https://doi.org/10.1140/epjc/s10052-020-7834-9
Regular Article - Experimental Physics
Mixed higher-order anisotropic flow and nonlinear response coefficients of charged particles in 
collisions at ![$$\sqrt{\smash [b]{s_{_{\mathrm {NN}}}}} = 2.76$$](/articles/epjc/abs/2020/06/10052_2020_Article_7834/10052_2020_Article_7834_tex_eq2.png)
and 5.02
1
Yerevan Physics Institute, Yerevan, Armenia
2
Institut für Hochenergiephysik, Wien, Austria
3
Institute for Nuclear Problems, Minsk, Belarus
4
Universiteit Antwerpen, Antwerp, Belgium
5
Vrije Universiteit Brussel, Brussels, Belgium
6
Université Libre de Bruxelles, Brussels, Belgium
7
Ghent University, Ghent, Belgium
8
Université Catholique de Louvain, Louvain-la-Neuve, Belgium
9
Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil
10
Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
11
Universidade Estadual Paulista, Universidade Federal do ABC, São Paulo, Brazil
12
Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria
13
University of Sofia, Sofia, Bulgaria
14
Beihang University, Beijing, China
15
Institute of High Energy Physics, Beijing, China
16
State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China
17
Tsinghua University, Beijing, China
18
Universidad de Los Andes, Bogotá, Colombia
19
Universidad de Antioquia, Medellín, Colombia
20
Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia
21
Faculty of Science, University of Split, Split, Croatia
22
Institute Rudjer Boskovic, Zagreb, Croatia
23
University of Cyprus, Nicosia, Cyprus
24
Charles University, Prague, Czech Republic
25
Escuela Politecnica Nacional, Quito, Ecuador
26
Universidad San Francisco de Quito, Quito, Ecuador
27
Academy of Scientific Research and Technology of the Arab Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt
28
National Institute of Chemical Physics and Biophysics, Tallinn, Estonia
29
Department of Physics, University of Helsinki, Helsinki, Finland
30
Helsinki Institute of Physics, Helsinki, Finland
31
Lappeenranta University of Technology, Lappeenranta, Finland
32
IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
33
Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de Paris, Paris, France
34
Université de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France
35
Centre de Calcul de l’Institut National de Physique Nucleaire et de Physique des Particules, CNRS/IN2P3, Villeurbanne, France
36
Université de Lyon, Université Claude Bernard Lyon 1, CNRS-IN2P3, Institut de Physique Nucléaire de Lyon, Villeurbanne, France
37
Georgian Technical University, Tbilisi, Georgia
38
Tbilisi State University, Tbilisi, Georgia
39
RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany
40
RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany
41
RWTH Aachen University, III. Physikalisches Institut B, Aachen, Germany
42
Deutsches Elektronen-Synchrotron, Hamburg, Germany
43
University of Hamburg, Hamburg, Germany
44
Karlsruher Institut fuer Technologie, Karlsruhe, Germany
45
Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi, Greece
46
National and Kapodistrian University of Athens, Athens, Greece
47
National Technical University of Athens, Athens, Greece
48
University of Ioánnina, Ioannina, Greece
49
MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary
50
Wigner Research Centre for Physics, Budapest, Hungary
51
Institute of Nuclear Research ATOMKI, Debrecen, Hungary
52
Institute of Physics, University of Debrecen, Debrecen, Hungary
53
Eszterhazy Karoly University, Karoly Robert Campus, Gyongyos, Hungary
54
Indian Institute of Science (IISc), Bangalore, India
55
National Institute of Science Education and Research, HBNI, Bhubaneswar, India
56
Panjab University, Chandigarh, India
57
University of Delhi, Delhi, India
58
Saha Institute of Nuclear Physics, HBNI, Kolkata, India
59
Indian Institute of Technology Madras, Madras, India
60
Bhabha Atomic Research Centre, Mumbai, India
61
Tata Institute of Fundamental Research-A, Mumbai, India
62
Tata Institute of Fundamental Research-B, Mumbai, India
63
Indian Institute of Science Education and Research (IISER), Pune, India
64
Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
65
University College Dublin, Dublin, Ireland
66
INFN Sezione di Bari, Università di Bari, Politecnico di Bari, Bari, Italy
