
==== 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

39115154
12925
10.1140/epjc/s10052-024-12925-0
Regular Article - Experimental Physics
Constraints on anomalous Higgs boson couplings from its production and decay using the WW channel in proton–proton collisions at s=13TeV
CMS CollaborationHayrapetyan A. 1
http://orcid.org/0009-0000-0684-6742
Tumasyan A. 1189
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Adam W. 2
Andrejkovic J. W. 2
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Bergauer T. 2
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Dragicevic M. 2
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Templ S. 2
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cms-publication-committee-chair@cern.ch

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1 https://ror.org/00ad27c73 grid.48507.3e 0000 0004 0482 7128 Yerevan Physics Institute, Yerevan, Armenia
2 https://ror.org/039shy520 grid.450258.e 0000 0004 0625 7405 Institut für Hochenergiephysik, Vienna, Austria
3 https://ror.org/008x57b05 grid.5284.b 0000 0001 0790 3681 Universiteit Antwerpen, Antwerp, Belgium
4 https://ror.org/006e5kg04 grid.8767.e 0000 0001 2290 8069 Vrije Universiteit Brussel, Brussels, Belgium
5 https://ror.org/01r9htc13 grid.4989.c 0000 0001 2348 6355 Université Libre de Bruxelles, Brussels, Belgium
6 https://ror.org/00cv9y106 grid.5342.0 0000 0001 2069 7798 Ghent University, Ghent, Belgium
7 https://ror.org/02495e989 grid.7942.8 0000 0001 2294 713X Université Catholique de Louvain, Louvain-la-Neuve, Belgium
8 https://ror.org/02wnmk332 grid.418228.5 0000 0004 0643 8134 Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil
9 https://ror.org/0198v2949 grid.412211.5 0000 0004 4687 5267 Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
10 grid.410543.7 0000 0001 2188 478X Universidade Estadual Paulista, Universidade Federal do ABC, São Paulo, Brazil
11 grid.410344.6 0000 0001 2097 3094 Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria
12 https://ror.org/02jv3k292 grid.11355.33 0000 0001 2192 3275 University of Sofia, Sofia, Bulgaria
13 https://ror.org/04xe01d27 grid.412182.c 0000 0001 2179 0636 Instituto De Alta Investigación, Universidad de Tarapacá, Casilla 7 D, Arica, Chile
14 https://ror.org/00wk2mp56 grid.64939.31 0000 0000 9999 1211 Beihang University, Beijing, China
15 https://ror.org/03cve4549 grid.12527.33 0000 0001 0662 3178 Department of Physics, Tsinghua University, Beijing, China
16 https://ror.org/03v8tnc06 grid.418741.f 0000 0004 0632 3097 Institute of High Energy Physics, Beijing, China
17 grid.11135.37 0000 0001 2256 9319 State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China
18 https://ror.org/0064kty71 grid.12981.33 0000 0001 2360 039X Sun Yat-Sen University, Guangzhou, China
19 https://ror.org/04c4dkn09 grid.59053.3a 0000 0001 2167 9639 University of Science and Technology of China, Hefei, China
20 https://ror.org/036trcv74 grid.260474.3 0000 0001 0089 5711 Nanjing Normal University, Nanjing, China
21 grid.8547.e 0000 0001 0125 2443 Institute of Modern Physics and Key Laboratory of Nuclear Physics and Ion-beam Application (MOE)-Fudan University, Shanghai, China
22 https://ror.org/00a2xv884 grid.13402.34 0000 0004 1759 700X Zhejiang University, Hangzhou, Zhejiang China
23 https://ror.org/02mhbdp94 grid.7247.6 0000 0004 1937 0714 Universidad de Los Andes, Bogotá, Colombia
24 https://ror.org/03bp5hc83 grid.412881.6 0000 0000 8882 5269 Universidad de Antioquia, Medellín, Colombia
25 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
26 https://ror.org/00m31ft63 grid.38603.3e 0000 0004 0644 1675 Faculty of Science, University of Split, Split, Croatia
