Eur. Phys. J. C (2025) 85: 72
https://doi.org/10.1140/epjc/s10052-024-13606-8

Regular Article - Experimental Physics

Measurement of multidifferential cross sections for dijet production in proton–proton collisions at $\sqrt{s}=13\mathrm{Te}\mathrm{V}$

¹ Yerevan Physics Institute, Yerevan, Armenia
² Institut für Hochenergiephysik, Vienna, Austria
³ Universiteit Antwerpen, Antwerpen, Belgium
⁴ Vrije Universiteit Brussel, Brussel, Belgium
⁵ Université Libre de Bruxelles, Bruxelles, Belgium
⁶ Ghent University, Ghent, Belgium
⁷ Université Catholique de Louvain, Louvain-la-Neuve, Belgium
⁸ Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil
⁹ Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
¹⁰ Universidade Estadual Paulista, Universidade Federal do ABC, São Paulo, Brazil
¹¹ Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria
¹² University of Sofia, Sofia, Bulgaria
¹³ Instituto De Alta Investigación, Universidad de Tarapacá, Casilla 7 D, Arica, Chile
¹⁴ Beihang University, Beijing, China
¹⁵ Department of Physics, Tsinghua University, Beijing, China
¹⁶ Institute of High Energy Physics, Beijing, China
¹⁷ State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China
¹⁸ Sun Yat-Sen University, Guangzhou, China
¹⁹ University of Science and Technology of China, Hefei, China
²⁰ Institute of Modern Physics and Key Laboratory of Nuclear Physics and Ion-beam Application (MOE)-Fudan University, Shanghai, China
²¹ Zhejiang University, Hangzhou, Zhejiang, China
²² Universidad de Los Andes, Bogota, Colombia
²³ Universidad de Antioquia, Medellin, Colombia
²⁴ Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia
²⁵ Faculty of Science, University of Split, Split, Croatia
²⁶ Institute Rudjer Boskovic, Zagreb, Croatia
²⁷ University of Cyprus, Nicosia, Cyprus
²⁸ Charles University, Prague, Czech Republic
²⁹ Escuela Politecnica Nacional, Quito, Ecuador
³⁰ Universidad San Francisco de Quito, Quito, Ecuador
³¹ Academy of Scientific Research and Technology of the Arab Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt
³² Center for High Energy Physics (CHEP-FU), Fayoum University, El-Fayoum, Egypt
³³ National Institute of Chemical Physics and Biophysics, Tallinn, Estonia
³⁴ Department of Physics, University of Helsinki, Helsinki, Finland
³⁵ Helsinki Institute of Physics, Helsinki, Finland
³⁶ Lappeenranta-Lahti University of Technology, Lappeenranta, Finland
³⁷ IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
³⁸ Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
³⁹ Université de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France
⁴⁰ Institut de Physique des 2 Infinis de Lyon (IP2I ), Villeurbanne, France
⁴¹ Georgian Technical University, Tbilisi, Georgia
⁴² I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
⁴³ III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany
⁴⁴ III. Physikalisches Institut B, RWTH Aachen University, Aachen, Germany
⁴⁵ Deutsches Elektronen-Synchrotron, Hamburg, Germany
⁴⁶ University of Hamburg, Hamburg, Germany
⁴⁷ Karlsruher Institut fuer Technologie, Karlsruhe, Germany
⁴⁸ Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi, Greece
⁴⁹ National and Kapodistrian University of Athens, Athens, Greece
⁵⁰ National Technical University of Athens, Athens, Greece
⁵¹ University of Ioánnina, Ioánnina, Greece
⁵² HUN-REN Wigner Research Centre for Physics, Budapest, Hungary
⁵³ MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary
⁵⁴ Institute of Nuclear Research ATOMKI, Debrecen, Hungary
⁵⁵ Institute of Physics, University of Debrecen, Debrecen, Hungary
⁵⁶ Karoly Robert Campus, MATE Institute of Technology, Gyongyos, Hungary
⁵⁷ Panjab University, Chandigarh, India
⁵⁸ University of Delhi, Delhi, India
⁵⁹ Saha Institute of Nuclear Physics, HBNI, Kolkata, India
