Eur. Phys. J. C (2025) 85: 729
https://doi.org/10.1140/epjc/s10052-025-14178-x

Regular Article - Experimental Physics

Measurement of $W^{\pm }$-boson differential cross-sections in proton–proton collisions with low pile-up data at $\sqrt{s}=5.02$ TeV and $13\text{TeV}$ with the ATLAS detector

¹ Department of Physics, University of Adelaide, Adelaide, Australia
² Department of Physics, University of Alberta, Edmonton, AB, Canada
³ Department of Physics, Ankara University, Ankara, Türkiye
⁴ Division of Physics, TOBB University of Economics and Technology, Ankara, Türkiye
⁵ LAPP, Université Savoie Mont Blanc, CNRS/IN2P3, Annecy, France
⁶ APC, Université Paris Cité, CNRS/IN2P3, Paris, France
⁷ High Energy Physics Division, Argonne National Laboratory, Argonne, IL, USA
⁸ Department of Physics, University of Arizona, Tucson, AZ, USA
⁹ Department of Physics, University of Texas at Arlington, Arlington, TX, USA
¹⁰ Physics Department, National and Kapodistrian University of Athens, Athens, Greece
¹¹ Physics Department, National Technical University of Athens, Zografou, Greece
¹² Department of Physics, University of Texas at Austin, Austin, TX, USA
¹³ Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan
¹⁴ Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona, Spain
¹⁵ Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China
¹⁶ Physics Department, Tsinghua University, Beijing, China
¹⁷ Institute of Physics, University of Belgrade, Belgrade, Serbia
¹⁸ Department for Physics and Technology, University of Bergen, Bergen, Norway
¹⁹ Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
²⁰ University of California, Berkeley, CA, USA
²¹ Institut für Physik, Humboldt Universität zu Berlin, Berlin, Germany
²² Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern, Switzerland
²³ School of Physics and Astronomy, University of Birmingham, Birmingham, UK
²⁴ Department of Physics, Bogazici University, Istanbul, Türkiye
²⁵ Department of Physics Engineering, Gaziantep University, Gaziantep, Türkiye
²⁶ Department of Physics, Istanbul University, Istanbul, Türkiye
²⁷ Facultad de Ciencias y Centro de Investigaciónes, Universidad Antonio Nariño, Bogotá, Colombia
²⁸ Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia
²⁹ Dipartimento di Fisica e Astronomia A. Righi, Università di Bologna, Bologna, Italy
³⁰ INFN Sezione di Bologna, Bologna, Italy
³¹ Physikalisches Institut, Universität Bonn, Bonn, Germany
³² Department of Physics, Boston University, Boston, MA, USA
³³ Department of Physics, Brandeis University, Waltham, MA, USA
³⁴ Transilvania University of Brasov, Brasov, Romania
³⁵ Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania
³⁶ Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi, Romania
³⁷ National Institute for Research and Development of Isotopic and Molecular Technologies, Physics Department, Cluj-Napoca, Romania
³⁸ National University of Science and Technology Politechnica, Bucharest, Romania
³⁹ West University in Timisoara, Timisoara, Romania
⁴⁰ Faculty of Physics, University of Bucharest, Bucharest, Romania
⁴¹ Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovak Republic
⁴² Department of Subnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice, Slovak Republic
⁴³ Physics Department, Brookhaven National Laboratory, Upton, NY, USA
⁴⁴ Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, y CONICET, Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
⁴⁵ California State University, CA, United States of America
⁴⁶ Cavendish Laboratory, University of Cambridge, Cambridge, UK
⁴⁷ Department of Physics, University of Cape Town, Cape Town, South Africa
⁴⁸ iThemba Labs, Western Cape, South Africa
⁴⁹ Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg, South Africa
⁵⁰ National Institute of Physics, University of the Philippines Diliman (Philippines), Quezon City, Philippines
⁵¹ University of South Africa, Department of Physics, Pretoria, South Africa
⁵² University of Zululand, KwaDlangezwa, Ongoye, South Africa
⁵³ School of Physics, University of the Witwatersrand, Johannesburg, South Africa
⁵⁴ Department of Physics, Carleton University, Ottawa, ON, Canada
⁵⁵ Faculté des Sciences Ain Chock, Université Hassan II de Casablanca, Casablanca, Morocco
⁵⁶ Faculté des Sciences, Université Ibn-Tofail, Kénitra, Morocco
