
==== 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

12268
10.1140/epjc/s10052-023-12268-2
Regular Article - Experimental Physics
Luminosity determination using Z boson production at the CMS experiment
CMS CollaborationHayrapetyan A. 1
http://orcid.org/0009-0000-0684-6742
Tumasyan A. 1185
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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Valle A. Escalante Del 2
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Hussain P.S. 2
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Jeitler M. 2186
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Krammer N. 2
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Liko D. 2
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Mikulec I. 2
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Schieck J. 2186
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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. 2186
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Darwish M.R. 3187
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Janssen T. 3
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Mechelen P. Van 3
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Bols E.S. 4
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Tlisova I. 184
http://orcid.org/0000-0002-2106-4041
Toropin A. 184
http://orcid.org/0000-0002-7602-2527
Uvarov L. 184
http://orcid.org/0000-0002-7007-9020
Uzunian A. 184
Vorobyev A. 184
http://orcid.org/0000-0001-6590-6266
Voytishin N. 184
Yuldashev B. S. 184286
http://orcid.org/0000-0002-1964-6106
Zarubin A. 184
http://orcid.org/0000-0001-6171-9682
Zhizhin I. 184
http://orcid.org/0000-0001-7178-5907
Zhokin A. 184
cms-publication-committee-chair@cern.ch

