
==== Front
Eur Phys J C Part Fields
Eur Phys J C Part Fields
The European Physical Journal. C, Particles and Fields
1434-6044
1434-6052
Springer Berlin Heidelberg Berlin/Heidelberg

39185726
13116
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 s=13TeV
CMS CollaborationHayrapetyan A. 1
http://orcid.org/0009-0000-0684-6742
Tumasyan A. 1189
http://orcid.org/0000-0001-9099-4341
Adam W. 2
Andrejkovic J. W. 2
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Bergauer T. 2
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Chatterjee S. 2
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Damanakis K. 2
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Dragicevic M. 2
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Hussain P. S. 2
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Jeitler M. 2190
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Krammer N. 2
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Li A. 2
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Liko D. 2
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Mikulec I. 2
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Schieck J. 2190
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Schöfbeck R. 2
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Schwarz D. 2
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Sonawane M. 2
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Templ S. 2
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Waltenberger W. 2
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Wulz C.-E. 2190
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Darwish M. R. 3191
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Janssen T. 3
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Bols E. S. 4
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cms-publication-committee-chair@cern.ch

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1 https://ror.org/00ad27c73 grid.48507.3e 0000 0004 0482 7128 Yerevan Physics Institute, Yerevan, Armenia
2 https://ror.org/039shy520 grid.450258.e 0000 0004 0625 7405 Institut für Hochenergiephysik, Vienna, Austria
3 https://ror.org/008x57b05 grid.5284.b 0000 0001 0790 3681 Universiteit Antwerpen, Antwerpen, Belgium
4 https://ror.org/006e5kg04 grid.8767.e 0000 0001 2290 8069 Vrije Universiteit Brussel, Brussels, Belgium
5 https://ror.org/01r9htc13 grid.4989.c 0000 0001 2348 6355 Université Libre de Bruxelles, Brussels, Belgium
6 https://ror.org/00cv9y106 grid.5342.0 0000 0001 2069 7798 Ghent University, Ghent, Belgium
7 https://ror.org/02495e989 grid.7942.8 0000 0001 2294 713X Université Catholique de Louvain, Louvain-la-Neuve, Belgium
8 https://ror.org/02wnmk332 grid.418228.5 0000 0004 0643 8134 Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil
9 https://ror.org/0198v2949 grid.412211.5 0000 0004 4687 5267 Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
10 grid.412368.a 0000 0004 0643 8839 Universidade Estadual Paulista, Universidade Federal do ABC, São Paulo, Brazil
11 grid.410344.6 0000 0001 2097 3094 Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria
12 https://ror.org/02jv3k292 grid.11355.33 0000 0001 2192 3275 University of Sofia, Sofia, Bulgaria
13 https://ror.org/04xe01d27 grid.412182.c 0000 0001 2179 0636 Instituto De Alta Investigación, Universidad de Tarapacá, Casilla 7 D, Arica, Chile
14 https://ror.org/00wk2mp56 grid.64939.31 0000 0000 9999 1211 Beihang University, Beijing, China
15 https://ror.org/03cve4549 grid.12527.33 0000 0001 0662 3178 Department of Physics, Tsinghua University, Beijing, China
16 https://ror.org/03v8tnc06 grid.418741.f 0000 0004 0632 3097 Institute of High Energy Physics, Beijing, China
17 grid.11135.37 0000 0001 2256 9319 State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China
18 https://ror.org/0064kty71 grid.12981.33 0000 0001 2360 039X Sun Yat-Sen University, Guangzhou, China
19 https://ror.org/04c4dkn09 grid.59053.3a 0000 0001 2167 9639 University of Science and Technology of China, Hefei, China
20 https://ror.org/036trcv74 grid.260474.3 0000 0001 0089 5711 Nanjing Normal University, Nanjing, China
21 grid.8547.e 0000 0001 0125 2443 Institute of Modern Physics and Key Laboratory of Nuclear Physics and Ion-beam Application (MOE)-Fudan University, Shanghai, China
22 https://ror.org/00a2xv884 grid.13402.34 0000 0004 1759 700X Zhejiang University, Hangzhou, Zhejiang China
23 https://ror.org/02mhbdp94 grid.7247.6 0000 0004 1937 0714 Universidad de Los Andes, Bogotá, Colombia
24 https://ror.org/03bp5hc83 grid.412881.6 0000 0000 8882 5269 Universidad de Antioquia, Medellin, Colombia
25 https://ror.org/00m31ft63 grid.38603.3e 0000 0004 0644 1675 University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Split, Croatia
26 https://ror.org/00m31ft63 grid.38603.3e 0000 0004 0644 1675 Faculty of Science, University of Split, Split, Croatia
27 https://ror.org/02mw21745 grid.4905.8 0000 0004 0635 7705 Institute Rudjer Boskovic, Zagreb, Croatia
28 https://ror.org/02qjrjx09 grid.6603.3 0000 0001 2116 7908 University of Cyprus, Nicosia, Cyprus
29 https://ror.org/024d6js02 grid.4491.8 0000 0004 1937 116X Charles University, Prague, Czech Republic
30 https://ror.org/01gb99w41 grid.440857.a 0000 0004 0485 2489 Escuela Politecnica Nacional, Quito, Ecuador
31 https://ror.org/01r2c3v86 grid.412251.1 0000 0000 9008 4711 Universidad San Francisco de Quito, Quito, Ecuador
32 grid.423564.2 0000 0001 2165 2866 Academy of Scientific Research and Technology of the Arab Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt
33 https://ror.org/023gzwx10 grid.411170.2 0000 0004 0412 4537 Center for High Energy Physics (CHEP-FU), Fayoum University, El-Fayoum, Egypt
34 https://ror.org/03eqd4a41 grid.177284.f 0000 0004 0410 6208 National Institute of Chemical Physics and Biophysics, Tallinn, Estonia
35 https://ror.org/040af2s02 grid.7737.4 0000 0004 0410 2071 Department of Physics, University of Helsinki, Helsinki, Finland
36 https://ror.org/01x2x1522 grid.470106.4 0000 0001 1106 2387 Helsinki Institute of Physics, Helsinki, Finland
37 https://ror.org/0208vgz68 grid.12332.31 0000 0001 0533 3048 Lappeenranta-Lahti University of Technology, Lappeenranta, Finland
38 https://ror.org/03xjwb503 grid.460789.4 0000 0004 4910 6535 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
39 grid.508893.f Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
40 https://ror.org/00pg6eq24 grid.11843.3f 0000 0001 2157 9291 CNRS, IPHC UMR 7178, Université de Strasbourg, Strasbourg, France
41 https://ror.org/02avf8f85 Institut de Physique des 2 Infinis de Lyon (IP2I ), Villeurbanne, France
42 https://ror.org/00aamz256 grid.41405.34 0000 0001 0702 1187 Georgian Technical University, Tbilisi, Georgia
43 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany
44 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany
45 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X RWTH Aachen University, III. Physikalisches Institut B, Aachen, Germany
46 https://ror.org/01js2sh04 grid.7683.a 0000 0004 0492 0453 Deutsches Elektronen-Synchrotron, Hamburg, Germany
47 https://ror.org/00g30e956 grid.9026.d 0000 0001 2287 2617 University of Hamburg, Hamburg, Germany
48 https://ror.org/04t3en479 grid.7892.4 0000 0001 0075 5874 Karlsruher Institut fuer Technologie, Karlsruhe, Germany
49 grid.6083.d 0000 0004 0635 6999 Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi, Greece
50 https://ror.org/04gnjpq42 grid.5216.0 0000 0001 2155 0800 National and Kapodistrian University of Athens, Athens, Greece
51 grid.4241.3 0000 0001 2185 9808 National Technical University of Athens, Athens, Greece
52 https://ror.org/01qg3j183 grid.9594.1 0000 0001 2108 7481 University of Ioánnina, Ioannina, Greece
53 grid.419766.b 0000 0004 1759 8344 HUN-REN Wigner Research Centre for Physics, Budapest, Hungary
54 https://ror.org/01jsq2704 grid.5591.8 0000 0001 2294 6276 MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary
55 https://ror.org/02xf66n48 grid.7122.6 0000 0001 1088 8582 Faculty of Informatics, University of Debrecen, Debrecen, Hungary
56 grid.418861.2 0000 0001 0674 7808 Institute of Nuclear Research ATOMKI, Debrecen, Hungary
57 Karoly Robert Campus, MATE Institute of Technology, Gyongyos, Hungary
58 https://ror.org/04p2sbk06 grid.261674.0 0000 0001 2174 5640 Panjab University, Chandigarh, India
59 https://ror.org/04gzb2213 grid.8195.5 0000 0001 2109 4999 University of Delhi, Delhi, India
60 https://ror.org/0491yz035 grid.473481.d 0000 0001 0661 8707 Saha Institute of Nuclear Physics, HBNI, Kolkata, India
61 https://ror.org/03v0r5n49 grid.417969.4 0000 0001 2315 1926 Indian Institute of Technology Madras, Madras, India
62 https://ror.org/03ht1xw27 grid.22401.35 0000 0004 0502 9283 Tata Institute of Fundamental Research-A, Mumbai, India
63 https://ror.org/03ht1xw27 grid.22401.35 0000 0004 0502 9283 Tata Institute of Fundamental Research-B, Mumbai, India
64 https://ror.org/02r2k1c68 grid.419643.d 0000 0004 1764 227X National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute, Bhubaneswar, Odisha India
65 https://ror.org/028qa3n13 grid.417959.7 0000 0004 1764 2413 Indian Institute of Science Education and Research (IISER), Pune, India
66 grid.411751.7 0000 0000 9908 3264 Isfahan University of Technology, Isfahan, Iran
67 https://ror.org/04xreqs31 grid.418744.a 0000 0000 8841 7951 Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
68 https://ror.org/05m7pjf47 grid.7886.1 0000 0001 0768 2743 University College Dublin, Dublin, Ireland
69 grid.4466.0 0000 0001 0578 5482 INFN Sezione di Bari, Università di Bari, Politecnico di Bari, Bari, Italy
70 grid.6292.f 0000 0004 1757 1758 INFN Sezione di Bologna, Università di Bologna, Bologna, Italy
71 grid.8158.4 0000 0004 1757 1969 INFN Sezione di Catania, Università di Catania, Catania, Italy
72 https://ror.org/02vv5y108 grid.470204.5 0000 0001 2231 4148 INFN Sezione di Firenze, Università di Firenze, Firenze, Italy
73 https://ror.org/049jf1a25 grid.463190.9 0000 0004 0648 0236 INFN Laboratori Nazionali di Frascati, Frascati, Italy
74 grid.5606.5 0000 0001 2151 3065 INFN Sezione di Genova, Università di Genova, Genoa, Italy
75 https://ror.org/03xejxm22 grid.470207.6 0000 0004 8390 4143 INFN Sezione di Milano-Bicocca, Università di Milano-Bicocca, Milan, Italy
76 grid.508348.2 INFN Sezione di Napoli, Università di Napoli ’Federico II’, Napoli, Italy; Università della Basilicata, Potenza, Italy; Scuola Superiore Meridionale (SSM), Naples, Italy
77 grid.11696.39 0000 0004 1937 0351 INFN Sezione di Padova, Università di Padova, Padova, Italy; Università di Trento, Trento, Italy
78 grid.8982.b 0000 0004 1762 5736 INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
79 grid.9027.c 0000 0004 1757 3630 INFN Sezione di Perugia, Università di Perugia, Perugia, Italy
80 grid.9024.f 0000 0004 1757 4641 INFN Sezione di Pisa, Università di Pisa, Scuola Normale Superiore di Pisa, Pisa, Italy; Università di Siena, Siena, Italy
81 grid.7841.a INFN Sezione di Roma, Sapienza Università di Roma, Rome, Italy
82 https://ror.org/01vj6ck58 grid.470222.1 0000 0004 7471 9712 INFN Sezione di Torino, Università di Torino, Torino, Italy; Università del Piemonte Orientale, Novara, Italy