⁵⁷ Faculté des Sciences Semlalia, LPHEA-Marrakech, Université Cadi Ayyad, Marrakech, Morocco
⁵⁸ LPMR, Faculté des Sciences, Université Mohamed Premier, Oujda, Morocco
⁵⁹ Faculté des sciences, Université Mohammed V, Rabat, Morocco
⁶⁰ Institute of Applied Physics, Mohammed VI Polytechnic University, Ben Guerir, Morocco
⁶¹ CERN, Geneva, Switzerland
⁶² Affiliated with an Institute Formerly Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
⁶³ Affiliated with an International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
⁶⁴ Enrico Fermi Institute, University of Chicago, Chicago, IL, USA
⁶⁵ LPC, CNRS/IN2P3, Université Clermont Auvergne, Clermont-Ferrand, France
⁶⁶ Nevis Laboratory, Columbia University, Irvington, NY, USA
⁶⁷ Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
⁶⁸ Dipartimento di Fisica, Università della Calabria, Rende, Italy
⁶⁹ Laboratori Nazionali di Frascati, INFN Gruppo Collegato di Cosenza, Cosenza, Italy
⁷⁰ Physics Department, Southern Methodist University, Dallas, TX, USA
⁷¹ National Centre for Scientific Research “Demokritos”, Agia Paraskevi, Greece
⁷² Department of Physics, Stockholm University, Stockholm, Sweden
⁷³ Oskar Klein Centre, Stockholm, Sweden
⁷⁴ Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen, Germany
⁷⁵ Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
⁷⁶ Institut für Kern- und Teilchenphysik, Technische Universität Dresden, Dresden, Germany
⁷⁷ Department of Physics, Duke University, Durham, NC, USA
⁷⁸ SUPA-School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK
⁷⁹ INFN e Laboratori Nazionali di Frascati, Frascati, Italy
⁸⁰ Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany
⁸¹ II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany
⁸² Département de Physique Nucléaire et Corpusculaire, Université de Genève, Geneva, Switzerland
⁸³ Dipartimento di Fisica, Università di Genova, Genoa, Italy
⁸⁴ INFN Sezione di Genova, Genoa, Italy
⁸⁵ II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany
⁸⁶ SUPA-School of Physics and Astronomy, University of Glasgow, Glasgow, UK
⁸⁷ LPSC, CNRS/IN2P3, Grenoble INP, Université Grenoble Alpes, Grenoble, France
⁸⁸ Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA, USA
⁸⁹ Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei, China
⁹⁰ Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
⁹¹ Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
⁹² Department of Physics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong
⁹³ Department of Physics, University of Hong Kong, Hong Kong, China
⁹⁴ Department of Physics and Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
⁹⁵ Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
⁹⁶ IJCLab, CNRS/IN2P3, Université Paris-Saclay, 91405, Orsay, France
⁹⁷ Centro Nacional de Microelectrónica (IMB-CNM-CSIC), Barcelona, Spain
⁹⁸ Department of Physics, Indiana University, Bloomington, IN, USA
⁹⁹ INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy
¹⁰⁰ ICTP, Trieste, Italy
¹⁰¹ Dipartimento Politecnico di Ingegneria e Architettura, Università di Udine, Udine, Italy
¹⁰² INFN Sezione di Lecce, Lecce, Italy
¹⁰³ Dipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy
¹⁰⁴ INFN Sezione di Milano, Milan, Italy
¹⁰⁵ Dipartimento di Fisica, Università di Milano, Milan, Italy
¹⁰⁶ INFN Sezione di Napoli, Naples, Italy
¹⁰⁷ Dipartimento di Fisica, Università di Napoli, Naples, Italy
¹⁰⁸ INFN Sezione di Pavia, Pavia, Italy
¹⁰⁹ Dipartimento di Fisica, Università di Pavia, Pavia, Italy
¹¹⁰ INFN Sezione di Pisa, Pisa, Italy
¹¹¹ Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy
¹¹² INFN Sezione di Roma, Rome, Italy
¹¹³ Dipartimento di Fisica, Sapienza Università di Roma, Rome, Italy
¹¹⁴ INFN Sezione di Roma Tor Vergata, Rome, Italy
¹¹⁵ Dipartimento di Fisica, Università di Roma Tor Vergata, Rome, Italy
¹¹⁶ INFN Sezione di Roma Tre, Rome, Italy
¹¹⁷ Dipartimento di Matematica e Fisica, Università Roma Tre, Rome, Italy
¹¹⁸ INFN-TIFPA, Povo, Italy
¹¹⁹ Università degli Studi di Trento, Trento, Italy
¹²⁰ Universität Innsbruck, Department of Astro and Particle Physics, Innsbruck, Austria
¹²¹ University of Iowa, Iowa City, IA, USA
¹²² Department of Physics and Astronomy, Iowa State University, Ames, IA, USA
¹²³ Istinye University, Sariyer, Istanbul, Türkiye
