https://doi.org/10.1140/epjc/s10052-024-13116-7
Regular Article
Measurement of multijet azimuthal correlations and determination of the strong coupling in proton-proton collisions at 
1
Yerevan Physics Institute, Yerevan, Armenia
2
Institut für Hochenergiephysik, Vienna, Austria
3
Universiteit Antwerpen, Antwerpen, Belgium
4
Vrije Universiteit Brussel, Brussels, Belgium
5
Université Libre de Bruxelles, Brussels, Belgium
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Ghent University, Ghent, Belgium
7
Université Catholique de Louvain, Louvain-la-Neuve, Belgium
8
Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil
9
Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
10
Universidade Estadual Paulista, Universidade Federal do ABC, São Paulo, Brazil
11
Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria
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University of Sofia, Sofia, Bulgaria
13
Instituto De Alta Investigación, Universidad de Tarapacá, Casilla 7 D, Arica, Chile
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Beihang University, Beijing, China
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Department of Physics, Tsinghua University, Beijing, China
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Institute of High Energy Physics, Beijing, China
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State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China
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Sun Yat-Sen University, Guangzhou, China
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University of Science and Technology of China, Hefei, China
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Nanjing Normal University, Nanjing, China
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Institute of Modern Physics and Key Laboratory of Nuclear Physics and Ion-beam Application (MOE)-Fudan University, Shanghai, China
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Zhejiang University, Hangzhou, Zhejiang, China
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Universidad de Los Andes, Bogotá, Colombia
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Universidad de Antioquia, Medellin, Colombia
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University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Split, Croatia
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Faculty of Science, University of Split, Split, Croatia
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Institute Rudjer Boskovic, Zagreb, Croatia
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University of Cyprus, Nicosia, Cyprus
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Charles University, Prague, Czech Republic
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Escuela Politecnica Nacional, Quito, Ecuador
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Universidad San Francisco de Quito, Quito, Ecuador
32
Academy of Scientific Research and Technology of the Arab Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt
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Center for High Energy Physics (CHEP-FU), Fayoum University, El-Fayoum, Egypt
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National Institute of Chemical Physics and Biophysics, Tallinn, Estonia
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Department of Physics, University of Helsinki, Helsinki, Finland
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Helsinki Institute of Physics, Helsinki, Finland
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Lappeenranta-Lahti University of Technology, Lappeenranta, Finland
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IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
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Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
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CNRS, IPHC UMR 7178, Université de Strasbourg, Strasbourg, France
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Institut de Physique des 2 Infinis de Lyon (IP2I ), Villeurbanne, France
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Georgian Technical University, Tbilisi, Georgia
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RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany
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RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany
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RWTH Aachen University, III. Physikalisches Institut B, Aachen, Germany
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Deutsches Elektronen-Synchrotron, Hamburg, Germany
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University of Hamburg, Hamburg, Germany
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Karlsruher Institut fuer Technologie, Karlsruhe, Germany
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Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi, Greece
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National and Kapodistrian University of Athens, Athens, Greece
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National Technical University of Athens, Athens, Greece
52
University of Ioánnina, Ioannina, Greece
53
HUN-REN Wigner Research Centre for Physics, Budapest, Hungary
54
MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary
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Faculty of Informatics, University of Debrecen, Debrecen, Hungary
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Institute of Nuclear Research ATOMKI, Debrecen, Hungary
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Karoly Robert Campus, MATE Institute of Technology, Gyongyos, Hungary
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Panjab University, Chandigarh, India
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University of Delhi, Delhi, India
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Saha Institute of Nuclear Physics, HBNI, Kolkata, India
