The Pierre Auger Collaboration

# 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

A. Aab  IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands  P.
Abreu  Laboratório de Instrumentação e Física Experimental de Partículas – LIP
and Instituto Superior Técnico – IST, Universidade de Lisboa – UL, Lisboa,
Portugal  M. Aglietta  Osservatorio Astrofisico di Torino (INAF), Torino,
Italy  INFN, Sezione di Torino, Torino, Italy  I. Al Samarai  Laboratoire de
Physique Nucléaire et de Hautes Energies (LPNHE), Universités Paris 6 et Paris
7, CNRS-IN2P3, Paris, France  I.F.M. Albuquerque  Universidade de São Paulo,
Instituto de Física, São Paulo, SP, Brazil  I. Allekotte  Centro Atómico
Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de
Bariloche, Argentina  A. Almela  Instituto de Tecnologías en Detección y
Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina  Universidad
Tecnológica Nacional – Facultad Regional Buenos Aires, Buenos Aires, Argentina
J. Alvarez Castillo  Universidad Nacional Autónoma de México, México, D.F.,
México  J. Alvarez-Muñiz  Universidad de Santiago de Compostela, Santiago de
Compostela, Spain  G.A. Anastasi  Gran Sasso Science Institute (INFN),
L’Aquila, Italy  INFN Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila),
Italy  L. Anchordoqui  Department of Physics and Astronomy, Lehman College,
City University of New York, Bronx, NY, USA  B. Andrada  Instituto de
Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos
Aires, Argentina  S. Andringa  Laboratório de Instrumentação e Física
Experimental de Partículas – LIP and Instituto Superior Técnico – IST,
Universidade de Lisboa – UL, Lisboa, Portugal  C. Aramo  INFN, Sezione di
Napoli, Napoli, Italy  F. Arqueros  Universidad Complutense de Madrid, Madrid,
Spain  N. Arsene  Institute of Space Science, Bucharest-Magurele, Romania  H.
Asorey  Centro Atómico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET),
San Carlos de Bariloche, Argentina  Universidad Industrial de Santander,
Bucaramanga, Colombia  P. Assis  Laboratório de Instrumentação e Física
Experimental de Partículas – LIP and Instituto Superior Técnico – IST,
Universidade de Lisboa – UL, Lisboa, Portugal  J. Aublin  Laboratoire de
Physique Nucléaire et de Hautes Energies (LPNHE), Universités Paris 6 et Paris
7, CNRS-IN2P3, Paris, France  G. Avila  Observatorio Pierre Auger, Malargüe,
Argentina  Observatorio Pierre Auger and Comisión Nacional de Energía Atómica,
Malargüe, Argentina  A.M. Badescu  University Politehnica of Bucharest,
Bucharest, Romania  A. Balaceanu  “Horia Hulubei” National Institute for
Physics and Nuclear Engineering, Bucharest-Magurele, Romania  F. Barbato
Università di Napoli ”Federico II”, Dipartimento di Fisica “Ettore Pancini“,
Napoli, Italy  R.J. Barreira Luz  Laboratório de Instrumentação e Física
Experimental de Partículas – LIP and Instituto Superior Técnico – IST,
Universidade de Lisboa – UL, Lisboa, Portugal  J.J. Beatty  Ohio State
University, Columbus, OH, USA  K.H. Becker  Bergische Universität Wuppertal,
Department of Physics, Wuppertal, Germany  J.A. Bellido  University of
Adelaide, Adelaide, S.A., Australia  C. Berat  Laboratoire de Physique
Subatomique et de Cosmologie (LPSC), Université Grenoble-Alpes, CNRS/IN2P3,
Grenoble, France  M.E. Bertaina  Università Torino, Dipartimento di Fisica,
Torino, Italy  INFN, Sezione di Torino, Torino, Italy  X. Bertou  Centro
Atómico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de
Bariloche, Argentina  P.L. Biermann  Max-Planck-Institut für Radioastronomie,
Bonn, Germany  J. Biteau  Institut de Physique Nucléaire d’Orsay (IPNO),
Université Paris-Sud, Univ. Paris/Saclay, CNRS-IN2P3, Orsay, France  S.G.
Blaess  University of Adelaide, Adelaide, S.A., Australia  A. Blanco
Laboratório de Instrumentação e Física Experimental de Partículas – LIP and
Instituto Superior Técnico – IST, Universidade de Lisboa – UL, Lisboa,
Portugal  J. Blazek  Institute of Physics of the Czech Academy of Sciences,
Prague, Czech Republic  C. Bleve  Università del Salento, Dipartimento di
Matematica e Fisica “E. De Giorgi”, Lecce, Italy  INFN, Sezione di Lecce,
Lecce, Italy  M. Boháčová  Institute of Physics of the Czech Academy of
Sciences, Prague, Czech Republic  D. Boncioli  INFN Laboratori Nazionali del
Gran Sasso, Assergi (L’Aquila), Italy  now at Deutsches Elektronen-Synchrotron
(DESY), Zeuthen, Germany  C. Bonifazi  Universidade Federal do Rio de Janeiro,
Instituto de Física, Rio de Janeiro, RJ, Brazil  N. Borodai  Institute of
Nuclear Physics PAN, Krakow, Poland  A.M. Botti  Instituto de Tecnologías en
Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina
Karlsruhe Institute of Technology, Institut für Kernphysik, Karlsruhe, Germany
J. Brack  Colorado State University, Fort Collins, CO, USA  I. Brancus  “Horia
Hulubei” National Institute for Physics and Nuclear Engineering, Bucharest-
Magurele, Romania  T. Bretz  RWTH Aachen University, III. Physikalisches
Institut A, Aachen, Germany  A. Bridgeman  Karlsruhe Institute of Technology,
Institut für Kernphysik, Karlsruhe, Germany  F.L. Briechle  RWTH Aachen
University, III. Physikalisches Institut A, Aachen, Germany  P. Buchholz
Universität Siegen, Fachbereich 7 Physik – Experimentelle Teilchenphysik,
Siegen, Germany  A. Bueno  Universidad de Granada and C.A.F.P.E., Granada,
Spain  S. Buitink  IMAPP, Radboud University Nijmegen, Nijmegen, The
Netherlands  M. Buscemi  Università di Catania, Dipartimento di Fisica e
Astronomia, Catania, Italy  INFN, Sezione di Catania, Catania, Italy  K.S.
Caballero-Mora  Universidad Autónoma de Chiapas, Tuxtla Gutiérrez, Chiapas,
México  L. Caccianiga  Università di Milano, Dipartimento di Fisica, Milano,
Italy  A. Cancio  Universidad Tecnológica Nacional – Facultad Regional Buenos
Aires, Buenos Aires, Argentina  Instituto de Tecnologías en Detección y
Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina  F. Canfora
IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands  L. Caramete
Institute of Space Science, Bucharest-Magurele, Romania  R. Caruso  Università
di Catania, Dipartimento di Fisica e Astronomia, Catania, Italy  INFN, Sezione
di Catania, Catania, Italy  A. Castellina  Osservatorio Astrofisico di Torino
(INAF), Torino, Italy  INFN, Sezione di Torino, Torino, Italy  F. Catalani
Universidade de São Paulo, Instituto de Física, São Paulo, SP, Brazil  G.
Cataldi  INFN, Sezione di Lecce, Lecce, Italy  L. Cazon  Laboratório de
Instrumentação e Física Experimental de Partículas – LIP and Instituto
Superior Técnico – IST, Universidade de Lisboa – UL, Lisboa, Portugal  A.G.
Chavez  Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán,
México  J.A. Chinellato  Universidade Estadual de Campinas, IFGW, Campinas,
SP, Brazil  J. Chudoba  Institute of Physics of the Czech Academy of Sciences,
Prague, Czech Republic  R.W. Clay  University of Adelaide, Adelaide, S.A.,
Australia  A. Cobos  Instituto de Tecnologías en Detección y Astropartículas
(CNEA, CONICET, UNSAM), Buenos Aires, Argentina  R. Colalillo  Università di
Napoli ”Federico II”, Dipartimento di Fisica “Ettore Pancini“, Napoli, Italy
INFN, Sezione di Napoli, Napoli, Italy  A. Coleman  Pennsylvania State
University, University Park, PA, USA  L. Collica  INFN, Sezione di Torino,
Torino, Italy  M.R. Coluccia  Università del Salento, Dipartimento di
Matematica e Fisica “E. De Giorgi”, Lecce, Italy  INFN, Sezione di Lecce,
Lecce, Italy  R. Conceição  Laboratório de Instrumentação e Física
Experimental de Partículas – LIP and Instituto Superior Técnico – IST,
Universidade de Lisboa – UL, Lisboa, Portugal  G. Consolati  INFN, Sezione di
Milano, Milano, Italy  Politecnico di Milano, Dipartimento di Scienze e
Tecnologie Aerospaziali , Milano, Italy  F. Contreras  Observatorio Pierre
Auger, Malargüe, Argentina  Observatorio Pierre Auger and Comisión Nacional de
Energía Atómica, Malargüe, Argentina  M.J. Cooper  University of Adelaide,
Adelaide, S.A., Australia  S. Coutu  Pennsylvania State University, University
Park, PA, USA  C.E. Covault  Case Western Reserve University, Cleveland, OH,
USA  J. Cronin  University of Chicago, Enrico Fermi Institute, Chicago, IL,
USA  S. D’Amico  Università del Salento, Dipartimento di Ingegneria, Lecce,
Italy  INFN, Sezione di Lecce, Lecce, Italy  B. Daniel  Universidade Estadual
de Campinas, IFGW, Campinas, SP, Brazil  S. Dasso  Instituto de Astronomía y
Física del Espacio (IAFE, CONICET-UBA), Buenos Aires, Argentina  Departamento
de Física and Departamento de Ciencias de la Atmósfera y los Océanos, FCEyN,
Universidad de Buenos Aires and CONICET, Buenos Aires, Argentina  K. Daumiller
Karlsruhe Institute of Technology, Institut für Kernphysik, Karlsruhe, Germany
B.R. Dawson  University of Adelaide, Adelaide, S.A., Australia  R.M. de
Almeida  Universidade Federal Fluminense, EEIMVR, Volta Redonda, RJ, Brazil
S.J. de Jong  IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands
Nationaal Instituut voor Kernfysica en Hoge Energie Fysica (NIKHEF), Science
Park, Amsterdam, The Netherlands  G. De Mauro  IMAPP, Radboud University
Nijmegen, Nijmegen, The Netherlands  J.R.T. de Mello Neto  Universidade
Federal do Rio de Janeiro, Instituto de Física, Rio de Janeiro, RJ, Brazil
Universidade Federal do Rio de Janeiro (UFRJ), Observatório do Valongo, Rio de
Janeiro, RJ, Brazil  I. De Mitri  Università del Salento, Dipartimento di
Matematica e Fisica “E. De Giorgi”, Lecce, Italy  INFN, Sezione di Lecce,
Lecce, Italy  J. de Oliveira  Universidade Federal Fluminense, EEIMVR, Volta
Redonda, RJ, Brazil  V. de Souza  Universidade de São Paulo, Instituto de
Física de São Carlos, São Carlos, SP, Brazil  J. Debatin  Karlsruhe Institute
of Technology, Institut für Kernphysik, Karlsruhe, Germany  O. Deligny
Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud, Univ.
Paris/Saclay, CNRS-IN2P3, Orsay, France  M.L. Díaz Castro  Universidade
Estadual de Campinas, IFGW, Campinas, SP, Brazil  F. Diogo  Laboratório de
Instrumentação e Física Experimental de Partículas – LIP and Instituto
Superior Técnico – IST, Universidade de Lisboa – UL, Lisboa, Portugal  C.
Dobrigkeit  Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil
J.C. D’Olivo  Universidad Nacional Autónoma de México, México, D.F., México
Q. Dorosti  Universität Siegen, Fachbereich 7 Physik – Experimentelle
Teilchenphysik, Siegen, Germany  R.C. dos Anjos  Universidade Federal do
Paraná, Setor Palotina, Palotina, Brazil  M.T. Dova  IFLP, Universidad
Nacional de La Plata and CONICET, La Plata, Argentina  A. Dundovic
Universität Hamburg, II. Institut für Theoretische Physik, Hamburg, Germany
J. Ebr  Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic  R. Engel  Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, Germany  M. Erdmann  RWTH Aachen University, III.
Physikalisches Institut A, Aachen, Germany  M. Erfani  Universität Siegen,
Fachbereich 7 Physik – Experimentelle Teilchenphysik, Siegen, Germany  C.O.
Escobar  Fermi National Accelerator Laboratory, USA  J. Espadanal  Laboratório
de Instrumentação e Física Experimental de Partículas – LIP and Instituto
Superior Técnico – IST, Universidade de Lisboa – UL, Lisboa, Portugal  A.
Etchegoyen  Instituto de Tecnologías en Detección y Astropartículas (CNEA,
CONICET, UNSAM), Buenos Aires, Argentina  Universidad Tecnológica Nacional –
Facultad Regional Buenos Aires, Buenos Aires, Argentina  H. Falcke  IMAPP,
Radboud University Nijmegen, Nijmegen, The Netherlands  Stichting Astronomisch
Onderzoek in Nederland (ASTRON), Dwingeloo, The Netherlands  Nationaal
Instituut voor Kernfysica en Hoge Energie Fysica (NIKHEF), Science Park,
Amsterdam, The Netherlands  J. Farmer  University of Chicago, Enrico Fermi
Institute, Chicago, IL, USA  G. Farrar  New York University, New York, NY, USA
A.C. Fauth  Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil  N.
Fazzini  Fermi National Accelerator Laboratory, USA  F. Fenu  Università
Torino, Dipartimento di Fisica, Torino, Italy  INFN, Sezione di Torino,
Torino, Italy  B. Fick  Michigan Technological University, Houghton, MI, USA
J.M. Figueira  Instituto de Tecnologías en Detección y Astropartículas (CNEA,
CONICET, UNSAM), Buenos Aires, Argentina  A. Filipčič  Experimental Particle
Physics Department, J. Stefan Institute, Ljubljana, Slovenia  Center for
Astrophysics and Cosmology (CAC), University of Nova Gorica, Nova Gorica,
Slovenia  O. Fratu  University Politehnica of Bucharest, Bucharest, Romania
M.M. Freire  Instituto de Física de Rosario (IFIR) – CONICET/U.N.R. and
Facultad de Ciencias Bioquímicas y Farmacéuticas U.N.R., Rosario, Argentina
T. Fujii  University of Chicago, Enrico Fermi Institute, Chicago, IL, USA  A.
Fuster  Instituto de Tecnologías en Detección y Astropartículas (CNEA,
CONICET, UNSAM), Buenos Aires, Argentina  Universidad Tecnológica Nacional –
Facultad Regional Buenos Aires, Buenos Aires, Argentina  R. Gaior  Laboratoire
de Physique Nucléaire et de Hautes Energies (LPNHE), Universités Paris 6 et
Paris 7, CNRS-IN2P3, Paris, France  B. García  Instituto de Tecnologías en
Detección y Astropartículas (CNEA, CONICET, UNSAM), and Universidad
Tecnológica Nacional – Facultad Regional Mendoza (CONICET/CNEA), Mendoza,
Argentina  D. Garcia-Pinto  Universidad Complutense de Madrid, Madrid, Spain
F. Gaté  SUBATECH, École des Mines de Nantes, CNRS-IN2P3, Université de
Nantes, France  H. Gemmeke  Karlsruhe Institute of Technology, Institut für
Prozessdatenverarbeitung und Elektronik, Karlsruhe, Germany  A. Gherghel-Lascu
“Horia Hulubei” National Institute for Physics and Nuclear Engineering,
Bucharest-Magurele, Romania  P.L. Ghia  Institut de Physique Nucléaire d’Orsay
(IPNO), Université Paris-Sud, Univ. Paris/Saclay, CNRS-IN2P3, Orsay, France
U. Giaccari  Universidade Federal do Rio de Janeiro, Instituto de Física, Rio
de Janeiro, RJ, Brazil  M. Giammarchi  INFN, Sezione di Milano, Milano, Italy