287
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, Brussel, Belgium
5 https://ror.org/01r9htc13 grid.4989.c 0000 0001 2348 6355 Université Libre de Bruxelles, Bruxelles, 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 https://ror.org/02v51f717 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 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
21 https://ror.org/00a2xv884 grid.13402.34 0000 0004 1759 700X Zhejiang University, Hangzhou, Zhejiang China
22 https://ror.org/02mhbdp94 grid.7247.6 0000 0004 1937 0714 Universidad de Los Andes, Bogota, Colombia
23 https://ror.org/03bp5hc83 grid.412881.6 0000 0000 8882 5269 Universidad de Antioquia, Medellin, Colombia
24 https://ror.org/00m31ft63 grid.38603.3e 0000 0004 0644 1675 Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia
25 https://ror.org/00m31ft63 grid.38603.3e 0000 0004 0644 1675 Faculty of Science, University of Split, Split, Croatia
26 https://ror.org/02mw21745 grid.4905.8 0000 0004 0635 7705 Institute Rudjer Boskovic, Zagreb, Croatia
27 https://ror.org/02qjrjx09 grid.6603.3 0000 0001 2116 7908 University of Cyprus, Nicosia, Cyprus
28 https://ror.org/024d6js02 grid.4491.8 0000 0004 1937 116X Charles University, Prague, Czech Republic
29 https://ror.org/01gb99w41 grid.440857.a 0000 0004 0485 2489 Escuela Politecnica Nacional, Quito, Ecuador
30 https://ror.org/01r2c3v86 grid.412251.1 0000 0000 9008 4711 Universidad San Francisco de Quito, Quito, Ecuador
31 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
32 https://ror.org/023gzwx10 grid.411170.2 0000 0004 0412 4537 Center for High Energy Physics (CHEP-FU), Fayoum University, El-Fayoum, Egypt
33 https://ror.org/03eqd4a41 grid.177284.f 0000 0004 0410 6208 National Institute of Chemical Physics and Biophysics, Tallinn, Estonia
34 https://ror.org/040af2s02 grid.7737.4 0000 0004 0410 2071 Department of Physics, University of Helsinki, Helsinki, Finland
35 https://ror.org/01x2x1522 grid.470106.4 0000 0001 1106 2387 Helsinki Institute of Physics, Helsinki, Finland
36 https://ror.org/0208vgz68 grid.12332.31 0000 0001 0533 3048 Lappeenranta-Lahti University of Technology, Lappeenranta, Finland
37 https://ror.org/03xjwb503 grid.460789.4 0000 0004 4910 6535 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
38 grid.508893.f Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
39 https://ror.org/00pg6eq24 grid.11843.3f 0000 0001 2157 9291 Université de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France
40 https://ror.org/02avf8f85 Institut de Physique des 2 Infinis de Lyon (IP2I ), Villeurbanne, France
41 https://ror.org/00aamz256 grid.41405.34 0000 0001 0702 1187 Georgian Technical University, Tbilisi, Georgia
42 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
43 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany
44 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X III. Physikalisches Institut B, RWTH Aachen University, Aachen, Germany
45 https://ror.org/01js2sh04 grid.7683.a 0000 0004 0492 0453 Deutsches Elektronen-Synchrotron, Hamburg, Germany
46 https://ror.org/00g30e956 grid.9026.d 0000 0001 2287 2617 University of Hamburg, Hamburg, Germany
47 https://ror.org/04t3en479 grid.7892.4 0000 0001 0075 5874 Karlsruher Institut fuer Technologie, Karlsruhe, Germany
48 grid.6083.d 0000 0004 0635 6999 Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi, Greece
49 https://ror.org/04gnjpq42 grid.5216.0 0000 0001 2155 0800 National and Kapodistrian University of Athens, Athens, Greece
50 grid.4241.3 0000 0001 2185 9808 National Technical University of Athens, Athens, Greece
51 https://ror.org/01qg3j183 grid.9594.1 0000 0001 2108 7481 University of Ioánnina, Ioannina, Greece
52 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
53 https://ror.org/035dsb084 grid.419766.b 0000 0004 1759 8344 Wigner Research Centre for Physics, Budapest, Hungary
54 grid.418861.2 0000 0001 0674 7808 Institute of Nuclear Research ATOMKI, Debrecen, Hungary
55 https://ror.org/02xf66n48 grid.7122.6 0000 0001 1088 8582 Institute of Physics, University of Debrecen, Debrecen, Hungary
56 Karoly Robert Campus, MATE Institute of Technology, Gyongyos, Hungary
57 https://ror.org/04p2sbk06 grid.261674.0 0000 0001 2174 5640 Panjab University, Chandigarh, India
58 https://ror.org/04gzb2213 grid.8195.5 0000 0001 2109 4999 University of Delhi, Delhi, India
59 https://ror.org/0491yz035 grid.473481.d 0000 0001 0661 8707 Saha Institute of Nuclear Physics, HBNI, Kolkata, India
60 https://ror.org/03v0r5n49 grid.417969.4 0000 0001 2315 1926 Indian Institute of Technology Madras, Madras, India
61 https://ror.org/03ht1xw27 grid.22401.35 0000 0004 0502 9283 Tata Institute of Fundamental Research-A, Mumbai, India
62 https://ror.org/03ht1xw27 grid.22401.35 0000 0004 0502 9283 Tata Institute of Fundamental Research-B, Mumbai, India
63 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
64 https://ror.org/028qa3n13 grid.417959.7 0000 0004 1764 2413 Indian Institute of Science Education and Research (IISER), Pune, India
65 grid.411751.7 0000 0000 9908 3264 Isfahan University of Technology, Isfahan, Iran
66 https://ror.org/04xreqs31 grid.418744.a 0000 0000 8841 7951 Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
67 https://ror.org/05m7pjf47 grid.7886.1 0000 0001 0768 2743 University College Dublin, Dublin, Ireland
68 grid.4466.0 0000 0001 0578 5482 INFN Sezione di Bari, Università di Bari, Politecnico di Bari, Bari, Italy
69 grid.6292.f 0000 0004 1757 1758 INFN Sezione di Bologna, Università di Bologna, Bologna, Italy
70 grid.8158.4 0000 0004 1757 1969 INFN Sezione di Catania, Università di Catania, Catania, Italy
71 https://ror.org/02vv5y108 grid.470204.5 0000 0001 2231 4148 INFN Sezione di Firenze, Università di Firenze, Firenze, Italy
72 https://ror.org/049jf1a25 grid.463190.9 0000 0004 0648 0236 INFN Laboratori Nazionali di Frascati, Frascati, Italy
73 grid.5606.5 0000 0001 2151 3065 INFN Sezione di Genova, Università di Genova, Genoa, Italy
74 https://ror.org/03xejxm22 grid.470207.6 0000 0004 8390 4143 INFN Sezione di Milano-Bicocca, Università di Milano-Bicocca, Milan, Italy
75 https://ror.org/015kcdd40 grid.470211.1 0000 0004 8343 7696 INFN Sezione di Napoli, Università di Napoli ’Federico II’, Napoli, Italy; Università della Basilicata, Potenza, Italy;, Università G. Marconi, Rome, Italy
76 grid.11696.39 0000 0004 1937 0351 INFN Sezione di Padova, Università di Padova, Padova, Italy; Università di Trento, Trento, Italy
77 grid.8982.b 0000 0004 1762 5736 INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
78 grid.9027.c 0000 0004 1757 3630 INFN Sezione di Perugia, Università di Perugia, Perugia, Italy
79 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
80 grid.7841.a INFN Sezione di Roma, Sapienza Università di Roma, Rome, Italy
81 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
82 grid.5133.4 0000 0001 1941 4308 INFN Sezione di Trieste, Università di Trieste, Trieste, Italy
83 https://ror.org/040c17130 grid.258803.4 0000 0001 0661 1556 Kyungpook National University, Daegu, Korea
84 https://ror.org/05kzjxq56 grid.14005.30 0000 0001 0356 9399 Chonnam National University, Institute for Universe and Elementary Particles, Kwangju, Korea
85 https://ror.org/046865y68 grid.49606.3d 0000 0001 1364 9317 Hanyang University, Seoul, Korea
86 https://ror.org/047dqcg40 grid.222754.4 0000 0001 0840 2678 Korea University, Seoul, Korea
87 https://ror.org/01zqcg218 grid.289247.2 0000 0001 2171 7818 Kyung Hee University, Department of Physics, Seoul, Korea
88 https://ror.org/00aft1q37 grid.263333.4 0000 0001 0727 6358 Sejong University, Seoul, Korea
89 https://ror.org/04h9pn542 grid.31501.36 0000 0004 0470 5905 Seoul National University, Seoul, Korea
90 https://ror.org/05en5nh73 grid.267134.5 0000 0000 8597 6969 University of Seoul, Seoul, Korea
91 https://ror.org/01wjejq96 grid.15444.30 0000 0004 0470 5454 Yonsei University, Department of Physics, Seoul, Korea
92 https://ror.org/04q78tk20 grid.264381.a 0000 0001 2181 989X Sungkyunkwan University, Suwon, Korea
93 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
94 https://ror.org/00twb6c09 grid.6973.b 0000 0004 0567 9729 Riga Technical University, Riga, Latvia
95 https://ror.org/05g3mes96 grid.9845.0 0000 0001 0775 3222 University of Latvia (LU), Riga, Latvia
96 https://ror.org/03nadee84 grid.6441.7 0000 0001 2243 2806 Vilnius University, Vilnius, Lithuania
97 https://ror.org/00rzspn62 grid.10347.31 0000 0001 2308 5949 National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia
98 grid.11893.32 0000 0001 2193 1646 Universidad de Sonora (UNISON), Hermosillo, Mexico
99 grid.512574.0 Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico
100 https://ror.org/05vss7635 grid.441047.2 0000 0001 2156 4794 Universidad Iberoamericana, Mexico City, Mexico
101 https://ror.org/03p2z7827 grid.411659.e 0000 0001 2112 2750 Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
102 https://ror.org/02drrjp49 grid.12316.37 0000 0001 2182 0188 University of Montenegro, Podgorica, Montenegro
103 https://ror.org/03y7q9t39 grid.21006.35 0000 0001 2179 4063 University of Canterbury, Christchurch, New Zealand
104 grid.412621.2 0000 0001 2215 1297 National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan
105 grid.9922.0 0000 0000 9174 1488 AGH University of Krakow, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland
106 https://ror.org/00nzsxq20 grid.450295.f 0000 0001 0941 0848 National Centre for Nuclear Research, Swierk, Poland
107 https://ror.org/039bjqg32 grid.12847.38 0000 0004 1937 1290 Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland
108 https://ror.org/01hys1667 grid.420929.4 Laboratório de Instrumentação e Física Experimental de Partículas, Lisbon, Portugal
109 https://ror.org/02qsmb048 grid.7149.b 0000 0001 2166 9385 Faculty of Physics, University of Belgrade, Belgrade, Serbia
110 grid.7149.b 0000 0001 2166 9385 VINCA Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia
111 https://ror.org/05xx77y52 grid.420019.e 0000 0001 1959 5823 Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain
112 https://ror.org/01cby8j38 grid.5515.4 0000 0001 1957 8126 Universidad Autónoma de Madrid, Madrid, Spain
113 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
114 grid.7821.c 0000 0004 1770 272X Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain
115 https://ror.org/02phn5242 grid.8065.b 0000 0001 2182 8067 University of Colombo, Colombo, Sri Lanka
116 https://ror.org/033jvzr14 grid.412759.c 0000 0001 0103 6011 University of Ruhuna, Department of Physics, Matara, Sri Lanka
117 https://ror.org/01ggx4157 grid.9132.9 0000 0001 2156 142X CERN, European Organization for Nuclear Research, Geneva, Switzerland
118 https://ror.org/03eh3y714 grid.5991.4 0000 0001 1090 7501 Paul Scherrer Institut, Villigen, Switzerland
119 grid.5801.c 0000 0001 2156 2780 ETH Zurich-Institute for Particle Physics and Astrophysics (IPA), Zurich, Switzerland
120 https://ror.org/02crff812 grid.7400.3 0000 0004 1937 0650 Universität Zürich, Zurich, Switzerland
121 https://ror.org/00944ve71 grid.37589.30 0000 0004 0532 3167 National Central University, Chung-Li, Taiwan
122 https://ror.org/05bqach95 grid.19188.39 0000 0004 0546 0241 National Taiwan University (NTU), Taipei, Taiwan
123 https://ror.org/028wp3y58 grid.7922.e 0000 0001 0244 7875 Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand
124 https://ror.org/05wxkj555 grid.98622.37 0000 0001 2271 3229 Physics Department, Science and Art Faculty, Çukurova University, Adana, Turkey
125 https://ror.org/014weej12 grid.6935.9 0000 0001 1881 7391 Physics Department, Middle East Technical University, Ankara, Turkey
126 https://ror.org/03z9tma90 grid.11220.30 0000 0001 2253 9056 Bogazici University, Istanbul, Turkey
127 https://ror.org/059636586 grid.10516.33 0000 0001 2174 543X Istanbul Technical University, Istanbul, Turkey
128 https://ror.org/03a5qrr21 grid.9601.e 0000 0001 2166 6619 Istanbul University, Istanbul, Turkey
129 grid.466758.e Institute for Scintillation Materials of National Academy of Science of Ukraine, Kharkiv, Ukraine
130 https://ror.org/00183pc12 grid.425540.2 0000 0000 9526 3153 National Science Centre, Kharkiv Institute of Physics and Technology, Kharkiv, Ukraine
131 https://ror.org/0524sp257 grid.5337.2 0000 0004 1936 7603 University of Bristol, Bristol, UK
132 https://ror.org/03gq8fr08 grid.76978.37 0000 0001 2296 6998 Rutherford Appleton Laboratory, Didcot, UK
133 https://ror.org/041kmwe10 grid.7445.2 0000 0001 2113 8111 Imperial College, London, UK
134 grid.7728.a 0000 0001 0724 6933 Brunel University, Uxbridge, UK
135 https://ror.org/005781934 grid.252890.4 0000 0001 2111 2894 Baylor University, Waco, TX USA
136 https://ror.org/047yk3s18 grid.39936.36 0000 0001 2174 6686 Catholic University of America, Washington, DC USA
137 https://ror.org/03xrrjk67 grid.411015.0 0000 0001 0727 7545 The University of Alabama, Tuscaloosa, AL USA
138 https://ror.org/05qwgg493 grid.189504.1 0000 0004 1936 7558 Boston University, Boston, MA USA
139 https://ror.org/05gq02987 grid.40263.33 0000 0004 1936 9094 Brown University, Providence, RI USA
140 https://ror.org/05t99sp05 grid.468726.9 0000 0004 0486 2046 University of California, Davis, Davis, CA USA
141 grid.19006.3e 0000 0000 9632 6718 University of California, Los Angeles, CA USA
142 https://ror.org/05t99sp05 grid.468726.9 0000 0004 0486 2046 University of California, Riverside, Riverside, CA USA
143 https://ror.org/05t99sp05 grid.468726.9 0000 0004 0486 2046 University of California, San Diego, La Jolla, CA USA
144 grid.133342.4 0000 0004 1936 9676 Department of Physics, University of California, Santa Barbara, Santa Barbara, CA USA
145 https://ror.org/05dxps055 grid.20861.3d 0000 0001 0706 8890 California Institute of Technology, Pasadena, CA USA
146 https://ror.org/05x2bcf33 grid.147455.6 0000 0001 2097 0344 Carnegie Mellon University, Pittsburgh, PA USA
147 https://ror.org/02ttsq026 grid.266190.a 0000 0000 9621 4564 University of Colorado Boulder, Boulder, CO USA
148 https://ror.org/05bnh6r87 grid.5386.8 0000 0004 1936 877X Cornell University, Ithaca, NY USA
149 https://ror.org/020hgte69 grid.417851.e 0000 0001 0675 0679 Fermi National Accelerator Laboratory, Batavia, IL USA
150 https://ror.org/02y3ad647 grid.15276.37 0000 0004 1936 8091 University of Florida, Gainesville, FL USA
151 https://ror.org/05g3dte14 grid.255986.5 0000 0004 0472 0419 Florida State University, Tallahassee, FL USA
152 https://ror.org/04atsbb87 grid.255966.b 0000 0001 2229 7296 Florida Institute of Technology, Melbourne, FL USA
153 https://ror.org/02mpq6x41 grid.185648.6 0000 0001 2175 0319 University of Illinois Chicago, Chicago, Chicago, USA
154 https://ror.org/036jqmy94 grid.214572.7 0000 0004 1936 8294 The University of Iowa, Iowa City, IA USA
155 https://ror.org/00za53h95 grid.21107.35 0000 0001 2171 9311 Johns Hopkins University, Baltimore, MD USA
156 https://ror.org/001tmjg57 grid.266515.3 0000 0001 2106 0692 The University of Kansas, Lawrence, KS USA
157 https://ror.org/05p1j8758 grid.36567.31 0000 0001 0737 1259 Kansas State University, Manhattan, KS USA
158 https://ror.org/041nk4h53 grid.250008.f 0000 0001 2160 9702 Lawrence Livermore National Laboratory, Livermore, CA USA
159 https://ror.org/047s2c258 grid.164295.d 0000 0001 0941 7177 University of Maryland, College Park, MD USA