83 grid.5133.4 0000 0001 1941 4308 INFN Sezione di Trieste, Università di Trieste, Trieste, Italy
84 https://ror.org/040c17130 grid.258803.4 0000 0001 0661 1556 Kyungpook National University, Daegu, Korea
85 grid.411733.3 0000 0004 0532 811X Department of Mathematics and Physics-GWNU, Gangneung, Korea
86 https://ror.org/05kzjxq56 grid.14005.30 0000 0001 0356 9399 Chonnam National University, Institute for Universe and Elementary Particles, Kwangju, Korea
87 https://ror.org/046865y68 grid.49606.3d 0000 0001 1364 9317 Hanyang University, Seoul, Korea
88 https://ror.org/047dqcg40 grid.222754.4 0000 0001 0840 2678 Korea University, Seoul, Korea
89 https://ror.org/01zqcg218 grid.289247.2 0000 0001 2171 7818 Department of Physics, Kyung Hee University, Seoul, Korea
90 https://ror.org/00aft1q37 grid.263333.4 0000 0001 0727 6358 Sejong University, Seoul, Korea
91 https://ror.org/04h9pn542 grid.31501.36 0000 0004 0470 5905 Seoul National University, Seoul, Korea
92 https://ror.org/05en5nh73 grid.267134.5 0000 0000 8597 6969 University of Seoul, Seoul, Korea
93 https://ror.org/01wjejq96 grid.15444.30 0000 0004 0470 5454 Yonsei University, Department of Physics, Seoul, Korea
94 https://ror.org/04q78tk20 grid.264381.a 0000 0001 2181 989X Sungkyunkwan University, Suwon, Korea
95 https://ror.org/02gqgne03 grid.472279.d 0000 0004 0418 1945 College of Engineering and Technology, American University of the Middle East (AUM), Dasman, Kuwait
96 https://ror.org/00twb6c09 grid.6973.b 0000 0004 0567 9729 Riga Technical University, Riga, Latvia
97 https://ror.org/05g3mes96 grid.9845.0 0000 0001 0775 3222 University of Latvia (LU), Riga, Latvia
98 https://ror.org/03nadee84 grid.6441.7 0000 0001 2243 2806 Vilnius University, Vilnius, Lithuania
99 https://ror.org/00rzspn62 grid.10347.31 0000 0001 2308 5949 National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia
100 grid.11893.32 0000 0001 2193 1646 Universidad de Sonora (UNISON), Hermosillo, Mexico
101 grid.512574.0 Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico
102 https://ror.org/05vss7635 grid.441047.2 0000 0001 2156 4794 Universidad Iberoamericana, Mexico City, Mexico
103 https://ror.org/03p2z7827 grid.411659.e 0000 0001 2112 2750 Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
104 https://ror.org/02drrjp49 grid.12316.37 0000 0001 2182 0188 University of Montenegro, Podgorica, Montenegro
105 https://ror.org/03y7q9t39 grid.21006.35 0000 0001 2179 4063 University of Canterbury, Christchurch, New Zealand
106 grid.412621.2 0000 0001 2215 1297 National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan
107 grid.9922.0 0000 0000 9174 1488 Faculty of Computer Science, Electronics and Telecommunications, AGH University of Krakow, Kraków, Poland
108 https://ror.org/00nzsxq20 grid.450295.f 0000 0001 0941 0848 National Centre for Nuclear Research, Swierk, Poland
109 https://ror.org/039bjqg32 grid.12847.38 0000 0004 1937 1290 Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland
110 grid.1035.7 0000000099214842 Warsaw University of Technology, Warsaw, Poland
111 https://ror.org/01hys1667 grid.420929.4 Laboratório de Instrumentação e Física Experimental de Partículas, Lisbon, Portugal
112 https://ror.org/02qsmb048 grid.7149.b 0000 0001 2166 9385 Faculty of Physics, University of Belgrade, Belgrade, Serbia
113 grid.7149.b 0000 0001 2166 9385 VINCA Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia
114 https://ror.org/05xx77y52 grid.420019.e 0000 0001 1959 5823 Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain
115 https://ror.org/01cby8j38 grid.5515.4 0000 0001 1957 8126 Universidad Autónoma de Madrid, Madrid, Spain
116 https://ror.org/006gksa02 grid.10863.3c 0000 0001 2164 6351 Universidad de Oviedo, Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA), Oviedo, Spain
117 grid.7821.c 0000 0004 1770 272X Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain
118 https://ror.org/02phn5242 grid.8065.b 0000 0001 2182 8067 University of Colombo, Colombo, Sri Lanka
119 https://ror.org/033jvzr14 grid.412759.c 0000 0001 0103 6011 Department of Physics, University of Ruhuna, Matara, Sri Lanka
120 https://ror.org/01ggx4157 grid.9132.9 0000 0001 2156 142X CERN, European Organization for Nuclear Research, Geneva, Switzerland
121 https://ror.org/03eh3y714 grid.5991.4 0000 0001 1090 7501 Paul Scherrer Institut, Villigen, Switzerland
122 grid.5801.c 0000 0001 2156 2780 ETH Zurich-Institute for Particle Physics and Astrophysics (IPA), Zurich, Switzerland
123 https://ror.org/02crff812 grid.7400.3 0000 0004 1937 0650 Universität Zürich, Zurich, Switzerland
124 https://ror.org/00944ve71 grid.37589.30 0000 0004 0532 3167 National Central University, Chung-Li, Taiwan
125 https://ror.org/05bqach95 grid.19188.39 0000 0004 0546 0241 National Taiwan University (NTU), Taipei, Taiwan
126 https://ror.org/028wp3y58 grid.7922.e 0000 0001 0244 7875 High Energy Physics Research Unit, Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand
127 https://ror.org/05wxkj555 grid.98622.37 0000 0001 2271 3229 Çukurova University, Physics Department, Science and Art Faculty, Adana, Turkey
128 https://ror.org/014weej12 grid.6935.9 0000 0001 1881 7391 Physics Department, Middle East Technical University, Ankara, Turkey
129 https://ror.org/03z9tma90 grid.11220.30 0000 0001 2253 9056 Bogazici University, Istanbul, Turkey
130 https://ror.org/059636586 grid.10516.33 0000 0001 2174 543X Istanbul Technical University, Istanbul, Turkey
131 https://ror.org/03a5qrr21 grid.9601.e 0000 0001 2166 6619 Istanbul University, Istanbul, Turkey
132 https://ror.org/0547yzj13 grid.38575.3c 0000 0001 2337 3561 Yildiz Technical University, Istanbul, Turkey
133 grid.466758.e Institute for Scintillation Materials of National Academy of Science of Ukraine, Kharkiv, Ukraine
134 https://ror.org/00183pc12 grid.425540.2 0000 0000 9526 3153 Kharkiv Institute of Physics and Technology, National Science Centre, Kharkiv, Ukraine
135 https://ror.org/0524sp257 grid.5337.2 0000 0004 1936 7603 University of Bristol, Bristol, UK
136 https://ror.org/03gq8fr08 grid.76978.37 0000 0001 2296 6998 Rutherford Appleton Laboratory, Didcot, UK
137 https://ror.org/041kmwe10 grid.7445.2 0000 0001 2113 8111 Imperial College, London, UK
138 grid.7728.a 0000 0001 0724 6933 Brunel University, Uxbridge, UK
139 https://ror.org/005781934 grid.252890.4 0000 0001 2111 2894 Baylor University, Waco, TX USA
140 https://ror.org/047yk3s18 grid.39936.36 0000 0001 2174 6686 Catholic University of America, Washington, DC USA
141 https://ror.org/03xrrjk67 grid.411015.0 0000 0001 0727 7545 The University of Alabama, Tuscaloosa, AL USA
142 https://ror.org/05qwgg493 grid.189504.1 0000 0004 1936 7558 Boston University, Boston, MA USA
143 https://ror.org/05gq02987 grid.40263.33 0000 0004 1936 9094 Brown University, Providence, RI USA
144 https://ror.org/05t99sp05 grid.468726.9 0000 0004 0486 2046 University of California, Davis, Davis, CA USA
145 grid.19006.3e 0000 0000 9632 6718 University of California, Los Angeles, CA USA
146 https://ror.org/05t99sp05 grid.468726.9 0000 0004 0486 2046 University of California, Riverside, Riverside, CA USA
147 https://ror.org/05t99sp05 grid.468726.9 0000 0004 0486 2046 University of California, San Diego, La Jolla, CA USA
148 grid.133342.4 0000 0004 1936 9676 Department of Physics, University of California, Santa Barbara, Santa Barbara, CA USA
149 https://ror.org/05dxps055 grid.20861.3d 0000 0001 0706 8890 California Institute of Technology, Pasadena, CA USA
150 https://ror.org/05x2bcf33 grid.147455.6 0000 0001 2097 0344 Carnegie Mellon University, Pittsburgh, PA USA
151 https://ror.org/02ttsq026 grid.266190.a 0000 0000 9621 4564 University of Colorado Boulder, Boulder, CO USA
152 https://ror.org/05bnh6r87 grid.5386.8 0000 0004 1936 877X Cornell University, Ithaca, NY USA
153 https://ror.org/020hgte69 grid.417851.e 0000 0001 0675 0679 Fermi National Accelerator Laboratory, Batavia, IL USA
154 https://ror.org/02y3ad647 grid.15276.37 0000 0004 1936 8091 University of Florida, Gainesville, FL USA
155 https://ror.org/05g3dte14 grid.255986.5 0000 0004 0472 0419 Florida State University, Tallahassee, FL USA
156 https://ror.org/04atsbb87 grid.255966.b 0000 0001 2229 7296 Florida Institute of Technology, Melbourne, FL USA
157 https://ror.org/02mpq6x41 grid.185648.6 0000 0001 2175 0319 University of Illinois Chicago, Chicago, USA
158 https://ror.org/036jqmy94 grid.214572.7 0000 0004 1936 8294 The University of Iowa, Iowa City, IA USA
159 https://ror.org/00za53h95 grid.21107.35 0000 0001 2171 9311 Johns Hopkins University, Baltimore, MD USA
160 https://ror.org/001tmjg57 grid.266515.3 0000 0001 2106 0692 The University of Kansas, Lawrence, KS USA
161 https://ror.org/05p1j8758 grid.36567.31 0000 0001 0737 1259 Kansas State University, Manhattan, KS USA
162 https://ror.org/041nk4h53 grid.250008.f 0000 0001 2160 9702 Lawrence Livermore National Laboratory, Livermore, CA USA
163 https://ror.org/047s2c258 grid.164295.d 0000 0001 0941 7177 University of Maryland, College Park, MD USA
164 https://ror.org/042nb2s44 grid.116068.8 0000 0001 2341 2786 Massachusetts Institute of Technology, Cambridge, MA USA
165 https://ror.org/017zqws13 grid.17635.36 0000 0004 1936 8657 University of Minnesota, Minneapolis, MN USA
166 https://ror.org/02teq1165 grid.251313.7 0000 0001 2169 2489 University of Mississippi, Oxford, MS USA
167 https://ror.org/043mer456 grid.24434.35 0000 0004 1937 0060 University of Nebraska-Lincoln, Lincoln, NE USA
168 grid.273335.3 0000 0004 1936 9887 State University of New York at Buffalo, Buffalo, NY USA
169 https://ror.org/04t5xt781 grid.261112.7 0000 0001 2173 3359 Northeastern University, Boston, MA USA
170 https://ror.org/000e0be47 grid.16753.36 0000 0001 2299 3507 Northwestern University, Evanston, IL USA
171 https://ror.org/00mkhxb43 grid.131063.6 0000 0001 2168 0066 University of Notre Dame, Notre Dame, IN USA
172 https://ror.org/00rs6vg23 grid.261331.4 0000 0001 2285 7943 The Ohio State University, Columbus, OH USA
173 https://ror.org/00hx57361 grid.16750.35 0000 0001 2097 5006 Princeton University, Princeton, NJ USA
174 https://ror.org/00wek6x04 grid.267044.3 0000 0004 0398 9176 University of Puerto Rico, Mayaguez, PR USA
175 https://ror.org/02dqehb95 grid.169077.e 0000 0004 1937 2197 Purdue University, West Lafayette, IN USA
176 https://ror.org/04keq6987 grid.504659.b 0000 0000 8864 7239 Purdue University Northwest, Hammond, IN USA
177 https://ror.org/008zs3103 grid.21940.3e 0000 0004 1936 8278 Rice University, Houston, TX USA
178 https://ror.org/022kthw22 grid.16416.34 0000 0004 1936 9174 University of Rochester, Rochester, NY USA
179 https://ror.org/0420db125 grid.134907.8 0000 0001 2166 1519 The Rockefeller University, New York, NY USA
180 https://ror.org/05vt9qd57 grid.430387.b 0000 0004 1936 8796 Rutgers, The State University of New Jersey, Piscataway, NJ USA
181 https://ror.org/020f3ap87 grid.411461.7 0000 0001 2315 1184 University of Tennessee, Knoxville, TN USA
182 https://ror.org/01f5ytq51 grid.264756.4 0000 0004 4687 2082 Texas A &M University, College Station, TX USA