¹²⁴ Departamento de Engenharia Elétrica, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil
¹²⁵ Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil
¹²⁶ Instituto de Física, Universidade de São Paulo, São Paulo, Brazil
¹²⁷ Rio de Janeiro State University, Rio de Janeiro, Brazil
¹²⁸ Federal University of Bahia, Bahia, Brazil
¹²⁹ KEK, High Energy Accelerator Research Organization, Tsukuba, Japan
¹³⁰ Graduate School of Science, Kobe University, Kobe, Japan
¹³¹ AGH University of Krakow, Faculty of Physics and Applied Computer Science, Kraków, Poland
¹³² Marian Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland
¹³³ Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland
¹³⁴ Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates
¹³⁵ University of Sharjah, Sharjah, United Arab Emirates
¹³⁶ Faculty of Science, Kyoto University, Kyoto, Japan
¹³⁷ Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka, Japan
¹³⁸ L2IT, CNRS/IN2P3, UPS, Université de Toulouse, Toulouse, France
¹³⁹ Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina
¹⁴⁰ Physics Department, Lancaster University, Lancaster, UK
¹⁴¹ Oliver Lodge Laboratory, University of Liverpool, Liverpool, UK
¹⁴² Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics, University of Ljubljana, Ljubljana, Slovenia
¹⁴³ Department of Physics and Astronomy, Queen Mary University of London, London, UK
¹⁴⁴ Department of Physics, Royal Holloway University of London, Egham, UK
¹⁴⁵ Department of Physics and Astronomy, University College London, London, UK
¹⁴⁶ Louisiana Tech University, Ruston, LA, USA
¹⁴⁷ Fysiska institutionen, Lunds universitet, Lund, Sweden
¹⁴⁸ Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid, Spain
¹⁴⁹ Institut für Physik, Universität Mainz, Mainz, Germany
¹⁵⁰ School of Physics and Astronomy, University of Manchester, Manchester, UK
¹⁵¹ CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
¹⁵² Department of Physics, University of Massachusetts, Amherst, MA, USA
¹⁵³ Department of Physics, McGill University, Montreal, QC, Canada
¹⁵⁴ School of Physics, University of Melbourne, Victoria, Australia
¹⁵⁵ Department of Physics, University of Michigan, Ann Arbor, MI, USA
¹⁵⁶ Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA
¹⁵⁷ Group of Particle Physics, University of Montreal, Montreal, QC, Canada
¹⁵⁸ Fakultät für Physik, Ludwig-Maximilians-Universität München, Munich, Germany
¹⁵⁹ Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Munich, Germany
¹⁶⁰ Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan
¹⁶¹ Department of Physics, Nanjing University, Nanjing, China
¹⁶² School of Science, Shenzhen Campus of Sun Yat-sen University, Shenzhen, China
¹⁶³ University of Chinese Academy of Science (UCAS), Beijing, China
¹⁶⁴ Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA
¹⁶⁵ Institute for Mathematics, Astrophysics and Particle Physics, Radboud University/Nikhef, Nijmegen, Netherlands
¹⁶⁶ Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, Netherlands
¹⁶⁷ Department of Physics, Northern Illinois University, DeKalb, IL, USA
¹⁶⁸ New York University Abu Dhabi, Abu Dhabi, United Arab Emirates
¹⁶⁹ United Arab Emirates University, Al Ain, United Arab Emirates
¹⁷⁰ Department of Physics, New York University, New York, NY, USA
¹⁷¹ Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo, Japan
¹⁷² Ohio State University, Columbus, OH, USA
¹⁷³ Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK, USA
¹⁷⁴ Department of Physics, Oklahoma State University, Stillwater, OK, USA
¹⁷⁵ Joint Laboratory of Optics, Palacký University, Olomouc, Czech Republic
¹⁷⁶ Institute for Fundamental Science, University of Oregon, Eugene, OR, USA
¹⁷⁷ Graduate School of Science, Osaka University, Osaka, Japan
¹⁷⁸ Department of Physics, University of Oslo, Oslo, Norway
¹⁷⁹ Department of Physics, Oxford University, Oxford, UK
¹⁸⁰ LPNHE, CNRS/IN2P3, Sorbonne Université, Université Paris Cité, Paris, France
¹⁸¹ Department of Physics, University of Pennsylvania, Philadelphia, PA, USA
¹⁸² Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA
¹⁸³ Laboratório de Instrumentação e Física Experimental de Partículas-LIP, Lisbon, Portugal
¹⁸⁴ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisbon, Portugal
¹⁸⁵ Departamento de Física, Universidade de Coimbra, Coimbra, Portugal
¹⁸⁶ Centro de Física Nuclear da Universidade de Lisboa, Lisbon, Portugal
