https://doi.org/10.1140/epjc/s10052-021-09570-2
Regular Article - Experimental Physics
Measurements of angular distance and momentum ratio distributions in three-jet and 
+ two-jet final states in 
collisions
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, Brussel, Belgium
6
Université Libre de Bruxelles, Bruxelles, 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
Department of Physics, Tsinghua University, Beijing, China
16
Institute of High Energy Physics, Beijing, China
17
State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China
18
Sun Yat-Sen University, Guangzhou, China
19
Institute of Modern Physics and Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Fudan University, Shanghai, China
20
Zhejiang University, Hangzhou, China
21
Universidad de Los Andes, Bogota, Colombia
22
Universidad de Antioquia, Medellin, Colombia
23
University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Split, Croatia
24
University of Split, Faculty of Science, Split, Croatia
25
Institute Rudjer Boskovic, Zagreb, Croatia
26
University of Cyprus, Nicosia, Cyprus
27
Charles University, Prague, Czech Republic
28
Escuela Politecnica Nacional, Quito, Ecuador
29
Universidad San Francisco de Quito, Quito, Ecuador
30
Academy of Scientific Research and Technology of the Arab Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt
31
Center for High Energy Physics (CHEP-FU), Fayoum University, El-Fayoum, Egypt
32
National Institute of Chemical Physics and Biophysics, Tallinn, Estonia
33
Department of Physics, University of Helsinki, Helsinki, Finland
34
Helsinki Institute of Physics, Helsinki, Finland
35
Lappeenranta University of Technology, Lappeenranta, Finland
36
IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
37
Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
38
Université de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France
39
Institut de Physique des 2 Infinis de Lyon (IP2I ), Villeurbanne, France
40
Georgian Technical University, Tbilisi, Georgia
41
RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany
42
III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany
43
III. Physikalisches Institut B, RWTH Aachen University, Aachen, Germany
44
Deutsches Elektronen-Synchrotron, Hamburg, Germany
45
University of Hamburg, Hamburg, Germany
46
Karlsruher Institut fuer Technologie, Karlsruhe, Germany
47
Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi, Athens, Greece
48
National and Kapodistrian University of Athens, Athens, Greece
49
National Technical University of Athens, Athens, Greece
50
University of Ioánnina, Ioannina, Greece
51
MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary
52
Wigner Research Centre for Physics, Budapest, Hungary
53
Institute of Nuclear Research ATOMKI, Debrecen, Hungary
54
Institute of Physics, University of Debrecen, Debrecen, Hungary
55
Eszterhazy Karoly University, Karoly Robert Campus, Gyongyos, Hungary
56
Indian Institute of Science (IISc), Bangalore, India
57
National Institute of Science Education and Research, HBNI, Bhubaneswar, India
58
Panjab University, Chandigarh, India
59
University of Delhi, Delhi, India
60
Saha Institute of Nuclear Physics, HBNI, Kolkata, India
61
Indian Institute of Technology Madras, Madras, India
62
Bhabha Atomic Research Centre, Mumbai, India
63
Tata Institute of Fundamental Research-A, Mumbai, India
64
Tata Institute of Fundamental Research-B, Mumbai, India
65
Indian Institute of Science Education and Research (IISER), Pune, India
66
Department of Physics, Isfahan University of Technology, Isfahan, Iran
67
Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
68
University College Dublin, Dublin, Ireland
69
INFN Sezione di Bari , Universit’a di Bari, Politecnico di Bari, Bari, Italy
70
INFN Sezione di Bologna, Università di Bologna, Bologna, Italy
71
INFN Sezione di Catania, Università di Catania, Catania, Italy
72
INFN Sezione di Firenze, Università di Firenze, Firenze, Italy
73
INFN Laboratori Nazionali di Frascati, Frascati, Italy
74
INFN Sezione di Genova, Università di Genova, Genoa, Italy
75
INFN Sezione di Milano-Bicocca, Università di Milano-Bicocca, Milan, Italy
76
INFN Sezione di Napoli , Università di Napoli ’Federico II’ , Napoli, Italy, Università della Basilicata , Potenza, Italy, Università G. Marconi, Rome, Italy
77
INFN Sezione di Padova , Università di Padova , Padova, Italy, Università di Trento, Trento, Italy