183 grid.264784.b 0000 0001 2186 7496 Texas Tech University, Lubbock, TX USA
184 https://ror.org/02vm5rt34 grid.152326.1 0000 0001 2264 7217 Vanderbilt University, Nashville, TN USA
185 https://ror.org/0153tk833 grid.27755.32 0000 0000 9136 933X University of Virginia, Charlottesville, VA USA
186 https://ror.org/01070mq45 grid.254444.7 0000 0001 1456 7807 Wayne State University, Detroit, MI USA
187 https://ror.org/01y2jtd41 grid.14003.36 0000 0001 2167 3675 University of Wisconsin-Madison, Madison, WI USA
188 grid.9132.9 0000 0001 2156 142X Authors Affiliated with an Institute or an International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
189 https://ror.org/00s8vne50 grid.21072.36 0000 0004 0640 687X Yerevan State University, Yerevan, Armenia
190 https://ror.org/04d836q62 grid.5329.d 0000 0004 1937 0669 TU Wien, Vienna, Austria
191 grid.442567.6 0000 0000 9015 5153 Institute of Basic and Applied Sciences, Faculty of Engineering, Arab Academy for Science, Technology and Maritime Transport, Alexandria, Egypt
192 https://ror.org/00cv9y106 grid.5342.0 0000 0001 2069 7798 Ghent University, Ghent, Belgium
193 https://ror.org/04wffgt70 grid.411087.b 0000 0001 0723 2494 Universidade Estadual de Campinas, Campinas, Brazil
194 https://ror.org/041yk2d64 grid.8532.c 0000 0001 2200 7498 Federal University of Rio Grande do Sul, Porto Alegre, Brazil
195 grid.412352.3 0000 0001 2163 5978 UFMS, Nova Andradina, Brazil
196 https://ror.org/036trcv74 grid.260474.3 0000 0001 0089 5711 Nanjing Normal University, Nanjing, China
197 https://ror.org/036jqmy94 grid.214572.7 0000 0004 1936 8294 Now at The University of Iowa, Iowa City, IA USA
198 https://ror.org/05qbk4x57 grid.410726.6 0000 0004 1797 8419 University of Chinese Academy of Sciences, Beijing, China
199 https://ror.org/02egfyg20 grid.464262.0 0000 0001 0318 1175 China Center of Advanced Science and Technology, Beijing, China
200 https://ror.org/05qbk4x57 grid.410726.6 0000 0004 1797 8419 University of Chinese Academy of Sciences, Beijing, China
201 https://ror.org/01g140v14 grid.495581.4 China Spallation Neutron Source, Guangdong, China
202 https://ror.org/00s13br28 grid.462338.8 0000 0004 0605 6769 Henan Normal University, Xinxiang, China
203 https://ror.org/01r9htc13 grid.4989.c 0000 0001 2348 6355 Université Libre de Bruxelles, Brussels, Belgium
204 https://ror.org/05g3mes96 grid.9845.0 0000 0001 0775 3222 University of Latvia (LU), Riga, Latvia
205 grid.9132.9 0000 0001 2156 142X An Institute or an International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
206 https://ror.org/00h55v928 grid.412093.d 0000 0000 9853 2750 Helwan University, Cairo, Egypt
207 https://ror.org/04w5f4y88 grid.440881.1 0000 0004 0576 5483 Zewail City of Science and Technology, Zewail, Egypt
208 https://ror.org/0066fxv63 grid.440862.c 0000 0004 0377 5514 British University in Egypt, Cairo, Egypt
209 https://ror.org/00cb9w016 grid.7269.a 0000 0004 0621 1570 Ain Shams University, Cairo, Egypt
210 https://ror.org/02dqehb95 grid.169077.e 0000 0004 1937 2197 Purdue University, West Lafayette, IN USA
211 https://ror.org/04k8k6n84 grid.9156.b 0000 0004 0473 5039 Université de Haute Alsace, Mulhouse, France
212 https://ror.org/03cve4549 grid.12527.33 0000 0001 0662 3178 Department of Physics, Tsinghua University, Beijing, China
213 https://ror.org/05fd1hd85 grid.26193.3f 0000 0001 2034 6082 Tbilisi State University, Tbilisi, Georgia
214 https://ror.org/04j5z3x06 grid.412290.c 0000 0000 8024 0602 The University of the State of Amazonas, Manaus, Brazil
215 grid.412176.7 0000 0001 1498 7262 Erzincan Binali Yildirim University, Erzincan, Turkey
216 https://ror.org/00g30e956 grid.9026.d 0000 0001 2287 2617 University of Hamburg, Hamburg, Germany
217 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany
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219 grid.7787.f 0000 0001 2364 5811 Bergische University Wuppertal (BUW), Wuppertal, Germany
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222 https://ror.org/01ggx4157 grid.9132.9 0000 0001 2156 142X CERN, European Organization for Nuclear Research, Geneva, Switzerland
223 grid.9132.9 0000 0001 2156 142X An Institute or an International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
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225 grid.418861.2 0000 0001 0674 7808 Institute of Nuclear Research ATOMKI, Debrecen, Hungary
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231 grid.34980.36 0000 0001 0482 5067 Indian Institute of Science (IISc), Bangalore, India
232 https://ror.org/028vtqb15 grid.462084.c 0000 0001 2216 7125 Birla Institute of Technology, Mesra, Mesra, India
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234 https://ror.org/01741jv66 grid.418915.0 0000 0004 0504 1311 Institute of Physics, Bhubaneswar, India
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237 https://ror.org/00af3sa43 grid.411751.7 0000 0000 9908 3264 Department of Physics, Isfahan University of Technology, Isfahan, Iran
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241 https://ror.org/02wdzfm91 grid.510931.f Centro Siciliano di Fisica Nucleare e di Struttura Della Materia, Catania, Italy
242 https://ror.org/00j0rk173 grid.440899.8 0000 0004 1780 761X Università degli Studi Guglielmo Marconi, Rome, Italy
243 https://ror.org/04swxte59 grid.508348.2 Scuola Superiore Meridionale, Università di Napoli ’Federico II’, Naples, Italy
244 https://ror.org/020hgte69 grid.417851.e 0000 0001 0675 0679 Fermi National Accelerator Laboratory, Batavia, IL USA
245 grid.5326.2 0000 0001 1940 4177 Consiglio Nazionale delle Ricerche-Istituto Officina dei Materiali, Perugia, Italy
246 https://ror.org/00twb6c09 grid.6973.b 0000 0004 0567 9729 Riga Technical University, Riga, Latvia
247 https://ror.org/00bw8d226 grid.412113.4 0000 0004 1937 1557 Department of Applied Physics, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Malaysia
248 https://ror.org/059ex5q34 grid.418270.8 0000 0004 0428 7635 Consejo Nacional de Ciencia y Tecnología, Mexico City, Mexico
249 grid.443373.4 0000 0001 0438 3334 Trincomalee Campus, Eastern University, Sri Lanka, Nilaveli, Sri Lanka
250 Saegis Campus, Nugegoda, Sri Lanka
251 https://ror.org/04gnjpq42 grid.5216.0 0000 0001 2155 0800 National and Kapodistrian University of Athens, Athens, Greece
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253 https://ror.org/02crff812 grid.7400.3 0000 0004 1937 0650 Universität Zürich, Zurich, Switzerland
254 https://ror.org/05kdjqf72 grid.475784.d 0000 0000 9532 5705 Stefan Meyer Institute for Subatomic Physics, Vienna, Austria
255 https://ror.org/049nhh297 grid.450330.1 0000 0001 2276 7382 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 https://ror.org/02s82rs08 grid.505922.9 Konya Technical University, Konya, Turkey
258 https://ror.org/017v96566 0000 0004 6412 5697 Izmir Bakircay University, Izmir, Turkey
259 https://ror.org/02s4gkg68 grid.411126.1 0000 0004 0369 5557 Adiyaman University, Adiyaman, Turkey
260 grid.411743.4 0000 0004 0369 8360 Bozok Universitetesi Rektörlügü, Yozgat, Turkey
261 https://ror.org/02kswqa67 grid.16477.33 0000 0001 0668 8422 Marmara University, Istanbul, Turkey
262 https://ror.org/010t24d82 grid.510982.7 Milli Savunma University, Istanbul, Turkey
263 https://ror.org/04v302n28 grid.16487.3c 0000 0000 9216 0511 Kafkas University, Kars, Turkey
264 grid.444283.d 0000 0004 0371 5255 Istanbul Okan University, Istanbul, Turkey
265 https://ror.org/04kwvgz42 grid.14442.37 0000 0001 2342 7339 Hacettepe University, Ankara, Turkey
266 grid.506076.2 0000 0004 1797 5496 Faculty of Engineering, Istanbul University-Cerrahpasa, Istanbul, Turkey
267 https://ror.org/0547yzj13 grid.38575.3c 0000 0001 2337 3561 Yildiz Technical University, Istanbul, Turkey
268 https://ror.org/006e5kg04 grid.8767.e 0000 0001 2290 8069 Vrije Universiteit Brussel, Brussels, Belgium
269 https://ror.org/01ryk1543 grid.5491.9 0000 0004 1936 9297 School of Physics and Astronomy, University of Southampton, Southampton, UK
270 https://ror.org/0524sp257 grid.5337.2 0000 0004 1936 7603 University of Bristol, Bristol, UK
271 https://ror.org/01v29qb04 grid.8250.f 0000 0000 8700 0572 IPPP Durham University, Durham, UK
272 https://ror.org/02bfwt286 grid.1002.3 0000 0004 1936 7857 Faculty of Science, Monash University, Clayton, Australia
273 grid.7605.4 0000 0001 2336 6580 Università di Torino, Turin, Italy
274 https://ror.org/05wnc7373 grid.446604.4 0000 0004 0583 4952 Bethel University, St. Paul, MN USA
275 https://ror.org/037vvf096 grid.440455.4 0000 0004 1755 486X Karamanoğlu Mehmetbey University, Karaman, Turkey
276 https://ror.org/05dxps055 grid.20861.3d 0000 0001 0706 8890 California Institute of Technology, Pasadena, CA USA
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278 https://ror.org/03hx84x94 grid.448543.a 0000 0004 0369 6517 Bingol University, Bingol, Turkey
279 https://ror.org/00aamz256 grid.41405.34 0000 0001 0702 1187 Georgian Technical University, Tbilisi, Georgia
280 https://ror.org/004ah3r71 grid.449244.b 0000 0004 0408 6032 Sinop University, Sinop, Turkey
281 https://ror.org/047g8vk19 grid.411739.9 0000 0001 2331 2603 Erciyes University, Kayseri, Turkey
282 https://ror.org/00d3pnh21 grid.443874.8 0000 0000 9463 5349 Horia Hulubei National Institute of Physics and Nuclear Engineering (IFIN-HH), Bucharest, Romania
283 https://ror.org/03vb4dm14 grid.412392.f 0000 0004 0413 3978 Texas A &M University at Qatar, Doha, Qatar
284 https://ror.org/040c17130 grid.258803.4 0000 0001 0661 1556 Kyungpook National University, Daegu, Korea
285 grid.9132.9 0000 0001 2156 142X Another Institute or International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
286 https://ror.org/008x57b05 grid.5284.b 0000 0001 0790 3681 Universiteit Antwerpen, Antwerpen, Belgium
287 https://ror.org/00ad27c73 grid.48507.3e 0000 0004 0482 7128 Yerevan Physics Institute, Yerevan, Armenia
288 https://ror.org/04t5xt781 grid.261112.7 0000 0001 2173 3359 Northeastern University, Boston, MA, USA
289 https://ror.org/041kmwe10 grid.7445.2 0000 0001 2113 8111 Imperial College, London, UK
290 grid.443859.7 0000 0004 0477 2171 Institute of Nuclear Physics of the Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
291 grid.9132.9 0000 0001 2156 142X CERN, 1211 Geneva 23, Switzerland
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Funded by SCOAP3.
A measurement is presented of a ratio observable that provides a measure of the azimuthal correlations among jets with large transverse momentum pT. This observable is measured in multijet events over the range of pT=360–3170GeV based on data collected by the CMS experiment in proton-proton collisions at a centre-of-mass energy of 13TeV, corresponding to an integrated luminosity of 134fb-1. 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 αS(mZ)=0.1177±0.0013(exp)-0.0073+0.0116(theo)=0.1177-0.0074+0.0117, where the total uncertainty is dominated by the scale dependence of the fixed-order predictions. A test of the running of αS in the TeV region shows no deviation from the expected NLO pQCD behaviour.