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Indian Institute of Technology Madras, Madras, India
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Tata Institute of Fundamental Research-A, Mumbai, India
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Tata Institute of Fundamental Research-B, Mumbai, India
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National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute, Bhubaneswar, Odisha, India
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Indian Institute of Science Education and Research (IISER), Pune, India
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Isfahan University of Technology, Isfahan, Iran
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Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
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University College Dublin, Dublin, Ireland
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INFN Sezione di Bari, Università di Bari, Politecnico di Bari, Bari, Italy
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INFN Sezione di Bologna, Università di Bologna, Bologna, Italy
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INFN Sezione di Catania, Università di Catania, Catania, Italy
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INFN Sezione di Firenze, Università di Firenze, Firenze, Italy
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INFN Laboratori Nazionali di Frascati, Frascati, Italy
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INFN Sezione di Genova, Università di Genova, Genoa, Italy
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INFN Sezione di Milano-Bicocca, Università di Milano-Bicocca, Milan, Italy
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INFN Sezione di Napoli, Università di Napoli ’Federico II’, Napoli, Italy; Università della Basilicata, Potenza, Italy; Scuola Superiore Meridionale (SSM), Naples, Italy
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INFN Sezione di Padova, Università di Padova, Padova, Italy; Università di Trento, Trento, Italy
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INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
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INFN Sezione di Perugia, Università di Perugia, Perugia, Italy
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INFN Sezione di Pisa, Università di Pisa, Scuola Normale Superiore di Pisa, Pisa, Italy; Università di Siena, Siena, Italy
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INFN Sezione di Roma, Sapienza Università di Roma, Rome, Italy
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INFN Sezione di Torino, Università di Torino, Torino, Italy; Università del Piemonte Orientale, Novara, Italy
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INFN Sezione di Trieste, Università di Trieste, Trieste, Italy
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Kyungpook National University, Daegu, Korea
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Department of Mathematics and Physics-GWNU, Gangneung, Korea
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Chonnam National University, Institute for Universe and Elementary Particles, Kwangju, Korea
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Hanyang University, Seoul, Korea
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Korea University, Seoul, Korea
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Department of Physics, Kyung Hee University, Seoul, Korea
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Sejong University, Seoul, Korea
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Seoul National University, Seoul, Korea
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University of Seoul, Seoul, Korea
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Yonsei University, Department of Physics, Seoul, Korea
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Sungkyunkwan University, Suwon, Korea
95
College of Engineering and Technology, American University of the Middle East (AUM), Dasman, Kuwait
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Riga Technical University, Riga, Latvia
97
University of Latvia (LU), Riga, Latvia
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Vilnius University, Vilnius, Lithuania
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National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia
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Universidad de Sonora (UNISON), Hermosillo, Mexico
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Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico
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Universidad Iberoamericana, Mexico City, Mexico
103
Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
104
University of Montenegro, Podgorica, Montenegro
105
University of Canterbury, Christchurch, New Zealand
106
National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan
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Faculty of Computer Science, Electronics and Telecommunications, AGH University of Krakow, Kraków, Poland
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National Centre for Nuclear Research, Swierk, Poland
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Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland
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Warsaw University of Technology, Warsaw, Poland
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Laboratório de Instrumentação e Física Experimental de Partículas, Lisbon, Portugal
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Faculty of Physics, University of Belgrade, Belgrade, Serbia
113
VINCA Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia
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Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain
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Universidad Autónoma de Madrid, Madrid, Spain
