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Abstract
The measurement of the flux of muons produced in cosmic ray air showers is essential for the study of primary cosmic rays. Such measurements are important in extensive air shower detectors to assess the energy spectrum and the chemical composition of the cosmic ray flux, complementary to the information provided by fluorescence detectors. Detailed simulations of the cosmic ray air showers are carried out, using codes such as CORSIKA, to estimate the muon flux at sea level. These simulations are based on the choice of hadronic interaction models, for which improvements have been implemented in the post-LHC era. In this work, a deficit in simulations that use state-of-the-art QCD models with respect to the measurement deep underwater with the KM3NeT neutrino detectors is reported. The KM3NeT/ARCA and KM3NeT/ORCA neutrino telescopes are sensitive to TeV muons originating mostly from primary cosmic rays with energies around 10 TeV. The predictions of state-of-the-art QCD models show that the deficit with respect to the data is constant in zenith angle; no dependency on the water overburden is observed. The observed deficit at a depth of several kilometres is compatible with the deficit seen in the comparison of the simulations and measurements at sea level.
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1 INFN, Sezione di Catania, (INFN-CT), Catania, Italy (GRID:grid.470198.3) (ISNI:0000 0004 1755 400X)
2 IPHC UMR 7178, Université de Strasbourg, CNRS, Strasbourg, France (GRID:grid.11843.3f) (ISNI:0000 0001 2157 9291); Université de Haute Alsace, Mulhouse Cedex, France (GRID:grid.9156.b) (ISNI:0000 0004 0473 5039)
3 Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France (GRID:grid.5399.6) (ISNI:0000 0001 2176 4817); University of Sharjah, Sharjah Academy for Astronomy, Space Sciences, and Technology, Sharjah, United Arab Emirates (GRID:grid.412789.1) (ISNI:0000 0004 4686 5317)
4 IFIC-Instituto de Física Corpuscular (CSIC-Universitat de València), Paterna, Spain (GRID:grid.470047.0) (ISNI:0000 0001 2178 9889)
5 Complesso Universitario di Monte S. Angelo, INFN, Sezione di Napoli, Naples, Italy (GRID:grid.4691.a) (ISNI:0000 0001 0790 385X); Università di Napoli “Federico II”, Dip. Scienze Fisiche “E. Pancini”, Complesso Universitario di Monte S. Angelo, Naples, Italy (GRID:grid.4691.a) (ISNI:0000 0001 0790 385X)
6 INFN, Sezione di Roma, Rome, Italy (GRID:grid.470218.8)
7 Universitat Politècnica de Catalunya, Laboratori d’Aplicacions Bioacústiques, Centre Tecnològic de Vilanova i la Geltrú, Vilanova i la Geltrú, Spain (GRID:grid.6835.8) (ISNI:0000 0004 1937 028X)
8 NCSR Demokritos, Institute of Nuclear and Particle Physics, Athens, Greece (GRID:grid.450262.7)
9 University of Granada, Dept. of Computer Architecture and Technology/CITIC, Granada, Spain (GRID:grid.4489.1) (ISNI:0000 0001 2167 8994)
10 Nantes Université, Subatech, IMT Atlantique, IN2P3-CNRS, Nantes, France (GRID:grid.4817.a) (ISNI:0000 0001 2189 0784)
11 Universitat Politècnica de València, Instituto de Investigación para la Gestión Integrada de las Zonas Costeras, Gandia, Spain (GRID:grid.157927.f) (ISNI:0000 0004 1770 5832)
12 Nikolaus-Fiebiger-Straße 2, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen Centre for Astroparticle Physics, Erlangen, Germany (GRID:grid.5330.5) (ISNI:0000 0001 2107 3311)
13 University Mohammed V in Rabat, Faculty of Sciences, Rabat, Morocco (GRID:grid.31143.34) (ISNI:0000 0001 2168 4024)
14 Université Paris Cité, CNRS, Astroparticule et Cosmologie, Paris, France (GRID:grid.508487.6) (ISNI:0000 0004 7885 7602)
15 INFN, Sezione di Genova, Genoa, Italy (GRID:grid.470205.4)