¹⁸⁷ Departamento de Física, Escola de Ciências, Universidade do Minho, Braga, Portugal
¹⁸⁸ Departamento de Física Teórica y del Cosmos, Universidad de Granada, Granada, Spain
¹⁸⁹ Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal
¹⁹⁰ Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic
¹⁹¹ Czech Technical University in Prague, Prague, Czech Republic
¹⁹² Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic
¹⁹³ Particle Physics Department, Rutherford Appleton Laboratory, Didcot, UK
¹⁹⁴ IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
¹⁹⁵ Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, CA, USA
¹⁹⁶ Departamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile
¹⁹⁷ Millennium Institute for Subatomic Physics at High Energy Frontier (SAPHIR), Santiago, Chile
¹⁹⁸ Instituto de Investigación Multidisciplinario en Ciencia y Tecnología y Departamento de Física, Universidad de La Serena, La Serena, Chile
¹⁹⁹ Universidad Andres Bello, Department of Physics, Santiago, Chile
²⁰⁰ Instituto de Alta Investigación, Universidad de Tarapacá, Arica, Chile
²⁰¹ Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile
²⁰² Department of Physics, Institute of Science, Tokyo, Japan
²⁰³ Department of Physics, University of Washington, Seattle, WA, USA
²⁰⁴ Institute of Frontier and Interdisciplinary Science and Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University, Qingdao, China
²⁰⁵ School of Physics, Zhengzhou University, China
²⁰⁶ State Key Laboratory of Dark Matter Physics, School of Physics and Astronomy, Shanghai Jiao Tong University, Key Laboratory for Particle Astrophysics and Cosmology (MOE), SKLPPC, Shanghai, China
²⁰⁷ State Key Laboratory of Dark Matter Physics, Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China
²⁰⁸ Department of Physics and Astronomy, University of Sheffield, Sheffield, UK
²⁰⁹ Department of Physics, Shinshu University, Nagano, Japan
²¹⁰ Department Physik, Universität Siegen, Siegen, Germany
²¹¹ Department of Physics, Simon Fraser University, Burnaby, BC, Canada
²¹² SLAC National Accelerator Laboratory, Stanford, CA, USA
²¹³ Department of Physics, Royal Institute of Technology, Stockholm, Sweden
²¹⁴ Departments of Physics and Astronomy, Stony Brook University, Stony Brook, NY, USA
²¹⁵ Department of Physics and Astronomy, University of Sussex, Brighton, UK
²¹⁶ School of Physics, University of Sydney, Sydney, Australia
²¹⁷ Institute of Physics, Academia Sinica, Taipei, Taiwan
²¹⁸ E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia
²¹⁹ High Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia
²²⁰ University of Georgia, Tbilisi, Georgia
²²¹ Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel
²²² Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel
²²³ Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece
²²⁴ International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo, Japan
²²⁵ Graduate School of Science and Technology, Tokyo Metropolitan University, Tokyo, Japan
²²⁶ Department of Physics, University of Toronto, Toronto, ON, Canada
²²⁷ TRIUMF, Vancouver, BC, Canada
²²⁸ Department of Physics and Astronomy, York University, Toronto, ON, Canada
²²⁹ Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan
²³⁰ Department of Physics and Astronomy, Tufts University, Medford, MA, USA
²³¹ Department of Physics and Astronomy, University of California Irvine, Irvine, CA, USA
²³² University of West Attica, Athens, Greece
²³³ Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden
²³⁴ Department of Physics, University of Illinois, Urbana, IL, USA
²³⁵ Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia-CSIC, Valencia, Spain
²³⁶ Department of Physics, University of British Columbia, Vancouver, BC, Canada
²³⁷ Department of Physics and Astronomy, University of Victoria, Victoria, BC, Canada
²³⁸ Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg, Germany
²³⁹ Department of Physics, University of Warwick, Coventry, UK
²⁴⁰ Waseda University, Tokyo, Japan
²⁴¹ Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, Israel
²⁴² Department of Physics, University of Wisconsin, Madison, WI, USA
²⁴³ Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal, Germany
²⁴⁴ Department of Physics, Yale University, New Haven, CT, USA
²⁴⁵ Yerevan Physics Institute, Yerevan, Armenia