78
INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
79
INFN Sezione di Perugia, Università di Perugia, Perugia, Italy
80
INFN Sezione di Pisa , Università di Pisa , Scuola Normale Superiore di Pisa , Pisa Italy, Università di Siena, Siena, Italy
81
INFN Sezione di Roma, Sapienza Università di Roma, Rome, Italy
82
INFN Sezione di Torino , Università di Torino , Torino Torino, Italy, Università del Piemonte Orientale, Novara, Italy
83
INFN Sezione di Trieste, Università di Trieste, Trieste, Italy
84
Kyungpook National University, Daegu, Korea
85
Chonnam National University, Institute for Universe and Elementary Particles, Kwangju, Korea
86
Hanyang University, Seoul, Korea
87
Korea University, Seoul, Korea
88
Kyung Hee University, Department of Physics, Seoul, Republic of Korea
89
Sejong University, Seoul, Korea
90
Seoul National University, Seoul, Korea
91
University of Seoul, Seoul, Korea
92
Department of Physics, Yonsei University, Seoul, Korea
93
Sungkyunkwan University, Suwon, Korea
94
Riga Technical University, Riga, Latvia
95
Vilnius University, Vilnius, Lithuania
96
National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia
97
Universidad de Sonora (UNISON), Hermosillo, Mexico
98
Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico
99
Universidad Iberoamericana, Mexico City, Mexico
100
Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
101
Universidad Autónoma de San Luis Potosí, San Luis Potosí, Mexico
102
University of Montenegro, Podgorica, Montenegro
103
University of Auckland, Auckland, New Zealand
104
University of Canterbury, Christchurch, New Zealand
105
National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan
106
AGH University of Science and Technology Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland
107
National Centre for Nuclear Research, Swierk, Poland
108
Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland
109
Laboratório de Instrumentação e Física Experimental de Partículas, Lisbon, Portugal
110
Joint Institute for Nuclear Research, Dubna, Russia
111
Petersburg Nuclear Physics Institute, Gatchina (St. Petersburg), Russia
112
Institute for Nuclear Research, Moscow, Russia
113
Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of NRC ‘Kurchatov Institute’, Moscow, Russia
114
Moscow Institute of Physics and Technology, Moscow, Russia
115
National Research Nuclear University ‘Moscow Engineering Physics Institute’ (MEPhI), Moscow, Russia
116
P.N. Lebedev Physical Institute, Moscow, Russia
117
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia
118
Novosibirsk State University (NSU), Novosibirsk, Russia
119
Institute for High Energy Physics of National Research Centre ‘Kurchatov Institute’, Protvino, Russia
120
National Research Tomsk Polytechnic University, Tomsk, Russia
121
Tomsk State University, Tomsk, Russia
122
University of Belgrade: Faculty of Physics and VINCA Institute of Nuclear Sciences, Belgrade, Serbia
123
Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain
124
Universidad Autónoma de Madrid, Madrid, Spain
125
Universidad de Oviedo, Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA), Oviedo, Spain
126
Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain
127
University of Colombo, Colombo, Sri Lanka
128
Department of Physics, University of Ruhuna, Matara, Sri Lanka
129
CERN, European Organization for Nuclear Research, Geneva, Switzerland
130
Paul Scherrer Institut, Villigen, Switzerland
131
ETH Zurich-Institute for Particle Physics and Astrophysics (IPA), Zurich, Switzerland
132
Universität Zürich, Zurich, Switzerland
133
National Central University, Chung-Li, Taiwan
134
National Taiwan University (NTU), Taipei, Taiwan
135
Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand
136
Physics Department, Science and Art Faculty, Çukurova University, Adana, Turkey
137
Physics Department, Middle East Technical University, Ankara, Turkey
138
Bogazici University, Istanbul, Turkey
139
Istanbul Technical University, Istanbul, Turkey
140
Istanbul University, Istanbul, Turkey
141
Institute for Scintillation Materials of National Academy of Science of Ukraine, Kharkov, Ukraine
142
National Scientific Center, Kharkov Institute of Physics and Technology, Kharkov, Ukraine
143
University of Bristol, Bristol, UK
144
Rutherford Appleton Laboratory, Didcot, UK
145
Imperial College, London, UK
146
Brunel University, Uxbridge, UK
147
Baylor University, Waco, USA