27 https://ror.org/02mw21745 grid.4905.8 0000 0004 0635 7705 Institute Rudjer Boskovic, Zagreb, Croatia
28 https://ror.org/02qjrjx09 grid.6603.3 0000 0001 2116 7908 University of Cyprus, Nicosia, Cyprus
29 https://ror.org/024d6js02 grid.4491.8 0000 0004 1937 116X Charles University, Prague, Czech Republic
30 https://ror.org/01gb99w41 grid.440857.a 0000 0004 0485 2489 Escuela Politecnica Nacional, Quito, Ecuador
31 https://ror.org/01r2c3v86 grid.412251.1 0000 0000 9008 4711 Universidad San Francisco de Quito, Quito, Ecuador
32 grid.423564.2 0000 0001 2165 2866 Academy of Scientific Research and Technology of the Arab Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt
33 https://ror.org/023gzwx10 grid.411170.2 0000 0004 0412 4537 Center for High Energy Physics (CHEP-FU), Fayoum University, El-Fayoum, Egypt
34 https://ror.org/03eqd4a41 grid.177284.f 0000 0004 0410 6208 National Institute of Chemical Physics and Biophysics, Tallinn, Estonia
35 https://ror.org/040af2s02 grid.7737.4 0000 0004 0410 2071 Department of Physics, University of Helsinki, Helsinki, Finland
36 https://ror.org/01x2x1522 grid.470106.4 0000 0001 1106 2387 Helsinki Institute of Physics, Helsinki, Finland
37 https://ror.org/0208vgz68 grid.12332.31 0000 0001 0533 3048 Lappeenranta-Lahti University of Technology, Lappeenranta, Finland
38 https://ror.org/03xjwb503 grid.460789.4 0000 0004 4910 6535 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
39 grid.10877.39 0000000121581279 Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
40 https://ror.org/00pg6eq24 grid.11843.3f 0000 0001 2157 9291 Université de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France
41 https://ror.org/02avf8f85 Institut de Physique des 2 Infinis de Lyon (IP2I ), Villeurbanne, France
42 https://ror.org/00aamz256 grid.41405.34 0000 0001 0702 1187 Georgian Technical University, Tbilisi, Georgia
43 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
44 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany
45 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X RWTH Aachen University, III. Physikalisches Institut B, Aachen, Germany
46 https://ror.org/01js2sh04 grid.7683.a 0000 0004 0492 0453 Deutsches Elektronen-Synchrotron, Hamburg, Germany
47 https://ror.org/00g30e956 grid.9026.d 0000 0001 2287 2617 University of Hamburg, Hamburg, Germany
48 https://ror.org/04t3en479 grid.7892.4 0000 0001 0075 5874 Karlsruher Institut fuer Technologie, Karlsruhe, Germany
49 grid.6083.d 0000 0004 0635 6999 Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Agia Paraskevi, Greece
50 https://ror.org/04gnjpq42 grid.5216.0 0000 0001 2155 0800 National and Kapodistrian University of Athens, Athens, Greece
51 grid.4241.3 0000 0001 2185 9808 National Technical University of Athens, Athens, Greece
52 https://ror.org/01qg3j183 grid.9594.1 0000 0001 2108 7481 University of Ioánnina, Ioannina, Greece
53 grid.419766.b 0000 0004 1759 8344 HUN-REN Wigner Research Centre for Physics, Budapest, Hungary
54 https://ror.org/01jsq2704 grid.5591.8 0000 0001 2294 6276 MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary
55 https://ror.org/02xf66n48 grid.7122.6 0000 0001 1088 8582 Faculty of Informatics, University of Debrecen, Debrecen, Hungary
56 grid.418861.2 0000 0001 0674 7808 Institute of Nuclear Research ATOMKI, Debrecen, Hungary
57 MATE Institute of Technology, Karoly Robert Campus, Gyongyos, Hungary
58 https://ror.org/04p2sbk06 grid.261674.0 0000 0001 2174 5640 Panjab University, Chandigarh, India
59 https://ror.org/04gzb2213 grid.8195.5 0000 0001 2109 4999 University of Delhi, Delhi, India