⁶⁰ Indian Institute of Technology Madras, Madras, India
⁶¹ Tata Institute of Fundamental Research-A, Mumbai, India
⁶² Tata Institute of Fundamental Research-B, Mumbai, India
⁶³ National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute, Bhubaneswar, Odisha, India
⁶⁴ Indian Institute of Science Education and Research (IISER), Pune, India
⁶⁵ Isfahan University of Technology, Isfahan, Iran
⁶⁶ Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
⁶⁷ University College Dublin, Dublin, Ireland
⁶⁸ INFN Sezione di Bari, Università di Bari, Politecnico di Bari, Bari, Italy
⁶⁹ INFN Sezione di Bologna, Università di Bologna, Bologna, Italy
⁷⁰ INFN Sezione di Catania, Università di Catania, Catania, Italy
⁷¹ INFN Sezione di Firenze, Università di Firenze, Firenze, Italy
⁷² INFN Laboratori Nazionali di Frascati, Frascati, Italy
⁷³ INFN Sezione di Genova, Università di Genova, Genoa, Italy
⁷⁴ INFN Sezione di Milano-Bicocca, Università di Milano-Bicocca, Milan, Italy
⁷⁵ INFN Sezione di Napoli, Università di Napoli ‘Federico II’, Napoli, Italy; Università della Basilicata, Potenza, Italy; Scuola Superiore Meridionale (SSM), Naples, Italy
⁷⁶ INFN Sezione di Padova, Università di Padova, Padova, Italy; Università di Trento, Trento, Italy
⁷⁷ INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
⁷⁸ INFN Sezione di Perugia, Università di Perugia, Perugia, Italy
⁷⁹ INFN Sezione di Pisa, Università di Pisa, Scuola Normale Superiore di Pisa, Pisa, Italy; Università di Siena, Siena, Italy
⁸⁰ INFN Sezione di Roma, Sapienza Università di Roma, Rome, Italy
⁸¹ INFN Sezione di Torino, Università di Torino, Torino, Italy; Università del Piemonte Orientale, Novara, Italy
⁸² INFN Sezione di Trieste, Università di Trieste, Trieste, Italy
⁸³ Kyungpook National University, Daegu, Korea
⁸⁴ Chonnam National University, Institute for Universe and Elementary Particles, Kwangju, Korea
⁸⁵ Hanyang University, Seoul, Korea
⁸⁶ Korea University, Seoul, Korea
⁸⁷ Kyung Hee University, Department of Physics, Seoul, Korea
⁸⁸ Sejong University, Seoul, Korea
⁸⁹ Seoul National University, Seoul, Korea
⁹⁰ University of Seoul, Seoul, Korea
⁹¹ Department of Physics, Yonsei University, Seoul, Korea
⁹² Sungkyunkwan University, Suwon, Korea
⁹³ College of Engineering and Technology, American University of the Middle East (AUM), Dasman, Kuwait
⁹⁴ Riga Technical University, Riga, Latvia
⁹⁵ University of Latvia (LU), Riga, Latvia
⁹⁶ Vilnius University, Vilnius, Lithuania
⁹⁷ National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia
⁹⁸ Universidad de Sonora (UNISON), Hermosillo, Mexico
⁹⁹ Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico
¹⁰⁰ Universidad Iberoamericana, Mexico City, Mexico
¹⁰¹ Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
¹⁰² University of Montenegro, Podgorica, Montenegro
¹⁰³ University of Canterbury, Christchurch, New Zealand
¹⁰⁴ National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan
¹⁰⁵ AGH University of Krakow, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland
¹⁰⁶ National Centre for Nuclear Research, Swierk, Poland
¹⁰⁷ Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland
¹⁰⁸ Warsaw University of Technology, Warsaw, Poland
¹⁰⁹ Laboratório de Instrumentação e Física Experimental de Partículas, Lisbon, Portugal
¹¹⁰ Faculty of Physics, University of Belgrade, Belgrade, Serbia
¹¹¹ VINCA Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia
¹¹² Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain
¹¹³ Universidad Autónoma de Madrid, Madrid, Spain
¹¹⁴ Universidad de Oviedo, Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA), Oviedo, Spain
¹¹⁵ Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain
¹¹⁶ University of Colombo, Colombo, Sri Lanka