148
Catholic University of America, Washington, DC, USA
149
The University of Alabama, Tuscaloosa, USA
150
Boston University, Boston, USA
151
Brown University, Providence, USA
152
University of California, Davis, Davis, USA
153
University of California, Los Angeles, USA
154
University of California, Riverside, Riverside, USA
155
University of California, San Diego, La Jolla, USA
156
Department of Physics, University of California, Santa Barbara, Santa Barbara, USA
157
California Institute of Technology, Pasadena, USA
158
Carnegie Mellon University, Pittsburgh, USA
159
University of Colorado Boulder, Boulder, USA
160
Cornell University, Ithaca, USA
161
Fermi National Accelerator Laboratory, Batavia, USA
162
University of Florida, Gainesville, USA
163
Florida State University, Tallahassee, USA
164
Florida Institute of Technology, Melbourne, USA
165
University of Illinois at Chicago (UIC), Chicago, USA
166
The University of Iowa, Iowa City, USA
167
Johns Hopkins University, Baltimore, USA
168
The University of Kansas, Lawrence, USA
169
Kansas State University, Manhattan, USA
170
Lawrence Livermore National Laboratory, Livermore, USA
171
University of Maryland, College Park, USA
172
Massachusetts Institute of Technology, Cambridge, USA
173
University of Minnesota, Minneapolis, USA
174
University of Mississippi, Oxford, USA
175
University of Nebraska-Lincoln, Lincoln, USA
176
State University of New York at Buffalo, Buffalo, USA
177
Northeastern University, Boston, USA
178
Northwestern University, Evanston, USA
179
University of Notre Dame, Notre Dame, USA
180
The Ohio State University, Columbus, USA
181
Princeton University, Princeton, USA
182
University of Puerto Rico, Mayaguez, USA
183
Purdue University, West Lafayette, USA
184
Purdue University Northwest, Hammond, USA
185
Rice University, Houston, USA
186
University of Rochester, Rochester, USA
187
Rutgers, The State University of New Jersey, Piscataway, USA
188
University of Tennessee, Knoxville, USA
189
Texas A&M University, College Station, USA
190
Texas Tech University, Lubbock, USA
191
Vanderbilt University, Nashville, USA
192
University of Virginia, Charlottesville, USA
193
Wayne State University, Detroit, USA
194
University of Wisconsin-Madison, Madison, WI, USA
195
Vienna University of Technology, Vienna, Austria
196
Institute of Basic and Applied Sciences, Faculty of Engineering, Arab Academy for Science, Technology and Maritime Transport, Alexandria, Egypt
197
Université Libre de Bruxelles, Bruxelles, Belgium
198
IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
199
Universidade Estadual de Campinas, Campinas, Brazil
200
Federal University of Rio Grande do Sul, Porto Alegre, Brazil
201
UFMS, Nova Andradina, Brazil
202
Universidade Federal de Pelotas, Pelotas, Brazil
203
University of Chinese Academy of Sciences, Beijing, China
204
Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of NRC ‘Kurchatov Institute’, Moscow, Russia
205
Joint Institute for Nuclear Research, Dubna, Russia
206
Cairo University, Cairo, Egypt
207
Helwan University, Cairo, Egypt
208
Zewail City of Science and Technology, Zewail, Egypt
209
British University in Egypt, Cairo, Egypt
210
Fayoum University, El-Fayoum, Egypt
211
Purdue University, West Lafayette, USA
212
Université de Haute Alsace, Mulhouse, France
213
Erzincan Binali Yildirim University, Erzincan, Turkey
214
CERN, European Organization for Nuclear Research, Geneva, Switzerland
215
III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany
216
University of Hamburg, Hamburg, Germany
217
Department of Physics, Isfahan University of Technology, Isfahan, Iran
218
Brandenburg University of Technology, Cottbus, Germany
219
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia
220
Institute of Physics, University of Debrecen, Debrecen, Hungary
221
Physics Department, Faculty of Science, Assiut University, Assiut, Egypt
222
MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary
223
Institute of Nuclear Research ATOMKI, Debrecen, Hungary
224
IIT Bhubaneswar, Bhubaneswar, India
225
Institute of Physics, Bhubaneswar, India
226
G.H.G. Khalsa College, Punjab, India
227
Shoolini University, Solan, India
228
University of Hyderabad, Hyderabad, India
229
University of Visva-Bharati, Santiniketan, India
230
Indian Institute of Technology (IIT), Mumbai, India
231
Deutsches Elektronen-Synchrotron, Hamburg, Germany
232