M. Giller  University of Łódź, Faculty of Astrophysics, Łódź, Poland  D. Głas
University of Łódź, Faculty of High-Energy Astrophysics,Łódź, Poland  C.
Glaser  RWTH Aachen University, III. Physikalisches Institut A, Aachen,
Germany  G. Golup  Centro Atómico Bariloche and Instituto Balseiro (CNEA-
UNCuyo-CONICET), San Carlos de Bariloche, Argentina  M. Gómez Berisso  Centro
Atómico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de
Bariloche, Argentina  P.F. Gómez Vitale  Observatorio Pierre Auger, Malargüe,
Argentina  Observatorio Pierre Auger and Comisión Nacional de Energía Atómica,
Malargüe, Argentina  N. González  Instituto de Tecnologías en Detección y
Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina  Karlsruhe
Institute of Technology, Institut für Kernphysik, Karlsruhe, Germany  A. Gorgi
Osservatorio Astrofisico di Torino (INAF), Torino, Italy  INFN, Sezione di
Torino, Torino, Italy  P. Gorham  University of Hawaii, Honolulu, HI, USA
A.F. Grillo  INFN Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila),
Italy  T.D. Grubb  University of Adelaide, Adelaide, S.A., Australia  F.
Guarino  Università di Napoli ”Federico II”, Dipartimento di Fisica “Ettore
Pancini“, Napoli, Italy  INFN, Sezione di Napoli, Napoli, Italy  G.P. Guedes
Universidade Estadual de Feira de Santana, Feira de Santana, Brazil  R.
Halliday  Case Western Reserve University, Cleveland, OH, USA  M.R. Hampel
Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET,
UNSAM), Buenos Aires, Argentina  P. Hansen  IFLP, Universidad Nacional de La
Plata and CONICET, La Plata, Argentina  D. Harari  Centro Atómico Bariloche
and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de Bariloche,
Argentina  T.A. Harrison  University of Adelaide, Adelaide, S.A., Australia
J.L. Harton  Colorado State University, Fort Collins, CO, USA  A. Haungs
Karlsruhe Institute of Technology, Institut für Kernphysik, Karlsruhe, Germany
T. Hebbeker  RWTH Aachen University, III. Physikalisches Institut A, Aachen,
Germany  D. Heck  Karlsruhe Institute of Technology, Institut für Kernphysik,
Karlsruhe, Germany  P. Heimann  Universität Siegen, Fachbereich 7 Physik –
Experimentelle Teilchenphysik, Siegen, Germany  A.E. Herve  Karlsruhe
Institute of Technology, Institut für Experimentelle Kernphysik (IEKP),
Karlsruhe, Germany  G.C. Hill  University of Adelaide, Adelaide, S.A.,
Australia  C. Hojvat  Fermi National Accelerator Laboratory, USA  E. Holt
Karlsruhe Institute of Technology, Institut für Kernphysik, Karlsruhe, Germany
Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET,
UNSAM), Buenos Aires, Argentina  P. Homola  Institute of Nuclear Physics PAN,
Krakow, Poland  J.R. Hörandel  IMAPP, Radboud University Nijmegen, Nijmegen,
The Netherlands  Nationaal Instituut voor Kernfysica en Hoge Energie Fysica
(NIKHEF), Science Park, Amsterdam, The Netherlands  P. Horvath  Palacky
University, RCPTM, Olomouc, Czech Republic  M. Hrabovský  Palacky University,
RCPTM, Olomouc, Czech Republic  T. Huege  Karlsruhe Institute of Technology,
Institut für Kernphysik, Karlsruhe, Germany  J. Hulsman  Instituto de
Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos
Aires, Argentina  Karlsruhe Institute of Technology, Institut für Kernphysik,
Karlsruhe, Germany  A. Insolia  Università di Catania, Dipartimento di Fisica
e Astronomia, Catania, Italy  INFN, Sezione di Catania, Catania, Italy  P.G.
Isar  Institute of Space Science, Bucharest-Magurele, Romania  I. Jandt
Bergische Universität Wuppertal, Department of Physics, Wuppertal, Germany
J.A. Johnsen  Colorado School of Mines, Golden, CO, USA  M. Josebachuili
Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET,
UNSAM), Buenos Aires, Argentina  J. Jurysek  Institute of Physics of the Czech
Academy of Sciences, Prague, Czech Republic  A. Kääpä  Bergische Universität
Wuppertal, Department of Physics, Wuppertal, Germany  O. Kambeitz  Karlsruhe
Institute of Technology, Institut für Experimentelle Kernphysik (IEKP),
Karlsruhe, Germany  K.H. Kampert  Bergische Universität Wuppertal, Department
of Physics, Wuppertal, Germany  B. Keilhauer  Karlsruhe Institute of
Technology, Institut für Kernphysik, Karlsruhe, Germany  N. Kemmerich
Universidade de São Paulo, Instituto de Física, São Paulo, SP, Brazil  E. Kemp
Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil  J. Kemp  RWTH
Aachen University, III. Physikalisches Institut A, Aachen, Germany  R.M.
Kieckhafer  Michigan Technological University, Houghton, MI, USA  H.O. Klages
Karlsruhe Institute of Technology, Institut für Kernphysik, Karlsruhe, Germany
M. Kleifges  Karlsruhe Institute of Technology, Institut für
Prozessdatenverarbeitung und Elektronik, Karlsruhe, Germany  J. Kleinfeller
Observatorio Pierre Auger, Malargüe, Argentina  R. Krause  RWTH Aachen
University, III. Physikalisches Institut A, Aachen, Germany  N. Krohm
Bergische Universität Wuppertal, Department of Physics, Wuppertal, Germany  D.
Kuempel  RWTH Aachen University, III. Physikalisches Institut A, Aachen,
Germany  G. Kukec Mezek  Center for Astrophysics and Cosmology (CAC),
University of Nova Gorica, Nova Gorica, Slovenia  N. Kunka  Karlsruhe
Institute of Technology, Institut für Prozessdatenverarbeitung und Elektronik,
Karlsruhe, Germany  A. Kuotb Awad  Karlsruhe Institute of Technology, Institut
für Kernphysik, Karlsruhe, Germany  B.L. Lago  Centro Federal de Educação
Tecnológica Celso Suckow da Fonseca, Nova Friburgo, Brazil  D. LaHurd  Case
Western Reserve University, Cleveland, OH, USA  R.G. Lang  Universidade de São
Paulo, Instituto de Física de São Carlos, São Carlos, SP, Brazil  M. Lauscher
RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany  R.
Legumina  University of Łódź, Faculty of Astrophysics, Łódź, Poland  M.A.
Leigui de Oliveira  Universidade Federal do ABC, Santo André, SP, Brazil  A.
Letessier-Selvon  Laboratoire de Physique Nucléaire et de Hautes Energies
(LPNHE), Universités Paris 6 et Paris 7, CNRS-IN2P3, Paris, France  I. Lhenry-
Yvon  Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud,
Univ. Paris/Saclay, CNRS-IN2P3, Orsay, France  K. Link  Karlsruhe Institute of
Technology, Institut für Experimentelle Kernphysik (IEKP), Karlsruhe, Germany
D. Lo Presti  Università di Catania, Dipartimento di Fisica e Astronomia,
Catania, Italy  INFN, Sezione di Catania, Catania, Italy  L. Lopes
Laboratório de Instrumentação e Física Experimental de Partículas – LIP and
Instituto Superior Técnico – IST, Universidade de Lisboa – UL, Lisboa,
Portugal  R. López  Benemérita Universidad Autónoma de Puebla, Puebla, México
A. López Casado  Universidad de Santiago de Compostela, Santiago de
Compostela, Spain  R. Lorek  Case Western Reserve University, Cleveland, OH,
USA  Q. Luce  Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-
Sud, Univ. Paris/Saclay, CNRS-IN2P3, Orsay, France  A. Lucero  Instituto de
Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos
Aires, Argentina  Universidad Tecnológica Nacional – Facultad Regional Buenos
Aires, Buenos Aires, Argentina  M. Malacari  University of Chicago, Enrico
Fermi Institute, Chicago, IL, USA  M. Mallamaci  Università di Milano,
Dipartimento di Fisica, Milano, Italy  INFN, Sezione di Milano, Milano, Italy
D. Mandat  Institute of Physics of the Czech Academy of Sciences, Prague,
Czech Republic  P. Mantsch  Fermi National Accelerator Laboratory, USA  A.G.
Mariazzi  IFLP, Universidad Nacional de La Plata and CONICET, La Plata,
Argentina  I.C. Mariş  Université Libre de Bruxelles (ULB), Brussels, Belgium
G. Marsella  Università del Salento, Dipartimento di Matematica e Fisica “E.
De Giorgi”, Lecce, Italy  INFN, Sezione di Lecce, Lecce, Italy  D. Martello
Università del Salento, Dipartimento di Matematica e Fisica “E. De Giorgi”,
Lecce, Italy  INFN, Sezione di Lecce, Lecce, Italy  H. Martinez  Centro de
Investigación y de Estudios Avanzados del IPN (CINVESTAV), México, D.F.,
México  O. Martínez Bravo  Benemérita Universidad Autónoma de Puebla, Puebla,
México  J.J. Masías Meza  Departamento de Física and Departamento de Ciencias
de la Atmósfera y los Océanos, FCEyN, Universidad de Buenos Aires and CONICET,
Buenos Aires, Argentina  H.J. Mathes  Karlsruhe Institute of Technology,
Institut für Kernphysik, Karlsruhe, Germany  S. Mathys  Bergische Universität
Wuppertal, Department of Physics, Wuppertal, Germany  J. Matthews  Louisiana
State University, Baton Rouge, LA, USA  J.A.J. Matthews  University of New
Mexico, Albuquerque, NM, USA  G. Matthiae  Università di Roma “Tor Vergata”,
Dipartimento di Fisica, Roma, Italy  INFN, Sezione di Roma ”Tor Vergata”,
Roma, Italy  E. Mayotte  Bergische Universität Wuppertal, Department of
Physics, Wuppertal, Germany  P.O. Mazur  Fermi National Accelerator
Laboratory, USA  C. Medina  Colorado School of Mines, Golden, CO, USA  G.
Medina-Tanco  Universidad Nacional Autónoma de México, México, D.F., México
D. Melo  Instituto de Tecnologías en Detección y Astropartículas (CNEA,
CONICET, UNSAM), Buenos Aires, Argentina  A. Menshikov  Karlsruhe Institute of
Technology, Institut für Prozessdatenverarbeitung und Elektronik, Karlsruhe,
Germany  K.-D. Merenda  Colorado School of Mines, Golden, CO, USA  S. Michal
Palacky University, RCPTM, Olomouc, Czech Republic  M.I. Micheletti  Instituto
de Física de Rosario (IFIR) – CONICET/U.N.R. and Facultad de Ciencias
Bioquímicas y Farmacéuticas U.N.R., Rosario, Argentina  L. Middendorf  RWTH
Aachen University, III. Physikalisches Institut A, Aachen, Germany  L.
Miramonti  Università di Milano, Dipartimento di Fisica, Milano, Italy  INFN,
Sezione di Milano, Milano, Italy  B. Mitrica  “Horia Hulubei” National
Institute for Physics and Nuclear Engineering, Bucharest-Magurele, Romania  D.
Mockler  Karlsruhe Institute of Technology, Institut für Experimentelle
Kernphysik (IEKP), Karlsruhe, Germany  S. Mollerach  Centro Atómico Bariloche
and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de Bariloche,
Argentina  F. Montanet  Laboratoire de Physique Subatomique et de Cosmologie
(LPSC), Université Grenoble-Alpes, CNRS/IN2P3, Grenoble, France  C. Morello
Osservatorio Astrofisico di Torino (INAF), Torino, Italy  INFN, Sezione di
Torino, Torino, Italy  M. Mostafá  Pennsylvania State University, University
Park, PA, USA  A.L. Müller  Instituto de Tecnologías en Detección y
Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina  Karlsruhe
Institute of Technology, Institut für Kernphysik, Karlsruhe, Germany  G.
Müller  RWTH Aachen University, III. Physikalisches Institut A, Aachen,
Germany  M.A. Muller  Universidade Estadual de Campinas, IFGW, Campinas, SP,
Brazil  Universidade Federal de Pelotas, Pelotas, RS, Brazil  S. Müller
Karlsruhe Institute of Technology, Institut für Kernphysik, Karlsruhe, Germany
Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET,
UNSAM), Buenos Aires, Argentina  R. Mussa  INFN, Sezione di Torino, Torino,
Italy  I. Naranjo  Centro Atómico Bariloche and Instituto Balseiro (CNEA-
UNCuyo-CONICET), San Carlos de Bariloche, Argentina  L. Nellen  Universidad
Nacional Autónoma de México, México, D.F., México  P.H. Nguyen  University of
Adelaide, Adelaide, S.A., Australia  M. Niculescu-Oglinzanu  “Horia Hulubei”
National Institute for Physics and Nuclear Engineering, Bucharest-Magurele,
Romania  M. Niechciol  Universität Siegen, Fachbereich 7 Physik –
Experimentelle Teilchenphysik, Siegen, Germany  L. Niemietz  Bergische
Universität Wuppertal, Department of Physics, Wuppertal, Germany  T. Niggemann
RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany  D.
Nitz  Michigan Technological University, Houghton, MI, USA  D. Nosek  Charles
University, Faculty of Mathematics and Physics, Institute of Particle and
Nuclear Physics, Prague, Czech Republic  V. Novotny  Charles University,
Faculty of Mathematics and Physics, Institute of Particle and Nuclear Physics,
Prague, Czech Republic  L. Nožka  Palacky University, RCPTM, Olomouc, Czech
Republic  L.A. Núñez  Universidad Industrial de Santander, Bucaramanga,
Colombia  L. Ochilo  Universität Siegen, Fachbereich 7 Physik – Experimentelle
Teilchenphysik, Siegen, Germany  F. Oikonomou  Pennsylvania State University,
University Park, PA, USA  A. Olinto  University of Chicago, Enrico Fermi
Institute, Chicago, IL, USA  M. Palatka  Institute of Physics of the Czech
Academy of Sciences, Prague, Czech Republic  J. Pallotta  Centro de
Investigaciones en Láseres y Aplicaciones, CITEDEF and CONICET, Villa
Martelli, Argentina  P. Papenbreer  Bergische Universität Wuppertal,
Department of Physics, Wuppertal, Germany  G. Parente  Universidad de Santiago
de Compostela, Santiago de Compostela, Spain  A. Parra  Benemérita Universidad
Autónoma de Puebla, Puebla, México  T. Paul  Department of Physics and
Astronomy, Lehman College, City University of New York, Bronx, NY, USA  M.
Pech  Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic  F. Pedreira  Universidad de Santiago de Compostela, Santiago de
Compostela, Spain  J. Pȩkala  Institute of Nuclear Physics PAN, Krakow, Poland
R. Pelayo  Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías
Avanzadas del Instituto Politécnico Nacional (UPIITA-IPN), México, D.F.,
México  J. Peña-Rodriguez  Universidad Industrial de Santander, Bucaramanga,
Colombia  L. A. S. Pereira  Universidade Estadual de Campinas, IFGW, Campinas,
SP, Brazil  M. Perlin  Instituto de Tecnologías en Detección y Astropartículas
(CNEA, CONICET, UNSAM), Buenos Aires, Argentina  L. Perrone  Università del
Salento, Dipartimento di Matematica e Fisica “E. De Giorgi”, Lecce, Italy
INFN, Sezione di Lecce, Lecce, Italy  C. Peters  RWTH Aachen University, III.
Physikalisches Institut A, Aachen, Germany  S. Petrera  Gran Sasso Science
Institute (INFN), L’Aquila, Italy  INFN Laboratori Nazionali del Gran Sasso,
Assergi (L’Aquila), Italy  J. Phuntsok  Pennsylvania State University,
University Park, PA, USA  R. Piegaia  Departamento de Física and Departamento