SCScience Committee Hayrapetyan A. http://dx.doi.org/10.13039/501100013699 Austrian Federal Ministry of Education, Science and Research BMBWF (Bundesministerium für Bildung, Wissenschaft, Forschung) [name change from BMWFW] Tumasyan A. http://dx.doi.org/10.13039/501100002428 Austrian Science Fund FWF Adam W. http://dx.doi.org/10.13039/501100002661 Belgian Fonds de la Recherche Scientifique FRS - FNRS Andrejkovic J. W. http://dx.doi.org/10.13039/501100003130 Belgian Fonds voor Wetenschappelijk Onderzoek FWO Bergauer T. http://dx.doi.org/10.13039/501100003593 CNPq Conselho Nacional de Desenvolvimento Cientifico e Tecnelógica Chatterjee S. http://dx.doi.org/10.13039/501100002322 CAPES Coordenação de Aperfeiçoamento de Pessoal de Nível Superior Damanakis K. http://dx.doi.org/10.13039/501100004586 FAPERJ Fundação de Amparo à Pesquisa do Estado de Rio de Janeiro Dragicevic M. http://dx.doi.org/10.13039/501100004263 FAPERGS Fundação de Amparo À Pesquisa do Estado do Rio Grande do Sul Hussain P. S. http://dx.doi.org/10.13039/501100001807 FAPESP Fundação de Amparo à Pesquisa do Estado de São Paulo Jeitler M. http://dx.doi.org/10.13039/501100005992 Bulgarian Ministry of Education and Science MES Krammer N. http://dx.doi.org/10.13039/501100003336 Bulgarian National Science Fund BNSF Li A. http://dx.doi.org/10.13039/100012470 CERN CERN [Conseil Européen pour la Recherche Nucléaire] Liko D. http://dx.doi.org/10.13039/501100002367 Chinese Academy of Sciences CAS Mikulec I. http://dx.doi.org/10.13039/501100002855 Ministry of Science and Technology MOST Schieck J. http://dx.doi.org/10.13039/501100001809 Chinese National Natural Science Foundation of China NSFC Schöfbeck R. http://dx.doi.org/10.13039/100007637 Colombian Funding Agency (MINICIENCIAS) Departamento Administriva de Ciencia, Tecnología e Innovación, now Ministerio de Ciencia Tecnología e Innovación Schwarz D. http://dx.doi.org/10.13039/501100006588 Croatian Ministry of Science, Education and Sport Ministarstvo Znanosti, Obrazovanja i Sporta; MSES Sonawane M. http://dx.doi.org/10.13039/501100004488 Croatian Science Foundation Hrvatska Zaklada za Znanost; CSF Templ S. http://dx.doi.org/10.13039/501100001810 Research and Innovation Foundation RIF Waltenberger W. http://dx.doi.org/10.13039/501100004299 SENESCYT Secretaría de Educación Superior, Ciencia, Tecnología e Innovación Wulz C.-E. http://dx.doi.org/10.13039/501100002301 Estonian Research Council via PRG780, PRG803, RVTT3 and TK202 Eesti Teadusagentuur; ERC IUT Darwish M. R. Ministry of Education and Research via TK202MoER Janssen T. http://dx.doi.org/10.13039/501100002341 Academy of Finland Suomen Akatemia Van Mechelen P. Finnish Ministry of Education and Culture MEC Bols E. S. Helsinki Institute of Physics HIP D’Hondt J. http://dx.doi.org/10.13039/501100004794 Institut National de Physique Nucléaire et de Physique des Particules IN2P3 Dansana S. http://dx.doi.org/10.13039/501100004794 Centre National de la Recherche Scientifique CNRS De Moor A. http://dx.doi.org/10.13039/501100006489 Commissariat à l’Énergie Atomique et aux Énergies Alternatives CEA Delcourt M. http://dx.doi.org/10.13039/501100004801 Shota Rustaveli National Science Foundation SRNSF El Faham H. http://dx.doi.org/10.13039/501100002347 Bundesministerium für Bildung und Forschung BMBF Lowette S. http://dx.doi.org/10.13039/501100001659 Deutsche Forschungsgemeinschaft DFG Makarenko I. http://dx.doi.org/10.13039/501100001656 Helmholtz-Gemeinschaft Deutscher Forschungszentren HGF Müller D. http://dx.doi.org/10.13039/501100003448 General Secretariat for Research and Innovation GSRI Sahasransu A. R. http://dx.doi.org/10.13039/501100011019 National Research, Development and Innovation Office NKFIH: Nemzeti Kutatási, Fejlesztési és Innováció Hivatal Tavernier S. http://dx.doi.org/10.13039/501100001502 Department of Atomic Energy DAE Tytgat M. http://dx.doi.org/10.13039/501100001409 Department of Science and Technology DST Van Onsem G. P. ICSC -National Research Centre for High Performance Computing, Big Data and Quantum Computing, funded by the EU NexGeneration programFAIR - Future Artificial Intelligence Research; funded by the EU NexGeneration programhttp://dx.doi.org/10.13039/501100006115 Institute for Research in Fundamental Studies IPM Clerbaux B. http://dx.doi.org/10.13039/501100001602 Science Foundation SFI Das A. K. http://dx.doi.org/10.13039/501100004007 Istituto Nazionale di Fisica Nucleare INFN De Lentdecker G. http://dx.doi.org/10.13039/501100004085 Korean Ministry of Education, Science and Technology previously listed was MSIP, Ministry of Science, ICT, and Future Planning Favart L. http://dx.doi.org/10.13039/501100003725 National Research Foundation of Korea (NRF) previously listed was WCU (World Class University) Hohov D. http://dx.doi.org/10.13039/501100001864 MES Ministry of Education and Science Jaramillo J. http://dx.doi.org/10.13039/501100004504 Research Council of Lithuania (LMTLT), agreement No. VS-19 Lietuvos Mokslo Taryba Khalilzadeh A. http://dx.doi.org/10.13039/501100003093 Ministry of Education ?Ministry of Higher Education, Malaysia Lee K. http://dx.doi.org/10.13039/501100004386 University of Malaya http://dx.doi.org/10.13039/501100006348 BUAP Benemérita Universidad Autónoma de Puebla Malara A. http://dx.doi.org/10.13039/501100008688 CINVESTAV Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional Paredes S. http://dx.doi.org/10.13039/501100003141 CONACYT Consejo Nacional de Ciencia y Tecnología Pétré L. LNSLaboratorio Nacional de Supercómputo del Sureste Postiau N. http://dx.doi.org/10.13039/100010096 SEP Secretaría de Educación Pública Thomas L. http://dx.doi.org/10.13039/501100005324 UASLP Universidad Autónoma de San Luis Potosí Vanden Bemden M. MOSMinistry of Science Vander Velde C. http://dx.doi.org/10.13039/501100003524 Ministry of Business, Innovation and Employment MBIE Vanlaer P. http://dx.doi.org/10.13039/501100008689 Pakistan Atomic Energy Commission PAEC De Coen M. http://dx.doi.org/10.13039/501100004569 Ministry of Educaton and Science Ministerstwo Edukacji I Nauki; MES [was MSHE, Ministerstwo Nauki i Szkolnictwa Wyższego] Dobur D. http://dx.doi.org/10.13039/501100004442 National Science Centre Narodowe Centrum Nauki; NSC Hong Y. http://dx.doi.org/10.13039/501100001871 Fundação para a Ciência e a Tecnologia, CERN/FIS-PAR/0025/2019 and CERN/FIS-INS/0032/2019 FCT Knolle J. http://dx.doi.org/10.13039/501100004564 Ministry of Education, Science and Technological Development of Serbia MESTD Lambrecht L. http://dx.doi.org/10.13039/501100011033 MCIN/AEI/10.13039/501100011033, ERDF “a way of making Europe” MCIN/AEI (Ministerio de Ciencia e Innovación/Agencia Estatal de Investigación) Mestdach G. http://dx.doi.org/10.13039/501100008530 Fondo Europeo de Desarrollo Regional, Spain FEDER (ERDF) Amarilo K. Mota https://doi.org/10.13039/100011941 Plan de Ciencia, Tecnología e Innovación del Principado de Asturias PCTI Rendón C. http://dx.doi.org/10.13039/501100008981 MOSTR Ministry of Science, Technology, and Research Samalan A. ETH BoardEidgenössische Technische Hochschule (ETH) Zürich Skovpen K. http://dx.doi.org/10.13039/501100003006 ETH Zurich Eidgenössische Technische Hochschule (ETH) Zürich Van Den Bossche N. http://dx.doi.org/10.13039/501100004219 PSI Paul Scherrer Institut van der Linden J. http://dx.doi.org/10.13039/501100001711 SNF Swiss National Science Foundation (Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung) Wezenbeek L. UniZHUniversität Zürich Benecke A. Canton ZurichSERState Secretariat for Education and Research (Education, Research, and Innovation: SERI) Bruno G. http://dx.doi.org/10.13039/501100004663 Ministry of Science and Technology http://dx.doi.org/10.13039/501100016204 Ministry of Higher Education, Science, Research and Innovation MHESI Delaere C. http://dx.doi.org/10.13039/501100004192 National Science and Technology Development Agency of Thailand NSTDA Donertas I. S. http://dx.doi.org/10.13039/501100004410 Scientific and Technical Research Council of Turkey Türkiye Bilimsel ve Teknolojik Araştirma Kurumu Giammanco A. http://dx.doi.org/10.13039/100010440 Turkish Atomic Energy Authority Türkiye Atom Enerjisi Kurumu Jaffel K. http://dx.doi.org/10.13039/501100004742 National Academy of Sciences of Ukraine http://dx.doi.org/10.13039/501100000271 Science and Technology Facilities Council http://dx.doi.org/10.13039/100000015 US Department of Energy http://dx.doi.org/10.13039/100000001 US National Science Foundation Marie-Curie programmehttp://dx.doi.org/10.13039/501100000781 European Research Council and EPLANET (European Union) ERC doi only Tumasyan A. http://dx.doi.org/10.13039/501100000921 European Research Council/European Cooperation in Science and Technology), Action CA16108 COST Adam W. Individual Horizon 2020 Grant, contract Nos. 675440, 724704, 752730, 758316, 765710, 824093, 101115353, 101002207 (European Union) http://dx.doi.org/10.13039/501100004117 Leventis Foundation http://dx.doi.org/10.13039/100000879 Alfred P. Sloan Foundation http://dx.doi.org/10.13039/100005156 Alexander von Humboldt Foundation Alexander von Humboldt-Stiftung Damanakis K. Science Committee, project no. 22rl-037Belgian Federal Science Policy Officehttp://dx.doi.org/10.13039/501100003134 Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium) http://dx.doi.org/10.13039/501100003132 Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium) http://dx.doi.org/10.13039/501100002661 Belgian Fonds de la Recherche Scientifique, "Excellence of Science - EOS" - be.h project n. 30820817 FRS - FNRS Li A. http://dx.doi.org/10.13039/501100003130 Belgian Fonds voor Wetenschappelijk Onderzoek, "Excellence of Science - EOS" - be.h project n. 30820817 FWO Liko D. http://dx.doi.org/10.13039/501100009592 Beijing Municipal Science & Technology Commission, No. Z191100007219010 https://dx.doi.org/10.13039/501100012226 Fundamental Research Funds for the Central Universities http://dx.doi.org/10.13039/501100001823 Ministry of Education, Youth and Sports (MEYS) of the Czech Republic Ministerstvo Školství, Mládeže a Tělovýchovy SRNSF Schöfbeck R. Schwarz D. http://dx.doi.org/10.13039/501100001659 Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy - EXC 2121 "Quantum Universe" – 390833306 http://dx.doi.org/10.13039/501100001659 Deutsche Forschungsgemeinschaft (DFG), project number 400140256 - GRK2497 http://dx.doi.org/10.13039/501100013209 Hellenic Foundation for Research and Innovation, Project Number 2288 HFRI Waltenberger W. http://dx.doi.org/10.13039/501100003825 Hungarian Academy of Sciences Magyar Tudományos Akadémia Wulz C.-E. http://dx.doi.org/10.13039/501100011019 New National Excellence Program - ÚNKP, the NKFIH research grants K 131991, K 133046, K 138136, K 143460, K 143477, K 146913, K 146914, K 147048, 2020-2.2.1-ED-2021-00181, and TKP2021-NKTA-64 (Hungary); ÚNKP: Új Nemzeti Kiválósági Program Darwish M. R. Council of Scientific and Industrial Research, Indiahttp://dx.doi.org/10.13039/501100005375 Latvian Council of Science Latvijas Zinātnes Padome Van Mechelen P. http://dx.doi.org/10.13039/501100004569 Ministy of Education and Science, project no. 2022/WK/14 Ministerstwo Edukacji I Nauki; MES Bols E. S. http://dx.doi.org/10.13039/501100004281 National Science Center, Opus 2021/41/B/ST2/01369 and 2021/43/B/ST2/01552 Narodowe Centrum Nauki D’Hondt J. http://dx.doi.org/10.13039/501100001871 Fundação para a Ciência e a Tecnologia, CEECIND/01334/2018 http://dx.doi.org/10.13039/100008982 National Priorities Research Program by Qatar National Research Fund Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia María de Maeztu, grant MDM-2017-0765 and projects PID2020-113705RB, PID2020-113304RB, PID2020-116262RB and PID2020-113341RB-I00https://doi.org/10.13039/100011941 Programa Severo Ochoa del Principado de Asturias http://dx.doi.org/10.13039/501100002873 CUAASC Chulalongkorn Academic into Its 2nd Century Project Advancement Project Lowette S. http://dx.doi.org/10.13039/501100004192 National Science, Research and Innovation Fund via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation, grant B37G660013 http://dx.doi.org/10.13039/100001201 Kavli Foundation http://dx.doi.org/10.13039/100007065 Nvidia Corporation hardware contribution: Titan Xp GPUs Sahasransu A. R. http://dx.doi.org/10.13039/100000928 Welch Foundation, contract C-1845 http://dx.doi.org/10.13039/100011223 Weston Havens Foundation Institut für Hochenergiephysik (HEPHY) using the Cloud Infrastructure Platform (CLIP), ViennaInter-University Institute for High Energies, Brusselshttp://dx.doi.org/10.13039/501100005041 Université Catholique de Louvain, Louvain-la-Neuve http://dx.doi.org/10.13039/501100009568 São Paulo Research and Analysis Center, São Paulo http://dx.doi.org/10.13039/501100006702 Universidade do Estado do Rio de Janeiro, Rio de Janeiro University of Sofia, Sofiahttp://dx.doi.org/10.13039/501100011181 Institute of High Energy Physics of the Chinese Academy of Sciences, Beijing http://dx.doi.org/10.13039/501100005789 National Institute of Chemical Physics and Biophysics, Tallinn Helsinki Institute of Physics, HelsinkiGrille de Recherche d’Ile de France (GRIF), Institut de recherche sur les lois fondamentales de l’Univers, CEA, Université Paris-Saclay, Gif-sur-Yvette, France and Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de ParisInstitut national de physique nucléaire et de physique des particules, IN2P3, VilleurbanneInstitut Pluridisciplinaire Hubert Curien (IPHC), Strasbourghttp://dx.doi.org/10.13039/501100001647 Deutsches Elektronen-Synchrotron, Hamburg http://dx.doi.org/10.13039/100009133 Karlsruher Institut für Technologie, Karlsruhe http://dx.doi.org/10.13039/501100007210 RWTH Aachen University, Aachen University of Ioánnina, Ioánninahttp://dx.doi.org/10.13039/501100014549 Wigner Research Centre for Physics, Budapest http://dx.doi.org/10.13039/501100001405 Tata Institute of Fundamental Research, Mumbai http://dx.doi.org/10.13039/501100004007 INFN CNAF, Bologna INFN Sezione di Bari, Università di Bari, Politecnico di Bari, Barihttp://dx.doi.org/10.13039/100009093 INFN Sezione di Pisa, Università di Pisa, Scuola Normale Superiore di Pisa, Pisa http://dx.doi.org/10.13039/501100004271 INFN Sezione di Roma, Sapienza Università di Roma, Rome INFN Sezione di Trieste, Università di Trieste, TriesteLaboratori Nazionali di Legnaro, Legnarohttp://dx.doi.org/10.13039/501100004253 National Centre for Physics, Quaid-I-Azam University, Islamabad Akademickie Centrum Komputerowe Cyfronet AGH, KrakowNational Centre for Nuclear Research, SwierkLaboratório de Instrumentação e Física Experimental de Partículas, Lisboahttp://dx.doi.org/10.13039/501100003693 Korea Institute of Science and Technology Information (KISTI), Daejeon http://dx.doi.org/10.13039/501100009613 Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, SantanderPort d’Informació Científica, Bellaterrahttp://dx.doi.org/10.13039/100012470 CERN, European Organization for Nuclear Research, Geneva Instrumentation and Detector Consortium, TaipeiNational Center for High-performance Computing (NCHC), Hsinchu Cityhttp://dx.doi.org/10.13039/501100004175 Middle East Technical University, Physics Department, Ankara National Scientific Center, Kharkov Institute of Physics and Technology, Kharkovhttp://dx.doi.org/10.13039/100008475 GridPP, Brunel University, Uxbridge http://dx.doi.org/10.13039/501100000761 GridPP, Imperial College, London http://dx.doi.org/10.13039/501100000851 GridPP, Queen Mary University of London, London GridPP, Royal Holloway, University of London, Londonhttp://dx.doi.org/10.13039/100014570 GridPP, Rutherford Appleton Laboratory, Didcot http://dx.doi.org/10.13039/501100005618 GridPP, University of Bristol, Bristol GridPP, University of Glasgow, Glasgowhttp://dx.doi.org/10.13039/100007492 Baylor University, Waco http://dx.doi.org/10.13039/100006961 California Institute of Technology, Pasadena http://dx.doi.org/10.13039/100006230 Fermi National Accelerator Laboratory, Batavia http://dx.doi.org/10.13039/100006919 Massachusetts Institute of Technology, Cambridge http://dx.doi.org/10.13039/100017223 National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility, Berkeley Open Science Grid (OSG) ConsortiumPittsburgh Supercomputing Center (PSC), Pittsburghhttp://dx.doi.org/10.13039/100006377 Purdue University, West Lafayette http://dx.doi.org/10.13039/100016353 San Diego Supercomputer Center (SDSC), La Jolla Texas Advanced Computing Center (TACC), Austinhttp://dx.doi.org/10.13039/100007911 University of California, San Diego, La Jolla http://dx.doi.org/10.13039/100007493 University of Colorado Boulder, Boulder http://dx.doi.org/10.13039/100009406 University of Florida, Gainesville http://dx.doi.org/10.13039/100008114 University of Nebraska-Lincoln, Lincoln http://dx.doi.org/10.13039/100007015 University of Wisconsin - Madison, Madison http://dx.doi.org/10.13039/100006537 Vanderbilt University, Nashville issue-copyright-statement© EDP Sciences, Societa Italiana di Fisica (SIF) and Springer-Verlag GmbH, DE, part of Springer Nature 2024
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pmcIntroduction

