Lang, R. G., Langner, N., Leigui de Oliveira, M. A., Lenok, V., Letessier-Selvon, A., Lhenry-Yvon, I., Lo Presti, D., Lopes, L., López, R., Lu, L., Luce, Q., Lucero, A., Lundquist, J. P., Machado Payeras, A., Mancarella, G., Mandat, D., Manning, B. C., Manshanden, J., Mantsch, P., Marafico, S., Mariazzi, A. G., Mariş, I. C., Marsella, G., Martello, D., Martinez, H., Martínez Bravo, O., Mastrodicasa, M., Mathes, H. J., Matthews, J., Matthiae, G., Mayotte, E., Mazur, P. O., Medina-Tanco, G., Melo, D., Menshikov, A., Merenda, K. -D., Michal, S., Micheletti, M. I., Miramonti, L., Mollerach, S., Montanet, F., Morello, C., Mostafá, M., Müller, A. L., Muller, M. A., Mulrey, K., Mussa, R., Muzio, M., Namasaka, W. M., Nasr-Esfahani, A., Nellen, L., Niculescu-Oglinzanu, M., Niechciol, M., Nitz, D., Nosek, D., Novotny, V., Nožka, L., Nucita, A., Núñez, L. A., Palatka, M., Pallotta, J., Papenbreer, P., Parente, G., Parra, A., Pech, M., Pedreira, F., Pȩkala, J., Pelayo, R., Peña-Rodriguez, J., Pereira Martins, E. E., Perez Armand, J., Pérez Bertolli, C., Perlin, M., Perrone, L., Petrera, S., Pierog, T., Pimenta, M., Pirronello, V., Platino, M., Pont, B., Pothast, M., Privitera, P., Prouza, M., Puyleart, A., Querchfeld, S., Rautenberg, J., Ravignani, D., Reininghaus, M., Ridky, J., Riehn, F., Risse, M., Rizi, V., Rodrigues de Carvalho, W., Rodriguez Rojo, J., Roncoroni, M. J., Roth, M., Roulet, E., Rovero, A. C., Ruehl, P., Saffi, S. J., Saftoiu, A., Salamida, F., Salazar, H., Salina, G., Sanabria Gomez, J. D., Sánchez, F., Santos, E. M., Santos, E., Sarazin, F., Sarmento, R., Sarmiento-Cano, C., Sato, R., Savina, P., Schäfer, C. M., Scherini, V., Schieler, H., Schimassek, M., Schimp, M., Schlüter, F., Schmidt, D., Scholten, O., Schovánek, P., Schröder, F. G., Schröder, S., Schulte, J., Sciutto, S. J., Scornavacche, M., Segreto, A., Sehgal, S., Shellard, R. C., Sigl, G., Silli, G., Sima, O., Šmída, R., Sommers, P., Soriano, J. F., Souchard, J., Squartini, R., Stadelmaier, M., Stanca, D., Stanič, S., Stasielak, J., Stassi, P., Streich, A., Suárez-Durán, M., Sudholz, T., Suomijärvi, T., Supanitsky, A. D., Šupík, J., Szadkowski, Z., Taboada, A., Tapia, A., Taricco, C., Timmermans, C., Tkachenko, O., Tobiska, P., Todero Peixoto, C. J., Tomé, B., Travaini, A., Travnicek, P., Trimarelli, C., Trini, M., Tueros, M., Ulrich, R., Unger, M., Vaclavek, L., Vacula, M., Valdés Galicia, J. F., Valore, L., Varela, E., Varma K.C., V., Vásquez-Ramírez, A., Veberič, D., Ventura, C., Vergara Quispe, I. D., Verzi, V., Vicha, J., Vink, J., Vorobiov, S., Wahlberg, H., Watanabe, C., Watson, A. A., Weber, M., Weindl, A., Wiencke, L., Wilczyński, H., Winchen, T., Wirtz, M., Wittkowski, D., Wundheiler, B., Yushkov, A., Zapparrata, O., Zas, E., Zavrtanik, D., Zavrtanik, M., Zehrer, L., and Zepeda, A. Wed .  
"Deep-Learning based Reconstruction of the Shower Maximum $X_{\mathrm{max}}$ using the Water-Cherenkov Detectors of the Pierre Auger Observatory".  United States.  https://doi.org/10.1088/1748-0221/16/07/p07019.  https://www.osti.gov/servlets/purl/1771163.