de Ciencias de la Atmósfera y los Océanos, FCEyN, Universidad de Buenos Aires
and CONICET, Buenos Aires, Argentina  T. Pierog  Karlsruhe Institute of
Technology, Institut für Kernphysik, Karlsruhe, Germany  M. Pimenta
Laboratório de Instrumentação e Física Experimental de Partículas – LIP and
Instituto Superior Técnico – IST, Universidade de Lisboa – UL, Lisboa,
Portugal  V. Pirronello  Università di Catania, Dipartimento di Fisica e
Astronomia, Catania, Italy  INFN, Sezione di Catania, Catania, Italy  M.
Platino  Instituto de Tecnologías en Detección y Astropartículas (CNEA,
CONICET, UNSAM), Buenos Aires, Argentina  M. Plum  RWTH Aachen University,
III. Physikalisches Institut A, Aachen, Germany  C. Porowski  Institute of
Nuclear Physics PAN, Krakow, Poland  R.R. Prado  Universidade de São Paulo,
Instituto de Física de São Carlos, São Carlos, SP, Brazil  P. Privitera
University of Chicago, Enrico Fermi Institute, Chicago, IL, USA  M. Prouza
Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic
E.J. Quel  Centro de Investigaciones en Láseres y Aplicaciones, CITEDEF and
CONICET, Villa Martelli, Argentina  S. Querchfeld  Bergische Universität
Wuppertal, Department of Physics, Wuppertal, Germany  S. Quinn  Case Western
Reserve University, Cleveland, OH, USA  R. Ramos-Pollan  Universidad
Industrial de Santander, Bucaramanga, Colombia  J. Rautenberg  Bergische
Universität Wuppertal, Department of Physics, Wuppertal, Germany  D. Ravignani
Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET,
UNSAM), Buenos Aires, Argentina  J. Ridky  Institute of Physics of the Czech
Academy of Sciences, Prague, Czech Republic  F. Riehn  Laboratório de
Instrumentação e Física Experimental de Partículas – LIP and Instituto
Superior Técnico – IST, Universidade de Lisboa – UL, Lisboa, Portugal  M.
Risse  Universität Siegen, Fachbereich 7 Physik – Experimentelle
Teilchenphysik, Siegen, Germany  P. Ristori  Centro de Investigaciones en
Láseres y Aplicaciones, CITEDEF and CONICET, Villa Martelli, Argentina  V.
Rizi  Università dell’Aquila, Dipartimento di Scienze Fisiche e Chimiche,
L’Aquila, Italy  INFN Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila),
Italy  W. Rodrigues de Carvalho  Universidade de São Paulo, Instituto de
Física, São Paulo, SP, Brazil  G. Rodriguez Fernandez  Università di Roma “Tor
Vergata”, Dipartimento di Fisica, Roma, Italy  INFN, Sezione di Roma ”Tor
Vergata”, Roma, Italy  J. Rodriguez Rojo  Observatorio Pierre Auger, Malargüe,
Argentina  D. Rogozin  Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, Germany  M.J. Roncoroni  Instituto de Tecnologías en
Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina
M. Roth  Karlsruhe Institute of Technology, Institut für Kernphysik,
Karlsruhe, Germany  E. Roulet  Centro Atómico Bariloche and Instituto Balseiro
(CNEA-UNCuyo-CONICET), San Carlos de Bariloche, Argentina  A.C. Rovero
Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA), Buenos
Aires, Argentina  P. Ruehl  Universität Siegen, Fachbereich 7 Physik –
Experimentelle Teilchenphysik, Siegen, Germany  S.J. Saffi  University of
Adelaide, Adelaide, S.A., Australia  A. Saftoiu  “Horia Hulubei” National
Institute for Physics and Nuclear Engineering, Bucharest-Magurele, Romania  F.
Salamida  Università dell’Aquila, Dipartimento di Scienze Fisiche e Chimiche,
L’Aquila, Italy  INFN Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila),
Italy  H. Salazar  Benemérita Universidad Autónoma de Puebla, Puebla, México
A. Saleh  Center for Astrophysics and Cosmology (CAC), University of Nova
Gorica, Nova Gorica, Slovenia  F. Salesa Greus  Pennsylvania State University,
University Park, PA, USA  G. Salina  INFN, Sezione di Roma ”Tor Vergata”,
Roma, Italy  F. Sánchez  Instituto de Tecnologías en Detección y
Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina  P. Sanchez-
Lucas  Universidad de Granada and C.A.F.P.E., Granada, Spain  E.M. Santos
Universidade de São Paulo, Instituto de Física, São Paulo, SP, Brazil  E.
Santos  Instituto de Tecnologías en Detección y Astropartículas (CNEA,
CONICET, UNSAM), Buenos Aires, Argentina  F. Sarazin  Colorado School of
Mines, Golden, CO, USA  R. Sarmento  Laboratório de Instrumentação e Física
Experimental de Partículas – LIP and Instituto Superior Técnico – IST,
Universidade de Lisboa – UL, Lisboa, Portugal  C. Sarmiento-Cano  Instituto de
Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos
Aires, Argentina  R. Sato  Observatorio Pierre Auger, Malargüe, Argentina  M.
Schauer  Bergische Universität Wuppertal, Department of Physics, Wuppertal,
Germany  V. Scherini  INFN, Sezione di Lecce, Lecce, Italy  H. Schieler
Karlsruhe Institute of Technology, Institut für Kernphysik, Karlsruhe, Germany
M. Schimp  Bergische Universität Wuppertal, Department of Physics, Wuppertal,
Germany  D. Schmidt  Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, Germany  Instituto de Tecnologías en Detección y
Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina  O. Scholten
KVI – Center for Advanced Radiation Technology, University of Groningen,
Groningen, The Netherlands  also at Vrije Universiteit Brussels, Brussels,
Belgium  P. Schovánek  Institute of Physics of the Czech Academy of Sciences,
Prague, Czech Republic  F.G. Schröder  Karlsruhe Institute of Technology,
Institut für Kernphysik, Karlsruhe, Germany  S. Schröder  Bergische
Universität Wuppertal, Department of Physics, Wuppertal, Germany  A. Schulz
Karlsruhe Institute of Technology, Institut für Experimentelle Kernphysik
(IEKP), Karlsruhe, Germany  J. Schumacher  RWTH Aachen University, III.
Physikalisches Institut A, Aachen, Germany  S.J. Sciutto  IFLP, Universidad
Nacional de La Plata and CONICET, La Plata, Argentina  A. Segreto  INAF –
Istituto di Astrofisica Spaziale e Fisica Cosmica di Palermo, Palermo, Italy
INFN, Sezione di Catania, Catania, Italy  A. Shadkam  Louisiana State
University, Baton Rouge, LA, USA  R.C. Shellard  Centro Brasileiro de
Pesquisas Fisicas, Rio de Janeiro, RJ, Brazil  G. Sigl  Universität Hamburg,
II. Institut für Theoretische Physik, Hamburg, Germany  G. Silli  Instituto de
Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos
Aires, Argentina  Karlsruhe Institute of Technology, Institut für Kernphysik,
Karlsruhe, Germany  O. Sima  University of Bucharest, Physics Department,
Bucharest, Romania  A. Śmiałkowski  University of Łódź, Faculty of
Astrophysics, Łódź, Poland  R. Šmída  Karlsruhe Institute of Technology,
Institut für Kernphysik, Karlsruhe, Germany  B. Smith  School of Physics and
Astronomy, University of Leeds, Leeds, United Kingdom  G.R. Snow  University
of Nebraska, Lincoln, NE, USA  P. Sommers  Pennsylvania State University,
University Park, PA, USA  S. Sonntag  Universität Siegen, Fachbereich 7 Physik
– Experimentelle Teilchenphysik, Siegen, Germany  R. Squartini  Observatorio
Pierre Auger, Malargüe, Argentina  D. Stanca  “Horia Hulubei” National
Institute for Physics and Nuclear Engineering, Bucharest-Magurele, Romania  S.
Stanič  Center for Astrophysics and Cosmology (CAC), University of Nova
Gorica, Nova Gorica, Slovenia  J. Stasielak  Institute of Nuclear Physics PAN,
Krakow, Poland  P. Stassi  Laboratoire de Physique Subatomique et de
Cosmologie (LPSC), Université Grenoble-Alpes, CNRS/IN2P3, Grenoble, France  M.
Stolpovskiy  Laboratoire de Physique Subatomique et de Cosmologie (LPSC),
Université Grenoble-Alpes, CNRS/IN2P3, Grenoble, France  F. Strafella
Università del Salento, Dipartimento di Matematica e Fisica “E. De Giorgi”,
Lecce, Italy  INFN, Sezione di Lecce, Lecce, Italy  A. Streich  Karlsruhe
Institute of Technology, Institut für Experimentelle Kernphysik (IEKP),
Karlsruhe, Germany  F. Suarez  Instituto de Tecnologías en Detección y
Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina  Universidad
Tecnológica Nacional – Facultad Regional Buenos Aires, Buenos Aires, Argentina
M. Suarez Durán  Universidad Industrial de Santander, Bucaramanga, Colombia
T. Sudholz  University of Adelaide, Adelaide, S.A., Australia  T. Suomijärvi
Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud, Univ.
Paris/Saclay, CNRS-IN2P3, Orsay, France  A.D. Supanitsky  Instituto de
Astronomía y Física del Espacio (IAFE, CONICET-UBA), Buenos Aires, Argentina
J. Šupík  Palacky University, RCPTM, Olomouc, Czech Republic  J. Swain
Northeastern University, Boston, MA, USA  Z. Szadkowski  University of Łódź,
Faculty of High-Energy Astrophysics,Łódź, Poland  A. Taboada  Karlsruhe
Institute of Technology, Institut für Experimentelle Kernphysik (IEKP),
Karlsruhe, Germany  O.A. Taborda  Centro Atómico Bariloche and Instituto
Balseiro (CNEA-UNCuyo-CONICET), San Carlos de Bariloche, Argentina  V.M.
Theodoro  Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil  C.
Timmermans  Nationaal Instituut voor Kernfysica en Hoge Energie Fysica
(NIKHEF), Science Park, Amsterdam, The Netherlands  IMAPP, Radboud University
Nijmegen, Nijmegen, The Netherlands  C.J. Todero Peixoto  Universidade de São
Paulo, Escola de Engenharia de Lorena, Lorena, SP, Brazil  L. Tomankova
Karlsruhe Institute of Technology, Institut für Kernphysik, Karlsruhe, Germany
B. Tomé  Laboratório de Instrumentação e Física Experimental de Partículas –
LIP and Instituto Superior Técnico – IST, Universidade de Lisboa – UL, Lisboa,
Portugal  G. Torralba Elipe  Universidad de Santiago de Compostela, Santiago
de Compostela, Spain  P. Travnicek  Institute of Physics of the Czech Academy
of Sciences, Prague, Czech Republic  M. Trini  Center for Astrophysics and
Cosmology (CAC), University of Nova Gorica, Nova Gorica, Slovenia  R. Ulrich
Karlsruhe Institute of Technology, Institut für Kernphysik, Karlsruhe, Germany
M. Unger  Karlsruhe Institute of Technology, Institut für Kernphysik,
Karlsruhe, Germany  M. Urban  RWTH Aachen University, III. Physikalisches
Institut A, Aachen, Germany  J.F. Valdés Galicia  Universidad Nacional
Autónoma de México, México, D.F., México  I. Valiño  Universidad de Santiago
de Compostela, Santiago de Compostela, Spain  L. Valore  Università di Napoli
”Federico II”, Dipartimento di Fisica “Ettore Pancini“, Napoli, Italy  INFN,
Sezione di Napoli, Napoli, Italy  G. van Aar  IMAPP, Radboud University
Nijmegen, Nijmegen, The Netherlands  P. van Bodegom  University of Adelaide,
Adelaide, S.A., Australia  A.M. van den Berg  KVI – Center for Advanced
Radiation Technology, University of Groningen, Groningen, The Netherlands  A.
van Vliet  IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands  E.
Varela  Benemérita Universidad Autónoma de Puebla, Puebla, México  B. Vargas
Cárdenas  Universidad Nacional Autónoma de México, México, D.F., México  G.
Varner  University of Hawaii, Honolulu, HI, USA  R.A. Vázquez  Universidad de
Santiago de Compostela, Santiago de Compostela, Spain  D. Veberič  Karlsruhe
Institute of Technology, Institut für Kernphysik, Karlsruhe, Germany  C.
Ventura  Universidade Federal do Rio de Janeiro (UFRJ), Observatório do
Valongo, Rio de Janeiro, RJ, Brazil  I.D. Vergara Quispe  IFLP, Universidad
Nacional de La Plata and CONICET, La Plata, Argentina  V. Verzi  INFN, Sezione
di Roma ”Tor Vergata”, Roma, Italy  J. Vicha  Institute of Physics of the
Czech Academy of Sciences, Prague, Czech Republic  L. Villaseñor  Universidad
Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán, México  S. Vorobiov
Center for Astrophysics and Cosmology (CAC), University of Nova Gorica, Nova
Gorica, Slovenia  H. Wahlberg  IFLP, Universidad Nacional de La Plata and
CONICET, La Plata, Argentina  O. Wainberg  Instituto de Tecnologías en
Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina
Universidad Tecnológica Nacional – Facultad Regional Buenos Aires, Buenos
Aires, Argentina  D. Walz  RWTH Aachen University, III. Physikalisches
Institut A, Aachen, Germany  A.A. Watson  School of Physics and Astronomy,
University of Leeds, Leeds, United Kingdom  M. Weber  Karlsruhe Institute of
Technology, Institut für Prozessdatenverarbeitung und Elektronik, Karlsruhe,
Germany  A. Weindl  Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, Germany  L. Wiencke  Colorado School of Mines, Golden,
CO, USA  H. Wilczyński  Institute of Nuclear Physics PAN, Krakow, Poland  C.
Wileman  School of Physics and Astronomy, University of Leeds, Leeds, United
Kingdom  M. Wirtz  RWTH Aachen University, III. Physikalisches Institut A,
Aachen, Germany  D. Wittkowski  Bergische Universität Wuppertal, Department of
Physics, Wuppertal, Germany  B. Wundheiler  Instituto de Tecnologías en
Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina
L. Yang  Center for Astrophysics and Cosmology (CAC), University of Nova
Gorica, Nova Gorica, Slovenia  A. Yushkov  Instituto de Tecnologías en
Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina
E. Zas  Universidad de Santiago de Compostela, Santiago de Compostela, Spain
D. Zavrtanik  Center for Astrophysics and Cosmology (CAC), University of Nova
Gorica, Nova Gorica, Slovenia  Experimental Particle Physics Department, J.
Stefan Institute, Ljubljana, Slovenia  M. Zavrtanik  Experimental Particle
Physics Department, J. Stefan Institute, Ljubljana, Slovenia  Center for
Astrophysics and Cosmology (CAC), University of Nova Gorica, Nova Gorica,
Slovenia  A. Zepeda  Centro de Investigación y de Estudios Avanzados del IPN
(CINVESTAV), México, D.F., México  B. Zimmermann  Karlsruhe Institute of
Technology, Institut für Prozessdatenverarbeitung und Elektronik, Karlsruhe,
Germany  M. Ziolkowski  Universität Siegen, Fachbereich 7 Physik –
Experimentelle Teilchenphysik, Siegen, Germany  Z. Zong  Institut de Physique
Nucléaire d’Orsay (IPNO), Université Paris-Sud, Univ. Paris/Saclay, CNRS-
IN2P3, Orsay, France  F. Zuccarello  Università di Catania, Dipartimento di
Fisica e Astronomia, Catania, Italy  INFN, Sezione di Catania, Catania, Italy
<EMAIL_ADDRESS>http://www.auger.org