16 LPC CAEN, Normandie Univ, ENSICAEN, UNICAEN, CNRS/IN2P3, Caen, France (GRID:grid.463917.e) (ISNI:0000 0004 0623 3905)
17 Czech Technical University in Prague, Institute of Experimental and Applied Physics, Prague, Czech Republic (GRID:grid.6652.7) (ISNI:0000 0001 2173 8213); Comenius University in Bratislava, Department of Nuclear Physics and Biophysics, Bratislava, Slovak Republic (GRID:grid.7634.6) (ISNI:0000 0001 0940 9708)
18 Nikhef, National Institute for Subatomic Physics, Amsterdam, Netherlands (GRID:grid.420012.5) (ISNI:0000 0004 0646 2193)
19 University Mohammed V in Rabat, Faculty of Sciences, Rabat, Morocco (GRID:grid.31143.34) (ISNI:0000 0001 2168 4024); Université Paris Cité, CNRS, Astroparticule et Cosmologie, Paris, France (GRID:grid.508487.6) (ISNI:0000 0004 7885 7602)
20 INFN, Sezione di Bologna, Bologna, Italy (GRID:grid.470193.8) (ISNI:0000 0004 8343 7610); Università di Bologna, Dipartimento di Fisica e Astronomia, Bologna, Italy (GRID:grid.6292.f) (ISNI:0000 0004 1757 1758)
21 Complesso Universitario di Monte S. Angelo, INFN, Sezione di Napoli, Naples, Italy (GRID:grid.4691.a) (ISNI:0000 0001 0790 385X); Università degli Studi della Campania “Luigi Vanvitelli”, Dipartimento di Matematica e Fisica, Caserta, Italy (GRID:grid.9841.4) (ISNI:0000 0001 2200 8888)
22 University of Hull, E. A. Milne Centre for Astrophysics, Hull, UK (GRID:grid.9481.4) (ISNI:0000 0004 0412 8669)
23 Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France (GRID:grid.5399.6) (ISNI:0000 0001 2176 4817)
24 INFN, Laboratori Nazionali del Sud, Catania, Italy (GRID:grid.466880.4) (ISNI:0000 0004 1757 4895)
25 North-West University, Centre for Space Research, Potchefstroom, South Africa (GRID:grid.25881.36) (ISNI:0000 0000 9769 2525)
26 University Mohammed I, Faculty of Sciences, BV Mohammed VI, Oujda, Morocco (GRID:grid.410890.4) (ISNI:0000 0004 1772 8348)
27 Complesso Universitario di Monte S. Angelo, INFN, Sezione di Napoli, Naples, Italy (GRID:grid.4691.a) (ISNI:0000 0001 0790 385X); Università di Salerno e INFN Gruppo Collegato di Salerno, Dipartimento di Fisica, Fisciano, Italy (GRID:grid.470211.1) (ISNI:0000 0004 8343 7696)
28 ISS, Măgurele, Romania (GRID:grid.450283.8)
29 Nikhef, National Institute for Subatomic Physics, Amsterdam, Netherlands (GRID:grid.420012.5) (ISNI:0000 0004 0646 2193); University of Amsterdam, Institute of Physics/IHEF, Amsterdam, Netherlands (GRID:grid.7177.6) (ISNI:0000 0000 8499 2262)
30 Nikhef, National Institute for Subatomic Physics, Amsterdam, Netherlands (GRID:grid.420012.5) (ISNI:0000 0004 0646 2193); TNO, Technical Sciences, Delft, Netherlands (GRID:grid.4858.1) (ISNI:0000 0001 0208 7216)
31 INFN, Sezione di Roma, Rome, Italy (GRID:grid.470218.8); Università La Sapienza, Dipartimento di Fisica, Rome, Italy (GRID:grid.7841.a)
32 INFN, Sezione di Bologna, Bologna, Italy (GRID:grid.470193.8) (ISNI:0000 0004 8343 7610); Università di Bologna, Dipartimento di Ingegneria dell’Energia Elettrica e dell’Informazione ”Guglielmo Marconi”, Cesena, Italy (GRID:grid.6292.f) (ISNI:0000 0004 1757 1758)
33 Cadi Ayyad University, Physics Department, Faculty of Science Semlalia, Marrakech, Morocco (GRID:grid.411840.8) (ISNI:0000 0001 0664 9298)
34 University of the Witwatersrand, Wits, School of Physics, Johannesburg, South Africa (GRID:grid.11951.3d) (ISNI:0000 0004 1937 1135)
35 INFN, Laboratori Nazionali del Sud, Catania, Italy (GRID:grid.466880.4) (ISNI:0000 0004 1757 4895); Università di Catania (INFN-CT), Dipartimento di Fisica e Astronomia “Ettore Majorana”, Catania, Italy (GRID:grid.8158.4) (ISNI:0000 0004 1757 1969)
36 INFN, Sezione di Bologna, Bologna, Italy (GRID:grid.470193.8) (ISNI:0000 0004 8343 7610)
37 INFN, Sezione di Bari, Bari, Italy (GRID:grid.470190.b)