160 https://ror.org/042nb2s44 grid.116068.8 0000 0001 2341 2786 Massachusetts Institute of Technology, Cambridge, MA USA
161 https://ror.org/017zqws13 grid.17635.36 0000 0004 1936 8657 University of Minnesota, Minneapolis, MN USA
162 https://ror.org/02teq1165 grid.251313.7 0000 0001 2169 2489 University of Mississippi, Oxford, MS USA
163 https://ror.org/043mer456 grid.24434.35 0000 0004 1937 0060 University of Nebraska-Lincoln, Lincoln, NE USA
164 grid.273335.3 0000 0004 1936 9887 State University of New York at Buffalo, Buffalo, NY USA
165 https://ror.org/04t5xt781 grid.261112.7 0000 0001 2173 3359 Northeastern University, Boston, MA USA
166 https://ror.org/000e0be47 grid.16753.36 0000 0001 2299 3507 Northwestern University, Evanston, IL USA
167 https://ror.org/00mkhxb43 grid.131063.6 0000 0001 2168 0066 University of Notre Dame, Notre Dame, IN USA
168 https://ror.org/00rs6vg23 grid.261331.4 0000 0001 2285 7943 The Ohio State University, Columbus, OH USA
169 https://ror.org/00hx57361 grid.16750.35 0000 0001 2097 5006 Princeton University, Princeton, NJ USA
170 https://ror.org/00wek6x04 grid.267044.3 0000 0004 0398 9176 University of Puerto Rico, Mayaguez, PR USA
171 https://ror.org/02dqehb95 grid.169077.e 0000 0004 1937 2197 Purdue University, West Lafayette, IN USA
172 https://ror.org/04keq6987 grid.504659.b 0000 0000 8864 7239 Purdue University Northwest, Hammond, IN USA
173 https://ror.org/008zs3103 grid.21940.3e 0000 0004 1936 8278 Rice University, Houston, TX USA
174 https://ror.org/022kthw22 grid.16416.34 0000 0004 1936 9174 University of Rochester, Rochester, NY USA
175 https://ror.org/0420db125 grid.134907.8 0000 0001 2166 1519 The Rockefeller University, New York, NY USA
176 https://ror.org/05vt9qd57 grid.430387.b 0000 0004 1936 8796 Rutgers, The State University of New Jersey, Piscataway, NJ USA
177 https://ror.org/020f3ap87 grid.411461.7 0000 0001 2315 1184 University of Tennessee, Knoxville, TN USA
178 https://ror.org/01f5ytq51 grid.264756.4 0000 0004 4687 2082 Texas A &M University, College Station, TX USA
179 grid.264784.b 0000 0001 2186 7496 Texas Tech University, Lubbock, TX USA
180 https://ror.org/02vm5rt34 grid.152326.1 0000 0001 2264 7217 Vanderbilt University, Nashville, TN USA
181 https://ror.org/0153tk833 grid.27755.32 0000 0000 9136 933X University of Virginia, Charlottesville, VA USA
182 https://ror.org/01070mq45 grid.254444.7 0000 0001 1456 7807 Wayne State University, Detroit, MI USA
183 https://ror.org/01y2jtd41 grid.14003.36 0000 0001 2167 3675 University of Wisconsin-Madison, Madison, WI USA
184 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
185 https://ror.org/00s8vne50 grid.21072.36 0000 0004 0640 687X Yerevan State University, Yerevan, Armenia
186 https://ror.org/04d836q62 grid.5329.d 0000 0004 1937 0669 TU Wien, Vienna, Austria
187 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
188 https://ror.org/00cv9y106 grid.5342.0 0000 0001 2069 7798 Ghent University, Ghent, Belgium
189 https://ror.org/04wffgt70 grid.411087.b 0000 0001 0723 2494 Universidade Estadual de Campinas, Campinas, Brazil
190 https://ror.org/041yk2d64 grid.8532.c 0000 0001 2200 7498 Federal University of Rio Grande do Sul, Porto Alegre, Brazil
191 grid.412352.3 0000 0001 2163 5978 UFMS, Nova Andradina, Brazil
192 https://ror.org/036trcv74 grid.260474.3 0000 0001 0089 5711 Nanjing Normal University, Nanjing, China
193 https://ror.org/036jqmy94 grid.214572.7 0000 0004 1936 8294 Now at The University of Iowa, Iowa City, IA USA
194 https://ror.org/05qbk4x57 grid.410726.6 0000 0004 1797 8419 University of Chinese Academy of Sciences, Beijing, China
195 https://ror.org/05qbk4x57 grid.410726.6 0000 0004 1797 8419 University of Chinese Academy of Sciences, Beijing, China
196 https://ror.org/01r9htc13 grid.4989.c 0000 0001 2348 6355 Université Libre de Bruxelles, Bruxelles, Belgium
197 grid.9132.9 0000 0001 2156 142X An institute or an international laboratory covered by a cooperation agreement with CERN, Geneva, Switzerland
198 https://ror.org/00h55v928 grid.412093.d 0000 0000 9853 2750 Helwan University, Cairo, Egypt
199 https://ror.org/04w5f4y88 grid.440881.1 0000 0004 0576 5483 Now at Zewail City of Science and Technology, Zewail, Egypt
200 https://ror.org/0066fxv63 grid.440862.c 0000 0004 0377 5514 British University in Egypt, Cairo, Egypt
201 grid.7269.a 0000 0004 0621 1570 Now at Ain Shams University, Cairo, Egypt
202 https://ror.org/028vtqb15 grid.462084.c 0000 0001 2216 7125 Birla Institute of Technology, Mesra, Mesra, India
203 https://ror.org/02dqehb95 grid.169077.e 0000 0004 1937 2197 Purdue University, West Lafayette, IN USA
204 https://ror.org/04k8k6n84 grid.9156.b 0000 0004 0473 5039 Université de Haute Alsace, Mulhouse, France
205 https://ror.org/03cve4549 grid.12527.33 0000 0001 0662 3178 Department of Physics, Tsinghua University, Beijing, China
206 https://ror.org/04j5z3x06 grid.412290.c 0000 0000 8024 0602 The University of the State of Amazonas, Manaus, Brazil
207 grid.412176.7 0000 0001 1498 7262 Erzincan Binali Yildirim University, Erzincan, Turkey
208 https://ror.org/00g30e956 grid.9026.d 0000 0001 2287 2617 University of Hamburg, Hamburg, Germany
209 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany
210 grid.411751.7 0000 0000 9908 3264 Isfahan University of Technology, Isfahan, Iran
211 grid.7787.f 0000 0001 2364 5811 Bergische University Wuppertal (BUW), Wuppertal, Germany
212 https://ror.org/02wxx3e24 grid.8842.6 0000 0001 2188 0404 Brandenburg University of Technology, Cottbus, Germany
213 https://ror.org/02nv7yv05 grid.8385.6 0000 0001 2297 375X Forschungszentrum Jülich, Juelich, Germany
214 https://ror.org/01ggx4157 grid.9132.9 0000 0001 2156 142X CERN, European Organization for Nuclear Research, Geneva, Switzerland
215 https://ror.org/01jaj8n65 grid.252487.e 0000 0000 8632 679X Physics Department, Faculty of Science, Assiut University, Assiut, Egypt
216 https://ror.org/035dsb084 grid.419766.b 0000 0004 1759 8344 Wigner Research Centre for Physics, Budapest, Hungary
217 https://ror.org/02xf66n48 grid.7122.6 0000 0001 1088 8582 Institute of Physics, University of Debrecen, Debrecen, Hungary
218 grid.418861.2 0000 0001 0674 7808 Institute of Nuclear Research ATOMKI, Debrecen, Hungary
219 grid.7399.4 0000 0004 1937 1397 Now at Universitatea Babes-Bolyai - Facultatea de Fizica, Cluj-Napoca, Romania
220 https://ror.org/02xf66n48 grid.7122.6 0000 0001 1088 8582 Faculty of Informatics, University of Debrecen, Debrecen, Hungary
221 https://ror.org/02qbzdk74 grid.412577.2 0000 0001 2176 2352 Punjab Agricultural University, Ludhiana, India
222 https://ror.org/04q2jes40 grid.444415.4 0000 0004 1759 0860 UPES-University of Petroleum and Energy Studies, Dehradun, India
223 https://ror.org/02y28sc20 grid.440987.6 0000 0001 2259 7889 University of Visva-Bharati, Santiniketan, India
224 https://ror.org/04a7rxb17 grid.18048.35 0000 0000 9951 5557 University of Hyderabad, Hyderabad, India
225 grid.34980.36 0000 0001 0482 5067 Indian Institute of Science (IISc), Bangalore, India
226 https://ror.org/04gx72j20 grid.459611.e 0000 0004 1774 3038 IIT Bhubaneswar, Bhubaneswar, India
227 https://ror.org/01741jv66 grid.418915.0 0000 0004 0504 1311 Institute of Physics, Bhubaneswar, India
228 https://ror.org/01js2sh04 grid.7683.a 0000 0004 0492 0453 Deutsches Elektronen-Synchrotron, Hamburg, Germany
229 https://ror.org/00af3sa43 grid.411751.7 0000 0000 9908 3264 Department of Physics, Isfahan University of Technology, Isfahan, Iran
230 https://ror.org/024c2fq17 grid.412553.4 0000 0001 0740 9747 Sharif University of Technology, Tehran, Iran
231 https://ror.org/04jf6jw55 grid.510412.3 Department of Physics, University of Science and Technology of Mazandaran, Behshahr, Iran
232 https://ror.org/02an8es95 grid.5196.b 0000 0000 9864 2490 Italian National Agency for New Technologies, Energy and Sustainable Economic Development, Bologna, Italy
233 https://ror.org/02wdzfm91 grid.510931.f Centro Siciliano di Fisica Nucleare e di Struttura Della Materia, Catania, Italy
234 https://ror.org/00j0rk173 grid.440899.8 0000 0004 1780 761X Università degli Studi Guglielmo Marconi, Rome, Italy
235 https://ror.org/04swxte59 grid.508348.2 Scuola Superiore Meridionale, Università di Napoli ’Federico II’, Naples, Italy
236 https://ror.org/020hgte69 grid.417851.e 0000 0001 0675 0679 Fermi National Accelerator Laboratory, Batavia, IL USA
237 grid.466875.e 0000 0004 1757 5572 Laboratori Nazionali di Legnaro dell’INFN, Legnaro, Italy
238 grid.4691.a 0000 0001 0790 385X Università di Napoli ’Federico II’, Naples, Italy
239 grid.5326.2 0000 0001 1940 4177 Consiglio Nazionale delle Ricerche-Istituto Officina dei Materiali, Perugia, Italy
240 https://ror.org/00twb6c09 grid.6973.b 0000 0004 0567 9729 Riga Technical University, Riga, Latvia
241 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
242 https://ror.org/059ex5q34 grid.418270.8 0000 0004 0428 7635 Consejo Nacional de Ciencia y Tecnología, Mexico City, Mexico
243 grid.443373.4 0000 0001 0438 3334 Trincomalee Campus, Eastern University, Sri Lanka, Nilaveli, Sri Lanka
244 grid.8982.b 0000 0004 1762 5736 INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
245 https://ror.org/04gnjpq42 grid.5216.0 0000 0001 2155 0800 National and Kapodistrian University of Athens, Athens, Greece
246 https://ror.org/02s376052 grid.5333.6 0000 0001 2183 9049 Ecole Polytechnique Fédérale Lausanne, Lausanne, Switzerland
247 https://ror.org/03prydq77 grid.10420.37 0000 0001 2286 1424 University of Vienna Faculty of Computer Science, Vienna, Austria
248 https://ror.org/02crff812 grid.7400.3 0000 0004 1937 0650 Universität Zürich, Zurich, Switzerland
249 https://ror.org/05kdjqf72 grid.475784.d 0000 0000 9532 5705 Stefan Meyer Institute for Subatomic Physics, Vienna, Austria
250 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
251 Near East University, Research Center of Experimental Health Science, Mersin, Turkey
252 https://ror.org/02s82rs08 grid.505922.9 Konya Technical University, Konya, Turkey
253 https://ror.org/017v96566 0000 0004 6412 5697 Izmir Bakircay University, Izmir, Turkey
254 https://ror.org/02s4gkg68 grid.411126.1 0000 0004 0369 5557 Adiyaman University, Adiyaman, Turkey
255 https://ror.org/013s3zh21 grid.411124.3 0000 0004 1769 6008 Necmettin Erbakan University, Konya, Turkey
256 grid.411743.4 0000 0004 0369 8360 Bozok Universitetesi Rektörlügü, Yozgat, Turkey
257 https://ror.org/02kswqa67 grid.16477.33 0000 0001 0668 8422 Marmara University, Istanbul, Turkey
258 https://ror.org/010t24d82 grid.510982.7 Milli Savunma University, Istanbul, Turkey
259 https://ror.org/04v302n28 grid.16487.3c 0000 0000 9216 0511 Kafkas University, Kars, Turkey
260 https://ror.org/04kwvgz42 grid.14442.37 0000 0001 2342 7339 Hacettepe University, Ankara, Turkey
261 grid.506076.2 0000 0004 1797 5496 Faculty of Engineering, Istanbul University-Cerrahpasa, Istanbul, Turkey
262 https://ror.org/0547yzj13 grid.38575.3c 0000 0001 2337 3561 Yildiz Technical University, Istanbul, Turkey
263 https://ror.org/006e5kg04 grid.8767.e 0000 0001 2290 8069 Vrije Universiteit Brussel, Brussel, Belgium
264 https://ror.org/01ryk1543 grid.5491.9 0000 0004 1936 9297 School of Physics and Astronomy, University of Southampton, Southampton, UK
265 https://ror.org/0524sp257 grid.5337.2 0000 0004 1936 7603 University of Bristol, Bristol, UK
266 https://ror.org/01v29qb04 grid.8250.f 0000 0000 8700 0572 IPPP Durham University, Durham, UK
267 https://ror.org/02bfwt286 grid.1002.3 0000 0004 1936 7857 Monash University, Faculty of Science, Clayton, Australia
268 grid.9132.9 0000 0001 2156 142X Now at an institute or an international laboratory covered by a cooperation agreement with CERN, Geneva, Switzerland
269 grid.7605.4 0000 0001 2336 6580 Università di Torino, Turin, Italy
270 https://ror.org/02faxbd19 grid.418297.1 0000 0000 8888 5173 Bethel University, St. Paul, MN USA
271 https://ror.org/037vvf096 grid.440455.4 0000 0004 1755 486X Karamanoğlu Mehmetbey University, Karaman, Turkey
272 https://ror.org/05dxps055 grid.20861.3d 0000 0001 0706 8890 California Institute of Technology, Pasadena, CA USA
273 https://ror.org/00znex860 grid.265465.6 0000 0001 2296 3025 United States Naval Academy, Annapolis, MD USA
274 https://ror.org/03hx84x94 grid.448543.a 0000 0004 0369 6517 Bingol University, Bingol, Turkey
275 https://ror.org/00aamz256 grid.41405.34 0000 0001 0702 1187 Georgian Technical University, Tbilisi, Georgia
276 https://ror.org/004ah3r71 grid.449244.b 0000 0004 0408 6032 Sinop University, Sinop, Turkey
277 https://ror.org/047g8vk19 grid.411739.9 0000 0001 2331 2603 Erciyes University, Kayseri, Turkey
278 https://ror.org/00d3pnh21 grid.443874.8 0000 0000 9463 5349 Horia Hulubei National Institute of Physics and Nuclear Engineering (IFIN-HH), Bucharest, Romania
279 https://ror.org/03vb4dm14 grid.412392.f 0000 0004 0413 3978 Texas A &M University at Qatar, Doha, Qatar
280 https://ror.org/040c17130 grid.258803.4 0000 0001 0661 1556 Kyungpook National University, Daegu, Korea
281 grid.9132.9 0000 0001 2156 142X Another institute or international laboratory covered by a cooperation agreement with CERN, Geneva, Switzerland
282 https://ror.org/008x57b05 grid.5284.b 0000 0001 0790 3681 Universiteit Antwerpen, Antwerpen, Belgium
283 https://ror.org/00ad27c73 grid.48507.3e 0000 0004 0482 7128 Yerevan Physics Institute, Yerevan, Armenia
284 https://ror.org/04t5xt781 grid.261112.7 0000 0001 2173 3359 Northeastern University, Boston, MA USA
285 https://ror.org/041kmwe10 grid.7445.2 0000 0001 2113 8111 Imperial College, London, UK
286 grid.443859.7 0000 0004 0477 2171 Institute of Nuclear Physics of the Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
287 grid.9132.9 0000 0001 2156 142X CERN, Geneva, Switzerland
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© The Author(s) 2024
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Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development.
The measurement of Z boson production is presented as a method to determine the integrated luminosity of CMS data sets. The analysis uses proton–proton collision data, recorded by the CMS experiment at the CERN LHC in 2017 at a center-of-mass energy of 13TeV. Events with Z bosons decaying into a pair of muons are selected. The total number of Z bosons produced in a fiducial volume is determined, together with the identification efficiencies and correlations from the same data set, in small intervals of 20pb-1 of integrated luminosity, thus facilitating the efficiency and rate measurement as a function of time and instantaneous luminosity. Using the ratio of the efficiency-corrected numbers of Z bosons, the precisely measured integrated luminosity of one data set is used to determine the luminosity of another. For the first time, a full quantitative uncertainty analysis of the use of Z  bosons for the integrated luminosity measurement is performed. The uncertainty in the extrapolation between two data sets, recorded in 2017 at low and high instantaneous luminosity, is less than 0.5%. We show that the Z boson rate measurement constitutes a precise method, complementary to traditional methods, with the potential to improve the measurement of the integrated luminosity.