###### Abstract

We present a new method for probing the hadronic interaction models at ultra-
high energy and extracting details about mass composition. This is done using
the time profiles of the signals recorded with the water-Cherenkov detectors
of the Pierre Auger Observatory. The profiles arise from a mix of the muon and
electromagnetic components of air-showers. Using the risetimes of the recorded
signals we define a new parameter, which we use to compare our observations
with predictions from simulations. We find, firstly, inconsistencies between
our data and predictions over a greater energy range and with substantially
more events than in previous studies. Secondly, by calibrating the new
parameter with fluorescence measurements from observations made at the Auger
Observatory, we can infer the depth of shower maximum Xmax for a sample of
over 81,000 events extending from 0.3 EeV to over 100 EeV. Above 30 EeV, the
sample is nearly fourteen times larger than currently available from
fluorescence measurements and extending the covered energy range by half a
decade. The energy dependence of $\langle$Xmax$\rangle$ is compared to
simulations and interpreted in terms of the mean of the logarithmic mass. We
find good agreement with previous work and extend the measurement of the mean
depth of shower maximum to greater energies than before, reducing
significantly the statistical uncertainty associated with the inferences about
mass composition.

###### pacs:

96.50.S-, 96.50.sb, 96.50.sd, 98.70.Sa

##  I Introduction

Our understanding of the properties of the highest-energy cosmic rays has
grown enormously over the last 12 years with the advent of data from the
Pierre Auger Observatory and the Telescope Array. These devices have been used
to study the energy spectrum, the mass composition and the distribution of
arrival directions of cosmic rays from 0.3 EeV to energies beyond 10 EeV.
While the features of the energy spectrum and of the arrival directions have
been well-characterised up to $\sim$100 EeV, the situation with regard to the
mass spectrum is less satisfactory because of the reliance on models of the
hadronic physics. This state of affairs arises for two reasons. Firstly, the
method that provides the best resolution, and therefore is the most potent for
measuring a mass-sensitive feature of extensive air-showers, is the
fluorescence technique. It has been exploited on an event-by-event basis to
determine the depth of shower maximum, i.e. the depth in the atmosphere at
which the energy deposition in the shower is greatest, but, as observations
are restricted to clear moonless-nights, the number of events is limited. For
example, in the Auger data so far reported (up to 31 December 2012) there are
227 events above 16 EeV r1 . For the same energy range, the event number from
the Telescope Array is smaller, 25 r2 . Secondly, to interpret the data sets
from the water-Cherenkov detectors and the fluorescence telescopes, one must
use the predictions of features of hadronic interactions, such as the cross-
sections for proton and pion interactions, the multiplicity and the
inelasticity, at centre-of-mass energies up to $\sim$300 TeV, well-beyond what
is accessible at the LHC r3 .

To overcome the limitations imposed by the relatively small number of events
accumulated with the fluorescence technique at the highest energies, use can
be made of data recorded with the water-Cherenkov detectors of the Observatory
which are operational nearly 100% of the time and thus yield substantially
more events at a given energy. In this paper, we describe a new method for
extracting information about the development of air showers from the time
profiles of the signals from the water-Cherenkov detectors.

Our method allows a comparison of the data with predictions from models of
parameters inferred directly from these detectors in which a signal from a mix
of the muon and electromagnetic components of air-showers is available. This
approach follows the line opened in four recent studies. From comparisons of
Auger observations with hadronic models it is argued that the latter are
inadequate to describe the various measurements r4 ; r5 ; r6 ; r7 . As in the
earlier work, we find that there are inconsistencies between the models and
the data: this is established over a greater energy range and with more events
than before.

The method also enables us to infer the depth of shower maximum (a dominantly
electromagnetic measurement) by calibrating the new parameter with
measurements from the fluorescence telescopes. We have determined Xmax for
about three times more events than available from these telescopes alone over
the range from $\sim$0.3 EeV to beyond 70 EeV: specifically for the two
surface detector configurations, the 750 and 1500 m arrays r8 , there are
27553 and 54022 events recorded respectively for which estimates of Xmax have
been possible. Of those, 49 events are in the range beyond 70 EeV, and 1586
above 20 EeV.

The structure of the paper is as follows. In section II features of the Pierre
Auger Observatory are briefly outlined. The measurement of the risetime of
signals from the water-Cherenkov detectors is described in section III and the
new parameter for studying the depth of shower maximum is introduced in
section IV. A comparison of the new parameter with predictions from hadronic
models is discussed in section V. Section VI presents the results on the
measurement of average Xmax from 0.3 EeV to beyond 70 EeV. A summary of the
conclusions is given in section VII.

##  II The Pierre Auger Observatory

The Pierre Auger Observatory is located near the city of Malargüe in the
Province of Mendoza, Argentina. It is a hybrid system, being a combination of
a large array of surface detectors and a set of fluorescence detectors, used
to study cosmic rays with energies above 0.1 EeV. Full details of the
instrumentation and the methods used for event reconstruction are given in r8
.

The work presented here is based on data gathered from 1 Jan 2004 to 31 Dec
2014 from the surface-detector array (SD), which covers an area of over 3000
km2. The array contains 1660 water-Cherenkov detectors, 1600 of which are
deployed on a hexagonal grid with 1500 m spacing with the remainder on a
lattice of 750 m covering 23.5 km2. We refer to these configurations as the
1500 m and 750 m arrays. The water-Cherenkov detectors are used to sample the
electromagnetic and muonic components of extensive air-showers. Each detector
contains 12 tonnes of ultra-pure water in a cylindrical container, lined with
Tyvec, 1.2 m deep and of 10 m2 area. The water is viewed by three
9”-photomultiplier tubes (PMTs). Signals from the anode and an amplified
signal from the last dynode of each PMT are digitised using 40 MHz 10-bit
Flash Analog to Digital Converters (FADCs): these are called the ‘high-gain’
and ‘low-gain’ channels in what follows. The responses of the detectors are
calibrated in units of the signal produced by a muon traversing the water
vertically at the center of the station: this unit is termed the “Vertical
Equivalent Muon” or VEM r9 . Air showers are identified using a 3-fold
coincidence, satisfied when a triangle of neighbouring stations is triggered
r10 . Using the six FADCs, 768 samples (over 19.2 $\mu$s) are recorded at each
triggered station. For the present analysis events are used that are confined
within the array so that an accurate reconstruction is ensured. This requires
that all six stations of the hexagon surrounding the detector with the highest
signal are operational and is known as the 6T5 condition. The arrival
directions are found from the relative arrival times of the shower front at
the triggered stations. The angular resolution is 0.8o for energies above 3
EeV for the 1500 m array and 1o for the 750 m-configuration r8 .

The estimator of the primary energy is the signal reconstructed at 1000 m
(1500 m array) or 450 m (750 m array) from the shower core, denoted by S(1000)
and S(450) respectively. These estimators are determined, together with the
core position, through a fit of the recorded signals (converted to units of
VEM after integration of the FADC traces) to a lateral distribution function
that describes the average rate of fall-off of the signals as a function of
the distance from the shower core. For S(1000) > 20 VEM (corresponding to an
energy of $\sim$3 EeV) showers are recorded with full efficiency over the
whole area of the array. For the 750 m array, the corresponding value of
S(450) for full efficiency is $\sim$60 VEM ($\sim$0.5 EeV). The accuracy of
the core location in lateral distance is $\sim$50 m (35 m) for the two
configurations. The uncertainty of S(1000), which is insensitive to the
lateral distribution function r11 , is 12% (3%) at 3 EeV (10 EeV) and for
S(450) the corresponding figure is 30% at 0.5 EeV.