38 Complesso Universitario di Monte S. Angelo, INFN, Sezione di Napoli, Naples, Italy (GRID:grid.4691.a) (ISNI:0000 0001 0790 385X)
39 Julius-Maximilians-Universität Würzburg, Fakultät für Physik und Astronomie, Institut für Theoretische Physik und Astrophysik, Lehrstuhl für Astronomie, Würzburg, Germany (GRID:grid.8379.5) (ISNI:0000 0001 1958 8658)
40 Comenius University in Bratislava, Department of Nuclear Physics and Biophysics, Bratislava, Slovak Republic (GRID:grid.7634.6) (ISNI:0000 0001 0940 9708)
41 Western Sydney University, School of Computing, Engineering and Mathematics, Penrith, Australia (GRID:grid.1029.a) (ISNI:0000 0000 9939 5719)
42 INFN, Sezione di Genova, Genoa, Italy (GRID:grid.470205.4); Università di Genova, Genoa, Italy (GRID:grid.5606.5) (ISNI:0000 0001 2151 3065)
43 University of Granada, Dpto. de Física Teórica y del Cosmos & C.A.F.P.E., Granada, Spain (GRID:grid.4489.1) (ISNI:0000 0001 2167 8994)
44 NIOZ (Royal Netherlands Institute for Sea Research), Texel, The Netherlands (GRID:grid.10914.3d) (ISNI:0000 0001 2227 4609)
45 Nikhef, National Institute for Subatomic Physics, Amsterdam, Netherlands (GRID:grid.420012.5) (ISNI:0000 0004 0646 2193); Leiden University, Leiden Institute of Physics, Leiden, Netherlands (GRID:grid.5132.5) (ISNI:0000 0001 2312 1970)
46 AstroCeNT, Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Warsaw, Poland (GRID:grid.413454.3) (ISNI:0000 0001 1958 0162)
47 Tbilisi State University, Department of Physics, Tbilisi, Georgia (GRID:grid.26193.3f) (ISNI:0000 0001 2034 6082); The University of Georgia, Institute of Physics, Tbilisi, Georgia (GRID:grid.213876.9) (ISNI:0000 0004 1936 738X)
48 Université Paris Cité, CNRS, Astroparticule et Cosmologie, Paris, France (GRID:grid.508487.6) (ISNI:0000 0004 7885 7602); Institut Universitaire de France, Paris, France (GRID:grid.440891.0) (ISNI:0000 0001 1931 4817)
49 The University of Georgia, Institute of Physics, Tbilisi, Georgia (GRID:grid.213876.9) (ISNI:0000 0004 1936 738X)
50 IPHC UMR 7178, Université de Strasbourg, CNRS, Strasbourg, France (GRID:grid.11843.3f) (ISNI:0000 0001 2157 9291); INFN, Sezione di Bologna, Bologna, Italy (GRID:grid.470193.8) (ISNI:0000 0004 8343 7610)
51 Czech Technical University in Prague, Institute of Experimental and Applied Physics, Prague, Czech Republic (GRID:grid.6652.7) (ISNI:0000 0001 2173 8213)
52 INFN, Sezione di Bari, Bari, Italy (GRID:grid.470190.b); Tbilisi State University, Department of Physics, Tbilisi, Georgia (GRID:grid.26193.3f) (ISNI:0000 0001 2034 6082)
53 IPHC UMR 7178, Université de Strasbourg, CNRS, Strasbourg, France (GRID:grid.11843.3f) (ISNI:0000 0001 2157 9291)
54 University of Johannesburg, Department Physics, Auckland Park, South Africa (GRID:grid.412988.e) (ISNI:0000 0001 0109 131X)
55 INFN, Sezione di Genova, Genoa, Italy (GRID:grid.470205.4); LPC CAEN, Normandie Univ, ENSICAEN, UNICAEN, CNRS/IN2P3, Caen, France (GRID:grid.463917.e) (ISNI:0000 0004 0623 3905); Università di Genova, Genoa, Italy (GRID:grid.5606.5) (ISNI:0000 0001 2151 3065)
56 Tbilisi State University, Department of Physics, Tbilisi, Georgia (GRID:grid.26193.3f) (ISNI:0000 0001 2034 6082)
57 INFN, Sezione di Catania, (INFN-CT), Catania, Italy (GRID:grid.470198.3) (ISNI:0000 0004 1755 400X); Università di Catania (INFN-CT), Dipartimento di Fisica e Astronomia “Ettore Majorana”, Catania, Italy (GRID:grid.8158.4) (ISNI:0000 0004 1757 1969)
58 Laboratoire Univers et Particules de Montpellier, Montpellier Cédex 05, France (GRID:grid.464184.b) (ISNI:0000 0004 0382 470X)
59 Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Remeis Sternwarte, Bamberg, Germany (GRID:grid.5330.5) (ISNI:0000 0001 2107 3311)