67
INFN Sezione di Bologna, Università di Bologna, Bologna, Italy
68
INFN Sezione di Catania, Università di Catania, Catania, Italy
69
INFN Sezione di Firenze, Università di Firenze, Firenze, Italy
70
INFN Laboratori Nazionali di Frascati, Frascati, Italy
71
INFN Sezione di Genova, Università di Genova, Genoa, Italy
72
INFN Sezione di Milano-Bicocca, Università di Milano-Bicocca, Milan, Italy
73
INFN Sezione di Napoli, Università di Napoli ‘Federico II’ , Napoli, Italy, Università della Basilicata, Potenza, Italy, Università G. Marconi, Rome, Italy
74
INFN Sezione di Padova, Università di Padova, Padova, Italy, Università di Trento, Trento, Italy
75
INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
76
INFN Sezione di Perugia, Università di Perugia, Perugia, Italy
77
INFN Sezione di Pisa, Università di Pisa, Scuola Normale Superiore di Pisa, Pisa, Italy
78
INFN Sezione di Roma, Sapienza Università di Roma, Rome, Italy
79
INFN Sezione di Torino, Università di Torino, Torino, Italy, Università del Piemonte Orientale, Novara, Italy
80
INFN Sezione di Trieste, Università di Trieste, Trieste, Italy
81
Kyungpook National University, Daegu, Korea
82
Chonnam National University, Institute for Universe and Elementary Particles, Kwangju, Korea
83
Hanyang University, Seoul, Korea
84
Korea University, Seoul, Korea
85
Department of Physics, Kyung Hee University, Seoul, Korea
86
Sejong University, Seoul, Korea
87
Seoul National University, Seoul, Korea
88
University of Seoul, Seoul, Korea
89
Sungkyunkwan University, Suwon, Korea
90
Riga Technical University, Riga, Latvia
91
Vilnius University, Vilnius, Lithuania
92
National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia
93
Universidad de Sonora (UNISON), Hermosillo, Mexico
94
Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico
95
Universidad Iberoamericana, Mexico City, Mexico
96
Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
97
Universidad Autónoma de San Luis Potosí, San Luis Potosí, Mexico
98
University of Montenegro, Podgorica, Montenegro
99
University of Auckland, Auckland, New Zealand
100
University of Canterbury, Christchurch, New Zealand
101
National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan
102
Faculty of Computer Science, Electronics and Telecommunications, AGH University of Science and Technology, Kraków, Poland
103
National Centre for Nuclear Research, Swierk, Poland
104
Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland
105
Laboratório de Instrumentação e Física Experimental de Partículas, Lisbon, Portugal
106
Joint Institute for Nuclear Research, Dubna, Russia
107
Petersburg Nuclear Physics Institute, Gatchina (St. Petersburg), Russia
108
Institute for Nuclear Research, Moscow, Russia
109
Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of NRC ‘Kurchatov Institute’, Moscow, Russia
110
Moscow Institute of Physics and Technology, Moscow, Russia
111
National Research Nuclear University ‘Moscow Engineering Physics Institute’ (MEPhI), Moscow, Russia
112
P.N. Lebedev Physical Institute, Moscow, Russia
113
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia
114
Novosibirsk State University (NSU), Novosibirsk, Russia
115
Institute for High Energy Physics of National Research Centre ‘Kurchatov Institute’, Protvino, Russia
116
National Research Tomsk Polytechnic University, Tomsk, Russia
117
Tomsk State University, Tomsk, Russia
118
Faculty of Physics and VINCA Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia
119
Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain
120
Universidad Autónoma de Madrid, Madrid, Spain
121
Universidad de Oviedo, Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA), Oviedo, Spain
122
Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain
123
University of Colombo, Colombo, Sri Lanka
124
Department of Physics, University of Ruhuna, Matara, Sri Lanka
125
CERN, European Organization for Nuclear Research, Geneva, Switzerland
126
Paul Scherrer Institut, Villigen, Switzerland
127
ETH Zurich-Institute for Particle Physics and Astrophysics (IPA), Zurich, Switzerland
128
Universität Zürich, Zurich, Switzerland
129
National Central University, Chung-Li, Taiwan
130
National Taiwan University (NTU), Taipei, Taiwan
131
Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand