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 Valle A. Escalante Del http://dx.doi.org/10.13039/501100001807 FAPESP Fundação de Amparo à Pesquisa do Estado de São Paulo Hussain P.S. http://dx.doi.org/10.13039/501100005992 Bulgarian Ministry of Education and Science MES Jeitler M. http://dx.doi.org/10.13039/501100003336 Bulgarian National Science Fund BNSF Krammer N. 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/10.13039/501100003510 Ministry of Education and Research Haridus- ja Teadusministeerium; MoER Darwish M.R. http://dx.doi.org/10.13039/501100002301 Estonian Research Council via PRG780, PRG803, and PRG445 Eesti Teadusagentuur; ERC IUT Janssen T. http://dx.doi.org/10.13039/501100008530 European Regional Development Fund ERDF Mechelen P. Van http://dx.doi.org/10.13039/501100002341 Academy of Finland Suomen Akatemia Bols E.S. Finnish Ministry of Education and CultureMEC D’Hondt J. Helsinki Institute of PhysicsHIP Dansana S. http://dx.doi.org/10.13039/501100004794 Institut National de Physique Nucléaire et de Physique des Particules IN2P3 De Moor A. http://dx.doi.org/10.13039/501100004794 Centre National de la Recherche Scientifique CNRS Delcourt M. http://dx.doi.org/10.13039/501100006489 Commissariat à l’Énergie Atomique et aux Énergies Alternatives CEA Faham H. El 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 Morton A. http://dx.doi.org/10.13039/501100003448 General Secretariat for Research and Innovation GSRI Müller D. http://dx.doi.org/10.13039/501100011019 National Research, Development and Innovation Office NKFIH: Nemzeti Kutatási, Fejlesztési és Innováció Hivatal Sahasransu A.R. http://dx.doi.org/10.13039/501100001502 Department of Atomic Energy DAE Tavernier S. http://dx.doi.org/10.13039/501100001409 Department of Science and Technology DST Tytgat M. http://dx.doi.org/10.13039/501100006115 Institute for Research in Fundamental Studies IPM Putte S. Van http://dx.doi.org/10.13039/501100001602 Science Foundation SFI Vannerom D. http://dx.doi.org/10.13039/501100004007 Istituto Nazionale di Fisica Nucleare INFN Clerbaux B. 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 De Lentdecker G. http://dx.doi.org/10.13039/501100003725 National Research Foundation of Korea (NRF) previously listed was WCU (World Class University) Favart L. http://dx.doi.org/10.13039/501100001864 MES Ministry of Education and Science Hohov D. http://dx.doi.org/10.13039/501100008523 Lithuanian Academy of Sciences LAS or Lietuvos Mokslu̧ Akademija Jaramillo J. http://dx.doi.org/10.13039/501100003093 Ministry of Education Ministry of Higher Education, Malaysia Khalilzadeh A. http://dx.doi.org/10.13039/501100004386 University of Malaya http://dx.doi.org/10.13039/501100006348 BUAP Benemérita Universidad Autónoma de Puebla Mahdavikhorrami M. http://dx.doi.org/10.13039/501100008688 CINVESTAV Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional Malara A. http://dx.doi.org/10.13039/501100003141 CONACYT Consejo Nacional de Ciencia y Tecnología Paredes S. LNSLaboratorio Nacional de Supercómputo del Sureste Pétré L. http://dx.doi.org/10.13039/100010096 SEP Secretaría de Educación Pública Postiau N. http://dx.doi.org/10.13039/501100005324 UASLP Universidad Autónoma de San Luis Potosí Thomas L. MOSMinistry of Science Bemden M. Vanden http://dx.doi.org/10.13039/501100003524 Ministry of Business, Innovation and Employment MBIE Velde C. Vander http://dx.doi.org/10.13039/501100008689 Pakistan Atomic Energy Commission PAEC Vanlaer P. http://dx.doi.org/10.13039/501100004569 Ministry of Educaton and Science Ministerstwo Edukacji I Nauki; MES [was MSHE, Ministerstwo Nauki i Szkolnictwa Wyższego] De Coen M. http://dx.doi.org/10.13039/501100004442 National Science Centre Narodowe Centrum Nauki; NSC Dobur D. 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) Rendón C. https://doi.org/10.13039/100011941 Plan de Ciencia, Tecnología e Innovación del Principado de Asturias PCTI Samalan A. http://dx.doi.org/10.13039/501100008981 MOSTR Ministry of Science, Technology, and Research Skovpen K. ETH BoardEidgenössische Technische Hochschule (ETH) Zürich Bossche N. Van Den http://dx.doi.org/ETH Zurich10.13039/501100003006 ETH Zurich Eidgenössische Technische Hochschule (ETH) Zürich Wezenbeek L. http://dx.doi.org/PSI10.13039/501100004219 PSI Paul Scherrer Institut Benecke A. http://dx.doi.org/SNF10.13039/501100001711 SNF Swiss National Science Foundation (Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung) Bruno G. UniZHUniversität Zürich Caputo C. Canton ZurichSERState Secretariat for Education and Research (Education, Research, and Innovation: SERI) Donertas I.S. http://dx.doi.org/10.13039/501100004663 Ministry of Science and Technology Thailand Center of Excellence in PhysicsInstitute for the Promotion of Teaching Science and Technology of ThailandSpecial Task Force for Activating Researchhttp://dx.doi.org/10.13039/501100004192 National Science and Technology Development Agency of Thailand http://dx.doi.org/10.13039/501100004410 Scientific and Technical Research Council of Turkey Türkiye Bilimsel ve Teknolojik Araştirma Kurumu Mastrapasqua P. http://dx.doi.org/10.13039/100010440 Turkish Atomic Energy Authority Türkiye Atom Enerjisi Kurumu Mondal 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. http://dx.doi.org/10.13039/100010661 Horizon 2020 Grant, contract Nos. 675440, 724704, 752730, 758316, 765710, 824093 (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 Krammer N. 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 Schieck J. http://dx.doi.org/10.13039/501100004801 Shota Rustaveli National Science Foundation SRNSF Schöfbeck R. 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 Templ S. http://dx.doi.org/10.13039/501100003825 Hungarian Academy of Sciences Magyar Tudományos Akadémia Waltenberger W. http://dx.doi.org/10.13039/501100011019 New National Excellence Program - ÚNKP, the NKFIH research grants K 124845, K 124850, K 128713, K 128786, K 129058, K 131991, K 133046, K 138136, K 143460, K 143477, 2020-2.2.1-ED-2021-00181, and TKP2021-NKTA-64 ÚNKP: Új Nemzeti Kiválósági Program Wulz C.-E. Council of Scientific and Industrial Research, Indiahttp://dx.doi.org/10.13039/501100005375 Latvian Council of Science Latvijas Zinātnes Padome Janssen T. http://dx.doi.org/10.13039/501100004569 Ministy of Education and Science, project no. 2022/WK/14 Ministerstwo Edukacji I Nauki; MES Mechelen P. Van 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 Bols E.S. 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 Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chulalongkorn University (Thailand) http://dx.doi.org/10.13039/501100002873 CUAASC Chulalongkorn Academic into Its 2nd Century Project Advancement Project Lowette S. http://dx.doi.org/10.13039/100001201 Kavli Foundation http://dx.doi.org/10.13039/100007065 Nvidia Corporation hardware contribution: Titan Xp GPUs Morton A. 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 de recherche sur les lois fondamentales de l’Univers, CEA, Université Paris-Saclay, Gif-sur-YvetteInstitut national de physique nucléaire et de physique des particules, IN2P3, VilleurbanneInstitut Pluridisciplinaire Hubert Curien (IPHC), StrasbourgLaboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseauhttp://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/10.13039/501100002531 Kyungpook National University, Daegu http://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 CSCS - 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pmcIntroduction