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@article{osti_1771163,

  title        = {Deep-Learning based Reconstruction of the Shower Maximum $X_{\mathrm{max}}$ using the Water-Cherenkov Detectors of the Pierre Auger Observatory},

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

  abstractNote = {The atmospheric depth of the air shower maximum Xmax is an observable commonly used for the determination of the nuclear mass composition of ultra-high energy cosmic rays. Direct measurements of Xmax 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 Xmax 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 Xmax. 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 Xmax 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 g/cm2 at energies above 2 × 1019 eV.},

  doi          = {10.1088/1748-0221/16/07/p07019},

  journal      = {Journal of Instrumentation},

  number       = 07,

  volume       = 16,

  place        = {United States},

  year         = {Wed Jul 14 00:00:00 EDT 2021},

  month        = {Wed Jul 14 00:00:00 EDT 2021}

}

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Here, we describe the method devised to reconstruct inclined cosmic-ray air showers with zenith angles greater than 60° detected with the surface array of the Pierre Auger Observatory. The measured signals at the ground level are fitted to muon density distributions predicted with atmospheric cascade models to obtain the relative shower size as an overall normalization parameter. The method is evaluated using simulated showers to test its performance. The energy of the cosmic rays is calibrated using a sub-sample of events reconstructed with both the fluorescence and surface array techniques. The reconstruction method described here provides the basis of complementarymore »« less
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https://doi.org/10.1088/1475-7516/2014/08/019

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Title: Deep-Learning based Reconstruction of the Shower Maximum $$X_{\mathrm{max}}$$ using the Water-Cherenkov Detectors of the Pierre Auger Observatory

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A generalized description of the signal size in extensive air shower detectors and its applications journal, January 2017

Reconstruction of events recorded with the surface detector of the Pierre Auger Observatory journal, October 2020

Deep Residual Learning for Image Recognition conference, June 2016

Muons in air showers at the Pierre Auger Observatory: Mean number in highly inclined events journal, February 2015

The Pierre Auger Cosmic Ray Observatory journal, July 2015

Measurement of the Depth of Maximum of Extensive Air Showers above 10 18 eV journal, March 2010

A generalized description of the time dependent signals in extensive air shower detectors and its applications journal, February 2017

Geant4—a simulation toolkit journal, July 2003

Measurements of the cosmic ray composition with air shower experiments journal, May 2012

Trigger and aperture of the surface detector array of the Pierre Auger Observatory journal, January 2010

Angular and energy distributions of charged particles in electron-photon cascades in air journal, October 1982

A deep learning-based reconstruction of cosmic ray-induced air showers journal, January 2018

The offline software framework of the Pierre Auger Observatory journal, October 2007

Measurement of the Proton-Air Cross Section at s = 57 TeV with the Pierre Auger Observatory journal, August 2012

Inferences on mass composition and tests of hadronic interactions from 0.3 to 100 EeV using the water-Cherenkov detectors of the Pierre Auger Observatory journal, December 2017

Measurements of the cosmic ray composition with air shower experiments journal, May 2012

A generalized description of the signal size in extensive air shower detectors and its applications journal, January 2017

A deep learning-based reconstruction of cosmic ray-induced air showers journal, January 2018

Angular and energy distributions of charged particles in electron-photon cascades in air journal, October 1982

A generalized description of the signal size in extensive air shower detectors and its applications
journal, January 2017

Reconstruction of events recorded with the surface detector of the Pierre Auger Observatory
journal, October 2020

Deep Residual Learning for Image Recognition
conference, June 2016

Muons in air showers at the Pierre Auger Observatory: Mean number in highly inclined events
journal, February 2015

The Pierre Auger Cosmic Ray Observatory
journal, July 2015

Measurement of the Depth of Maximum of Extensive Air Showers above $10^{18} eV$
journal, March 2010

A generalized description of the time dependent signals in extensive air shower detectors and its applications
journal, February 2017

Geant4—a simulation toolkit
journal, July 2003

Measurements of the cosmic ray composition with air shower experiments
journal, May 2012

Trigger and aperture of the surface detector array of the Pierre Auger Observatory
journal, January 2010

Angular and energy distributions of charged particles in electron-photon cascades in air
journal, October 1982

A deep learning-based reconstruction of cosmic ray-induced air showers
journal, January 2018

The offline software framework of the Pierre Auger Observatory
journal, October 2007

Measurement of the Proton-Air Cross Section at $\sqrt{s} = 57 TeV$ with the Pierre Auger Observatory
journal, August 2012

Inferences on mass composition and tests of hadronic interactions from 0.3 to 100 EeV using the water-Cherenkov detectors of the Pierre Auger Observatory
journal, December 2017

Measurements of the cosmic ray composition with air shower experiments
journal, May 2012

A generalized description of the signal size in extensive air shower detectors and its applications
journal, January 2017

A deep learning-based reconstruction of cosmic ray-induced air showers
journal, January 2018

Angular and energy distributions of charged particles in electron-photon cascades in air
journal, October 1982