https://doi.org/10.1140/epjc/s10052-021-09538-2
Regular Article - Experimental Physics
Precision luminosity measurement in proton–proton collisions at 
in 2015 and 2016 at CMS
1
Yerevan Physics Institute, Yerevan, Armenia
2
Institut für Hochenergiephysik, Vienna, Austria
3
Institute for Nuclear Problems, Minsk, Belarus
4
Universiteit Antwerpen, Antwerp, Belgium
5
Vrije Universiteit Brussel, Brussels, Belgium
6
Université Libre de Bruxelles, Brussels, Belgium
7
Ghent University, Ghent, Belgium
8
Université Catholique de Louvain, Louvain-la-Neuve, Belgium
9
Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil
10
Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
11
Universidade Estadual Paulista, Universidade Federal do ABC, São Paulo, Brazil
12
Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria
13
University of Sofia, Sofia, Bulgaria
14
Beihang University, Beijing, China
15
Department of Physics, Tsinghua University, Beijing, China
16
Institute of High Energy Physics, Beijing, China
17
State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China
18
Sun Yat-Sen University, Guangzhou, China
19
Institute of Modern Physics and Key Laboratory of Nuclear Physics and Ion-beam Application (MOE)-Fudan University, Shanghai, China
20
Zhejiang University, Hangzhou, China
21
Universidad de Los Andes, Bogotá, Colombia
22
Universidad de Antioquia, Medellín, Colombia
23
Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia
24
Faculty of Science, University of Split, Split, Croatia
25
Institute Rudjer Boskovic, Zagreb, Croatia
26
University of Cyprus, Nicosia, Cyprus
27
Charles University, Prague, Czech Republic
28
Escuela Politecnica Nacional, Quito, Ecuador
29
Universidad San Francisco de Quito, Quito, Ecuador
30
Academy of Scientific Research and Technology of the Arab Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt
31
Center for High Energy Physics (CHEP-FU), Fayoum University, El-Fayoum, Egypt
32
National Institute of Chemical Physics and Biophysics, Tallinn, Estonia
33
Department of Physics, University of Helsinki, Helsinki, Finland
34
Helsinki Institute of Physics, Helsinki, Finland
35
Lappeenranta University of Technology, Lappeenranta, Finland
36
IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
37
Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
38
Université de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France
39
Institut de Physique des 2 Infinis de Lyon (IP2I ), Villeurbanne, France
40
Georgian Technical University, Tbilisi, Georgia
41
I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
42
III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany
43
III. Physikalisches Institut B, RWTH Aachen University, Aachen, Germany
44
Deutsches Elektronen-Synchrotron, Hamburg, Germany
45
University of Hamburg, Hamburg, Germany
46
Karlsruher Institut fuer Technologie, Karlsruhe, Germany
47
Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi, Greece
48
National and Kapodistrian University of Athens, Athens, Greece
49
National Technical University of Athens, Athens, Greece
50
University of Ioánnina, Ioannina, Greece
51
MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary
52
Wigner Research Centre for Physics, Budapest, Hungary
53
Institute of Nuclear Research ATOMKI, Debrecen, Hungary
54
Institute of Physics, University of Debrecen, Debrecen, Hungary
55
Eszterhazy Karoly University, Karoly Robert Campus, Gyongyos, Hungary
56
Indian Institute of Science (IISc), Bangalore, India
57
National Institute of Science Education and Research, HBNI, Bhubaneswar, India
58
Panjab University, Chandigarh, India
59
University of Delhi, Delhi, India
60
Saha Institute of Nuclear Physics, HBNI, Kolkata, India
61
Indian Institute of Technology Madras, Chennai, India
62
Bhabha Atomic Research Centre, Mumbai, India
63
Tata Institute of Fundamental Research-A, Mumbai, India
64
Tata Institute of Fundamental Research-B, Mumbai, India
65
Indian Institute of Science Education and Research (IISER), Pune, India
66
Department of Physics, Isfahan University of Technology, Isfahan, Iran
67
Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
68
University College Dublin, Dublin, Ireland
69
INFN Sezione di Bari, Universit’a di Bari, Politecnico di Bari, Bari, Italy
70
INFN Sezione di Bologna, Università di Bologna, Bologna, Italy
71
INFN Sezione di Catania, Università di Catania, Catania, Italy
72
INFN Sezione di Firenze, Università di Firenze, Florence, Italy
73
INFN Laboratori Nazionali di Frascati, Frascati, Italy
74
INFN Sezione di Genova, Università di Genova, Genoa, Italy
75