In the CERN LHC, during the Run 2 data-taking period in 2015–2018, about 300 million events with Z bosons decaying into pairs of muons were recorded by the CMS experiment. Precision cross section measurements were performed [1–6] that provide (i) important tests of theoretical calculations [7–9]; (ii) input to fits of the parton distribution functions (PDFs) of the proton [10–13]; and (iii) constraints on backgrounds to searches for new physics [14].

Events with a Z boson decaying into a pair of muons have a remarkably clean experimental signature and a large cross section that facilitates high-precision measurements. Samples of Z bosons are also used as standard tools for detector calibrations and efficiency studies. The precisely known Z boson mass and width [15] are used to calibrate energy scales and momenta and to determine the detector resolution [16, 17]. Efficiencies for lepton triggering, reconstruction, and identification are determined using the “tag-and-probe” method [1, 16–18].

The large Drell–Yan (DY) cross section for the production of Z  bosons, and the possibility of simultaneously determining both the yield and the detection efficiency in situ, i.e., from the same event sample, make the process useful for precision measurements of the integrated luminosity. This was discussed before the start of the LHC [19]. During LHC operation, measurements of the Z boson rate already proved to be a useful and independent method for the LHC machine operators and experiments to monitor the relative instantaneous luminosity delivered to the ATLAS and CMS experiments [20]. The use of Z boson production as a measure of relative luminosities was also explored by the ATLAS experiment [21].

Both muons from the Z boson decay are detectable within the fiducial volume of the CMS detector in about one third of the Z  boson events. The fiducial Z boson cross section in proton–proton (pp) collisions at 13TeV has been measured to be [3]1 σZB(Z→μ+μ-)=694±6(syst)±17(lumi)\,pb.

Theoretical predictions are available up to next-to-next-to-next-to-leading order (N3LO) [9] in quantum chromodynamics (QCD). Electroweak corrections, including mixed QCD-electroweak corrections, are also available [7, 22, 23]. The current uncertainty in the prediction of the fiducial cross section is about 3%, and mainly originates from limited knowledge of proton PDFs and higher-order corrections [8]. Within this uncertainty, the integrated luminosity can be directly determined from the measured number of Z bosons corrected for efficiencies.

In practice, precision luminosity calibrations at the LHC are obtained from van der Meer (vdM) scan data [21, 24–29], which are more precise than the theory predictions for the Z boson cross section. In vdM scans, which are performed at low instantaneous luminosity with zero crossing angle between the two beams, the two beams are separated in two orthogonal directions transverse to the parallel beam axes. In each scan step, for a given beam separation, the event rate measured in the luminosity detectors is recorded to determine the beam overlap area. Together with the beam currents and the measured head-on collision rate, a luminosity calibration constant, referred to as the visible cross section, is determined. A full vdM scan campaign takes about six hours per experiment and is usually performed once per year, with specifically configured beams to maximize the accuracy and precision of the measurement. A detailed description of vdM scans is reported in Ref. [29].

The most precise integrated luminosity measurement in CMS to date, achieved for the 2016 data-taking period, has a total uncertainty of 1.2% [29]. Roughly half of the total uncertainty is due to the luminosity integration over the full year of data taking. This uncertainty, in turn, is composed of the uncertainty in the extrapolation of the visible cross section obtained in the vdM scan to standard data-taking conditions at high instantaneous luminosity, and the uncertainty in the integration of the instantaneous luminosity over time, obtained from comparisons between different luminosity measurements. In the 2017 data, presented in this paper, the average number of collisions per bunch crossing, usually referred to as pileup, was 32 [30]. In Run 2, peak instantaneous luminosities as high as 20nb-1s-1 were reached, corresponding to a pileup of more than 50. For the high-luminosity LHC (HL-LHC), a pileup of up to 200 is expected [31] likely leading to an increase in uncertainty with the conventional methods due to the larger extrapolation.

In this paper, we explore an approach originally proposed in Ref. [32]. The measurement of the Z boson rate is used as an alternative method for the extrapolation and integration of the luminosity calibration. The Z boson counting complements conventional luminosity measurements obtained from the CMS luminosity systems, which are taken as reference luminosity. The fiducial Z boson production cross section is defined as σfidZ=NZ/L, where NZ stands for the efficiency-corrected number of reconstructed Z boson events and L for the integrated luminosity. Since σfidZ is identical for all data sets of the same center-of-mass energy, the ratio of NZ for two data sets can be used to transfer the luminosity calibration from one data set to another, without input from theoretical predictions or precise knowledge of σfidZ. For the first time, a full quantitative uncertainty analysis of the use of Z bosons for the integrated luminosity measurement is performed.

We choose two independent data sets of Z boson events, both recorded by the CMS experiment in 2017: a data set with a bunch luminosity corresponding to about three pp collisions per bunch crossing, referred to in the following as “lowPU ”; and the bulk of CMS pp collision data recorded in 2017 with a typical pileup of 32, denoted as “highPU ”. The luminosity of the lowPU data is used to determine that of the highPU data via the relation2 LhighPU=NhighPUZNlowPUZLlowPU.

For both sets of data, the individual trigger and selection efficiencies are determined in situ, in intervals of 20pb-1, thus enhancing the sensitivity to possible variations due to changes in beam conditions or detector response as a function of time. Using the integrated luminosity for the lowPU data, which has an uncertainty of 1.7% [33], the integrated luminosity LhighPU and its uncertainty are determined from Eq. (2), and compared with the result from the conventional integrated luminosity measurement. Due to the cleaner signature, better resolution, and smaller backgrounds, the analysis of Z boson decays into muons is more accurate than electrons. In this paper, only the decays of Z bosons into muons are used.

The paper is structured as follows. After a brief outline of the CMS detector in Sect. 2, the analysis of the Z boson event sample is described in Sect. 3. The reconstructed number of Z bosons and the trigger and selection efficiencies are extracted from fits to the data. Acceptance corrections and correlations between the efficiencies for the muon track components and among the two muon tracks are studied as a function of pileup. Subsequently, in Sect. 4, the luminosity information obtained from Z boson counting is compared with the results from conventional luminosity measurements. In Sect. 5, the benefits and advantages of Z boson counting for luminosity measurements are discussed. The paper concludes with a summary in Sect. 6.

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 magnet volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter, each composed of a barrel and two endcap sections. Forward calorimeters extend the pseudorapidity (η) coverage provided by the barrel and endcap detectors. The muon system consists of gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, is reported in Ref. [34].