In the standard model of particle physics, the strong interaction between partons (quarks and gluons) is described by the theory of quantum chromodynamics (QCD). A key property of the strong interaction is “asymptotic freedom”, which characterizes the decreasing value of the coupling αS(Q) for increasingly larger momentum transfer Q that corresponds to smaller distances between the interacting partons. This property is a consequence of the non-Abelian nature of QCD, and can be theoretically derived from the renormalization group equations (RGE) [1–3]. Although the RGE cannot predict the absolute value of αS(Q), they can accurately determine its evolution as a function of the energy scale Q [4]. By comparing experimental measurements to perturbative QCD (pQCD) predictions for a given observable, the value of αS(Q) can be extracted at various scales [5, 6]. To compare various αS(Q) determinations, it is standard practice to evolve them to a common scale given by the mass of the Z boson, Q=mZ. The current world-average value of the QCD coupling at this reference scale is αS(mZ)=0.1180±0.0009 [5].

This paper reports a new extraction of the αS(Q) coupling from multijet measurements at various energy scales in proton-proton (pp) collisions at the CERN LHC. For this purpose, a ratio observable RΔϕ(pT), related to the azimuthal correlations among jets, is measured as a function of the jet transverse momentum pT. Similar ratio observables, based on either the distance in the plane of rapidity and azimuthal angle among jets, RΔR(pT) [7], or on the dijet azimuthal decorrelations, RΔϕ(HT) [8, 9], have already been used to extract the αS(Q) coupling at hadron colliders. The RΔϕ(pT) observable is defined as:1 RΔϕ(pT)=∑i=1Njet(pT)Nnbr(i)(Δϕ,pTminnbr)Njet(pT),

where the denominator Njet(pT) simply counts the number of jets in a given jet pT bin, and the numerator sums the number of neighbouring jets, Nnbr(i), around each jet i in the same pT bin. A neighbouring jet must exceed a minimum transverse momentum of pTminnbr and be separated from jet i within a specified interval of azimuthal distance Δϕ: Δϕmin<Δϕ<Δϕmax. In fixed-order predictions of jet production based on pQCD calculations, the leading-order (LO) 2→2 process is characterized by an azimuthal separation of Δϕ=π. Since the sum in the numerator runs over all jets, this would lead to two entries at pT=pT,1=pT,2. At next-to-leading order (NLO), the radiation of a third hard parton can give rise to a 3-jet topology with Δϕ between 2π/3 and π with respect to the jet opposite to the hemisphere with radiation (Fig. 1, right diagrams). Hence, by fixing the azimuthal distance for neighbouring jets to 2π/3<Δϕ<7π/8 in Eq. (1), the dijet case is avoided, and the numerator is different from zero only for events with three jets or more, whose LO cross section is proportional to αS3. Also here, a jet pair fulfilling both the selection in pTminnbr and in Δϕ leads to two entries, but potentially at different jet pT values. On the other hand, the denominator corresponds to the inclusive jet cross section, which at LO is proportional to αS2, such that the RΔϕ(pT) observable is directly proportional to αS, at the lowest order. A representative illustration, indicating the entries to the numerator and denominator of the RΔϕ(pT) ratio, is shown in the left and right panels of Fig. 1 for a 2-jet and a 3-jet event, respectively.Fig. 1 Example of the number of entries contributing to the numerator and denominator of the RΔϕ(pT) ratio, Eq. (1), for 2-jet (left) and 3-jet (right) events, with all jets having pT>pTminnbr=100GeV. The 2-jet topology does not contribute (null numerator) to the RΔϕ(pT) ratio when the azimuthal distance for neighbouring jets is fixed to 2π/3<Δϕ<7π/8. In the 3-jet topology, each jet is considered as a reference, and its azimuthal separations (Δϕ,1 and Δϕ,2) to other neighbouring jets (with pT,1nbr and pT,2nbr) are computed. Each neighbouring jet with Δϕ within the specified interval increments the entries of the numerator, whereas the denominator simply counts the number of jets in the event

In the ratio defined by Eq. (1) many experimental systematic uncertainties – such as those from the integrated luminosity, the jet energy scale (JES), and the jet energy resolution (JER) – cancel entirely or to a large extent. In addition, theoretical uncertainties – such as nonperturbative (NP) and parton distribution function (PDF) uncertainties – are reduced.

To rigorously account for correlations between the numerator and denominator, it is useful to consider the more general, two-dimensional jet-counting quantity, N(pT,n), which is a function of the i-th jet’s pT and of the number n of neighbouring jets that satisfy the additional selection criteria for pTminnbr and Δϕ. Then, using N(pT,n), it can be shown that the RΔϕ(pT) observable can be also formulated as:2 RΔϕ(pT)=∑nnN(pT,n)∑nN(pT,n).

Such a definition allows a multidimensional unfolding of the more general quantity N(pT,n) to be performed, instead of a separate unfolding of the numerator and denominator of Eq. (1).

The measurement is performed using data collected with the CMS detector, during the LHC Run 2 data-taking period (2016–2018), corresponding to an integrated luminosity of 134fb-1 at a centre-of-mass energy of 13TeV [10–12]. Previous determinations of the strong coupling constant αS(mZ) using jets at hadron colliders have been reported by the CDF [13] and D0 [7, 14] Collaborations in proton-antiproton collisions at s=1.8 and 1.96TeV at the Fermilab Tevatron. At the LHC, determinations have been reported using pp collision data from the ATLAS and CMS Collaborations at s=7 [15–22], 8 [9, 21–25], and 13 [26–29, 29–32]TeV.

The paper is organized as follows. In Sect. 2 a brief description of the CMS detector is given. In Sect. 3 the event reconstruction is described. Section 4 details the measurement of the RΔϕ(pT) observable. Experimental results and theoretical predictions for the RΔϕ(pT) observable are compared in Sect. 5. The determination of αS(mZ) and the investigation of the running of the αS(Q) coupling are presented in Sect. 6. Finally, a summary of the paper is given in Sect. 7.

Tabulated results are provided in the HEPData record for this analysis [33].

The CMS detector

The central feature of the CMS apparatus is a superconducting solenoid of 6\,m internal diameter, providing a magnetic field of 3.8\,T. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections. Forward calorimeters extend the pseudorapidity coverage provided by the barrel and endcap detectors. Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid.

The electromagnetic calorimeter consists of 75 848 lead tungstate crystals, which provide coverage in pseudorapidity |η|<1.48 in a barrel region (EB) and 1.48<|η|<3.0 in two endcap regions (EE). Preshower detectors consisting of two planes of silicon sensors interleaved with a total of three radiation lengths of lead are located in front of each EE detector.

In the region |η|<1.74, the HCAL cells have widths of 0.087 in pseudorapidity and 0.087 in azimuth (ϕ). In the η–ϕ plane, and for |η|<1.48, the HCAL cells map on to 5×5 arrays of ECAL crystals to form calorimeter towers projecting radially outwards from close to the nominal interaction point. For |η|>1.74, the coverage of the towers increases progressively to a maximum of 0.174 in Δη and Δϕ. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [34].

Events of interest are selected using a two-tiered trigger system. The first level (L1), composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of around 100\,kHz within a fixed latency of about 4μs [35]. The second level, known as the high-level trigger (HLT), consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing and reduces the event rate to around 1\,kHz before data storage [36].

Event reconstruction

The global event reconstruction – also called particle-flow (PF) event reconstruction [37] – aims to reconstruct and identify each individual particle in an event, with an optimized combination of all subdetector information. In this process, the identification of the particle type (photon, electron, muon, charged hadron, neutral hadron) plays an important role in the determination of the particle direction and energy. Photons (e.g., coming from π0decays or from electron bremsstrahlung) are identified as ECAL energy clusters not linked to the extrapolation of any charged particle trajectory to the ECAL. Electrons (e.g., coming from photon conversions in the tracker material or from bottom quark (b) hadron semileptonic decays) are identified as a primary charged particle track and potentially many ECAL energy clusters corresponding to this track extrapolation to the ECAL and to possible bremsstrahlung photons emitted along the way through the tracker material. Muons (e.g., from bhadron semileptonic decays) are identified as tracks in the central tracker consistent with either a track or several hits in the muon system, and associated with calorimeter deposits compatible with the muon hypothesis. Charged hadrons are identified as charged particle tracks neither identified as electrons, nor as muons. Finally, neutral hadrons are identified as HCAL energy clusters not linked to any charged-hadron trajectory, or as a combined ECAL and HCAL energy excess with respect to the expected charged-hadron energy deposit.