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Universidad de Oviedo, Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA), Oviedo, Spain
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Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain
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University of Colombo, Colombo, Sri Lanka
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Department of Physics, University of Ruhuna, Matara, Sri Lanka
120
CERN, European Organization for Nuclear Research, Geneva, Switzerland
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Paul Scherrer Institut, Villigen, Switzerland
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ETH Zurich-Institute for Particle Physics and Astrophysics (IPA), Zurich, Switzerland
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Universität Zürich, Zurich, Switzerland
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National Central University, Chung-Li, Taiwan
125
National Taiwan University (NTU), Taipei, Taiwan
126
High Energy Physics Research Unit, Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand
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Çukurova University, Physics Department, Science and Art Faculty, Adana, Turkey
128
Physics Department, Middle East Technical University, Ankara, Turkey
129
Bogazici University, Istanbul, Turkey
130
Istanbul Technical University, Istanbul, Turkey
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Istanbul University, Istanbul, Turkey
132
Yildiz Technical University, Istanbul, Turkey
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Institute for Scintillation Materials of National Academy of Science of Ukraine, Kharkiv, Ukraine
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Kharkiv Institute of Physics and Technology, National Science Centre, Kharkiv, Ukraine
135
University of Bristol, Bristol, UK
136
Rutherford Appleton Laboratory, Didcot, UK
137
Imperial College, London, UK
138
Brunel University, Uxbridge, UK
139
Baylor University, Waco, TX, USA
140
Catholic University of America, Washington, DC, USA
141
The University of Alabama, Tuscaloosa, AL, USA
142
Boston University, Boston, MA, USA
143
Brown University, Providence, RI, USA
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University of California, Davis, Davis, CA, USA
145
University of California, Los Angeles, CA, USA
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University of California, Riverside, Riverside, CA, USA
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University of California, San Diego, La Jolla, CA, USA
148
Department of Physics, University of California, Santa Barbara, Santa Barbara, CA, USA
149
California Institute of Technology, Pasadena, CA, USA
150
Carnegie Mellon University, Pittsburgh, PA, USA
151
University of Colorado Boulder, Boulder, CO, USA
152
Cornell University, Ithaca, NY, USA
153
Fermi National Accelerator Laboratory, Batavia, IL, USA
154
University of Florida, Gainesville, FL, USA
155
Florida State University, Tallahassee, FL, USA
156
Florida Institute of Technology, Melbourne, FL, USA
157
University of Illinois Chicago, Chicago, USA
158
The University of Iowa, Iowa City, IA, USA
159
Johns Hopkins University, Baltimore, MD, USA
160
The University of Kansas, Lawrence, KS, USA
161
Kansas State University, Manhattan, KS, USA
162
Lawrence Livermore National Laboratory, Livermore, CA, USA
163
University of Maryland, College Park, MD, USA
164
Massachusetts Institute of Technology, Cambridge, MA, USA
165
University of Minnesota, Minneapolis, MN, USA
166
University of Mississippi, Oxford, MS, USA
167
University of Nebraska-Lincoln, Lincoln, NE, USA
168
State University of New York at Buffalo, Buffalo, NY, USA
169
Northeastern University, Boston, MA, USA
170
Northwestern University, Evanston, IL, USA
171
University of Notre Dame, Notre Dame, IN, USA
172
The Ohio State University, Columbus, OH, USA
173
Princeton University, Princeton, NJ, USA
174
University of Puerto Rico, Mayaguez, PR, USA
175
Purdue University, West Lafayette, IN, USA
176
Purdue University Northwest, Hammond, IN, USA
177
Rice University, Houston, TX, USA
178
University of Rochester, Rochester, NY, USA
179
The Rockefeller University, New York, NY, USA
180
Rutgers, The State University of New Jersey, Piscataway, NJ, USA
181
University of Tennessee, Knoxville, TN, USA
182
Texas A &M University, College Station, TX, USA
183
Texas Tech University, Lubbock, TX, USA
184
Vanderbilt University, Nashville, TN, USA
185
University of Virginia, Charlottesville, VA, USA
186
Wayne State University, Detroit, MI, USA
187
University of Wisconsin-Madison, Madison, WI, USA
188
Authors Affiliated with an Institute or an International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
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Yerevan State University, Yerevan, Armenia
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TU Wien, Vienna, Austria
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Institute of Basic and Applied Sciences, Faculty of Engineering, Arab Academy for Science, Technology and Maritime Transport, Alexandria, Egypt
192
Ghent University, Ghent, Belgium
193
Universidade Estadual de Campinas, Campinas, Brazil
194
Federal University of Rio Grande do Sul, Porto Alegre, Brazil
195
UFMS, Nova Andradina, Brazil
196
Nanjing Normal University, Nanjing, China
197
Now at The University of Iowa, Iowa City, IA, USA
198
University of Chinese Academy of Sciences, Beijing, China
199
China Center of Advanced Science and Technology, Beijing, China
200
University of Chinese Academy of Sciences, Beijing, China
201
China Spallation Neutron Source, Guangdong, China
202
Henan Normal University, Xinxiang, China
203
Université Libre de Bruxelles, Brussels, Belgium
204
University of Latvia (LU), Riga, Latvia
205
An Institute or an International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
206
Helwan University, Cairo, Egypt
207
Zewail City of Science and Technology, Zewail, Egypt
208
British University in Egypt, Cairo, Egypt
209
Ain Shams University, Cairo, Egypt