The silicon tracker measures charged particles in the pseudorapidity range |η|<3.0 [35, 36]. An iterative approach is used to build tracker tracks, executing a sequence of tracking algorithms, each with slightly distinct logic [17]. Muons are measured in the range |η|<2.4, with detection planes made using three technologies: drift tubes, cathode strip chambers, and resistive plate chambers. Matching muons to tracks measured in the silicon tracker results in a relative transverse momentum (pT) resolution of 1% in the barrel and 3% in the endcaps, for muons with pT of about 100GeV  [17]. The particle-flow (PF) algorithm [37] reconstructs and identifies each individual particle in an event, combining information from the various CMS detector components. Jets are clustered using the anti-kT jet finding algorithm [38, 39] with the tracks assigned to candidate vertices as inputs, and the associated missing transverse momentum pTmiss, taken as the negative vector pT sum of those jets [40]. The primary vertex (PV) is taken to be the vertex with the largest ∑pT2 of its associated tracks, as described in Section 9.4 of Ref. [41].

Events of interest are selected using a two-tiered trigger system. The first level (L1), comprised 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 4 μ s [42]. 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 [43].

During LHC Run 2, the main CMS luminosity subdetectors (luminometers) were the silicon pixel detector, the hadron forward calorimeter (HF), the pixel luminosity telescope (PLT) [44], and the fast beam conditions monitor (BCM1F) [45]. A separate data acquisition system is used to collect and store HF, PLT, and BCM1F data, as well as LHC beam-related data. A more detailed description of the CMS luminosity system is reported in Ref. [29]. For all comparisons in this paper, the reference integrated luminosity is obtained with the CMS luminometers, calibrated as described in Ref. [33] and using offline-calibrated corrections for the afterglow effects in the HF luminosity measurement.

The analysis described in this paper is largely independent of Monte Carlo (MC) simulations. However, MC simulations are used for two purposes: to determine the expected DY invariant mass distribution of the signal measured in the CMS detector; and to study possible biases in the pileup-dependent measurement of the muon track-finding efficiencies. Simulated event samples of the DY process, Z/γ∗→ℓℓ, are produced at leading order using the MadGraph 5_amc@nlo (v2.6.5) [46] generator, interfaced with pythia (v8.240) [47] for the parton shower simulation. The parameters describing the modeling of the parton shower and underlying event are based on the CP5 tune [48]. The generated MC events are passed through a full simulation of the detector using Geant4  [49].

The Z boson candidate selection and efficiency determination

The events were recorded using a single-muon trigger (HLT muon) that requires at least one muon candidate with pT>24GeV and loose isolation criteria [50]. The lowPU data were recorded using different, looser trigger configurations than those used for the highPU data. To obtain identical trigger configurations for the two data sets, the trigger decision in the lowPU was recalculated from raw data using the trigger configuration of the highPU data.

Based on the offline reconstruction, selected muon candidates consist of an “outer” standalone track in the muon system, matched to an “inner” track reconstructed in the silicon tracker [35]. The outer track is required to have signals in at least two muon detector planes. The inner track must have at least one valid hit in the silicon pixel detector and hits in more than five strip tracker layers. The matching is done by comparing parameters of the two tracks propagated onto a common surface. A combined Kalman filter fit [51] is performed in which the information from the inner and outer tracks is used to obtain a “global” muon track. For global muons, the inner and outer tracks are required to have pT>20GeV, lie within |η|<2.4, and to be matched within ΔR=(Δη)2+(Δϕ)2<0.3. Quality criteria on the global muon track fit are imposed, and it is required that the muon candidate is also reconstructed with the PF algorithm [37]. No requirements are imposed on the impact parameters of the muon track. Isolation criteria are omitted to maintain efficiency also at high pileup. For muons with pT<200GeV, i.e., about 99% of identified muon candidates, the track parameters are taken from the inner track. In other cases, the track parameters are determined by combining information from the inner and outer tracks. For all muon tracks, pT>25GeV is required to ensure that the trigger efficiency reaches a plateau.

A Z boson candidate is identified as a pair of opposite-charge muons with an invariant mass of 60<mμμ<120GeV. At least one of the two muon candidates is required to be matched with an HLT muon within ΔR<0.1. To obtain the actual number of produced Z bosons, the number of reconstructed and selected Z  boson candidates, the trigger efficiency, the muon-identification efficiency, as well as the background arising from nonresonant production, are determined from dedicated fits to the data, as explained in the following.

Trigger efficiency and signal extraction

The trigger efficiency and the number of Z boson candidates are determined from fits to the invariant dimuon mass distributions of mutually exclusive sets of events with exactly one (N1) or exactly two (N2) selected muons matched to an HLT muon. The observables N1 and N2 follow the relations3 N1=2ϵHLTμ(1-CHLTϵHLTμ)ϵIDZNZ+N1bkg,N2=CHLT(ϵHLTμ)2ϵIDZNZ+N2bkg.

Here, the quantity ϵHLTμ refers to the HLT muon trigger efficiency. The correction factor CHLT accounts for the correlation between the HLT efficiencies of the two muons. A value of CHLT>1 indicates a positive correlation between the two muons, i.e., an increased probability for the second muon to pass the HLT if the first muon passes it. The determination of CHLT is presented in Sect. 3.2. The terms N1bkg and N2bkg describe the contributions from nonresonant backgrounds. The reconstruction efficiency ϵIDZ is separately determined from the data, as described in Sect. 3.3.Fig. 1 The upper panels show the reconstructed invariant mass distributions of Z boson candidates in a 20pb-1 sample of data for events where one (upper) or two (lower) muons pass the single-muon trigger selection. The blue curve shows the fitted background contribution and the red curve illustrates the modeled signal-plus-background contribution. The error bars indicate the statistical uncertainties. The numbers of signal and background candidates are given by Nisig=Ni-Nibkg and Nibkg, respectively. Also indicated are the χ2 values per degree of freedom (dof). The lower panels contain the pulls of the distributions, defined as the difference between the data and the fit model in each bin, divided by the statistical uncertainty estimated from the expected number of entries given by the model

A fit is performed to two histograms binned in mμμ for Z  candidates contributing to N1 and N2 in which ϵHLTμ and NZ are two free parameters. In the fit, the signal is modeled by a histogram template generated from simulated Z→μμ events, convolved with a Gaussian function to take into account muon momentum scale and resolution differences between data and simulation. A falling exponential function is used to describe the nonresonant background. In Fig. 1, examples of two distributions and the results of the fits are presented. The sample shown here corresponds to an integrated luminosity of 20pb-1, yielding about 12 000 Z boson candidates.

Muon trigger correlation

The correlation between the trigger efficiencies of the two HLT muons is described by the correction factor CHLT, as introduced in Eq. (3). The dependence of CHLT on the pileup is of particular interest in this analysis because it does not cancel in the ratio in Eq. (2), and thus constitutes an important source of systematic uncertainty. The correlation was investigated in simulation, and it is largely understood to originate from isolation requirements in the trigger selection.

We determine CHLT from an MC simulation sample of Z→μμ events. As a proxy to the amount of pileup in a given event, we use the number of reconstructed PVs, NPV, an observable that is directly accessible event-by-event in both data and simulation. At fixed pileup, the distribution of NPV approximately follows a Poisson distribution with a mean at about 80% of the true pileup, as determined from DY simulation.

In the simulation, CHLT is obtained directly, by rearranging Eq. (3), as4 CHLT=4NZϵIDZN2sigN1sig+2N2sig2,

where N1sig and N2sig are the number of signal events, corresponding to N1-N1bkg and N2-N2bkg in the data.

We use data to validate the result for CHLT obtained in the simulation. To this end, events are analyzed that are triggered independently of the muon trigger, namely by using the trigger condition pTmiss>120GeV in which the contribution from muons is not included. This pTmiss trigger also records Z boson candidates for which the number of HLT muons is zero, and, thus, an additional relation for the number of reconstructed Z boson candidates with no HLT muons, denoted as N0, is obtained,5 N0=(1-2ϵHLTμ+CHLT(ϵHLTμ)2)ϵIDZNZ+N0bkg.

Together with Eq. (3), we obtain three equations for N0, N1, and N2 with three unknowns, ϵHLTμ, CHLT, and ϵIDZNZ. The correction factor CHLT can thus be determined from the number of signal events in the three categories, each obtained from a fit. The fits are performed separately in six bins of NPV where the number of bins and their boundaries are chosen such that the number of events per bin are similar.

The result is presented in Fig. 2. The red lines indicate the expectation from the simulation in which CHLT is at the level of 0.1–0.2% above unity for NPV∼30. Within the limited statistical precision of the data, good agreement of the simulation with the data is observed. We assign a systematic uncertainty of 100% of the correction, which is represented by the gray band in the figure.Fig. 2 Correction factor CHLT for the correlation between the measured muon trigger efficiencies of the two muons as a function of the number of reconstructed primary vertices, NPV, in the simulation (lines) and the data (points). The data points are drawn at the mean value of NPV in each bin of the measurement. The horizontal error bars on the points show the bin width, and the vertical error bars show the statistical uncertainty. The gray band indicates the ±100% uncertainty in the correction factor

Muon identification and reconstruction efficiency

The efficiency to reconstruct a Z boson, ϵIDZ, depends on the muon identification and reconstruction efficiency ϵIDμ for each of the two muons. In the simulation, the pileup-dependent correlation between the two identified muons is of the order of 0.01%, and thus ϵIDZ=CID(ϵIDμ)2. The value for CID≈1.0001 is taken from simulation and applied as a function of NPV. The muon efficiency ϵIDμ is defined independently of the HLT muon efficiency, such that the total number of produced Z bosons is obtained from Eq. (3).