¹¹⁷ Department of Physics, University of Ruhuna, Matara, Sri Lanka
¹¹⁸ CERN, European Organization for Nuclear Research, Geneva, Switzerland
¹¹⁹ Paul Scherrer Institut, Villigen, Switzerland
¹²⁰ ETH Zurich-Institute for Particle Physics and Astrophysics (IPA), Zurich, Switzerland
¹²¹ Universität Zürich, Zurich, Switzerland
¹²² National Central University, Chung-Li, Taiwan
¹²³ National Taiwan University (NTU), Taipei, Taiwan
¹²⁴ High Energy Physics Research Unit, Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand
¹²⁵ Physics Department, Science and Art Faculty, Çukurova University, Adana, Turkey
¹²⁶ Physics Department, Middle East Technical University, Ankara, Turkey
¹²⁷ Bogazici University, Istanbul, Turkey
¹²⁸ Istanbul Technical University, Istanbul, Turkey
¹²⁹ Istanbul University, Istanbul, Turkey
¹³⁰ Institute for Scintillation Materials of National Academy of Science of Ukraine, Kharkiv, Ukraine
¹³¹ National Science Centre, Kharkiv Institute of Physics and Technology, Kharkiv, Ukraine
¹³² University of Bristol, Bristol, UK
¹³³ Rutherford Appleton Laboratory, Didcot, UK
¹³⁴ Imperial College, London, UK
¹³⁵ Brunel University, Uxbridge, UK
¹³⁶ Baylor University, Waco, TX, USA
¹³⁷ Catholic University of America, Washington, DC, USA
¹³⁸ The University of Alabama, Tuscaloosa, AL, USA
¹³⁹ Boston University, Boston, MA, USA
¹⁴⁰ Brown University, Providence, RI, USA
¹⁴¹ University of California, Davis, Davis, CA, USA
¹⁴² University of California, Los Angeles, CA, USA
¹⁴³ University of California, Riverside, Riverside, CA, USA
¹⁴⁴ University of California, San Diego, La Jolla, CA, USA
¹⁴⁵ Department of Physics, University of California, Santa Barbara, Santa Barbara, CA, USA
¹⁴⁶ California Institute of Technology, Pasadena, CA, USA
¹⁴⁷ Carnegie Mellon University, Pittsburgh, PA, USA
¹⁴⁸ University of Colorado Boulder, Boulder, CO, USA
¹⁴⁹ Cornell University, Ithaca, NY, USA
¹⁵⁰ Fermi National Accelerator Laboratory, Batavia, IL, USA
¹⁵¹ University of Florida, Gainesville, FL, USA
¹⁵² Florida State University, Tallahassee, FL, USA
¹⁵³ Florida Institute of Technology, Melbourne, FL, USA
¹⁵⁴ University of Illinois Chicago, Chicago, USA
¹⁵⁵ The University of Iowa, Iowa City, IA, USA
¹⁵⁶ Johns Hopkins University, Baltimore, MD, USA
¹⁵⁷ The University of Kansas, Lawrence, KS, USA
¹⁵⁸ Kansas State University, Manhattan, KS, USA
¹⁵⁹ Lawrence Livermore National Laboratory, Livermore, CA, USA
¹⁶⁰ University of Maryland, College Park, MD, USA
¹⁶¹ Massachusetts Institute of Technology, Cambridge, MA, USA
¹⁶² University of Minnesota, Minneapolis, MN, USA
¹⁶³ University of Mississippi, Oxford, MS, USA
¹⁶⁴ University of Nebraska-Lincoln, Lincoln, NE, USA
¹⁶⁵ State University of New York at Buffalo, Buffalo, NY, USA
¹⁶⁶ Northeastern University, Boston, MA, USA
¹⁶⁷ Northwestern University, Evanston, IL, USA
¹⁶⁸ University of Notre Dame, Notre Dame, IN, USA
¹⁶⁹ The Ohio State University, Columbus, OH, USA
¹⁷⁰ Princeton University, Princeton, NJ, USA
¹⁷¹ University of Puerto Rico, Mayaguez, PR, USA
¹⁷² Purdue University, West Lafayette, IN, USA
¹⁷³ Purdue University Northwest, Hammond, IN, USA
¹⁷⁴ Rice University, Houston, TX, USA
¹⁷⁵ University of Rochester, Rochester, NY, USA
¹⁷⁶ The Rockefeller University, New York, NY, USA
¹⁷⁷ Rutgers, The State University of New Jersey, Piscataway, NJ, USA
¹⁷⁸ University of Tennessee, Knoxville, TN, USA
¹⁷⁹ Texas A&M University, College Station, TX, USA
¹⁸⁰ Texas Tech University, Lubbock, TX, USA
¹⁸¹ Vanderbilt University, Nashville, TN, USA
¹⁸² University of Virginia, Charlottesville, VA, USA
¹⁸³ Wayne State University, Detroit, MI, USA
¹⁸⁴ University of Wisconsin-Madison, Madison, WI, USA