The energy of photons is obtained from the ECAL measurement. The energy of electrons is determined from a combination of the track momentum at the main interaction vertex, the corresponding ECAL cluster energy, and the energy sum of all bremsstrahlung photons attached to the track. The energy of muons is obtained from the corresponding track momentum. The energy of charged hadrons is determined from a combination of the track momentum and the corresponding ECAL and HCAL energies, corrected for the response function of the calorimeters to hadronic showers. Finally, the energy of neutral hadrons is obtained from the corresponding corrected ECAL and HCAL energies.Table 1 The different HLT pT thresholds used in the measurement and the corresponding integrated luminosities for each data-taking year

pTthresh (GeV)		40	60	80	140	200	260	320	400	450	500	
	2016	0.0497	0.328	1.00	10.1	85.8	518	1526	4590	33,500	–	
L (pb-1)	2017	0.182	0.505	2.53	26.6	189	469	1230	7690	9660	41,500	
	2018	0.0151	0.419	2.17	47.1	202	466	1240	3720	7390	59,800	

The primary vertex (PV) is taken to be the vertex corresponding to the hardest scattering in the event, evaluated using tracking information alone, as described in Section 9.4.1 of Ref. [38]. For each event, hadronic jets are clustered from the reconstructed particle candidates using the infrared and collinear safe anti-kT algorithm [39, 40] with a distance parameter of R=0.7. This choice of the parameter R enables the compatibility with previous results from the CMS Collaboration at s=7 [16] and 13 [30]TeV. Jet momentum is determined as the vectorial sum of all particle momenta in the jet, and is found from simulation to be, on average, within 5 to 10% of the true momentum over the whole pT spectrum and detector acceptance. Additional pp interactions within the same, or nearby, bunch crossings (pileup) can contribute additional tracks and calorimetric energy depositions to the jet momentum. To mitigate this effect, charged particles identified to be originating from pileup vertices are discarded, and an offset correction is applied to correct for the remaining contributions [41]. The JES corrections are derived from simulation to bring the measured response of jets to that of particle-level jets on average. In situ measurements of the momentum balance in dijet, photon+jet, Z+jet, and multijet events are used to account for any residual differences in the jet energy scale between the measured data and simulation [42]. The jet energy resolution amounts typically to 15–20% at 30GeV, 10% at 100GeV, and 5% at 1TeV [42]. Additional selection criteria are applied to each jet to remove jets potentially dominated by anomalous contributions from various subdetector components or reconstruction failures [43].

The missing transverse momentum vector p→Tmiss is computed as the negative vector sum of the transverse momenta of all the PF candidates in an event, and its magnitude is denoted as pTmiss [44]. The p→Tmiss is modified to account for corrections to the energy scale of the reconstructed jets in the event.

During the 2016-2017 data taking, a gradual shift in the timing of the inputs of the ECAL L1 trigger in the region at |η|>2.0 caused a specific trigger inefficiency [45], called “prefiring” hereafter. For events containing a jet with pT≳100GeV in the region 2.5<|η|<3.0, the efficiency loss is ≈10–20%, depending on pT, η, and data-taking period.

Data analysis

Event selection criteria

Each event is required to have at least one offline-reconstructed PV with z coordinate satisfying the criterion |zPV|<24cm and radial distance from the interaction point ρPV<2cm. Anomalous high-pTmiss events can be due to a variety of reconstruction failures, detector malfunctions, or noncollision backgrounds. Such events are rejected by event filters that are designed to identify more than 85–90% of the spurious high-pTmiss events with a mistagging rate less than 0.1% [44]. Only events that have been accepted by at least one single-jet trigger path (described in Sect. 4.2) are included in the measurement. For the rejection of poorly reconstructed jets and jets originating from detector noise, additional quality criteria are applied to them based on their constituents [43].

The measurement is based on an inclusive jet sample that contains only jets reconstructed within the rapidity range |y|<2.5 and with transverse momenta pT>50GeV. The pTminnbr threshold and azimuthal separation interval for neighbouring jets as defined in Eq. (1), are set to 100GeV and 2π/3<Δϕ<7π/8, respectively. This choice was motivated by statistical optimization, extending the phase space as much as possible, and guaranteeing that the NLO predictions remain valid and soft effects are negligible.

Triggers

The analysis is based on single-jet triggers that require at least one jet with pT above a given threshold (pTthresh) to be present in the event. Table 1 shows the different HLT thresholds along with the effective integrated luminosities recorded by the triggers for 2016, 2017 and 2018. All triggers in Table 1 were prescaled, apart from trigger 450 for 2016, and trigger 500 for 2017 and 2018. The efficiency for each trigger is estimated as a function of leading-jet pT using a lower-threshold trigger, except for the lowest-threshold trigger efficiency. The latter is estimated using a tag-and-probe method applied to dijet topologies, which counts the jets reconstructed with the offline PF algorithm that can be matched to HLT jets, considering only the jets leading and subleading in pT. The data consist of events selected with a combination of triggers in mutually exclusive leading-jet pT intervals. The usage of a specific trigger is enabled only in phase-space regions where its efficiency is larger than 99.5% and disabled in phase-space regions where the efficiency of a higher-threshold trigger is larger than 99.5%. The jet-counting variables are combined event-by-event by applying weights to account for the trigger prescales of each data sample.Table 2 Values of the RΔϕ(pT) observable in different pT intervals, and associated experimental uncertainties

pT (GeV)	RΔϕ(pT)	Stat. (%)	JES (%)	Prefiring (%)	JER (%)	PU (%)	MCmodel (%)	
360–430	0.25	0.26	0.74	0.06	0.08	0.01	–	
430–510	0.26	0.23	0.69	0.09	0.06	0.02	–	
510–600	0.27	0.19	0.67	0.12	0.05	0.02	–	
600–700	0.27	0.18	0.66	0.13	0.04	0.02	0.01	
700–800	0.28	0.18	0.65	0.12	0.04	0.02	0.01	
800–920	0.28	0.20	0.65	0.10	0.04	0.02	0.01	
920–1050	0.27	0.27	0.66	0.07	0.05	0.02	–	
1050–1190	0.27	0.39	0.67	0.05	0.06	0.02	–	
1190–1340	0.27	0.58	0.70	0.03	0.07	0.02	–	
1340–1500	0.26	0.90	0.75	0.02	0.08	0.02	–	
1500–1680	0.26	1.34	0.84	0.01	0.11	0.02	–	
1680–1870	0.25	2.16	0.98	–	0.14	0.02	–	
1870–2070	0.24	3.42	1.21	–	0.19	0.02	–	
2070–2300	0.21	5.66	1.62	–	0.27	0.02	–	
2300–2560	0.22	8.23	2.36	–	0.39	0.02	–	
2560–3170	0.21	10.49	5.00	–	0.77	0.01	–	

Unfolding

To compare the experimental data with theoretical predictions, the measured distributions must be corrected for detector effects, such as finite pT resolution and limited detector acceptance. The detector effects are parameterized through a response matrix built from simulated event samples using pythia  8.240 [46] with tunes CUETP8M1 [47] and CP5 [48], where reconstructed-level jets are matched to generator-level jets as explained next. First, the generated jets in each event are ordered by decreasing pT. Then, each generated jet is matched to the reconstructed jet with the highest pT, within a cone of radius ΔR=(Δη)2+(Δϕ)2=0.35 (where Δη and Δϕ are the angular differences in pseudorapidity and azimuthal angle between the generated and reconstructed jets). The probability matrix A corresponds to the row-by-row normalized response matrix. Each element Aij represents the probability of a jet produced in (generator-level) bin j to be observed in (reconstructed-level) bin i. The detector effects are corrected through an unfolding procedure that accounts for bin migrations, background (fake jets, i.e., reconstructed-level jets that could not be matched to generator-level jets), and inefficiencies (missed jets, i.e., generator-level jets that could not be matched to reconstructed-level jets), and corrects the measurement from the detector level to the level of stable particles (except neutrinos) with mean decay-lengths larger than cτ=10\,mm (where τ denotes the mean proper lifetime of the particle).

The unfolding procedure is implemented using the TUnfold package [49]. The determination of the particle-level distribution (x) is performed with the matrix pseudoinverse method [50] using a detector-level distribution (y) with twice the number of bins of the particle-level distribution. The latter are defined in Table 2 (first column) and are chosen to ensure that the bin sizes remain at least twice as large as the jet pT resolution. The unfolding solution arises from the minimization of the quantity3 χ2=Ax+b-yT(V-1)Ax+b-y,

where b is the background obtained from simulated events, and V is the covariance matrix (corrected for the background) of the detector-level data including their statistical uncertainties and correlations. Instead of unfolding separately the numerator and denominator of Eq. (1), a multidimensional unfolding of the more general, equivalent quantity N(pT,n) is performed, which rigorously accounts for the numerator-denominator statistical correlations following Eq. (2).

Figure 2 shows the probability matrix for the N(pT,n) quantity. The number of events with n≥4 is small, and n=3 is the maximum number of neighbouring jets shown here. The condition number (defined as the absolute value of the ratio between the largest and smallest matrix eigenvalues) for the matrix A is ≈5.5, which means that the unfolding problem is well-conditioned, and therefore no additional regularization is required.Fig. 2 Probability matrix for the N(pT,n) distribution built using pythia8 simulated events. The horizontal axis corresponds to the generator-level jet pT, and the vertical axis to the reconstructed-level jet pT. The 4×4 structure of the matrix corresponds to the bins of neighbouring jets n (labelled in the uppermost row and rightmost column), and indicates migrations among those bins. The horizontal and vertical axes of each cell correspond to the pT of the jets, and each cell indicates the migrations among the jet pT bins. The range of colours covers from 10-6 to 1, and indicates the probability of migrations from a given (generator) particle-level bin to the corresponding (reconstructed) detector-level bin

Experimental uncertainties

The experimental uncertainties contain statistical and systematic sources that propagate to the measured distributions. The statistical uncertainties are obtained from the covariance matrix, extracted at the particle level from the N(pT,n) distribution along with the RΔϕ(pT) observable, as described in Sect. 4.3. The bin-to-bin correlation matrix at the particle level is shown in Fig. 3, where the value 1 (-1) corresponds to fully (anti)correlated bins. The diagonal elements of the correlation matrix are by construction always unity, and the off-diagonal elements represent the bin-to-bin (anti)correlations, where the highest (lowest) value is 0.49 (-0.57). The statistical uncertainties in the RΔϕ(pT) measurement remain below 1% up to ≈1.5TeV increasing to about 10% at ≈3TeV.

The calibration of the reconstructed jet energy is performed through a series of successive stages implemented in the JES correction procedure [42], as described in Sect. 3. The JES uncertainty is composed of 27 individual uncorrelated contributions, which are investigated one-by-one considering a ±1 standard-deviation variation from their nominal value. Each variation is applied at the detector level and propagated to the particle-level measurement by repeating the unfolding procedure. Finally, the total JES uncertainty is computed as the quadratic sum of individual JES uncertainty sources, and remains below 1% up to ≈1.5TeV increasing to about 5% at ≈3TeV. Additional variations of the trigger prefiring corrections described in Sect. 3 are applied in the same manner. The uncertainties from prefiring corrections in the RΔϕ(pT) measurement are smaller than 0.13%.

In simulated samples, a detailed modelling of the CMS detector is included based on the Geant4 toolkit [51]. The JER obtained in the detector simulation is generally better than that in the actual detector. Therefore, the energy of reconstructed jets in simulation is smeared out, so that the simulated JER matches the one measured in experimental data. The JER uncertainty is estimated by varying the smearing factors within ±1 standard deviations from their nominal values, and propagated to the particle-level measurement by repeating the unfolding procedure. The JER uncertainty in the RΔϕ(pT) measurement is below 0.8%.