To determine ϵIDμ, the following factorization ansatz is used:6 ϵIDμ=ϵID|GloμϵGlo|StaμϵSta|Trkμ1cT&P,

where the efficiency ϵID|Gloμ is the fraction of global muons that fulfill the full set of muon identification requirements; the efficiency ϵGlo|Staμ is the global muon efficiency, given by the fraction of standalone muons that also qualify as global muon; and the efficiency ϵSta|Trkμ is the standalone muon efficiency, defined as the fraction of muons with good inner tracks that are matched within ΔR<0.3 to outer standalone muon tracks with pT>20GeV and |η|<2.4. To obtain an unbiased set of inner tracks for the measurement of the efficiency ϵSta|Trkμ, inner tracks that are seeded from the extrapolation of outer standalone muon tracks are excluded. The term cT&P accounts for the correlations between the efficiency terms in Eq. (6). The pileup dependence of the correction from cT&P between the lowPU and the highPU data sets is estimated from simulation to be about 0.01%.

The efficiencies are determined from the data using a “tag-and-probe” methodology [1]. Identified muon candidates that are matched to the HLT muon are selected as “tag”. For each tag, a probe muon candidate of opposite charge is selected under the condition that the muon candidate pair has an invariant mass between 60 and 120GeV. The efficiency ϵx|yμ is then measured as7 ϵx|yμ=npnp+nf,

where y denotes the reference sample of muon candidates and x is the probe criterion. The numbers np and nf correspond to the number of events that pass and fail the test criterion, respectively.

For each of the efficiencies, and in bins of 20pb-1, fits to the mμμ distributions of the passing and failing distributions are performed. In the fits, the same shapes as described in Sect. 3.1 are used to describe the signal. In the histograms with passing probes, the background contribution is low and a falling exponential is used. In the case of failing probes, the nonresonant background is much larger and a more complex analytic function, comprising an exponential at high mass above the Z boson resonance and an error function at low mass, is fit. To ensure a bias-free measurement of ϵGlo|Staμ, the outer standalone muon track parameters are used to determine mμμ for the passing and failing probes. Since the resolution of these tracks is much worse, the invariant mass requirement is widened to 50–130GeV. In the case that, in a given event, the probe muon also fulfills the tag muon requirements, the tag-and-probe muons are indistinguishable and both muons are used as probes. Quantitative results for the measurement of the efficiencies are presented in Sect. 4.

Acceptance correction

To determine the true number of Z bosons in the visible phase space, an acceptance correction for losses, or gains, due to the finite resolution of the reconstructed muon tracks is required. The correction affects the number of reconstructed Z bosons itself. The efficiencies are also affected, primarily in the matching of inner and outer tracks, and, to a lesser extent, if muon tracks for passing and for failing probes have different resolutions. The size of the correction is determined from the simulation by comparing the efficiency-corrected number of Z bosons as obtained from the measurement with the generated number of Z bosons in the visible phase space, as defined for bare leptons after final-state radiation (FSR), but before detector simulation.

For outer muon tracks, resolution effects lead to an acceptance correction of about 1.35%, which is independent of pileup and constant over the full year of data taking. For inner tracks, the acceptance correction is 0.15% at low pileup, and it is negligibly small for the highPU data set. This pileup dependency of 0.15% is applied as an additional correction, and an uncertainty of 100% of the correction is assigned. For a direct cross section measurement, the size of the bias could be further reduced through optimized track selection criteria. However, for this analysis it suffices that the pileup-independent components of the acceptance correction cancel in the cross section ratio.Fig. 3 Upper: the efficiency-corrected Z boson rate, compared to the reference luminosity measurement, in the LHC fill 6255, recorded on September 29, 2017 [33]. Each bin corresponds to about 20pb-1, as determined by the reference measurement. For shape comparison, the integrated Z boson rate is normalized to the reference integrated luminosity. The panel at the bottom shows the ratio of the two measurements. The vertical error bars show the statistical uncertainty in the Z boson rate. Lower: the measured single-muon efficiencies as functions of time for the same LHC fill. The vertical error bars show the statistical uncertainty in the efficiency

The L1 trigger corrections

The term “prefiring” describes the effect that a trigger decision is assigned to a bunch crossing preceding the one in which the collision actually took place. In the CMS experiment, the triggering and readout of events in adjacent bunch crossings is vetoed in the trigger logic. However, due to the limited time resolution of the muon system, the assignment of muon candidates to bunch crossings can be wrong, and thus lead to a loss of good events, i.e., a trigger inefficiency. Since the tag-and-probe efficiency measurement is insensitive to this effect, the inefficiency due to prefiring is measured in a dedicated analysis. During the 2017 data taking, measurable prefiring occurred at nonnegligible rates for the L1 muon and ECAL triggers [42, 50]. For the L1 muon trigger, a correction for trigger inefficiency of 0.6% was found, independent of pileup and time. In contrast, losses due to prefiring of the ECAL require a pileup-dependent correction of 0.05–0.2% for the pileup range 0–50. The prefiring from ECAL triggers is caused mainly by initial or final state radiation, pileup jets, or the underlying event. The impact on the lowPU data was somewhat larger due to the lower ECAL trigger thresholds, and for the lowPU data a correction of 0.6% is applied.

Results and uncertainties

The procedures described above to measure the number of reconstructed Z bosons and their efficiencies are applied to the data in bins of 20pb-1. Since the amount of data at the end of a fill does not usually add up to 20pb-1, the last bin is included as long as it contains more than 10pb-1. In case the last bin contains <10pb-1 it is merged with the second to last. Altogether, in 2017 about 2000 such bins are defined.

Normalized Z boson rate

In Fig. 3, the measured Z boson rate and efficiencies are shown for the data recorded during a typical LHC fill of the highPU data-taking period in 2017. In this fill, pp collision data were recorded continuously for about 16 h. An integrated luminosity of about 515pb-1 was accumulated, corresponding to 25 bins of 20pb-1 each, and the last bin contains the remaining 15pb-1 of data. The instantaneous luminosity decreased from initially 15nb-1s-1, corresponding to a pileup of about 50, to about one third of the initial value. In Fig. 3 (upper), a comparison between the conventional measurement of the recorded luminosity and the measurement using the Z boson rate is shown. The integral of the measured Z boson rate is normalized to the integral of the reference luminosity. The shapes of the two independent measurements agree very well. In Fig. 3 (lower), the muon trigger and identification efficiencies, ϵHLTμ and ϵIDμ, separated into its different components, as applied to the respective time intervals, are presented. In particular, a significant dependence on time, and thus on pileup, is seen for the HLT muon efficiency for which a rise by about 3% is measured as the pileup decreases in the course of the fill.

To compare the relative linearity between the measurement of the Z  boson rate and the CMS reference luminosity, the fiducial cross section for Z boson production, normalized to the average Z  boson cross section, is studied as a function of the instantaneous luminosity. The result is shown in Fig. 4, where the average instantaneous luminosity in each 20pb-1 bin is used to assign an instantaneous luminosity bin from which the average cross section is obtained. The straight-line fit to the data yields a value of 0.2% below unity for the intercept with the y-axis at low pileup. This value gives an estimate of the agreement between Z boson counting and reference luminosity measurement in the extrapolation from the low to the high pileup data.Fig. 4 Fiducial Z boson production cross section as a function of the instantaneous recorded luminosity, normalized to the average measured cross section. In each point, multiple measurements of the delivered Z boson rates are combined, the error bars correspond to the statistical uncertainties of the Z boson rate measurement. The leftmost point, highlighted in red, corresponds to the lowPU data. The result of a fit to a linear function is shown as a red line and the statistical uncertainties are covered by the gray band

Measurement of the absolute luminosity

Using Eq. (2), the integrated luminosity of the highPU data, referred to in the following as “Z luminosity”, is determined from the integrated luminosity of the lowPU data, using the ratio of the number of Z bosons recorded during the two periods, corrected for reconstruction and trigger efficiencies as determined in intervals of 20pb-1. In the ratio, all correlated uncertainties cancel, as detailed in the following section.

In Fig. 5, the distribution of the ratios between the Z luminosity and the reference luminosity as obtained from the CMS luminosity systems is shown. Each entry in the histogram corresponds to an interval of 20pb-1 in the highPU data recorded in 2017. The central values of both measurements are in good agreement with a difference of 0.3%. The standard deviation of about 1.2% is predominantly of statistical nature, and close to the expectation for the pure statistical uncertainty of about 12 000 Z boson candidates reconstructed in intervals of 20pb-1 each. The ratio of Z luminosity and reference luminosity as a function of the integrated luminosity is shown in Fig. 6. This figure shows a good stability of the Z luminosity measurement over the full year. No significant patterns in time are observed.

Statistical and systematic uncertainties, and additional cross checks

The uncertainties in the analysis were studied with the focus on the ratio r=NhighPUZ/NlowPUZ of the Z boson counts between two data samples in 2017 as presented in Eq. (2). The full list of considered sources of uncertainty in the cross sections and their ratio is given in Table 1, and described in the following.

Statistical uncertainties are driven by the number of available Z  bosons and also include the statistical uncertainty in the efficiencies. As mentioned above, in one interval of 20pb-1, about 12 000 Z bosons candidates with two muons in the final state are available, leading to an average statistical uncertainty of 1.17%. For all intervals combined, the statistical uncertainty for the full 2017 highPU data is negligibly small. The lowPU data set corresponds to an integrated luminosity of about 200pb-1, and this contributes a statistical uncertainty of about 0.35%.

As discussed in Sect. 3.2, the correction factor for correlations in the trigger efficiencies of the two muons CHLT is determined from data and simulation; it is about 0.1% above unity for the highPU sample, consistently for data and MC simulation. The uncertainty in CHLT is assigned to be 100% of the correction.

Possible correlations between the two identified muons and imperfect factorization of muon identification and reconstruction efficiencies were discussed in Sect. 3.3. The simulation shows negligible effects, and corrections at the level of 0.01% are applied. The corresponding uncertainties are estimated to be 100% of the correction.

The limited resolution of the reconstructed muon tracks leads to a bias in the measurement, as described in Sect. 3.4. The bias from the inner track resolution is smaller, but pileup dependent, and remains in the ratio with a magnitude of 0.15%. The outer track resolution leads to a large bias, but is mostly pileup independent and cancels in the ratio. A correction is derived from simulation and two independent sources of uncertainty, estimated to be 100% of the correction each, are assigned each for the inner and outer tracks, respectively.