The conversions from S(450) and S(1000) to energy are derived using subsets of
showers that trigger the fluorescence detector and the surface array
independently (‘hybrid events’) using well-established methods r12 . The
statistical uncertainty in the energy determination is about 16% (12%) for the
two reference energies of the 1500 m array and 15% at 0.5 EeV for the 750 m
array. The absolute energy scale, determined using the fluorescence detector,
has a systematic uncertainty of 14% r13 .

Twenty-four telescopes (each with a field of view of 30o$\times$30o) form the
Fluorescence Detector (FD). They are distributed in sets of six at four
observation sites. The FD overlooks the SD array and collects the fluorescence
light produced as the shower develops in the atmosphere. Its duty cycle
amounts to $\sim$15% since it operates exclusively on clear moonless nights.
The 750 m array is overlooked from one observation site by three high-
elevation telescopes (HEAT) with a field of view covering elevations from 30o
to 60o, thus allowing the study of lower energy showers. Those low energy
showers are detected closer to the detector; therefore we need a higher
elevation field of view to contain also this kind of events.

##  III The Risetime and its Measurement

###  III.1 Overview of the risetime concept

In the study described below, we use the risetime of the signals from the
water-Cherenkov detectors to extract information about the development of
showers. A single parameter, namely the time for the signal to increase from
10% to 50% of the final magnitude of the integrated signal, t1/2, is used to
characterize the signal at each station. This parameter was used for the first
demonstration of the existence of ‘between-shower’ fluctuations in an early
attempt to get information about the mass of the cosmic rays at $\sim$1 EeV
r14 . That work was carried out using data from the Haverah Park array in
England where the water-Cherenkov detectors were of 1.2 m deep (identical to
those of the Auger Observatory) and of area 34 m2.

The choice of this parameter is based on the experimental work by Linsley and
Scarsi r15 . They showed that at distances of more than about 100 m from the
shower core, the early part of the shower signal is dominated by muons. Direct
measurements of muons using magnetic spectrographs established that the mean
momentum of muons beyond 100 m was more than 1 GeV: this leads to the
conclusion that the geometrical effects dominate the temporal spread of the
muons at a detector. This is illustrated in Fig. 1 for a shower arriving in
the vertical direction where it can be seen that the muons arriving from lower
down in the shower arrive later at a detector than those that arise from
higher up. Furthermore it is evident that at larger distances from the shower
axis, the muons will be more dispersed in time than at smaller distances,
leading to the dependence of the risetime on distance found experimentally
(Fig. 2). Because the muons are relatively energetic, the effects of velocity
difference, of deflections in the geomagnetic field and of Coulomb scattering
is small although these factors were taken into account even in the earliest
Monte Carlo studies of the phenomenon r16 . By contrast the electrons and
photons of an air shower have mean energies of about 10 MeV so that the
arrival of the electromagnetic component of the shower is delayed with respect
to the muons because of the multiple scattering of the electrons. The delay of
the electromagnetic component with respect to the muons also increases with
distance.

Figure 1: Qualitative sketch of how geometrical effects affect the temporal
spread of the muons at a detector.

The risetime is found experimentally to be a function of distance, zenith
angle and energy (Fig. 2). At 1000 m from the shower axis, for a vertical
event of 10 EeV, t1/2 $\sim$380 ns. This value increases slowly with energy
and decreases with zenith angle. At large angles and/or small distances t1/2
can be comparable to the 25 ns resolution of the FADCs and this fact restricts
the data that are used below. The fastest risetime, measured in very inclined
showers or with single muons, is 40 ns and is an indication of the limitations
set by the measurement technique and hence guides our selection of distance
and angular ranges.

Because of the size of the Auger Observatory and the large separation of the
detectors, it is necessary to take account of the fact that a detector that is
struck early in the passage of the shower across the array will have a slower
risetime than one that is struck later, even if the two detectors are at the
same axial distance from the shower core. This asymmetry arises from a complex
combination of attenuation of the electromagnetic component as the shower
develops and because of the different part of the angular distribution of
muons (more strictly of the parent pions) that is sampled at different
positions across the array. The attenuation of the electromagnetic component
of a shower across an array was first discussed by Greisen r17 . A detailed
description of the asymmetry that is observed, and of its power for testing
hadronic interaction models, has been given recently r6 . For the present
study, the asymmetry is taken into account by referencing each risetime to
that which would be recorded at a hypothetical detector situated at 90o with
respect to the direction of the shower axis projected onto the ground, and at
the same axial distance from the shower core, as the station at which a
measurement is made. The amplitude of the asymmetry is a function of zenith
angle, axial distance and energy: at 40o, 750 m and 10 EeV it is $\sim$15%.

The magnitudes of the risetimes that are measured in a particular shower
depend upon the development of the shower. As the energy increases, the mean
position of the point of maximum development of the shower moves deeper into
the atmosphere and thus the risetimes will, on average, be slower than for a
lower energy event. Because muons dominate the shower to an increasing extent
at large zenith angles, because the electromagnetic component suffers
increased attenuation, the risetimes are expected to be faster at a detector
that is at the same distance from the axis of the shower but in the vertical
direction. The magnitude of the energy, distance and zenith angle effects that
can be inferred qualitatively from Fig. 1 are evident in the data shown in
Fig. 2.

From these considerations, it follows that studying the risetimes of showers
provides a method of measuring the shower development and thus of deducing the
mass composition. Details of the study are presented below where the risetime
properties are also compared with predictions from Monte Carlo calculations
using different hadronic models.

|
---|---
|

Figure 2:  (Top left) The risetime as a function of distance to the shower
core for two different intervals of sec $\theta$ in the energy range 19.0 <
log (E/eV) < 19.2. (Top right) The risetime as a function of distance for two
different energy bands in the angular range 1.20 < sec $\theta$ < 1.30.
(Bottom left) Illustration of the spread in the risetimes as a function of
distance for events in the energy range 19.1 < log (E/eV) < 19.2. (Bottom
right) Illustration of the variation of risetime with zenith angle for events
in the energy range 19.1 < log (E/eV) < 19.2. All plots are based on
experimental data

###  III.2 Determination of the accuracy of measurements of t1/2

The uncertainty in a measurement of t1/2 is found empirically from the data
and will be described in some detail as it plays an essential role in the
determination of the new parameter, introduced in section IV, used to
characterize shower development. The uncertainty can be obtained by using sets
of detectors placed 11 m apart (known as ‘twins’) and also by using detectors
that lie at similar distances from the shower core (‘pairs’). Measurements
made using twins and pairs cover different distance ranges. With twins we can
parameterize the uncertainty with a sufficient number of events only between
300 m and 1200 m from the shower core. With pairs we can cover distances from
600 m to 1800 m. It is then natural to combine both sets of measurements to
avoid as much as possible relying on extrapolations when estimating the
uncertainty in the measurement of t1/2.

The twin detectors give two independent measurements of the risetime at what
is effectively a single point in the shower plane. Differences in the values
of t1/2 at the twins arise from the limitations set by the sampling of the
shower front by a detector of finite size (10 m2) and from the measurement
uncertainties intrinsic to the FADC system. For the more-numerous pairs there
are the additional complications that arise from the asymmetry effect and from
the difference in distance of the pairs from the shower core.

####  III.2.1 Assessment of measurement uncertainty using twin detectors

In the surface-detector array there are 14 sets of twins and seven sets of
triplets (three detectors on a triangular grid each separated by 11 m): the
triplets are also referred to as ‘twins’. We parameterize the uncertainty by
splitting the data in different bins of distance to the core, zenith angle and
detector signal. This implies that a precise parameterization of the
uncertainty demands a large amount of data. To cope with this requirement we
must combine all twin measurements that belong to events reconstructed at
either of the arrays. A total of $\sim$83 000 twin measurements are available
from the two arrays for zenith angles below 60o and above energies of 0.3 EeV
and 1 EeV for events that trigger the two arrays. The cuts on energy and
zenith angle are very loose to enhance the number of events available for
analysis. Likewise the criteria applied at detector level and detailed in
Table 1 are mild to keep the selection efficiency as high as possible. We
discard detectors that recorded a small number of particles or located far
from the core to avoid biases in the signal measurement. For very large
signals, the risetime measurements approach the instrumental resolution and
therefore are discarded. The cut on |Si – Smean| in Table 1 is made to deal
with cases where one signal is typically around 5 VEM and the other, possibly
because of an upward fluctuation, is relatively large. Such twins are
rejected.

The average uncertainty in a risetime measurement, $\sigma$1/2, is given by

$\sigma_{1/2}=\frac{\sqrt{\pi}}{2}\left\langle\left|t_{1/2}^{1}-t_{1/2}^{2}\right|\right\rangle$
(1)

where the superscripts define each member of the twin. As twin detectors are
only 11 m apart no correction is necessary for the azimuthal asymmetry.

Table 1: Selection of twin detectors used to assess the risetime uncertainty. | 750 m array | 1500 m array
---|---|---
Cuts | Number of twins | Efficiency | Number of twins | Efficiency
Pre-twin selection | 41 100 | 1.00 | 41 934 | 1.00
5 < S/VEM < 800 | 34 461 | 0.84 | 35 704 | 0.85
r < 2000 m | 34 459 | 0.83 | 35 620 | 0.84
|Si-Smean|< 0.25 Smean | 28 466 | 0.69 | 29 832 | 0.71

The data have been divided into seven sec $\theta$ intervals (of width 0.1)
and six distance ranges (see Fig. 3 left). The mean values of $\sigma$1/2 as a
function of signal size, S, are fitted with the function

$\sigma_{1/2}\,=\sqrt{\left(\frac{J(r,\theta)}{\sqrt{S}}\right)^{2}+\left(\sqrt{2}\frac{25\,\text{ns}}{\sqrt{12}}\right)^{2}}$
(2)

The first term in this function represents the differences seen between the
two detectors while the second term arises from the digitisation of the signal
in time intervals of 25 ns.

J is found from a linear function, J(r,$\theta$) = po($\theta$) + p1($\theta$)
r, and the fitted values of po and p1 as functions of sec $\theta$ are

$\begin{array}[]{l}p_{0}(\theta)=(-340\pm 30)+(186\pm 20)\,\sec\theta\\\
p_{1}(\theta)=(0.94\pm 0.03)+(-0.44\pm 0.01)\,\sec\theta\end{array}$ (3)

where p0 units are (ns VEM1/2) and p1 units are (ns VEM1/2 m-1).

####  III.2.2 Assessment of measurement uncertainty using pairs of detectors

For the purposes of this study, a pair of detectors is defined as any two
detectors in the same shower where the difference in distance from the shower
core, (|r2 – r1|) is less than 100 m, irrespective of azimuth angle. After
applying the cuts previously discussed, there are $\sim$50% more pair
measurements than there are measurements from twins. This sample is large
enough to allow us to limit this study to pairs of detectors from the 1500 m
array only. However, corrections have to be made for the asymmetry and,
because of the array spacing, there are no data below 600 m. Additionally a
correction must be made because the risetimes are at different axial
distances: for a 100 m separation this difference is $\sim$30 ns, assuming a
linear dependence of risetime with distance (see Fig. 2). Before applying this
correction the mean time difference for pairs was (14.750 $\pm$ 0.002) ns:
after correction the average difference was (0.140 $\pm$ 0.002) ns.

Figure 3:  (Left) Uncertainty obtained with pair detectors as a function of
the station signal for vertical events (1.00< sec $\theta$ <1.10). Each line
is the result of the fits performed for different distance ranges. Each point
represents the average measurements of at least 10 pair detectors. (Right) The
parameter J(r, $\theta$) as a function of the distance to the core for the
same zenith angle range.

From a similar analysis to that described for the twin detectors, the fits for
p0 and p1 have the parameterisations

$\begin{array}[]{l}p_{0}(\theta)=(-447\pm 30)+(224\pm 20)\,\sec\theta\\\
p_{1}(\theta)=(1.12\pm 0.03)+(-0.51\pm 0.02)\,\sec\theta.\end{array}$ (4)

The variation of J with distance is also shown in Fig. 3.

The differences in the values of p0 and p1 from the two analyses arise because
they cover different distance ranges and different energy ranges. To optimize
the determination of $\sigma$1/2 for the risetimes measured at each station,
we adopt the following parameterisations for p0 and p1 for different core
ranges

$\begin{array}[]{l}p_{0}(\theta)=\begin{cases}(-340\pm 30)+(186\pm
20)\,\sec\theta,\,\,r\leq\,650\,\text{m}\\\ (-447\pm 30)+(224\pm
20)\,\sec\theta,\,\,r>\,650\,\text{m}\\\ \end{cases}\\\
p_{1}(\theta)=\begin{cases}(0.94\pm 0.03)+(-0.44\pm
0.01)\,\sec\theta,\,\,r\leq\,650\,\text{m}\\\ (1.12\pm 0.03)+(-0.51\pm
0.02)\,\sec\theta,\,\,r>\,650\,\text{m}\\\ \end{cases}\end{array}$ (5)

We have set the break point at 650 m because at this distance the
uncertainties given by the two parameterizations agree within their
statistical uncertainties (2-3 ns).

##  IV The new parameter $\Delta_{s}$ and its determination for individual
air-showers

###  IV.1 Introduction to the Delta method

When a large number of risetimes is recorded in an event, it is possible to
characterize that event by a single time just as the size of an event is
designated by S(1000), the signal size at 1000 m from the shower axis. This
approach is only practical at high energies, as several measurements are
needed to estimate the risetime at 1000 m by extrapolation r18 . Here, to
obtain a large sample of data over a wide range of energies, an alternative
method of using risetime measurements is introduced. We have determined for
the two arrays independent relationships that describe the risetimes as a
function of distance in a narrow range of energy (see section IV.3). We call
these functions ‘benchmarks’, and risetimes at particular stations, after
correction for the asymmetry effect, are compared with the relevant times from
the benchmark, $t_{\text{1/2}}^{\text{bench}}$, in units of the accuracy with
which they are determined. The approach is illustrated in Fig. 4: the
benchmarks are, of course, zenith-angle dependent (see Fig. 2). We use the
term ‘Delta method’ to refer to this approach in what follows.