The probability distribution for the number of pp interactions per bunch crossing is represented by pileup (PU) profiles. To account for differences between the measured and simulated PU profiles, the simulated events are reweighted using the PU distribution of the experimental data as a reference. An additional systematic uncertainty, which remains below 0.03%, is evaluated by varying the PU profile correction in the simulation. The model dependence introduced by unfolding is estimated from the difference in the RΔϕ(pT) distribution unfolded with response matrices obtained from pythia8 and MadGraph 5_amc@nlo  2.6 [52, 53] interfaced with pythia8. Additionally, the model dependence for inefficiencies (missed jets) and backgrounds (misreconstructed jets) is studied by varying separately their rates within an estimate of 5%, which largely covers the model dependence of migrations in and out of the phase space. The total model dependence uncertainties (MCmodel) are negligible (<0.01%) compared with other uncertainties for the bulk of the spectrum. The trigger efficiency uncertainties are also negligible in the RΔϕ(pT) measurement. The RΔϕ(pT) observable values along with all the experimental uncertainties are shown in Table 2.Fig. 3 Bin-to-bin correlation matrix for the RΔϕ(pT) distribution at the particle level, where the value 1 (-1) corresponds to fully (anti)correlated bins. For illustration purposes, only bins with (anti)correlations larger (smaller) than 0.05 (-0.05) are shown also as text

Fig. 4 The RΔϕ(pT) observable as a function of pT, compared with MC generator predictions at LO (left) and at NLO (right) accuracy. The LO predictions are obtained with pythia8 tunes CUETP8M1 and CUETP8M2, and herwig++ tune UE-EE-5-CTEQ6L1 MC event generators. The NLO predictions are obtained with powheg interfaced with each of the aforementioned MC event generators. The experimental data are represented with black dots and the MC predictions with coloured lines. The lower panel of each plot shows the ratio between MC predictions and experimental data. The total experimental uncertainties are indicated by the vertical error bars (upper panels) and coloured band (lower panels) correspondingly

Table 3 Default and range of αS(mZ) values used in the different NLO PDF sets

PDF set	Default αS(mZ)	Alternative αS(mZ)	
ABMP16 [78]	0.1191	0.114–0.123	
CT18 [79]	0.1180	0.110–0.124	
MSHT20 [80]	0.1200	0.108–0.130	
NNPDF3.1 [81]	0.1180	0.106–0.130	

Fig. 5 Theoretical predictions for the cross sections corresponding to the numerator (left) and denominator (right) of the RΔϕ(pT) ratio, Eq. (1), obtained using the NNPDF3.1 NLO PDF set. The coloured bands represent the LO and NLO scale uncertainties derived with a six-point variation of μR and μF from the central reference value. The lower panels show the ratios to the respective LO predictions

Fig. 6 Nonperturbative correction factors for the numerator (upper left) and denominator (upper right) of the RΔϕ(pT) ratio, Eq. (1), using pythia8 with tunes CUETP8M1 and CUETP8M2, herwig++ with tune UE-EE-5-CTEQ6L1, and POWHEG interfaced with each of them. The lower plot shows the NP correction factors (blue line) for RΔϕ(pT) and their uncertainties

Theoretical predictions

Monte Carlo event generators predictions

Experimental data are compared with predictions from herwig++  2.7.1 [54], pythia  8.240 [46], and powheg  2.0 [55] Monte Carlo (MC) event generators obtained using the Rivet toolkit [56]. The herwig++ event generator computes the matrix elements (MEs) at LO accuracy for 2→2 QCD scattering processes. The parton shower (PS) is simulated through successive angular-ordered emissions, and the cluster fragmentation model [57] is used for the hadronization. The underlying event (UE) activity is obtained from the simulation of multiparton interactions (MPIs) tuned to experimental data. The set of herwig++ parameters used in this analysis is that of the UE-EE-5-CTEQ6L1 tune [58] based on the CTEQ6.1M LO PDF set [59]. Similarly to herwig++, in pythia8 the MEs are calculated at LO accuracy for 2→2 QCD scattering processes. The PS is simulated through successive pT-ordered emissions and the hadronization mechanism employs the Lund string model [60]. Two different sets of parameters are used for pythia8, the CUETP8M1 tune [47] based on the NNPDF2.3 LO PDF set [61, 62] and the CUETP8M2 tune [63] based on the NNPDF3.0 LO PDF set [64]. The powheg [65, 66] generator, based on the Powheg box [55], generates 2→2 matrix elements at NLO accuracy, as well as 2→3 matrix elements at LO accuracy and uses the NNPDF3.0 NLO PDF set [64]. To simulate the PS, hadronization, and MPI processes, powheg is interfaced either with pythia8 or with herwig++.

Figure 4 (left) shows the particle-level data for the RΔϕ(pT) observable compared with the predictions of pythia8 tunes CUETP8M1 and CUETP8M2, and herwig++ tune UE-EE-5-CTEQ6L1 LO MC event generators. The lower panels show the corresponding ratios between the MC predictions and the measured data. Figure 4 (right) illustrates the particle-level RΔϕ(pT) observable compared with powheg interfaced with pythia8 tunes CUETP8M1 and CUETP8M2, and herwig++ tune UE-EE-5-CTEQ6L1 results. The corresponding lower panels show the ratios between the powheg predictions and the measurement. The coloured band on both lower panels represents the total experimental uncertainties.

From 360 up to around 800GeV, the RΔϕ(pT) distribution rises as the phase space for the production of a third jet increases. Then, the distribution reaches a plateau up to around 1200GeV, followed by a decrease due to the running of αS, and the reduced amount of gluon scatterings.

The predictions from LO herwig++ and LO pythia8 tune CUETP8M1 overestimate the measurement by ≈20% and ≈12–18%, respectively. On the other hand, the predictions from the (LO) pythia8 tune CUETP8M2 give a good description of the data. Besides the PDF set, the main differences between the parameters of the two pythia8 tunes are the value of αS used for the initial-state shower αSISR, the MPI infrared regularization scale pT0ref, and the amount of colour reconnection. Among the NLO MC predictions based on powheg, the powheg interfaced with pythia8 tune CUETP8M2 gives the best description, being ≈5–6% away from the measurement. Finally, powheg interfaced with herwig++ tune UE-EE-5-CTEQ6L1 or with pythia8 tune CUETP8M1 overestimate the RΔϕ(pT) measurement by ≈12% and ≈10%, respectively.

Fixed-order predictions

Fixed-order theoretical predictions for the RΔϕ(pT) observable are obtained up to NLO accuracy in pQCD with the NLOJet++ program [67, 68] within the fastNLO framework [69, 70]. The predictions are extracted for several PDF sets available via the lhapdf library [71], using their default value for the strong coupling constant αS(mZ), and alternative values, as shown in Table 3. The central reference values μ0 for the renormalization (μR) and factorization (μF) scales are defined as:4 μR=μF=H^T/2,

where H^T is the scalar sum of the transverse momenta of all partons in the event. This choice follows recommendations detailed in Ref. [72], which favour H^T over pT,jet and discourage the use of pT,max=pT,1 as the central scale choice for inclusive jet cross sections. For 3-jet ratio observables such as RΔϕ(pT), Refs. [73, 74] conclude that H^T/2 is slightly preferred for comparisons with theoretical predictions at next-to-NLO accuracy. The uncertainties related to missing higher-order terms of the perturbative series are estimated using the conventional recipe [75–77], i.e., by varying μR and μF around the reference scale μ0 within six combinations: (μR/μ0,μF/μ0)=(1/2,1/2), (1/2, 1), (1, 1/2), (1, 2), (2, 1), (2, 2). An envelope is constructed from the various combinations, where the edges define the scale uncertainties.Fig. 7 Electroweak corrections for the numerator (blue) and denominator (green) of Eq. (1), and for the RΔϕ(pT) ratio itself (red). The solid lines correspond to the additive combination of NLO EW corrections to the QCD process (NLO QCD+EW), and the markers represent the multiplicative combination (NLO QCD×EW)

Fig. 8 The RΔϕ(pT) observable as a function of pT, compared with fixed-order theoretical calculations at NLO accuracy using the ABMP16 (upper left), CT18 (upper right), MSHT20 (lower left), and NNPDF3.1 (lower right) NLO PDF sets. The experimental data are indicated with blue dots (with error bars representing the total experimental uncertainty), the theoretical prediction for the default αS(mZ) for each PDF set with black solid lines, the scale uncertainties with red bands, and the PDF uncertainties with green bands. The lower panel of each plot shows the ratio between experimental data and theoretical predictions

Theoretical calculations are performed separately for the cross sections corresponding to the jet counts in the numerator and denominator of the RΔϕ(pT) ratio defined in Eq. (1). The predictions using NNPDF3.1 for the numerator (left) and denominator (right) differential cross sections (dσ/dpT) at LO and NLO accuracy are shown in Fig. 5, along with the scale uncertainties (coloured bands). The lower panels in this figure display the ratios to the respective LO predictions, where the so-called NLO pQCD K factors (NLO/LO) are about 1.30–1.55 for the numerator and 1.20–1.35 for the denominator (1.08–1.15 for their ratio). The LO and NLO scale uncertainty bands overlap over the whole phase space. The NLO scale uncertainties are in the range 9–17% for the numerator and 5–10% for the denominator.

To compare fixed-order predictions at parton level with unfolded data, the former must be corrected for NP effects due to MPI and hadronization (HAD). Based on PS generators, the NP correction factors are evaluated from the ratio of the nominal over the generated cross sections when MPI and HAD effects are switched off:5 CNP=σPS+MPI+HADσPS.

The model dependence of CNP is investigated using different MC event generators, namely pythia8 with tunes CUETP8M1 and CUETP8M2, herwig++ with tune UE-EE-5-CTEQ6L1, and powheg interfaced with each one of them. A simple polynomial function a+bpTc (where a, b, and c are free parameters) is used to parameterize the dependence of CNP on jet pT for each MC event generator, to avoid statistical fluctuations in less populated regions of phase space. An envelope is constructed from the different MC predictions, where the central values are identified as the NP correction factors CNP and the edges define the corresponding uncertainties. Figure 6 shows the NP correction factors obtained for the numerator (upper left) and denominator (upper right) of the RΔϕ(pT) observable. The lower panels show the final NP correction factors CNP (blue line) for RΔϕ(pT). The red band is constructed from the envelope of individual ratios and represents the relevant uncertainties, which are less than 1%.Fig. 9 Sensitivity of the RΔϕ(pT) ratio to the strong coupling constant αS(mZ). The data are indicated with blue dots with error bars representing the total experimental uncertainty. In each plot, the lines represent fixed-order NLO theoretical calculations obtained with ABMP16 (upper left), CT18 (upper right), MSHT20 (lower left) and NNPDF3.1 (lower right) NLO PDF sets. Solid green (red) lines indicate maximum (minimum) values, and dotted black lines intermediate values of αS(mZ) for each PDF set

To further improve the accuracy, in particular at large jet pT, the theoretical predictions are complemented with electroweak (EW) corrections. The complete set of NLO corrections for three-jet production at the LHC is presented in Ref. [82]. To obtain the EW corrections for the RΔϕ(pT) observable, the sherpa event generator [83] is used, interfaced with recola [84, 85]. Further details on the implementation of the above interface as well as on the method used for the subtraction of NLO EW infrared divergences are reported in Refs. [86, 87], respectively. The pure NLO EW corrections for n-jet production are defined as:6 σnjNLO EW=σnjLO+σnjΔNLO1,

where σnjLO is the pure LO pQCD cross section and ΔNLO1 accounts for the virtual and real EW corrections. The additive and multiplicative combination of the above corrections to the cross sections are defined, respectively, as:7 σnjNLO QCD+EW=σnjLO+σnjΔNLO0+σnjΔNLO1,

8 σnjNLO QCD×EW=σnjLO1+σnjΔNLO0σnjLO1+σnjΔNLO1σnjLO,

where ΔNLO0 accounts for the virtual and real QCD corrections. Figure 7 shows the EW corrections obtained for the numerator and denominator cross sections, and for the RΔϕ(pT) ratio. The multiplicative combination, Eq. (8), is considered as the main result, whereas the additive combination, Eq. (7) is used as an uncertainty estimate. The relative change of the central αS(mZ) result (Sect. 6), when the additive combination is used as the main result, is smaller than 0.2%. The EW corrections for RΔϕ(pT) observable range from 0.2 to 5.0% and their relevant uncertainties from 0.01 to 0.53%.

Comparisons between the measurement and the theoretical predictions for the four different PDF sets are shown in Fig. 8. The PDF uncertainties in the RΔϕ(pT) predictions are evaluated at 68% confidence level for each PDF set following either the Hessian [88] or the MC [89] methods, and are about 1–2% in all cases. The scale uncertainties in RΔϕ(pT) predictions are dominant, ranging from 2 to 8%. In general, all predictions (based on the default αS(mZ) for each PDF set) are in agreement with the measurement within the experimental and theoretical uncertainties.

Determination of αS(mZ)

The sensitivity of the RΔϕ(pT) ratio to the strong coupling constant is investigated by varying αS(mZ) for each PDF set within the ranges presented in Table 3. The αS(mZ) value in the fixed-order matrix elements calculations is also adjusted accordingly. Figure 9 shows the results for each PDF set, where the solid green (red) curves represent the maximum (minimum) αS(mZ) values, and the dashed black curves correspond to intermediate αS(mZ) values in ΔαS(mZ)=±0.001 or ΔαS(mZ)=±0.002 steps. A large sensitivity of RΔϕ(pT) to variations of the strong coupling constant is observed for all PDF sets, and hence RΔϕ(pT) can be used for the determination of αS(mZ).Fig. 10 Minimization of the χ2 between experimental measurements and theoretical predictions for the RΔϕ(pT) ratio, with respect to αS(mZ) for the ABMP16, CT18, MSHT20, and NNPDF3.1 NLO PDF sets. In this plot, only experimental uncertainties are included in the covariance matrix. The minimum value of αS(mZ) found for each PDF set is indicated with a dashed line and corresponds to the central result. The experimental uncertainty is estimated from the αS(mZ) values for which the χ2 is increased by one unit with respect to the minimum value

Table 4 Results for αS(mZ), associated uncertainties, and goodness-of-fit per degree of freedom (χ2/ndof), obtained from the measured RΔϕ(pT) distribution compared with theoretical predictions using different NLO PDF sets

NLO PDF set	αS(mZ)	Exp.	NP	PDF	EW	Scale	χ2/ndof	
ABMP16	0.1197	0.0008	0.0007	0.0007	0.0002	-0.0042+0.0043	16/16	
CT18	0.1159	0.0013	0.0009	0.0014	0.0002	-0.0067+0.0099	19/16	
MSHT20	0.1166	0.0013	0.0008	0.0010	0.0003	-0.0063+0.0112	17/16	
NNPDF3.1	0.1177	0.0013	0.0011	0.0010	0.0003	-0.0068+0.0114	20/16	

Fig. 11 Determination of αS(mZ) from the RΔϕ(pT) ratio with the NNPDF3.1 PDF set (red), in comparison with previous NLO determinations of αS(mZ) from inclusive jet (magenta), dijet (green), and multijet (blue) measurements. The horizontal error bars indicate the total uncertainty (experimental and theoretical). The world-average αS(mZ) value is represented by the vertical dashed black line and its uncertainty by the yellow band

The value of αS(mZ) is determined by minimising the goodness-of-fit (χ2) between the experimental measurements and the theoretical predictions. The χ2 is defined as:9 χ2=∑ijN(Di-Ti)Cij-1(Dj-Tj),

where N is the number of measurements, Di are the experimental measurements, Ti are the theoretical predictions and Cij is the covariance matrix, which is composed of:10 C=Cstat+Cuncor+∑sourcesCJES+Cunfold+Cpref+CNP+CPDF+CEW,

where Cstat represents the statistical uncertainty, Cuncor is the numerical precision of the fixed-order predictions, which is assigned as uncorrelated uncertainty to each bin, CJES is the systematic uncertainty for each JES uncertainty source, Cunfold=CJER+CPU+CMCmodel is the systematic uncertainty induced through unfolding (representing the JER, pileup, and model uncertainties, respectively, described in Sect. 4.4), Cpref is the trigger prefiring uncertainty [45], and CNP, CPDF, and CEW are the NP, PDF, and EW uncertainties, respectively.