132
Physics Department, Science and Art Faculty, Çukurova University, Adana, Turkey
133
Physics Department, Middle East Technical University, Ankara, Turkey
134
Bogazici University, Istanbul, Turkey
135
Istanbul Technical University, Istanbul, Turkey
136
Istanbul University, Istanbul, Turkey
137
Institute for Scintillation Materials of National Academy of Science of Ukraine, Kharkov, Ukraine
138
National Scientific Center, Kharkov Institute of Physics and Technology, Kharkov, Ukraine
139
University of Bristol, Bristol, UK
140
Rutherford Appleton Laboratory, Didcot, UK
141
Imperial College, London, UK
142
Brunel University, Uxbridge, UK
143
Baylor University, Waco, USA
144
Catholic University of America, Washington DC, USA
145
The University of Alabama, Tuscaloosa, USA
146
Boston University, Boston, USA
147
Brown University, Providence, USA
148
University of California, Davis, Davis, USA
149
University of California, Los Angeles, USA
150
University of California, Riverside, Riverside, USA
151
University of California, San Diego, La Jolla, USA
152
Department of Physics, University of California, Santa Barbara, Santa Barbara, USA
153
California Institute of Technology, Pasadena, USA
154
Carnegie Mellon University, Pittsburgh, USA
155
University of Colorado Boulder, Boulder, USA
156
Cornell University, Ithaca, USA
157
Fermi National Accelerator Laboratory, Batavia, USA
158
University of Florida, Gainesville, USA
159
Florida International University, Miami, USA
160
Florida State University, Tallahassee, USA
161
Florida Institute of Technology, Melbourne, USA
162
University of Illinois at Chicago (UIC), Chicago, USA
163
The University of Iowa, Iowa City, USA
164
Johns Hopkins University, Baltimore, USA
165
The University of Kansas, Lawrence, USA
166
Kansas State University, Manhattan, USA
167
Lawrence Livermore National Laboratory, Livermore, USA
168
University of Maryland, College Park, USA
169
Massachusetts Institute of Technology, Cambridge, USA
170
University of Minnesota, Minneapolis, USA
171
University of Mississippi, Oxford, USA
172
University of Nebraska-Lincoln, Lincoln, USA
173
State University of New York at Buffalo, Buffalo, USA
174
Northeastern University, Boston, USA
175
Northwestern University, Evanston, USA
176
University of Notre Dame, Notre Dame, USA
177
The Ohio State University, Columbus, USA
178
Princeton University, Princeton, USA
179
University of Puerto Rico, Mayagüez, USA
180
Purdue University, West Lafayette, USA
181
Purdue University Northwest, Hammond, USA
182
Rice University, Houston, USA
183
University of Rochester, Rochester, USA
184
Rutgers, The State University of New Jersey, Piscataway, USA
185
University of Tennessee, Knoxville, USA
186
Texas A&M University, College Station, USA
187
Texas Tech University, Lubbock, USA
188
Vanderbilt University, Nashville, USA
189
University of Virginia, Charlottesville, USA
190
Wayne State University, Detroit, USA
191
University of Wisconsin-Madison, Madison, WI, USA
192
CERN, 1211, Geneva 23, Switzerland
* e-mail: cms-publication-committee-chair@cern.ch
Received:
19
October
2019
Accepted:
14
March
2020
Published online:
13
June
2020
Anisotropies in the initial energy density distribution of the quark-gluon plasma created in high energy heavy ion collisions lead to anisotropies in the azimuthal distributions of the final-state particles known as collective anisotropic flow. Fourier harmonic decomposition is used to quantify these anisotropies. The higher-order harmonics can be induced by the same order anisotropies (linear response) or by the combined influence of several lower order anisotropies (nonlinear response) in the initial state. The mixed higher-order anisotropic flow and nonlinear response coefficients of charged particles are measured as functions of transverse momentum and centrality in collisions at nucleon-nucleon center-of-mass energies and 5.02 with the CMS detector. The results are compared with viscous hydrodynamic calculations using several different initial conditions, as well as microscopic transport model calculations. None of the models provides a simultaneous description of the mixed higher-order flow harmonics and nonlinear response coefficients.
© CERN for the benefit of the CMS collaboration, 2020