Figure 4:  Schematic diagram to illustrate the Delta method.

Thus for each measurement of t1/2 at a single detector, i, an estimate of
$\Delta_{i}=\left(t_{\text{1/2}}-t_{\text{1/2}}^{\text{bench}}\right)/\sigma_{\text{1/2}}$
is made. Each shower is then characterised by $\Delta_{s}$, the average of
these estimates for the N selected stations.

$\Delta_{s}=\frac{1}{N}\sum\limits_{stations}\Delta_{i}$ (6)

###  IV.2 Data selection

The data from the water-Cherenkov arrays were collected between 1 Jan 2004
(2008 for the 750 m spacing) and 31 Dec 2014. The first selection, of 6T5
events, has already been discussed. Other selections for the two arrays are
shown in Table 2.

Table 2:  Quality cuts applied to the events of the 750 m and the 1500 m arrays. $\epsilon$ stands for the overall efficiency. The explanation for the different cuts can be found in the text. 750 m array | 1500 m array
---|---
Quality cuts | Events |  $\epsilon$ (%) | Quality cuts | Events |  $\epsilon$ (% )
17.5 < log (E/eV) < 18.5 | 159 795 | 100.0 | log (E/eV) > 18.5 | 217 469 | 100.0
sec $\theta$ < 1.30 | 72 907 | 45.6 | sec $\theta$ < 1.45 | 97 981 | 45.0
6T5 trigger | 29 848 | 18.7 | 6T5 trigger | 67 764 | 31.0
Reject bad periods | 28 773 | 18.0 | Reject bad periods | 63 856 | 29.0
$\geq$ 3 selected stations | 27 553 | 17.2 |  $\geq$ 3 selected stations | 54 022 | 24.8

The lower energy cuts are made to select events that trigger the arrays with
100% efficiency. The upper energy cut in the 750 m array is made to set aside
events in overlapping energy regions that will be used later to cross-check
the robustness of the method. As previously discussed, at large angles t1/2
can be comparable to the 25 ns resolution of the FADCs and this fact restricts
the usable angular range. The cut in zenith angle is lower for the 750 m array
than for the 1500 m array because the stations tend to be closer to the core
and the limitations set by the sampling speed of the FADCs become more
important at larger angles and small distances. We rejected data taking
periods where the performance of the array of surface detectors was not
optimal. At least three selected stations are required for an event to be
included in the data samples.

The stations used within each event must fulfil the following criteria. The
stations cannot be saturated in the low-gain channel since risetimes cannot be
obtained from such signals. The signals recorded by the stations must be
bigger than 3 VEM and 5 VEM for the 750 m and the 1500 m arrays respectively.
Those cuts guarantee that no bias towards primaries of a particular type is
introduced: the difference in selection efficiency for protons and iron is
less than 5% for all energy bins. The selected stations must lie within a
given distance range from the position of the reconstructed core of the
shower. The lower range of distance, 300 m, is selected to avoid the problems
set by the inability of the recording system to record fast pulses (see
section III.1), while the upper ranges (800 m (1400 m) for the 750 m (1500 m)
array) are chosen to span what is consistent with unbiased selection. For the
highest energies this has been extended to 2000 m as the signal sizes in such
events are sufficiently large to give accurate measurements. For the 750 and
1500 m arrays the overall selection efficiencies at station level are 52% and
56% respectively. This translates into 113,661 and 210,709 detectors for the
750 m and the 1500 m arrays respectively.

Using simulations, we have searched for biases that might be introduced into
inferences about mass composition as a result of these cuts. The difference
between the overall selection efficiencies for protons and Fe-nuclei are
smaller than 2%. The upper limit on the energy cut in the 750 m data
eliminates only 2% of the events. This cut, and the lower energy limit for the
1500 m array, are relaxed later to study the overlap region in detail.

For the 750 and 1500 m arrays, the mean numbers of selected stations per event
satisfying the selection criteria defined in Table 2 are 4.0 and 3.6
respectively. In the analysis discussed below, selected events are required to
have 3 or more values of $\Delta_{i}$, but, for an arrival direction study, in
which it is desirable to separate light from heavy primaries, one could
envisage using two stations, or even one, to infer the state of development of
the shower, albeit with more limited accuracy.

###  IV.3 Determination of the benchmarks for the 750 and 1500 m arrays

The determination of the benchmarks, which define the average behaviour of the
risetimes as a function of distance and zenith angle, is fundamental to the
success of the technique. Essentially the same procedures have been adopted
for both arrays. For each detector two time traces are recorded on high-gain
and low-gain channels. The risetime of a detector is computed according to the
following procedure: in the case where no saturation occurs, the risetime is
obtained from the trace corresponding to the high-gain channel. If this
channel is saturated, we use the trace from the low-gain channel to compute
the risetime. If the low-gain signal is saturated as well, which can occur for
stations close to the core in high-energy events, that station is not selected
for this analysis. Further details of the recording procedures are given in r8
.

In computing the benchmarks, account must be taken of the fact that the
risetimes measured for a station in the two channels are not identical, as
illustrated in Fig. 5. During the digitization process, a threshold is imposed
that removes very small signals. The net effect of this threshold affects the
low-gain traces much more, since their signals are smaller due to the lower
signal-to-noise ratio when compared to the one associated to high-gain traces.
The influence of tails in the determination of the integrated signal is
therefore reduced for low-gain signals and as a consequence the risetime
measurement is affected. This instrumental effect makes it necessary to obtain
benchmarks for the high-gain and the low-gain traces independently.

Figure 5: (Left) Risetimes as a function of core distance for events with and
without saturation in the high-gain channel. We have selected events with
energies 19.0 < log (E/eV) <19.2 and zenith angles 1.00 < sec $\theta$ <1.10.
(Right) Same as left plot but this time we show average values to make more
evident the difference between measurements when the saturation of the high-
gain channel is present.

As shown in Table 2 the energy ranges covered by the two arrays are 17.5 < log
(E/eV) < 18.5 (750 m spacing) and log (E/eV) >18.5 (1500 m spacing). The
energy bins chosen for the benchmarks of the 750 and 1500 m arrays are 17.7 <
log (E/eV) < 17.8 and 19.1 < log (E/eV) < 19.2 respectively. The choices for
the benchmarks are most effective in dealing with the high-gain/low-gain
problem just discussed. They guarantee that we reject a reduced number of
detectors where the low and the high-gain channels are simultaneously
saturated and therefore allow a definition of the benchmark over a broad
distance range. In addition, this implies that the distance intervals used to
fit the behaviour of the risetimes computed either with the low or the high-
gain traces are sufficiently long to avoid compromising the quality of the
fit.

A fit is first made to the data from the low-gain channels using the relation

$t_{\text{1/2}}^{\text{low-gain
trace}}=40\,\text{ns}+\sqrt{A(\theta)^{2}+B(\theta)r^{2}}-A(\theta)$ (7)

where A and B are free parameters. The reason for adopting 40 ns as a limit
was explained in section III.1. Other functions were tested: this one gave
consistently lower values of reduced $\chi^{2}$ over the range of angles and
energies used for the two arrays.

Having used low-gain traces to evaluate A and B, the signals from high-gain
traces are now fitted with the function

$t_{\text{1/2}}^{\text{high-gain
trace}}=40\,\text{ns}+N(\theta)\left(\sqrt{A(\theta)^{2}+B(\theta)r^{2}}-A(\theta)\right)$
(8)

in which there is one free parameter, $N(\theta)$, that describes the shift
between the measurements in the two channels. Examples of the quality of the
fits of these functions to the data are shown in Fig. LABEL:fi5 and Fig. 7 for
two angular ranges for each of the two arrays.

Figure 6: Examples of benchmark fit for the 750 m array. (Top panels) 1.00 <
sec $\theta$ < 1.05. (Bottom panels) 1.15 < sec $\theta$ < 1.20. The solid
(dashed) line corresponds to the fit done to the risetimes computed using the
low-gain (high-gain) trace.

Figure 7: Examples of benchmark fit for the 1500 m array. (Top panels) 1.00 <
sec $\theta$ < 1.05. (Bottom panels) 1.25 < sec $\theta$ < 1.30. The solid
(dashed) line corresponds to the fit done to the risetimes computed using the
low-gain (high-gain) trace.

In the right-hand plots of each pair, the mean and RMS deviations of the fits
are seen to be consistent with 0 and 1, as expected for pull distributions r17
. The uncertainty in the axial distance has not been included in the fits as
it is only around 2% for the distances in question.

Fits were made for A, B and $N(\theta)$ in six intervals of sec $\theta$
ranges 1.0 – 1.30 and 1.0 – 1.45 for the 750 m and 1500 m arrays respectively.
In all six cases the $\chi^{2}$-values of the fits are between 1 and 1.2. To
obtain the final parameterization of A, B and N as a function of $\theta$ fits
have been made using the following functions

$\begin{array}[]{l}A(\theta)=a_{0}+a_{1}(\sec\theta)^{-4}\\\
B(\theta)=b_{0}+b_{1}(\sec\theta)^{-4}\\\
N(\theta)=n_{0}+n_{1}(\sec\theta)^{2}+n_{2}e^{\sec\theta}\end{array}$ (9)

where the seven coefficients, a0, a1 etc., are determined for the two arrays.
This set of functions has been empirically chosen. It guarantees that, for the
energy bins for which the benchmarks are defined, the mean value of
$\Delta_{s}$ shows a flat behaviour as function of sec $\theta$. This
naturally follows from the definition of $t_{\text{1/2}}^{\text{bench}}$.
Since it embodies the dependence on sec $\theta$, the numerator in the
definition of $\Delta_{i}$ has to be independent of the zenith angle.

We may thus define the benchmarks in terms of A, B and N as a function of sec
$\theta$, enabling an appropriate benchmark to be defined for the zenith angle
of the event under study. Thus $\Delta_{i}$ can be found for every station
that satisfies the selection criterion and the corresponding value of
$\Delta_{s}$ can be found for every selected event.

##  V Evolution of $\langle\Delta_{s}\rangle$ with energy and comparison with
model predictions

We now describe the observed variation of $\langle$$\Delta_{s}$$\rangle$, the
mean of $\Delta_{s}$ for a set of events, as a function of energy. The
selection criteria for this analysis were presented in Table 2. The variation
of $\langle$$\Delta_{s}$$\rangle$ with energy for the two arrays is shown in
Fig. 8. Note that at the benchmark energies, indicated by the vertical bands,
$\langle$$\Delta_{s}$$\rangle$ is zero, as expected by definition.

Figure 8: Evolution of $\langle$$\Delta_{s}$$\rangle$ as a function of energy
for the two surface arrays: 750 m (left), 1500 m (right). The grey bands show
the energy ranges where the benchmark functions were defined.

The results shown in Fig. 8 were obtained using the whole data set. We produce
similar plots but this time splitting data in different bands of sec $\theta$.
This exercise gives results that are consistent with the ones displayed in
Fig. 8. Searches for anomalous behaviour of the largest, the second largest
and the smallest signals separately have also been made: none was found.

To test the validity of hadronic models we can use
$\langle$$\Delta_{s}$$\rangle$. In previous works r4 ; r5 ; r6 ; r7  strong
evidence has been found that the models do not adequately describe the data
and that the problem lies with the predictions of the muon content of showers.
As the risetime is dominated by muons, $\langle$$\Delta_{s}$$\rangle$ is
expected to provide a further investigation of this problem that will be
useful because of the higher number of events and the extension to lower
energies.

Libraries of simulations for the QGSJETII-04 r19  and EPOS-LHC r20  models and
proton and iron primaries for zenith angles < 45o and 17.5 < log (E/eV) < 20
have been created. In making comparisons with data it is necessary to choose
which benchmarks to adopt. For consistency in what follows we use the
benchmarks determined from data (section IV). Different choices of benchmarks
would simply give shifts in the values of $\langle$$\Delta_{s}$$\rangle$,
which would be the same for each data set.

For this study, the uncertainties in the risetimes have been found from
simulations and adopting the ‘twins’ approach described in section III. The
results are shown in Fig. 9 where it is seen that the uncertainties from the
data are in good agreement with simulations using the QGSJETII-04 model at the
benchmark energy.

Figure 9: Risetime uncertainties estimated for protons (red lines), iron
nuclei (blue dashed lines) and data as a function of core distance. For a
clear view, the uncertainties corresponding to data are the average values.
The uncertainties have been evaluated for events with energies in the range
19.0 < log (E/eV) < 19.2. The regions bracketed by the lines indicate the
spread of the events simulated with QGSJETII-04 at a given distance.

A comparison of the evolution of $\langle$$\Delta_{s}$$\rangle$ with energy
from the data with those from models is shown in Fig. 10.

The main sources that contribute to the systematic uncertainty are: a seasonal
effect found when data are grouped according to the season of the year. It
amounts to 0.03 for the 1500 m data and it is due to the variable conditions
of pressure and temperature found in the atmosphere through the year. The UTC
time at which the data were recorded also introduces a small uncertainty in
our determination of $\langle$$\Delta_{s}$$\rangle$. Splitting data into
periods corresponding to day and night, we obtain a value of this uncertainty
of 0.01 for the 1500 m array data. Our observable also exhibits dependence
with the ageing effects of surface detectors. We take as a systematic
uncertainty the difference in $\langle$$\Delta_{s}$$\rangle$ found after
grouping our data into two samples, one running from 2004 to 2010 and the
other one from the years 2012 to 2014. For the 1500 m array, the difference
amounts to 0.04. A small dependence of $\langle$$\Delta_{s}$$\rangle$ with sec
$\theta$ is taken as source of systematics, its value being 0.02. Finally the
systematic uncertainty associated to the energy scale ($\pm$14%) results in a
systematic uncertainty on $\langle$$\Delta_{s}$$\rangle$ that amounts to 0.1.
Adding all these contributions in quadrature, the overall systematic
uncertainty in $\langle$$\Delta_{s}$$\rangle$ is 0.11 for the 1500 m array. A
similar study for the 750 m array gives an overall systematic uncertainty in
$\langle$$\Delta_{s}$$\rangle$ of 0.07. According to simulations, this is
about 10% of the separation between proton and iron nuclei. It is evident,
independent of which model is adopted, that the measurements suggest an
increase of the mean mass with energy above $\sim$2.5 EeV if the hadronic
models are correct.