INFN Sezione di Milano-Bicocca, Università di Milano-Bicocca, Milan, Italy
76
INFN Sezione di Napoli, Università di Napoli ‘Federico II’, Naples, Italy, Università della Basilicata, Potenza, Italy, Università G. Marconi, Rome, Italy
77
INFN Sezione di Padova, Università di Padova, Padua, Italy, Università di Trento, Trento, Italy
78
INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
79
INFN Sezione di Perugia, Università di Perugia, Perugia, Italy
80
INFN Sezione di Pisa, Università di Pisa, Scuola Normale Superiore di Pisa, Pisa, Italy, Università di Siena, Siena, Italy
81
INFN Sezione di Roma, Sapienza Università di Roma, Rome, Italy
82
INFN Sezione di Torino, Università di Torino, Turin, Italy, Università del Piemonte Orientale, Novara, Italy
83
INFN Sezione di Trieste, Università di Trieste, Trieste, Italy
84
Kyungpook National University, Daegu, Korea
85
Institute for Universe and Elementary Particles, Chonnam National University, Kwangju, Korea
86
Hanyang University, Seoul, Korea
87
Korea University, Seoul, Korea
88
Department of Physics, Kyung Hee University, Seoul, Republic of Korea
89
Sejong University, Seoul, Korea
90
Seoul National University, Seoul, Korea
91
University of Seoul, Seoul, Korea
92
Department of Physics, Yonsei University, Seoul, Korea
93
Sungkyunkwan University, Suwon, Korea
94
College of Engineering and Technology, American University of the Middle East (AUM), Egaila, Kuwait
95
Riga Technical University, Riga, Latvia
96
Vilnius University, Vilnius, Lithuania
97
National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia
98
Universidad de Sonora (UNISON), Hermosillo, Mexico
99
Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico
100
Universidad Iberoamericana, Mexico City, Mexico
101
Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
102
University of Montenegro, Podgorica, Montenegro
103
University of Auckland, Auckland, New Zealand
104
University of Canterbury, Christchurch, New Zealand
105
National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan
106
Faculty of Computer Science, Electronics and Telecommunications, AGH University of Science and Technology, Kraków, Poland
107
National Centre for Nuclear Research, Swierk, Poland
108
Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland
109
Laboratório de Instrumentação e Física Experimental de Partículas, Lisbon, Portugal
110
Joint Institute for Nuclear Research, Dubna, Russia
111
Petersburg Nuclear Physics Institute, Gatchina (St. Petersburg), Russia
112
Institute for Nuclear Research, Moscow, Russia
113
Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of NRC ‘Kurchatov Institute’, Moscow, Russia
114
Moscow Institute of Physics and Technology, Moscow, Russia
115
National Research Nuclear University ‘Moscow Engineering Physics Institute’ (MEPhI), Moscow, Russia
116
P.N. Lebedev Physical Institute, Moscow, Russia
117
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia
118
Novosibirsk State University (NSU), Novosibirsk, Russia
119
Institute for High Energy Physics of National Research Centre ‘Kurchatov Institute’, Protvino, Russia
120
National Research Tomsk Polytechnic University, Tomsk, Russia
121
Tomsk State University, Tomsk, Russia
122
Faculty of Physics and VINCA Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia
123
Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain
124
Universidad Autónoma de Madrid, Madrid, Spain
125
Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA), Universidad de Oviedo, Oviedo, Spain
126
Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain
127
University of Colombo, Colombo, Sri Lanka
128
Department of Physics, University of Ruhuna, Matara, Sri Lanka
129
CERN, European Organization for Nuclear Research, Geneva, Switzerland
130
Paul Scherrer Institut, Villigen, Switzerland
131
ETH Zurich-Institute for Particle Physics and Astrophysics (IPA), Zurich, Switzerland
132
Universität Zürich, Zurich, Switzerland
133
National Central University, Chung-Li, Taiwan
134
National Taiwan University (NTU), Taipei, Taiwan
135
Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand
136
Physics Department, Science and Art Faculty, Çukurova University, Adana, Turkey
137
Physics Department, Middle East Technical University, Ankara, Turkey
138
Bogazici University, Istanbul, Turkey
139
Istanbul Technical University, Istanbul, Turkey
140
Istanbul University, Istanbul, Turkey
141
Institute for Scintillation Materials of National Academy of Science of Ukraine, Kharkov, Ukraine
142
National Scientific Center, Kharkov Institute of Physics and Technology, Kharkov, Ukraine
143