Systematic uncertainties in the L1 muon prefiring corrections, described in Sect. 3.5, cancel completely in the ratio, whereas the uncertainties due to ECAL prefiring have a different magnitude between the two data sets and cancel only partially. The remaining uncertainty is estimated to be 20% of the nominal correction [42].Fig. 5 Distribution of the ratio of integrated luminosities between Z boson counting and the reference luminometer. The entries, each corresponding to one interval of 20pb-1 of highPU data, are weighted with the respective measured luminosity

The extraction of the signal and background contributions was studied using alternative fit models. For the signal model, the Gaussian resolution function convolved with the histogram template is varied. First, the histogram template is used alone, i.e., fully relying on the simulation and leaving no further degrees of freedom to the fit. Secondly, the histogram template is convolved with a Crystal Ball function [52], which has four free parameters and gives the fit more freedom to incorporate possible differences between data and simulation. Thirdly, the histogram template is constructed from generator-level post-FSR leptons, instead of mirroring the selection at detector level. This template is then convolved with a Crystal Ball function. The three variations lead to changes in the extracted numbers of Z bosons, and the efficiencies, in both the highPU and lowPU data sets. While the trends are correlated, the relative magnitudes are different, and this leads to a significant residual uncertainty. The envelope of the three variations is taken to quantify this uncertainty.

The two types of background models are varied independently. For the categories with major background contributions, the Das function [53], a wide Gaussian distribution with exponential tails is used as an alternative function, which has four free parameters, as opposed to three for the nominal model. In the other cases, the falling exponential is substituted by a uniform distribution.Fig. 6 The luminosity as measured from Z bosons divided by the reference luminosity as a function of the integrated luminosity for the 2017 highPU data. Each green point represents the ratio from one measurement of the number of Z bosons. The blue lines show the averages of 50 consecutive measurements, corresponding to an average of 1fb-1 of data. The gray band has a width of 1.5%, corresponding to the uncertainty in the ratio of the integrated reference luminosities from the lowPU to the one of highPU  [33]

Table 1 Summary of the uncertainties in the number of delivered Z bosons in the 2017 highPU and lowPU data, and their ratio. The symbol δ denotes the relative uncertainty, i.e., δx=Δx/x. The systematic and statistical uncertainties are added in quadrature to obtain the total uncertainty

	δNhighPUZ [%]	δNlowPUZ [%]	δ(NhighPUZ/NlowPUZ) [%]	
HLT correlation CHLT	±0.1	±0.06	±0.04	
Dimuon correlation CID	±0.00	∓0.01	±0.01	
Inner-outer track correlation cT&P	±0.01	∓0.01	±0.01	
Inner track resolution	±0.01	±0.16	∓0.15	
Outer track resolution	±1.35	±1.36	∓0.01	
L1 muon prefiring	±0.15	±0.15	0	
ECAL prefiring	±0.04	±0.14	∓0.10	
Signal modeling up	-0.63	-0.75	+0.19	
Signal modeling down	+0.51	+0.71	-0.21	
Background modeling up	-0.15	-0.31	+0.16	
Background modeling down	-0.09	-0.05	-0.04	
Systematic up	+1.45	+1.56	+0.31	
Systematic down	-1.50	-1.60	-0.28	
Statistical	±0.03	±0.35	±0.35	
Total up	+1.45	+1.60	+0.47	
Total down	-1.50	-1.64	-0.45	

The total systematic uncertainty is obtained by adding the systematic uncertainties listed in Table 1 in quadrature. In combination with the statistical uncertainty of 0.35%, the total uncertainty to transfer the luminosity from the lowPU data to the highPU data in 2017 is8 δr=-0.28%+0.31%(syst)±0.35%(stat)=-0.45%+0.47%,

where the statistical uncertainty is due to the limited size of the lowPU data set. The systematic uncertainty is driven by the uncertainties in the signal modeling, followed by the background modeling and acceptance corrections. Overall, a total uncertainty of about 0.5% is obtained.

Multiple cross-checks were performed to test the robustness of the result. The size of the luminosity bin was varied from 20 down to 15 and up to 30pb-1, and negligible differences with respect to the nominal measurement were found. It was further verified that the measurement is independent of the choice of the bin width chosen for the mμμ distribution, by varying it by factors of 1/2 and 2. Independence of the result on the chosen fit interval was tested using two alternative ranges: a more narrow interval from mμμ∈[70,110]GeV and a wider interval from mμμ∈[50,130]GeV. Both variations have a strong impact on NZ since the phase space of the measurement changes, but, as expected, the effect cancels almost completely in the ratio. The results of these cross checks are summarized in Table 2.Table 2 Summary of cross checks performed by varying the length of the luminosity interval, the bin width of the mμμ histograms, and the range of the fit. As in Table 1, the resulting variations of the number of Z bosons in the 2017 highPU and lowPU data, and their ratio, are shown. The δ denotes the relative variations, i.e., δx=Δx/x

	δNhighPUZ [%]	δNlowPUZ [%]	δ(NhighPUZ/NlowPUZ) [%]	
Lum. bin size 30pb-1	-0.05	-0.01	-0.04	
Lum. bin size 15pb-1	+0.04	+0.07	-0.03	
Mass bin width 1GeV	-0.02	-0.06	+0.03	
Mass bin width 0.25GeV	-0.01	+0.01	-0.02	
Mass range [50,130]GeV	+1.25	+1.24	+0.00	
Mass range [70,110]GeV	-2.32	-2.26	-0.05	

Discussion and outlook

With an uncertainty in the transfer factor of about 0.5% for the 2017 data, this analysis shows that Z boson counting can provide an independent and competitive method to extrapolate and integrate luminosity calibrations. The results from Z boson counting are independent of the conventional luminosity measurements. They can be treated as uncorrelated in combinations, which can lead to significant improvements in the combined uncertainty.

Taking the current precision of 1.7% for the integrated luminosity in the lowPU data [33], the integrated luminosity in the highPU 2017 data could potentially be determined to a precision of better than 1.8%, in contrast to the preliminary uncertainty of the reference luminosity measurement of 2.3% [33].

A unique aspect of Z boson counting is that the relevant efficiency corrections as a function of time can be calibrated from the same event sample. This feature makes the method robust not only against small changes in detector response, but also across different detector configurations. In general, once a precision measurement of the integrated luminosity is available, such as that for the lowPU data in 2017, the integrated luminosity for all data recorded at the same center-of-mass energy can be determined using the Z boson counting. However, each transfer between data sets requires detailed studies of the correlations of the muon trigger and the reconstruction efficiencies.

In this paper, the full analysis was presented for the data from 2017, when a dedicated and sufficiently large sample of lowPU data was recorded. Under such conditions, a large fraction of the systematic uncertainties cancels in the ratio. For the most precise CMS measurement of the luminosity to date [29], published for 2016, an extrapolation and integration uncertainty of 0.7% was reported. For 2016, no lowPU data set was recorded. Further studies on the impact of different detector conditions would be required to extrapolate from the 2016 data set. If, hypothetically, an extrapolation uncertainty of 0.5% for Z boson counting were achievable also in the 2016 data, the uncertainty of 1.2% in the total integrated luminosity for 2016 could be improved to 1.1%.

The dominant contribution to the uncertainty comes from the statistical uncertainty, which is driven by the size of the lowPU data sample. The lowPU data recorded in 2017 correspond to an integrated luminosity of about 200pb-1. A significant increase of the sample size, e.g., by a factor 3 or 4, would make the statistical uncertainty negligible.

In the coming years, during the ongoing LHC Run 3 and beyond, additional measurements and studies on the main systematic uncertainties will be performed, and that is expected to improve the precision of the method further. Furthermore, the method is expected to contribute substantially to the combination of integrated luminosity measurements for different data sets. In the longer term, pileup conditions of up to 200 pp collisions per bunch crossing are expected at the HL-LHC [31]. In both Run 3 and at the HL-LHC, the uncertainties due to extrapolation from vdM conditions to standard data taking are expected to remain substantial. In such conditions, the method of Z boson counting has the potential to provide significant improvements.

Summary

The precision measurement of the Z boson production rate provides a complementary method to transfer integrated luminosity measurements between data sets. This study makes use of events with Z bosons decaying into a pair of muons. The data were recorded with the CMS experiment at the CERN LHC in 2017, at a proton–proton center-of-mass energy of 13TeV. The integrated luminosity of a larger data sample recorded in 2017 is obtained from that of a smaller data set recorded at lower pileup using the ratio of the efficiency-corrected numbers of Z bosons counted in the two data sets. The full set of efficiencies and correlation correction factors for triggering, reconstruction, and selection are determined in intervals of 20pb-1 from the same Z boson data samples. Monte Carlo simulations are used only to describe the shape of the resonant Z boson signal and for the study of possible biases of the method. A detailed quantitative study of the systematic uncertainties and their dependencies on pileup is performed for the first time. In the integrated luminosity ratio, the systematic uncertainties cancel almost completely, with the exception of the pileup-dependent effects. The resulting uncertainty in the ratio is 0.5%. With its high precision, the Z boson counting is competitive with and independent of conventional methods for the extrapolation and integration of luminosity.

Acknowledgements

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 centers and personnel of the Worldwide LHC Computing Grid and other centers 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); MoER, ERC PUT and ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); 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); LAS (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 program and the European Research Council and Horizon 2020 Grant, contract Nos. 675440, 724704, 752730, 758316, 765710, 824093, 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 124845, K 124850, K 128713, K 128786, K 129058, K 131991, K 133046, K 138136, K 143460, K 143477, 2020-2.2.1-ED-2021-00181, and TKP2021-NKTA-64 (Hungary); the Council of Science and Industrial Research, India; 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 B05F650021 (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

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Release and preservation of data used by the CMS Collaboration as the basis for publications is guided by the CMS policy as stated in https://cms-docdb.cern.ch/cgibin/PublicDocDB/RetrieveFile?docid=6032 &filename=CMSDataPolicyV1.2.pdf &version=2. CMS data preservation, re-use and open access policy.]

Declarations

Conflict of interest

The authors declare that they have no conflict of interest.

T. Tuuva, M. Narain, S. Wimpenny, G. R. Snow, A. Vorobyev: Deceased.
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