Figure 10: $\langle$$\Delta_{s}$$\rangle$ as a function of the energy for the
two surface arrays. Brackets correspond to the systematic uncertainties. Data
are compared to the predictions obtained from simulations.

Assuming the superposition model is valid and since
$\langle$$\Delta_{s}$$\rangle$ is proportional to the logarithm of the energy
(Fig. 8), the mean value of the natural logarithm of A (the atomic weight of
an element) can be found from the following equation

$\langle\ln A\rangle=\ln
56\frac{\langle\Delta_{s}\rangle_{\text{p}}-\langle\Delta_{s}\rangle_{\text{data}}}{\langle\Delta_{s}\rangle_{\text{p}}-\langle\Delta_{s}\rangle_{\text{Fe}}}$
(10)

The results of this transformation for two models are shown in Fig. 11 and are
compared with the Auger measurements of Xmax made with the FD r21 . While the
absolute values of $\langle$ln A$\rangle$ for the Delta method and the FD Xmax
differ from each other, the trend in $\langle$ln A$\rangle$ with energy is
very similar. The observed difference arises because of the inadequate
description of the muon component in the models used to get the $\langle$ln
A$\rangle$ values. Notice that the electromagnetic cascade dominates the FD
measurement whereas the Delta method is of a parameter that is a mixture of
muons and the electromagnetic component. With substantially more events than
in previous studies, we observe that the inconsistency between data and model
predictions extends over a greater energy range than what was probed in past
works.

Figure 11: $\langle$ln A$\rangle$ as a function of energy for the Delta method
and for Xmax measurements done with the FD. QGSJetII-04 and EPOS-LHC have been
used as the reference hadronic models. Statistical uncertainties are shown as
bars. Brackets and shaded areas correspond to the systematic uncertainties
associated to the measurements done with the SD and FD data, respectively.

In Fig. 12, the Delta results are also compared with the results of the
analysis made using the asymmetry method r6  and with those from the study of
the depth of muon production r4

Figure 12: $\langle$ln A$\rangle$ as a function of the energy for analyses
using FD data and SD data from the 1500 m array. QGSJetII-04 and EPOS-LHC have
been used as the reference hadronic models. The results of the Delta method
are compared with those arising from the asymmetry analysis r6  (top panels)
and from the Muon Production Depth analysis r4  (bottom panels). Brackets
correspond to the systematic uncertainties.

For EPOS-LHC the results from the asymmetry analysis, which is also based on
risetimes and consequently on signals which are a mixture of the muon and the
electromagnetic component, are in good agreement with the Delta results,
albeit within the rather large statistical uncertainties. By contrast, the
results from the MPD analysis, in which only muons are studied, give much
larger (and astrophysically unexpected) values of $\langle$ln A$\rangle$. This
once more indicates that the mechanisms of muon production in extensive air-
showers are not properly described in current hadronic models.

##  VI Correlation of $\Delta_{s}$ with the Depth of Shower Maximum

We now address the correlation of $\Delta_{s}$ with the depth of shower
maximum, Xmax. As remarked earlier, we would not expect a 1:1 correlation
between these parameters because the muon/electromagnetic mix incident on the
water-Cherenkov detectors changes in a complex, but well-understood, manner
with zenith angle, energy and distance. An idea of the correlation to be
expected can be gained through Monte Carlo studies.

Values of $\Delta_{s}$ and Xmax have been obtained from simulations of 1000
proton and 1000 iron nuclei showers made using the QGSJETII-04 model for the
benchmark bin of the 1500 m array. The results are shown for three stations in
Fig. 13. The fact that the Pearson’s correlation is less strong for Fe-nuclei
than for protons, reflects the enhanced dominance of muons in showers
initiated by Fe-primaries. The simulations give an indication of what is to be
expected when the measurements of $\Delta_{s}$ are compared with the Xmax
values in the hybrid events for which the reconstruction of both observables
is possible.

Figure 13: Pearson’s correlation of $\Delta_{s}$ and the true values of Xmax
for events simulated with QGSJETII-04 in the energy range 19.1 < log (E/eV) <
19.2. The left panel corresponds to iron nuclei; the right panel shows the
correlation for protons. Values of $\Delta_{s}$ are computed for three
stations.

To exploit the correlation using data, and hence extend the energy range and
the statistical significance of the elongation rate determined with the FD, it
is necessary to create empirical correlations using events in which both
$\Delta_{s}$and Xmax have been measured in the same events. For this study we
used the data discussed in r1  for the 1500 m array for the events with
energies > 3 EeV and a similar set of data from the 750 m array r21  for
events of lower energy. The selection of events is shown in Table 3.

Table 3: Set of cuts used to select events simultaneously reconstructed by the fluorescence and surface detectors. These events are used for calibration purposes. $\epsilon$ stands for the overall efficiency. HEAT data are obtained with a set of three fluorescence detectors that point to the higher zenith angles appropriate to the lower energies. 750 m array | 1500 m array
---|---
Quality cuts | Events |  $\epsilon$ (%) | Quality cuts | Events |  $\epsilon$ (% )
HEAT data | 12 003 | 100.0 | FD data | 19 759 | 100.0
FD & SD recon | 2 461 | 20.5 | FD & SD recon | 12 825 | 65.0
sec $\theta$ < 1.30 | 2 007 | 16.7 | sec $\theta$ < 1.45 | 9 625 | 49.0
6T5 trigger | 714 | 5.9 | 6T5 trigger | 7 361 | 37.0
$\geq$ 3 selected stations | 660 | 5.5 |  $\geq$ 3 selected stations | 4 025 | 20.0
log (E/eV) $\geq$ 17.5 | 252 | 2.1 | log (E/eV) $\geq$ 18.5 | 885 | 4.5

The $\Delta_{s}$and Xmax of the events selected for the purposes of
calibration are shown for the two arrays in Fig. 14. There are 252 and 885
events for the 750 m and 1500 m arrays respectively available for calibration
of which 161 have energies >10 EeV. The small number for the 750 m array
reflects the shorter period of operation and the relatively small area (23.5
km2) of the array. We have checked that the sample of events selected is
unbiased by comparing the elongation rate determined from the full data set
(from HEAT and standard fluorescence telescopes) with that found from the 252
and 885 events alone.

Figure 14:  (Left) Correlation of Xmax and $\Delta_{s}$ for the 252 events from the 750 m array. (Right) Correlation of Xmax and $\Delta_{s}$for the 885 events of the 1500 m array. Table 4: Coefficients obtained from the calibration of $\Delta_{s}$ and Xmax. | 750 m array | 1500 m array
---|---|---
Calibration parameters | Value (g cm-2) | Value (g cm -2)
a | 636 $\pm$ 20 | 699 $\pm$ 12
b | 96 $\pm$ 10 | 56 $\pm$ 3
c | 2.9 $\pm$ 1.2 | 3.6 $\pm$ 0.7

For the calibration we fit functions of the form

$X_{\text{max}}=a+b\Delta_{s}+c\log(E/\text{eV})$ (11)

to the two data sets. The term ‘b’ is dominant in the fit. The term ‘c’ is
included to accommodate the energy dependence of both variables. A fit
including a quadratic term in log (E/eV) does not modify our results. The
uncertainties in Xmax are taken from r1 . We have used the maximum likelihood
method to make the fits which give the coefficients listed in Table 4. The
three coefficients are not independent. Their Pearson’s correlations are
$\rho_{ab}$=-0.2, $\rho_{ac}$=-0.97 and $\rho_{bc}$=0.34. These correlations
are taken into account when evaluating the systematic uncertainty associated
with the calibration procedure.

We have also evaluated the systematic uncertainties associated with the
measurements of Xmax deduced from the surface detectors. These include the
seasonal, diurnal, ageing and $\theta$ dependence already discussed for
$\langle$$\Delta_{s}$$\rangle$ in section V that Xmax propagate to our
measurement. Now two further sources of systematic arise. One is related to
the uncertainty in the calibration parameters. We have propagated this
uncertainty taking into account the correlation of the parameters a, b and c.
For the 1500 m array, the differences in Xmax span from 3 g cm-2 at the lowest
energies to 5 g cm-2 at the upper end of the energy spectrum. We quote
conservatively as a systematic uncertainty the largest value found and
consider it constant for the whole energy range. A similar procedure for the
750 m array data results on a systematic uncertainty of 10 g cm-2. The
systematic uncertainty obtained in the measurement of Xmax with the FD
detector propagates directly into the values obtained with the SD data. In r1
the systematic uncertainty is given as a function of the energy. In this
analysis, the average of those values is quoted a systematic uncertainty that
is constant with energy. The values are shown for each effect and for each
array in Table 5.

The systematic uncertainties have been added in quadrature to give 14 and 11 g
cm-2 for the 750 and 1500 m arrays respectively.

The values of Xmax found from this analysis are shown as a function of energy
in Fig. 15. The resolution in the measurement of Xmax with the surface
detector data is 45 g cm-2.

Table 5: Breakdown of the systematic uncertainties of Xmax for the 750 m and 1500 m arrays. The systematic uncertainty obtained in the measurement of Xmax with the FD and HEAT detectors propagates directly into the values obtained with the SD data. The rest of systematic uncertainties quoted in this table are intrinsic to the Delta method. 750 m array | 1500 m array
---|---
Source |  Systematic uncertainty (g cm-2) |  Source |  Systematic uncertainty (g cm-2)
Uncertainty on calibration | 10.0 | Uncertainty on calibration | 5.0
Seasonal effect | 2.0 | Seasonal effect | 2.0
Diurnal dependence | 1.0 | Diurnal dependence | 1.0
Ageing | 3.0 | Ageing | 3.0
HEAT systematic uncertainty | 8.5 | FD systematic uncertainty | 8.5
Angular dependence | <1.0 | Angular dependence | 1.5
Total | 14.0 | Total | 11.0
Figure 15: Mean values of the Xmax distributions obtained with the data of the
750 m and 1500 m surface arrays as a function of the energy. The shaded area
indicates the systematic uncertainties. Data are compared to the predictions
from simulations of protons and iron nuclei for two different hadronic models.
The number of selected events in each energy bin is indicated.

In Fig. 16 measurements in the region of overlap between the two arrays are
shown. The agreement is satisfactory.

Figure 16: Same as Fig. 15 including additional Xmax measurements from the
surface detectors above and below 3 EeV. (Inset) Three energy bins have been
included below 3 EeV using the data of the 1500 m array and two measurements
added above 3 EeV use the data of the 750 m array. There is good agreement
between measurements in the overlap region. The brackets correspond to
systematic uncertainties.

In Fig. 17 the data of Fig. 15 are compared with measurements made with the
fluorescence detectors [21].

Figure 17: Evolution of $\langle$Xmax$\rangle$ as a function of energy. The
figure compares the mean values of the Xmax distributions measured by the
fluorescence and surface detectors of the Pierre Auger Observatory. In most
cases the uncertainties are smaller than the size of the symbols.

The agreement is good: the results from the surface detector alone are
statistically stronger and extend to higher energies.

###  VI.1 Interpretation of the measurements in terms of average mass

A comparison with hadronic models allows the expression of the average depth
of shower maxima in terms of the natural logarithm of the atomic mass
$\langle$ln A$\rangle$, following the procedure discussed in section V. The
evolution of $\langle$ln A$\rangle$ as a function of energy is shown in Fig.
18. In the energy range where the FD and SD measurements coincide, the
agreement is good. For both hadronic models the evolution of $\langle$ln
A$\rangle$ with energy is similar. However the EPOS-LHC model suggests a
heavier average composition. SD measurements have been used to confirm, with a
larger data set, what has already been observed with FD measurements, namely
that the primary flux of particles is predominantly composed of light
particles at around 2 EeV and that the average mass increases up to $\sim$40
EeV. Above this energy, the SD measurements can be used to draw inferences
about mass composition with good statistical power. The last two bins indicate
a possible change in the dependence of Xmax with energy above 50 EeV, with the
final point lying $\sim$3 sigma above the elongation rate fitted to data above
3 EeV. It is, therefore, possible that the increase of the primary mass with
energy is slowing at the highest energies but we need to reduce statistical
and systematic uncertainties further before strong conclusions can be drawn.
AugerPrime, the upgrade of the surface-detector array of the Pierre Auger
Observatory r22 , will significantly improve our capability to elucidate mass
composition on an event-by-event basis in the energy range of the flux
suppression.

Figure 18: $\langle$ln A$\rangle$ as a function of the energy. QGSJetII-04 and
EPOS-LHC have been used as the reference hadronic models. The results of the
Delta method are compared with those based on Xmax measurements done with the
FD r21 . Brackets and shaded areas correspond to the systematic uncertainties;
bars correspond to uncertainties of statistical nature.

##  VII Summary and Conclusions

We have described a new method for extracting relevant information from the
time profiles of the signals from the water-Cherenkov detectors of the Pierre
Auger Observatory. With it, we have been able to obtain information on the
evolution of the mean depth of shower maximum with energy over a larger energy
range than has been studied previously using over 81,000 events of which 123
are of energy >50 EeV. We have also been able to expand the discussions of the
mismatch between data and predictions from models based on extrapolations of
hadronic interactions from LHC energies. Specifically we have reported the
following:

  1. 1.