University of Bristol, Bristol, UK
144
Rutherford Appleton Laboratory, Didcot, UK
145
Imperial College, London, UK
146
Brunel University, Uxbridge, UK
147
Baylor University, Waco, USA
148
Catholic University of America, Washington, DC, USA
149
The University of Alabama, Tuscaloosa, USA
150
Boston University, Boston, USA
151
Brown University, Providence, USA
152
University of California, Davis, Davis, USA
153
University of California, Los Angeles, USA
154
University of California, Riverside, Riverside, USA
155
University of California, San Diego, La Jolla, USA
156
Department of Physics, University of California, Santa Barbara, Santa Barbara, USA
157
California Institute of Technology, Pasadena, USA
158
Carnegie Mellon University, Pittsburgh, USA
159
University of Colorado Boulder, Boulder, USA
160
Cornell University, Ithaca, USA
161
Fermi National Accelerator Laboratory, Batavia, USA
162
University of Florida, Gainesville, USA
163
Florida State University, Tallahassee, USA
164
Florida Institute of Technology, Melbourne, USA
165
University of Illinois at Chicago (UIC), Chicago, USA
166
The University of Iowa, Iowa City, USA
167
Johns Hopkins University, Baltimore, USA
168
The University of Kansas, Lawrence, USA
169
Kansas State University, Manhattan, USA
170
Lawrence Livermore National Laboratory, Livermore, USA
171
University of Maryland, College Park, USA
172
Massachusetts Institute of Technology, Cambridge, USA
173
University of Minnesota, Minneapolis, USA
174
University of Mississippi, Oxford, USA
175
University of Nebraska-Lincoln, Lincoln, USA
176
State University of New York at Buffalo, Buffalo, USA
177
Northeastern University, Boston, USA
178
Northwestern University, Evanston, USA
179
University of Notre Dame, Notre Dame, USA
180
The Ohio State University, Columbus, USA
181
Princeton University, Princeton, USA
182
University of Puerto Rico, Mayagüez, USA
183
Purdue University, West Lafayette, USA
184
Purdue University Northwest, Hammond, USA
185
Rice University, Houston, USA
186
University of Rochester, Rochester, USA
187
Rutgers, The State University of New Jersey, Piscataway, USA
188
University of Tennessee, Knoxville, USA
189
Texas A&M University, College Station, USA
190
Texas Tech University, Lubbock, USA
191
Vanderbilt University, Nashville, USA
192
University of Virginia, Charlottesville, USA
193
Wayne State University, Detroit, USA
194
University of Wisconsin-Madison, Madison, WI, USA
195
Vienna University of Technology, Vienna, Austria
196
Institute of Basic and Applied Sciences, Faculty of Engineering, Arab Academy for Science, Technology and Maritime Transport, Alexandria, Egypt
197
Université Libre de Bruxelles, Brussels, Belgium
198
Universidade Estadual de Campinas, Campinas, Brazil
199
Federal University of Rio Grande do Sul, Porto Alegre, Brazil
200
University of Chinese Academy of Sciences, Beijing, China
201
Department of Physics, Tsinghua University, Beijing, China
202
UFMS, Nova Andradina, Brazil
203
Department of Physics, Nanjing Normal University, Nanjing, China
204
The University of Iowa, Iowa City, USA
205
Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of NRC ‘Kurchatov Institute’, Moscow, Russia
206
Joint Institute for Nuclear Research, Dubna, Russia
207
Ain Shams University, Cairo, Egypt
208
Zewail City of Science and Technology, Zewail, Egypt
209
British University in Egypt, Cairo, Egypt
210
Purdue University, West Lafayette, USA
211
Université de Haute Alsace, Mulhouse, France
212
Erzincan Binali Yildirim University, Erzincan, Turkey
213
CERN, European Organization for Nuclear Research, Geneva, Switzerland
214
III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany
215
University of Hamburg, Hamburg, Germany
216
Department of Physics, Isfahan University of Technology, Isfahan, Iran
217
Brandenburg University of Technology, Cottbus, Germany
218
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia
219
Physics Department, Faculty of Science, Assiut University, Assiut, Egypt
220
Eszterhazy Karoly University, Karoly Robert Campus, Gyongyos, Hungary
221
Institute of Physics, University of Debrecen, Debrecen, Hungary
222
Institute of Nuclear Research ATOMKI, Debrecen, Hungary
223
MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary
224
Wigner Research Centre for Physics, Budapest, Hungary
225
IIT Bhubaneswar, Bhubaneswar, India
226
Institute of Physics, Bhubaneswar, India
227
G.H.G. Khalsa College, Punjab, India
228
Shoolini University, Solan, India
229
University of Hyderabad, Hyderabad, India
230
University of Visva-Bharati, Santiniketan, India
231