Sharif University of Technology, Tehran, Iran
233
Department of Physics, University of Science and Technology of Mazandaran, Behshahr, Iran
234
INFN Sezione di Bari , Università di Bari, Politecnico di Bari, Bari, Italy
235
Italian National Agency for New Technologies, Energy and Sustainable Economic Development, Bologna, Italy
236
Centro Siciliano di Fisica Nucleare e di Struttura Della Materia, Catania, Italy
237
Università di Napoli ’Federico II’, Naples, Italy
238
Riga Technical University, Riga, Latvia
239
Consejo Nacional de Ciencia y Tecnología, Mexico City, Mexico
240
Warsaw University of Technology, Institute of Electronic Systems, Warsaw, Poland
241
Institute for Nuclear Research, Moscow, Russia
242
National Research Nuclear University ‘Moscow Engineering Physics Institute’ (MEPhI), Moscow, Russia
243
St. Petersburg State Polytechnical University, St. Petersburg, Russia
244
University of Florida, Gainesville, USA
245
Imperial College, London, UK
246
P.N. Lebedev Physical Institute, Moscow, Russia
247
California Institute of Technology, Pasadena, USA
248
Budker Institute of Nuclear Physics, Novosibirsk, Russia
249
Faculty of Physics, University of Belgrade, Belgrade, Serbia
250
Trincomalee Campus, Eastern University, Nilaveli, Sri Lanka
251
INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
252
National and Kapodistrian University of Athens, Athens, Greece
253
Universität Zürich, Zurich, Switzerland
254
Stefan Meyer Institute for Subatomic Physics, Vienna, Austria
255
Laboratoire d’Annecy-le-Vieux de Physique des Particules, IN2P3-CNRS, Annecy-le-Vieux, France
256
Şırnak University, Sirnak, Turkey
257
Department of Physics, Tsinghua University, Beijing, China
258
Near East University, Research Center of Experimental Health Science, Nicosia, Turkey
259
Beykent University, Istanbul, Turkey
260
Application and Research Center for Advanced Studies (App. & Res. Cent. for Advanced Studies), Istanbul Aydin University, Istanbul, Turkey
261
Mersin University, Mersin, Turkey
262
Piri Reis University, Istanbul, Turkey
263
Adiyaman University, Adiyaman, Turkey
264
Ozyegin University, Istanbul, Turkey
265
Izmir Institute of Technology, Izmir, Turkey
266
Necmettin Erbakan University, Konya, Turkey
267
Bozok Universitetesi Rektörlügü, Yozgat, Turkey
268
Marmara University, Istanbul, Turkey
269
Milli Savunma University, Istanbul, Turkey
270
Kafkas University, Kars, Turkey
271
Istanbul Bilgi University, Istanbul, Turkey
272
Hacettepe University, Ankara, Turkey
273
School of Physics and Astronomy, University of Southampton, Southampton, UK
274
IPPP Durham University, Durham, UK
275
Monash University, Faculty of Science, Clayton, Australia
276
Bethel University, St. Paul, Minneapolis, USA
277
Karamanoğlu Mehmetbey University, Karaman, Turkey
278
Ain Shams University, Cairo, Egypt
279
Bingol University, Bingol, Turkey
280
Georgian Technical University, Tbilisi, Georgia
281
Sinop University, Sinop, Turkey
282
Mimar Sinan University, Istanbul, Turkey
283
Department of Physics, Nanjing Normal University, Nanjing, China
284
Texas A&M University at Qatar, Doha, Qatar
285
Kyungpook National University, Daegu, Korea
286
CERN, 1211, Geneva 23, Switzerland
f
cms-publication-committee-chair@cern.ch
Received:
17
February
2021
Accepted:
24
August
2021
Published online:
27
September
2021
Collinear (small-angle) and large-angle, as well as soft and hard radiations are investigated in three-jet and + two-jet events collected in proton-proton collisions at the LHC. The normalized production cross sections are measured as a function of the ratio of transverse momenta of two jets and their angular separation. The measurements in the three-jet and + two-jet events are based on data collected at a center-of-mass energy of 8
, corresponding to an integrated luminosity of 19.8
. The + two-jet events are reconstructed in the dimuon decay channel of the boson. The three-jet measurement is extended to include 
data corresponding to an integrated luminosity of 2.3. The results are compared to predictions from event generators that include parton showers, multiple parton interactions, and hadronization. The collinear and soft regions are in general well described by parton showers, whereas the regions of large angular separation are often best described by calculations using higher-order matrix elements.
© The Author(s) 2021
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