The comparison of the risetime data with fluorescence measurements reinforces
the conclusions reported previously r4 ; r5 ; r6 ; r7  that the modelling of
showers provides an inadequate description of air-shower data. The deductions
are made over a larger energy range and with smaller statistical uncertainties
than hitherto (Fig. 11 and Fig. 12).

  2. 2.

The depth of shower maximum has been measured from 0.3 EeV to 100 EeV using
data of the Surface Detector (Fig. 15).

  3. 3.

Data from the 750 m array of the Observatory have been used to derive mass
information for the first time.

  4. 4.

The mean measurements of Xmax have been compared with predictions from the
EPOS-LHC and QGSJetII04 models and estimates of $\langle$ln A$\rangle$
extracted (Fig. 18). While the EPOS-LHC model leads to larger values of
$\langle$ln A$\rangle$ than are found with the other model, both show the
general trend of the mean mass becoming smaller as the energy increases up to
$\sim$2 EeV, after which it rises slowly with energy up to about 50 EeV where
this rise seems to stop.

## Acknowledgments

The successful installation, commissioning, and operation of the Pierre Auger
Observatory would not have been possible without the strong commitment and
effort from the technical and administrative staff in Malargüe. We are very
grateful to the following agencies and organizations for financial support:

Argentina – Comisión Nacional de Energía Atómica; Agencia Nacional de
Promoción Científica y Tecnológica (ANPCyT); Consejo Nacional de
Investigaciones Científicas y Técnicas (CONICET); Gobierno de la Provincia de
Mendoza; Municipalidad de Malargüe; NDM Holdings and Valle Las Leñas; in
gratitude for their continuing cooperation over land access; Australia – the
Australian Research Council; Brazil – Conselho Nacional de Desenvolvimento
Científico e Tecnológico (CNPq); Financiadora de Estudos e Projetos (FINEP);
Fundação de Amparo à Pesquisa do Estado de Rio de Janeiro (FAPERJ); São Paulo
Research Foundation (FAPESP) Grants No. 2010/07359-6 and No. 1999/05404-3;
Ministério de Ciência e Tecnologia (MCT); Czech Republic – Grant No. MSMT CR
LG15014, LO1305, LM2015038 and CZ.02.1.01/0.0/0.0/16_013/0001402; France –
Centre de Calcul IN2P3/CNRS; Centre National de la Recherche Scientifique
(CNRS); Conseil Régional Ile-de-France; Département Physique Nucléaire et
Corpusculaire (PNC-IN2P3/CNRS); Département Sciences de l’Univers (SDU-
INSU/CNRS); Institut Lagrange de Paris (ILP) Grant No. LABEX ANR-10-LABX-63
within the Investissements d’Avenir Programme Grant No. ANR-11-IDEX-0004-02;
Germany – Bundesministerium für Bildung und Forschung (BMBF); Deutsche
Forschungsgemeinschaft (DFG); Finanzministerium Baden-Württemberg; Helmholtz
Alliance for Astroparticle Physics (HAP); Helmholtz-Gemeinschaft Deutscher
Forschungszentren (HGF); Ministerium für Innovation, Wissenschaft und
Forschung des Landes Nordrhein-Westfalen; Ministerium für Wissenschaft,
Forschung und Kunst des Landes Baden-Württemberg; Italy – Istituto Nazionale
di Fisica Nucleare (INFN); Istituto Nazionale di Astrofisica (INAF); Ministero
dell’Istruzione, dell’Universitá e della Ricerca (MIUR); CETEMPS Center of
Excellence; Ministero degli Affari Esteri (MAE); Mexico – Consejo Nacional de
Ciencia y Tecnología (CONACYT) No. 167733; Universidad Nacional Autónoma de
México (UNAM); PAPIIT DGAPA-UNAM; The Netherlands – Ministerie van Onderwijs,
Cultuur en Wetenschap; Nederlandse Organisatie voor Wetenschappelijk Onderzoek
(NWO); Stichting voor Fundamenteel Onderzoek der Materie (FOM); Poland –
National Centre for Research and Development, Grants No. ERA-NET-ASPERA/01/11
and No. ERA-NET-ASPERA/02/11; National Science Centre, Grants No.
2013/08/M/ST9/00322, No. 2013/08/M/ST9/00728 and No. HARMONIA
5–2013/10/M/ST9/00062, UMO-2016/22/M/ST9/00198; Portugal – Portuguese national
funds and FEDER funds within Programa Operacional Factores de Competitividade
through Fundação para a Ciência e a Tecnologia (COMPETE); Romania – Romanian
Authority for Scientific Research ANCS; CNDI-UEFISCDI partnership projects
Grants No. 20/2012 and No.194/2012 and PN 16 42 01 02; Slovenia – Slovenian
Research Agency; Spain – Comunidad de Madrid; Fondo Europeo de Desarrollo
Regional (FEDER) funds; Ministerio de Economía y Competitividad; Xunta de
Galicia; European Community 7th Framework Program Grant No.
FP7-PEOPLE-2012-IEF-328826; USA – Department of Energy, Contracts No. DE-
AC02-07CH11359, No. DE-FR02-04ER41300, No. DE-FG02-99ER41107 and No. DE-
SC0011689; National Science Foundation, Grant No. 0450696; The Grainger
Foundation; Marie Curie-IRSES/EPLANET; European Particle Physics Latin
American Network; European Union 7th Framework Program, Grant No.
PIRSES-2009-GA-246806; European Union’s Horizon 2020 research and innovation
programme (Grant No. 646623); and UNESCO.

## Appendix A: Data Tables

Table A1: Values of $\langle$$\Delta_{s}$$\rangle$ for the 750 m array. The fourth column shows the statistical uncertainty. For all measurements the systematic uncertainty amounts to 0.07. Log (E/eV) range |  $\langle$Log (E/eV) $\rangle$ |  $\langle$$\Delta_{s}$$\rangle$ |  $\sigma$stat($\langle$$\Delta_{s}$$\rangle$)
---|---|---|---
[17.5,17.6) | 17.55 | -0.157 | 0.009
[17.6,17.7) | 17.65 | -0.064 | 0.009
[17.7,17.8) | 17.75 | 0.004 | 0.008
[17.8,17.9) | 17.85 | 0.077 | 0.011
[17.9,18.0) | 17.95 | 0.170 | 0.014
[18.0,18.1) | 18.05 | 0.35 | 0.02
[18.1,18.2) | 18.15 | 0.41 | 0.03
[18.2,18.3) | 18.25 | 0.40 | 0.03
[18.3,18.4) | 18.35 | 0.54 | 0.03
[18.4,18.5) | 18.45 | 0.53 | 0.05
Table A2: Values of $\langle$$\Delta_{s}$$\rangle$ for the 1500 m array. The fourth column shows the statistical uncertainty. For all measurements the systematic uncertainty amounts to 0.11. Log (E/eV) range |  $\langle$Log (E/eV) $\rangle$ |  $\langle$$\Delta_{s}$$\rangle$ |  $\sigma$stat($\langle$$\Delta_{s}$$\rangle$)
---|---|---|---
[18.5,18.6) | 18.55 | -0.297 | 0.005
[18.6,18.7) | 18.65 | -0.242 | 0.006
[18.7,18.8) | 18.75 | -0.218 | 0.007
[18.8,18.9) | 18.85 | -0.163 | 0.009
[18.9,19.0) | 18.95 | -0.108 | 0.011
[19.0,19.1) | 19.05 | -0.056 | 0.012
[19.1,19.2) | 19.15 | 0.004 | 0.015
[19.2,19.3) | 19.25 | 0.077 | 0.020
[19.3,19.4) | 19.35 | 0.15 | 0.03
[19.4,19.5) | 19.45 | 0.11 | 0.03
[19.5,19.6) | 19.55 | 0.29 | 0.04
[19.6,19.7) | 19.64 | 0.20 | 0.04
[19.7,19.8) | 19.74 | 0.41 | 0.06
[19.8,$\infty$) | 19.88 | 0.60 | 0.06
Table A3: Values of $\langle$Xmax$\rangle$ for the 750 m array. The fourth column shows the statistical uncertainty. For all measurements the systematic uncertainty amounts to 14 g cm-2. Log (E/eV) range |  $\langle$Log (E/eV) $\rangle$ |  $\langle$Xmax/ g cm-2$\rangle$ |  $\sigma$stat($\langle$Xmax$\rangle$)/g cm-2
---|---|---|---
[17.5,17.6) | 17.55 | 687.2 | 0.5
[17.6,17.7) | 17.65 | 695.6 | 0.6
[17.7,17.8) | 17.75 | 699.9 | 0.8
[17.8,17.9) | 17.85 | 707 | 1.0
[17.9,18.0) | 17.95 | 716 | 1.0
[18.0,18.1) | 18.05 | 733 | 2.0
[18.1,18.2) | 18.15 | 738 | 3.0
[18.2,18.3) | 18.25 | 745 | 3.0
[18.3,18.4) | 18.35 | 759 | 4.0
[18.4,18.5) | 18.45 | 754 | 5.0
Table A4: Values of $\langle$Xmax$\rangle$ for the 1500 m array. The fourth column shows the statistical uncertainty. For all measurements the systematic uncertainty amounts to 11 g cm-2. Log (E/eV) range |  $\langle$Log (E/eV) $\rangle$ |  $\langle$Xmax/ g cm-2$\rangle$ |  $\sigma$stat($\langle$Xmax$\rangle$) /g cm-2
---|---|---|---
[18.5,18.6) | 18.55 | 750.7 | 0.3
[18.6,18.7) | 18.65 | 755.2 | 0.3
[18.7,18.8) | 18.75 | 756.4 | 0.4
[18.8,18.9) | 18.85 | 759.8 | 0.6
[18.9,19.0) | 18.95 | 763.0 | 0.6
[19.0,19.1) | 19.05 | 766.5 | 0.7
[19.1,19.2) | 19.15 | 769.6 | 0.9
[19.2,19.3) | 19.25 | 775 | 1.0
[19.3,19.4) | 19.35 | 780 | 2.0
[19.4,19.5) | 19.45 | 779 | 2.0
[19.5,19.6) | 19.55 | 788 | 2.0
[19.6,19.7) | 19.64 | 785 | 2.0
[19.7,19.8) | 19.74 | 795 | 3.0
[19.8,$\infty$) | 19.88 | 807 | 3.0

## References

  * (1) A. Aab et al. [Pierre Auger Collaboration], Phys. Rev. D 90, 122005 (2014) [arXiv:1409.4809 [astro-ph.HE]].
  * (2) R. U. Abbasi et al., Astropart. Phys. 64, 49 (2015) [arXiv:1408.1726 [astro-ph.HE]].
  * (3) A. Aab et al. [Pierre Auger Collaboration], Phys. Rev. D 90, 122006 (2014) [arXiv:1409.5083 [astro-ph.HE]].
  * (4) A. Aab et al. [Pierre Auger Collaboration], Phys. Rev. D 90, 012012 (2014) Addendum: [Phys. Rev. D 90, 039904 (2014)] Erratum: [Phys. Rev. D 92, 019903 (2015)] [arXiv:1407.5919 [hep-ex]].
  * (5) A. Aab et al. [Pierre Auger Collaboration], Phys. Rev. D 91, 032003 (2015) Erratum: [Phys. Rev. D 91, 059901 (2015)] [arXiv:1408.1421 [astro-ph.HE]].
  * (6) A. Aab et al. [Pierre Auger Collaboration], Phys. Rev. D 93, 072006 (2016) [arXiv:1604.00978 [astro-ph.HE]].
  * (7) A. Aab et al. [Pierre Auger Collaboration], Phys. Rev. Lett. 117, 192001 (2016) [arXiv:1610.08509 [hep-ex]].
  * (8) A. Aab et al. [Pierre Auger Collaboration], Nucl. Instrum. Meth. A 798, 172 (2015) [arXiv:1502.01323 [astro-ph.IM]].
  * (9) X. Bertou et al. [Pierre Auger Collaboration], Nucl. Instrum. Meth. A 568, 839 (2006).
  * (10) J. Abraham et al. [Pierre Auger Collaboration], Nucl. Instrum. Meth. A 613, 29 (2010) [arXiv:1111.6764 [astro-ph.IM]].
  * (11) D. Newton, J. Knapp, A.A. Watson, Astropart.Phys. 26, 414 (2007).
  * (12) J. Abraham et al. [Pierre Auger Collaboration], Phys. Rev. Lett. 101, 061101 (2008) [arXiv:0806.4302 [astro-ph]].
  * (13) V. Verzi, PoS ICRC 2015, 015 (2016).
  * (14) A. A. Watson and J. G. Wilson, J. Phys. A 7, 1199 (1974).
  * (15) J. Linsley and L. Scarsi, Phys. Rev. 128, 2384 (1962).
  * (16) A. J. Baxter, J. Phys. A 2, 50 (1969).
  * (17) K. Greisen, Ann. Rev. Nucl. Part. Sci. 10, 63 (1960).
  * (18) L. Demotier and L. Lyons, CDF/ANAL/PUBLIC/5776, 2002.
  * (19) Pierre Auger Collaboration in preparation.
  * (20) S. Ostapchenko, Phys. Rev. D 83, 014018 (2011) [arXiv:1010.1869 [hep-ph]].
  * (21) T. Pierog, I. Karpenko, J. M. Katzy, E. Yatsenko and K. Werner, Phys. Rev. C 92, 034906 (2015) [arXiv:1306.0121 [hep-ph]].
  * (22) A. Porcelli for the Pierre Auger Collaboration, PoS (ICRC2015) 420.
  * (23) A. Aab et al. [Pierre Auger Collaboration], arXiv:1604.03637 [astro-ph.IM].