Indian Institute of Technology (IIT), Mumbai, India
232
Deutsches Elektronen-Synchrotron, Hamburg, Germany
233
Sharif University of Technology, Tehran, Iran
234
Department of Physics, University of Science and Technology of Mazandaran, Behshahr, Iran
235
INFN Sezione di Bari, Università di Bari, Politecnico di Bari, Bari, Italy
236
Italian National Agency for New Technologies, Energy and Sustainable Economic Development, Bologna, Italy
237
Centro Siciliano di Fisica Nucleare e di Struttura Della Materia, Catania, Italy
238
Università di Napoli ‘Federico II’, Naples, Italy
239
Riga Technical University, Riga, Latvia
240
Consejo Nacional de Ciencia y Tecnología, Mexico City, Mexico
241
IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
242
Institute for Nuclear Research, Moscow, Russia
243
National Research Nuclear University ‘Moscow Engineering Physics Institute’ (MEPhI), Moscow, Russia
244
St. Petersburg State Polytechnical University, St. Petersburg, Russia
245
University of Florida, Gainesville, USA
246
Imperial College, London, UK
247
P.N. Lebedev Physical Institute, Moscow, Russia
248
California Institute of Technology, Pasadena, USA
249
INFN Sezione di Padova, Università di Padova, Università di Trento, Trento, Italy, Padua, Italy
250
Budker Institute of Nuclear Physics, Novosibirsk, Russia
251
Faculty of Physics, University of Belgrade, Belgrade, Serbia
252
Trincomalee Campus, Eastern University, Nilaveli, Sri Lanka
253
INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
254
National and Kapodistrian University of Athens, Athens, Greece
255
Ecole Polytechnique Fédérale Lausanne, Lausanne, Switzerland
256
Universität Zürich, Zurich, Switzerland
257
Stefan Meyer Institute for Subatomic Physics, Vienna, Austria
258
Laboratoire d’Annecy-le-Vieux de Physique des Particules, IN2P3-CNRS, Annecy-le-Vieux, France
259
Şırnak University, Sirnak, Turkey
260
Research Center of Experimental Health Science, Near East University, Nicosia, Turkey
261
Konya Technical University, Konya, Turkey
262
Faculty of Engineering, Istanbul University-Cerrahpasa, Istanbul, Turkey
263
Mersin University, Mersin, Turkey
264
Piri Reis University, Istanbul, Turkey
265
Adiyaman University, Adiyaman, Turkey
266
Ozyegin University, Istanbul, Turkey
267
Izmir Institute of Technology, Izmir, Turkey
268
Necmettin Erbakan University, Konya, Turkey
269
Bozok Universitetesi Rektörlügü, Yozgat, Turkey
270
Marmara University, Istanbul, Turkey
271
Milli Savunma University, Istanbul, Turkey
272
Kafkas University, Kars, Turkey
273
Istanbul Bilgi University, Istanbul, Turkey
274
Hacettepe University, Ankara, Turkey
275
Vrije Universiteit Brussel, Brussels, Belgium
276
School of Physics and Astronomy, University of Southampton, Southampton, UK
277
IPPP Durham University, Durham, UK
278
Faculty of Science, Monash University, Clayton, Australia
279
Bethel University, St. Paul, Minneapolis, USA
280
Karamanoğlu Mehmetbey University, Karaman, Turkey
281
Bingol University, Bingol, Turkey
282
Georgian Technical University, Tbilisi, Georgia
283
Sinop University, Sinop, Turkey
284
Mimar Sinan University, Istanbul, Turkey
285
Erciyes University, Kayseri, Turkey
286
Texas A&M University at Qatar, Doha, Qatar
287
Kyungpook National University, Daegu, Korea
288
CERN, 1211, Geneva 23, Switzerland
q
cms-publication-committee-chair@cern.ch
Received:
5
April
2021
Accepted:
9
August
2021
Published online:
9
September
2021
The measurement of the luminosity recorded by the CMS detector installed at LHC interaction point 5, using proton–proton collisions at 
in 2015 and 2016, is reported. The absolute luminosity scale is measured for individual bunch crossings using beam-separation scans (the van der Meer method), with a relative precision of 1.3 and 1.0% in 2015 and 2016, respectively. The dominant sources of uncertainty are related to residual differences between the measured beam positions and the ones provided by the operational settings of the LHC magnets, the factorizability of the proton bunch spatial density functions in the coordinates transverse to the beam direction, and the modeling of the effect of electromagnetic interactions among protons in the colliding bunches. When applying the van der Meer calibration to the entire run periods, the integrated luminosities when CMS was fully operational are 2.27 and 36.3 
in 2015 and 2016, with a relative precision of 1.6 and 1.2%, respectively. These are among the most precise luminosity measurements at bunched-beam hadron colliders.
© The Author(s) 2021
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