¹⁸⁵ Authors affiliated with an institute or an international laboratory covered by a cooperation agreement with CERN, Geneva, Switzerland
¹⁸⁶ Yerevan State University, Yerevan, Armenia
¹⁸⁷ TU Wien, Vienna, Austria
¹⁸⁸ Institute of Basic and Applied Sciences, Faculty of Engineering, Arab Academy for Science, Technology and Maritime Transport, Alexandria, Egypt
¹⁸⁹ Université Libre de Bruxelles, Bruxelles, Belgium
¹⁹⁰ Universidade Estadual de Campinas, Campinas, Brazil
¹⁹¹ Federal University of Rio Grande do Sul, Porto Alegre, Brazil
¹⁹² UFMS, Nova Andradina, Brazil
¹⁹³ University of Chinese Academy of Sciences, Beijing, China
¹⁹⁴ Nanjing Normal University, Nanjing, China
¹⁹⁵ Now at The University of Iowa, Iowa City, IA, USA
¹⁹⁶ an institute or an international laboratory covered by a cooperation agreement with CERN, Geneva, Switzerland
¹⁹⁷ Helwan University, Cairo, Egypt
¹⁹⁸ Now at Zewail City of Science and Technology, Zewail, Egypt
¹⁹⁹ British University in Egypt, Cairo, Egypt
²⁰⁰ Now at Ain Shams University, Cairo, Egypt
²⁰¹ Purdue University, West Lafayette, Indiana, USA
²⁰² Université de Haute Alsace, Mulhouse, France
²⁰³ Department of Physics, Tsinghua University, Beijing, China
²⁰⁴ The University of the State of Amazonas, Manaus, Brazil
²⁰⁵ Erzincan Binali Yildirim University, Erzincan, Turkey
²⁰⁶ University of Hamburg, Hamburg, Germany
²⁰⁷ III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany
²⁰⁸ Isfahan University of Technology, Isfahan, Iran
²⁰⁹ Bergische University Wuppertal (BUW), Wuppertal, Germany
²¹⁰ Brandenburg University of Technology, Cottbus, Germany
²¹¹ Forschungszentrum Jülich, Juelich, Germany
²¹² CERN, European Organization for Nuclear Research, Geneva, Switzerland
²¹³ Institute of Physics, University of Debrecen, Debrecen, Hungary
²¹⁴ Institute of Nuclear Research ATOMKI, Debrecen, Hungary
²¹⁵ Now at Universitatea Babes-Bolyai-Facultatea de Fizica, Cluj-Napoca, Romania
²¹⁶ Physics Department, Faculty of Science, Assiut University, Assiut, Egypt
²¹⁷ HUN-REN Wigner Research Centre for Physics, Budapest, Hungary
²¹⁸ Faculty of Informatics, University of Debrecen, Debrecen, Hungary
²¹⁹ Punjab Agricultural University, Ludhiana, India
²²⁰ UPES-University of Petroleum and Energy Studies, Dehradun, India
²²¹ University of Visva-Bharati, Santiniketan, India
²²² University of Hyderabad, Hyderabad, India
²²³ Indian Institute of Science (IISc), Bangalore, India
²²⁴ IIT Bhubaneswar, Bhubaneswar, India
²²⁵ Institute of Physics, Bhubaneswar, India
²²⁶ Deutsches Elektronen-Synchrotron, Hamburg, Germany
²²⁷ Now at Department of Physics, Isfahan University of Technology, Isfahan, Iran
²²⁸ Sharif University of Technology, Tehran, Iran
²²⁹ Department of Physics, University of Science and Technology of Mazandaran, Behshahr, Iran
²³⁰ Italian National Agency for New Technologies, Energy and Sustainable Economic Development, Bologna, Italy
²³¹ Centro Siciliano di Fisica Nucleare e di Struttura Della Materia, Catania, Italy
²³² Università degli Studi Guglielmo Marconi, Rome, Italy
²³³ Scuola Superiore Meridionale, Università di Napoli ’Federico II’, Naples, Italy
²³⁴ Fermi National Accelerator Laboratory, Batavia, IL, USA
²³⁵ Laboratori Nazionali di Legnaro dell’INFN, Legnaro, Italy
²³⁶ Università di Napoli ’Federico II’, Naples, Italy
²³⁷ Consiglio Nazionale delle Ricerche - Istituto Officina dei Materiali, Perugia, Italy
²³⁸ IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
²³⁹ Riga Technical University, Riga, Latvia
²⁴⁰ Department of Applied Physics, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Malaysia
²⁴¹ Consejo Nacional de Ciencia y Tecnología, Mexico City, Mexico
²⁴² Trincomalee Campus, Eastern University, Nilaveli, Sri Lanka
²⁴³ INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