The JES, unfolding, prefiring, NP, PDF, and EW uncertainties are considered as 100% correlated among pT bins, and are treated as multiplicative. Including only the experimental (statistical, JES, unfolding, and prefiring) uncertainties in the covariance matrix composition, the central αS(mZ) result is obtained by minimising the χ2 with respect to αS(mZ). The associated experimental uncertainty is estimated from the αS(mZ) values, for which the χ2 is increased by one unit with respect to the minimum value. Figure 10 illustrates the χ2 minimization curves for each PDF set, which result in the αS(mZ) values and their respective experimental uncertainties listed in Table 4.

The propagation of NP, PDF, and EW uncertainties is estimated separately by repeating the χ2 minimization procedure after including the relevant terms in Eq. (10). For the evaluation of scale uncertainties, the χ2 comparison between measurement and theoretical predictions is repeated for the six different combinations of μR and μF scales described in Sect. 5. The up/down scale uncertainties correspond to the difference between the highest/lowest and the nominal αS(mZ) values, respectively. All resulting αS(mZ) values for the different PDF sets are fully compatible among each other, as well as with the world average [5]. The spread of these αS(mZ) values from the different PDF sets shown in Table 4, is used for the assignment of an additional uncertainty in the final αS(mZ) result due to the PDF choice. This uncertainty is evaluated from the maximum difference among the αS(mZ) values determined using the NNPDF3.1 NLO PDF set, and all the other αS(mZ) values determined using the other PDF sets shown in Table 4. The final result from the present analysis using the NNPDF3.1 NLO PDF set is: αS(mZ)=0.1177-0.0068+0.0114(scale)±0.0013(exp)±0.0011(NP)±0.0010(PDF)±0.0003(EW)±0.0020(PDF choice). This result, in comparison with a selection of αS(mZ) determinations at NLO accuracy obtained from inclusive jet [7, 13, 15, 20, 24, 90–92], dijet [25], and multijet [7, 9, 16, 17, 19, 23, 91, 93–95] measurements is presented in Fig. 11.Table 5 Values of αS(mZ) and αS(Q) determined in four different jet pT fitting subregions corresponding to an average scale ⟨Q⟩ over each pT interval

pT range (GeV)	αS(mZ)	⟨Q⟩ (GeV)	αS(Q)	
360–700	0.1177-0.0067+0.0104	433.0	0.0967-0.0044+0.0066	
700–1190	0.1162-0.0073+0.0108	819.0	0.0878-0.0042+0.0060	
1190–1870	0.1159-0.0077+0.0112	1346.0	0.0830-0.0040+0.0055	
1870–3170	0.1118-0.0070+0.0110	2081.0	0.0775-0.0034+0.0051	

Fig. 12 Running of the strong coupling αS(Q) (dashed line) evolved using the current world-average value αS(mZ)=0.1180±0.0009 [5] together with its associated total uncertainty (yellow band). The four new extractions from the present analysis (Table 5) are shown as filled red circles, compared with results from the H1 [91, 94, 95], ZEUS [96], D0 [7, 14], CMS [16, 19, 20, 24], and ATLAS [9, 23] experiments. The vertical error bars indicate the total uncertainty (experimental and theoretical). All the experimental results shown in this figure are based on fixed-order predictions at NLO accuracy in pQCD

For the investigation of the running of the strong coupling, the fitted region of pT=360–3170GeV (16 points) is split into four pT subregions: 360–700, 700–1190, 1190–1870, and 1870–3170GeV (4 points each). The fitting procedure is repeated and the αS(mZ) and all the relevant uncertainties are determined in each subregion separately. The αS(mZ) values from each subregion are evolved to αS(Q), where Q is chosen as the jet pT and is calculated as a cross-section-weighted average (⟨Q⟩) for each subregion. This study is performed using the NNPDF3.1 NLO PDF set. The values of αS(mZ) and the results for αS(Q) evaluated at the respective ⟨Q⟩ for each fitted subregion are shown in Table 5.

Figure 12 shows the energy dependence predicted by the RGE (dashed line) using the current world-average value αS(mZ)=0.1180±0.0009 [5] together with its associated total uncertainty (yellow band). The results from the αS(Q) determinations in the four subregions presented in Table 5 are also shown, along with αS values determined at lower scales by the H1 [91, 94, 95], ZEUS [96], D0 [7, 14], CMS [16, 19, 20, 24], and ATLAS [9, 23] Collaborations. All results reported in this study are consistent with the energy dependence predicted by the RGE, and no deviation is observed from the expected behaviour up to ∼2TeV.

Summary

A measurement of the RΔϕ(pT) ratio, sensitive to azimuthal correlations in multijet events, has been presented using proton-proton collision data collected by the CMS experiment at a centre-of-mass energy of 13TeV and corresponding to an integrated luminosity of 134fb-1. The experimental data are compared with predictions from Monte Carlo (MC) event generators, pythia8 with tunes CUETP8M1 and CUETP8M2, herwig++ with tune UE-EE-5-CTEQ6L1, and powheg interfaced with each one of them. Deviations between data and MC predictions are observed in all cases, except for pythia8 tune CUETP8M2, which gives a good overall description of the measurement.

The measurement is also compared with fixed-order perturbative quantum chromodynamics (pQCD) predictions at next-to-leading-order (NLO) accuracy using the NLOJet++ package within the fastNLO framework. Those predictions are extracted for four different NLO parton distribution function (PDF) sets, ABMP16, CT18, MSHT20, and NNPDF3.1. Corrections for nonperturbative (NP) effects are evaluated using all the aforementioned MC event generators, and are applied to the fixed-order predictions. The predictions are additionally corrected for electroweak (EW) effects that become important at large jet transverse momenta. Generally, the fixed-order predictions are in agreement with the experimental data in the phase space of this analysis, and they provide a good description of the measured RΔϕ(pT) distribution for all PDF sets.

Based on a comparison of the measured RΔϕ(pT) distribution and the theoretical predictions, the strong coupling at the scale of the Z boson mass is: αS(mZ)=0.1177-0.0068+0.0114(scale)±0.0013(exp)±0.0011(NP)±0.0010(PDF)±0.0003(EW)±0.0020(PDF choice)=0.1177-0.0074+0.0117, using calculations based on the NNPDF3.1 NLO PDF set. Alternative αS(mZ) results obtained with other PDF sets are compatible among each other, as well as with the central result of this work, and with the current world average, αS(mZ)=0.1180±0.0009. The spread of the αS(mZ) values obtained from different PDF sets is used for the assignment of the “PDF choice” uncertainty quoted in the final strong coupling constant derived here. The dominant uncertainty in this measurement originates from the scale dependence of the NLO pQCD predictions, and is expected to be significantly reduced with the future inclusion of fixed-order predictions at next-to-NLO accuracy.

The evolution of the strong coupling as a function of the energy scale, αS(Q), has been tested up to Q≈2TeV, a higher scale than that probed in previous H1, ZEUS, D0, CMS, and ATLAS measurements. This test has been performed by choosing as energy scale Q the average jet transverse momentum in the different intervals considered, and no deviation from the expected NLO pQCD running of the strong coupling is observed.

Acknowledgements

We thank Max Reyer, Marek Schönherr and Steffen Schumann for providing the electroweak corrections for the RΔϕ(pT) observable within the sherpa framework. We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centres and personnel of the Worldwide LHC Computing Grid and other centres for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC, the CMS detector, and the supporting computing infrastructure provided by the following funding agencies: SC (Armenia), BMBWF and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, FAPERGS, and FAPESP (Brazil); MES and BNSF (Bulgaria); CERN; CAS, MoST, and NSFC (China); MINCIENCIAS (Colombia); MSES and CSF (Croatia); RIF (Cyprus); SENESCYT (Ecuador); ERC PRG, RVTT3 and MoER TK202 (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); SRNSF (Georgia); BMBF, DFG, and HGF (Germany); GSRI (Greece); NKFIH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Republic of Korea); MES (Latvia); LMTLT (Lithuania); MOE and UM (Malaysia); BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MOS (Montenegro); MBIE (New Zealand); PAEC (Pakistan); MES and NSC (Poland); FCT (Portugal); MESTD (Serbia); MCIN/AEI and PCTI (Spain); MOSTR (Sri Lanka); Swiss Funding Agencies (Switzerland); MST (Taipei); MHESI and NSTDA (Thailand); TUBITAK and TENMAK (Turkey); NASU (Ukraine); STFC (United Kingdom); DOE and NSF (USA). Individuals have received support from the Marie-Curie programme and the European Research Council and Horizon 2020 Grant, contract Nos. 675440, 724704, 752730, 758316, 765710, 824093, 101115353,101002207, and COST Action CA16108 (European Union); the Leventis Foundation; the Alfred P. Sloan Foundation; the Alexander von Humboldt Foundation; the Science Committee, project no. 22rl-037 (Armenia); the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the F.R.S.-FNRS and FWO (Belgium) under the “Excellence of Science – EOS” – be.h project n. 30820817; the Beijing Municipal Science & Technology Commission, No. Z191100007219010 and Fundamental Research Funds for the Central Universities (China); the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Shota Rustaveli National Science Foundation, grant FR-22-985 (Georgia); the Deutsche Forschungsgemeinschaft (DFG), under Germany’s Excellence Strategy – EXC 2121 “Quantum Universe” – 390833306, and under project number 400140256 - GRK2497; the Hellenic Foundation for Research and Innovation (HFRI), Project Number 2288 (Greece); the Hungarian Academy of Sciences, the New National Excellence Program - ÚNKP, the NKFIH research grants K 131991, K 133046, K 138136, K 143460, K 143477, K 146913, K 146914, K 147048, 2020-2.2.1-ED-2021-00181, and TKP2021-NKTA-64 (Hungary); the Council of Science and Industrial Research, India; ICSC – National Research Centre for High Performance Computing, Big Data and Quantum Computing and FAIR – Future Artificial Intelligence Research, funded by the EU NexGeneration program (Italy); the Latvian Council of Science; the Ministry of Education and Science, project no. 2022/WK/14, and the National Science Center, contracts Opus 2021/41/B/ST2/01369 and 2021/43/B/ST2/01552 (Poland); the Fundação para a Ciência e a Tecnologia, grant CEECIND/01334/2018 (Portugal); the National Priorities Research Program by Qatar National Research Fund; MCIN/AEI/10.13039/501100011033, ERDF “a way of making Europe”, and the Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia María de Maeztu, grant MDM-2017-0765 and Programa Severo Ochoa del Principado de Asturias (Spain); the Chulalongkorn Academic into Its 2nd Century Project Advancement Project, and the National Science, Research and Innovation Fund via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation, grant B37G660013 (Thailand); the Kavli Foundation; the Nvidia Corporation; the SuperMicro Corporation; the Welch Foundation, contract C-1845; and the Weston Havens Foundation (USA).

Data Availability Statement

Data cannot be made available for reasons disclosed in the data availability statement. [Authors’ comment: Release and preservation of data used by the CMS Collaboration as the basis for publications https://cms-docdb.cern.ch/cgi-bin/PublicDocDB/RetrieveFile?docid=6032&filename=CMSDataPolicyV1.2.pdf &version=2 CMS data preservation, re-use and open access policy.]

Code Availability Statement

This manuscript has associated code/software in a data repository. [Authors’comment: The CMS core software is publicly available on GitHub (https://github.com/cms-sw/cmssw).]

Declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Deceased: M. Narain, S. Wimpenny, A. Vorobyev.
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