²⁴⁶ Affiliated with an Institute Formerly Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
²⁴⁷ An-Najah National University, Nablus, Palestine
²⁴⁸ Borough of Manhattan Community College, City University of New York, New York, NY, USA
²⁴⁹ Center for High Energy Physics, Peking University, China
²⁵⁰ Center for Interdisciplinary Research and Innovation (CIRI-AUTH), Thessaloniki, Greece
²⁵¹ Centre of Physics of the Universities of Minho and Porto (CF-UM-UP), Porto, Portugal
²⁵² CERN, Geneva, Switzerland
²⁵³ CMD-AC UNEC Research Center, Azerbaijan State University of Economics (UNEC), Baku, Azerbaijan
²⁵⁴ Département de Physique Nucléaire et Corpusculaire, Université de Genève, Geneva, Switzerland
²⁵⁵ Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spain
²⁵⁶ Department of Financial and Management Engineering, University of the Aegean, Chios, Greece
²⁵⁷ Department of Mathematical Sciences, University of South Africa, Johannesburg, South Africa
²⁵⁸ Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei, China
²⁵⁹ Department of Physics, Bolu Abant Izzet Baysal University, Bolu, Türkiye
²⁶⁰ Department of Physics, California State University, Sacramento, USA
²⁶¹ Department of Physics, King’s College London, London, UK
²⁶² Department of Physics, Stanford University, Stanford, CA, USA
²⁶³ Department of Physics, Stellenbosch University, South Africa
²⁶⁴ Department of Physics, University of Fribourg, Fribourg, Switzerland
²⁶⁵ Department of Physics, University of Thessaly, Volos, Greece
²⁶⁶ Department of Physics, Westmont College, Santa Barbara, USA
²⁶⁷ Faculty of Physics, Sofia University, ‘St. Kliment Ohridski’, Sofia, Bulgaria
²⁶⁸ Hellenic Open University, Patras, Greece
²⁶⁹ Henan University, Kaifeng, China
²⁷⁰ Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
²⁷¹ Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain
²⁷² Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germany
²⁷³ Institute for Nuclear Research and Nuclear Energy (INRNE) of the Bulgarian Academy of Sciences, Sofia, Bulgaria
²⁷⁴ Institute of Applied Physics, Mohammed VI Polytechnic University, Ben Guerir, Morocco
²⁷⁵ Institute of Particle Physics (IPP), Toronto, Canada
²⁷⁶ Institute of Physics and Technology, Mongolian Academy of Sciences, Ulaanbaatar, Mongolia
²⁷⁷ Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan
²⁷⁸ Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia
²⁷⁹ National Institute of Physics, University of the Philippines Diliman (Philippines), Quezon City, Philippines
²⁸⁰ Technical University of Munich, Munich, Germany
²⁸¹ The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing, China
²⁸² TRIUMF, Vancouver, BC, Canada
²⁸³ Università di Napoli Parthenope, Naples, Italy
²⁸⁴ Department of Physics, University of Colorado, Boulder, CO, USA
²⁸⁵ University of Sienna, Sienna, Italy
²⁸⁶ University of the Western Cape, Cape Town, South Africa
²⁸⁷ Washington College, Chestertown, MD, USA
²⁸⁸ Yeditepe University, Physics Department, Istanbul, Türkiye
²⁸⁹ CERN, 1211, Geneva 23, Switzerland

^a atlas.publications@cern.ch

Received: 14 February 2025
Accepted: 10 April 2025
Published online: 2 July 2025

Abstract

High precision single-differential $W^{\pm }$-boson production cross-sections as a function of electron or muon transverse momentum $p_{\text{T}}$ or their pseudorapity $\eta$, as well as double-differential cross-sections as functions of these variables, are measured in proton–proton collisions at centre-of-mass energies $\sqrt{s}=5.02$ TeV and 13 TeV. The W-boson charge asymmetry as a function of lepton $\eta$ is also measured. The data, collected in dedicated runs at reduced instantaneous luminosity with the ATLAS detector at the Large Hadron Collider, correspond to integrated luminosities of 255 pb$_{}^{-1}$ at 5.02 TeV and 338 pb$_{}^{-1}$ at 13 TeV. The measurements are in agreement with Standard-Model predictions calculated at next-to-next-to-leading-order in the strong coupling constant ${\alpha }_s$ including transverse-momentum resummation at next-to-next-to-leading logarithmic accuracy using several parton distribution functions. The impact of the measured differential cross-sections as a function of lepton $\eta$ on the determination of these functions is studied using a profiling technique.