²⁴⁴ National and Kapodistrian University of Athens, Athens, Greece
²⁴⁵ Ecole Polytechnique Fédérale Lausanne, Lausanne, Switzerland
²⁴⁶ Universität Zürich, Zurich, Switzerland
²⁴⁷ Stefan Meyer Institute for Subatomic Physics, Vienna, Austria
²⁴⁸ Laboratoire d’Annecy-le-Vieux de Physique des Particules, IN2P3-CNRS, Annecy-le-Vieux, France
²⁴⁹ Near East University, Research Center of Experimental Health Science, Mersin, Turkey
²⁵⁰ Konya Technical University, Konya, Turkey
²⁵¹ Izmir Bakircay University, Izmir, Turkey
²⁵² Adiyaman University, Adiyaman, Turkey
²⁵³ Necmettin Erbakan University, Konya, Turkey
²⁵⁴ Bozok Universitetesi Rektörlügü, Yozgat, Turkey
²⁵⁵ Marmara University, Istanbul, Turkey
²⁵⁶ Milli Savunma University, Istanbul, Turkey
²⁵⁷ Kafkas University, Kars, Turkey
²⁵⁸ Hacettepe University, Ankara, Turkey
²⁵⁹ Faculty of Engineering, Istanbul University-Cerrahpasa, Istanbul, Turkey
²⁶⁰ Ozyegin University, Istanbul, Turkey
²⁶¹ Vrije Universiteit Brussel, Brussel, Belgium
²⁶² School of Physics and Astronomy, University of Southampton, Southampton, UK
²⁶³ University of Bristol, Bristol, UK
²⁶⁴ IPPP Durham University, Durham, UK
²⁶⁵ Monash University, Faculty of Science, Clayton, Australia
²⁶⁶ Università di Torino, Turin, Italy
²⁶⁷ Bethel University, St. Paul, MN, USA
²⁶⁸ Karamanoğlu Mehmetbey University, Karaman, Turkey
²⁶⁹ California Institute of Technology, Pasadena, CA, USA
²⁷⁰ United States Naval Academy, Annapolis, MD, USA
²⁷¹ Bingol University, Bingol, Turkey
²⁷² Georgian Technical University, Tbilisi, Georgia
²⁷³ Sinop University, Sinop, Turkey
²⁷⁴ Erciyes University, Kayseri, Turkey
²⁷⁵ Horia Hulubei National Institute of Physics and Nuclear Engineering (IFIN-HH), Bucharest, Romania
²⁷⁶ Texas A&M University at Qatar, Doha, Qatar
²⁷⁷ Kyungpook National University, Daegu, Korea
²⁷⁸ another institute or international laboratory covered by a cooperation agreement with CERN, Geneva, Switzerland
²⁷⁹ Universiteit Antwerpen, Antwerpen, Belgium
²⁸⁰ Yerevan Physics Institute, Yerevan, Armenia
²⁸¹ Northeastern University, Boston, MA, USA
²⁸² Now at another institute or international laboratory covered by a cooperation agreement with CERN, Geneva, Switzerland
²⁸³ Imperial College, London, UK
²⁸⁴ Institute of Nuclear Physics of the Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
²⁸⁵ CERN, 1211 Geneva 23, Switzerland

^a cms-publication-committee-chair@cern.ch

Received: 27 December 2023
Accepted: 12 November 2024
Published online: 24 January 2025

Abstract

A measurement of the dijet production cross section is reported based on proton–proton collision data collected in 2016 at $\sqrt{s}=13\mathrm{Te}\mathrm{V}$ by the CMS experiment at the CERN LHC, corresponding to an integrated luminosity of up to 36.3${\mathrm{fb}}^{-1}$. Jets are reconstructed with the anti-$k_{\text{T}}$ algorithm for distance parameters of $R=0.4$ and 0.8. Cross sections are measured double-differentially (2D) as a function of the largest absolute rapidity ${|y|}_{\max }$ of the two jets with the highest transverse momenta $p_{\text{T}}$ and their invariant mass $m_{1,2}$, and triple-differentially (3D) as a function of the rapidity separation $y^{\ast }$, the total boost $y_{\mathrm{b}}$, and either $m_{1,2}$ or the average $p_{\text{T}}$ of the two jets. The cross sections are unfolded to correct for detector effects and are compared with fixed-order calculations derived at next-to-next-to-leading order in perturbative quantum chromodynamics. The impact of the measurements on the parton distribution functions and the strong coupling constant at the mass of the $\mathrm{Z}$ boson is investigated, yielding a value of ${\alpha }_{\text{S}}(m_{\mathrm{Z}})=0.1179\pm 0.0019$.