210
Purdue University, West Lafayette, IN, USA
211
Université de Haute Alsace, Mulhouse, France
212
Department of Physics, Tsinghua University, Beijing, China
213
Tbilisi State University, Tbilisi, Georgia
214
The University of the State of Amazonas, Manaus, Brazil
215
Erzincan Binali Yildirim University, Erzincan, Turkey
216
University of Hamburg, Hamburg, Germany
217
RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany
218
Isfahan University of Technology, Isfahan, Iran
219
Bergische University Wuppertal (BUW), Wuppertal, Germany
220
Brandenburg University of Technology, Cottbus, Germany
221
Forschungszentrum Jülich, Juelich, Germany
222
CERN, European Organization for Nuclear Research, Geneva, Switzerland
223
An Institute or an International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
224
Institute of Physics, University of Debrecen, Debrecen, Hungary
225
Institute of Nuclear Research ATOMKI, Debrecen, Hungary
226
Universitatea Babes-Bolyai-Facultatea de Fizica, Cluj-Napoca, Romania
227
Physics Department, Faculty of Science, Assiut University, Assiut, Egypt
228
HUN-REN Wigner Research Centre for Physics, Budapest, Hungary
229
Punjab Agricultural University, Ludhiana, India
230
University of Visva-Bharati, Santiniketan, India
231
Indian Institute of Science (IISc), Bangalore, India
232
Birla Institute of Technology, Mesra, Mesra, India
233
IIT Bhubaneswar, Bhubaneswar, India
234
Institute of Physics, Bhubaneswar, India
235
University of Hyderabad, Hyderabad, India
236
Deutsches Elektronen-Synchrotron, Hamburg, Germany
237
Department of Physics, Isfahan University of Technology, Isfahan, Iran
238
Sharif University of Technology, Tehran, Iran
239
Department of Physics, University of Science and Technology of Mazandaran, Behshahr, Iran
240
Italian National Agency for New Technologies, Energy and Sustainable Economic Development, Bologna, Italy
241
Centro Siciliano di Fisica Nucleare e di Struttura Della Materia, Catania, Italy
242
Università degli Studi Guglielmo Marconi, Rome, Italy
243
Scuola Superiore Meridionale, Università di Napoli ’Federico II’, Naples, Italy
244
Fermi National Accelerator Laboratory, Batavia, IL, USA
245
Consiglio Nazionale delle Ricerche-Istituto Officina dei Materiali, Perugia, Italy
246
Riga Technical University, Riga, Latvia
247
Department of Applied Physics, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Malaysia
248
Consejo Nacional de Ciencia y Tecnología, Mexico City, Mexico
249
Trincomalee Campus, Eastern University, Sri Lanka, Nilaveli, Sri Lanka
250
Saegis Campus, Nugegoda, Sri Lanka
251
National and Kapodistrian University of Athens, Athens, Greece
252
Ecole Polytechnique Fédérale Lausanne, Lausanne, Switzerland
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
Near East University, Research Center of Experimental Health Science, Mersin, Turkey
257
Konya Technical University, Konya, Turkey
258
Izmir Bakircay University, Izmir, Turkey
259
Adiyaman University, Adiyaman, Turkey
260
Bozok Universitetesi Rektörlügü, Yozgat, Turkey
261
Marmara University, Istanbul, Turkey
262
Milli Savunma University, Istanbul, Turkey
263
Kafkas University, Kars, Turkey
264
Istanbul Okan University, Istanbul, Turkey
265
Hacettepe University, Ankara, Turkey
266
Faculty of Engineering, Istanbul University-Cerrahpasa, Istanbul, Turkey
267
Yildiz Technical University, Istanbul, Turkey
268
Vrije Universiteit Brussel, Brussels, Belgium
269
School of Physics and Astronomy, University of Southampton, Southampton, UK
270
University of Bristol, Bristol, UK
271
IPPP Durham University, Durham, UK
272
Faculty of Science, Monash University, Clayton, Australia
273
Università di Torino, Turin, Italy
274
Bethel University, St. Paul, MN, USA
275
Karamanoğlu Mehmetbey University, Karaman, Turkey
276
California Institute of Technology, Pasadena, CA, USA
277
United States Naval Academy, Annapolis, MD, USA
278
Bingol University, Bingol, Turkey
279
Georgian Technical University, Tbilisi, Georgia
280
Sinop University, Sinop, Turkey
281
Erciyes University, Kayseri, Turkey
282
Horia Hulubei National Institute of Physics and Nuclear Engineering (IFIN-HH), Bucharest, Romania
283
Texas A &M University at Qatar, Doha, Qatar
284
Kyungpook National University, Daegu, Korea
285
Another Institute or International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
286
Universiteit Antwerpen, Antwerpen, Belgium
287
Yerevan Physics Institute, Yerevan, Armenia
288
Northeastern University, Boston, MA, USA
289
Imperial College, London, UK
290
Institute of Nuclear Physics of the Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
291
CERN, 1211, Geneva 23, Switzerland
a
cms-publication-committee-chair@cern.ch
Received:
24
April
2024
Accepted:
11
July
2024
Published online:
21
August
2024
A measurement is presented of a ratio observable that provides a measure of the azimuthal correlations among jets with large transverse momentum 
. This observable is measured in multijet events over the range of 
–
based on data collected by the CMS experiment in proton-proton collisions at a centre-of-mass energy of 13
, corresponding to an integrated luminosity of 134
. The results are compared with predictions from Monte Carlo parton-shower event generator simulations, as well as with fixed-order perturbative quantum chromodynamics (pQCD) predictions at next-to-leading-order (NLO) accuracy obtained with different parton distribution functions (PDFs) and corrected for nonperturbative and electroweak effects. Data and theory agree within uncertainties. From the comparison of the measured observable with the pQCD prediction obtained with the NNPDF3.1 NLO PDFs, the strong coupling at the Z boson mass scale is 
, where the total uncertainty is dominated by the scale dependence of the fixed-order predictions. A test of the running of 
in the region shows no deviation from the expected NLO pQCD behaviour.
Deceased: M. Narain, S. Wimpenny, A. Vorobyev.
© The Author(s) 2024
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