60 https://ror.org/0491yz035 grid.473481.d 0000 0001 0661 8707 Saha Institute of Nuclear Physics, HBNI, Kolkata, India
61 https://ror.org/03v0r5n49 grid.417969.4 0000 0001 2315 1926 Indian Institute of Technology Madras, Chennai, India
62 https://ror.org/03ht1xw27 grid.22401.35 0000 0004 0502 9283 Tata Institute of Fundamental Research-A, Mumbai, India
63 https://ror.org/03ht1xw27 grid.22401.35 0000 0004 0502 9283 Tata Institute of Fundamental Research-B, Mumbai, India
64 https://ror.org/02r2k1c68 grid.419643.d 0000 0004 1764 227X National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute, Bhubaneswar, Odisha India
65 https://ror.org/028qa3n13 grid.417959.7 0000 0004 1764 2413 Indian Institute of Science Education and Research (IISER), Pune, India
66 grid.411751.7 0000 0000 9908 3264 Isfahan University of Technology, Isfahan, Iran
67 https://ror.org/04xreqs31 grid.418744.a 0000 0000 8841 7951 Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
68 https://ror.org/05m7pjf47 grid.7886.1 0000 0001 0768 2743 University College Dublin, Dublin, Ireland
69 INFN Sezione di Bari, Università di Bari, Politecnico di Bari, Bari, Italy
70 grid.470193.8 0000 0004 8343 7610 INFN Sezione di Bologna, Università di Bologna, Bologna, Italy
71 grid.470198.3 0000 0004 1755 400X INFN Sezione di Catania, Università di Catania, Catania, Italy
72 https://ror.org/02vv5y108 grid.470204.5 0000 0001 2231 4148 INFN Sezione di Firenze, Università di Firenze, Florence, Italy
73 https://ror.org/049jf1a25 grid.463190.9 0000 0004 0648 0236 INFN Laboratori Nazionali di Frascati, Frascati, Italy
74 grid.470205.4 INFN Sezione di Genova, Università di Genova, Genoa, Italy
75 https://ror.org/03xejxm22 grid.470207.6 0000 0004 8390 4143 INFN Sezione di Milano-Bicocca, Università di Milano-Bicocca, Milan, Italy
76 grid.470211.1 0000 0004 8343 7696 INFN Sezione di Napoli, Università di Napoli ‘Federico II’, Naples, Italy; Università della Basilicata, Potenza, Italy; Scuola Superiore Meridionale (SSM), Naples, Italy
77 grid.11696.39 0000 0004 1937 0351 INFN Sezione di Padova, Università di Padova, Padova, Italy; Università di Trento, Trento, Italy
78 INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
79 grid.470215.5 INFN Sezione di Perugia, Università di Perugia, Perugia, Italy
80 grid.9024.f 0000 0004 1757 4641 INFN Sezione di Pisa, Università di Pisa, Scuola Normale Superiore di Pisa, Pisa, Italy; Università di Siena, Siena, Italy
81 grid.470218.8 INFN Sezione di Roma, Sapienza Università di Roma, Rome, Italy
82 https://ror.org/01vj6ck58 grid.470222.1 0000 0004 7471 9712 INFN Sezione di Torino, Università di Torino, Turin, Italy; Università del Piemonte Orientale, Novara, Italy
83 grid.470223.0 0000 0004 1760 7175 INFN Sezione di Trieste, Università di Trieste, Trieste, Italy
84 https://ror.org/040c17130 grid.258803.4 0000 0001 0661 1556 Kyungpook National University, Daegu, Korea
85 grid.411733.3 0000 0004 0532 811X Department of Mathematics and Physics, GWNU, Gangneung, Korea
86 https://ror.org/05kzjxq56 grid.14005.30 0000 0001 0356 9399 Institute for Universe and Elementary Particles, Chonnam National University, Kwangju, Korea
87 https://ror.org/046865y68 grid.49606.3d 0000 0001 1364 9317 Hanyang University, Seoul, Korea
88 https://ror.org/047dqcg40 grid.222754.4 0000 0001 0840 2678 Korea University, Seoul, Korea
89 https://ror.org/01zqcg218 grid.289247.2 0000 0001 2171 7818 Department of Physics, Kyung Hee University, Seoul, Korea
90 https://ror.org/00aft1q37 grid.263333.4 0000 0001 0727 6358 Sejong University, Seoul, Korea
91 https://ror.org/04h9pn542 grid.31501.36 0000 0004 0470 5905 Seoul National University, Seoul, Korea
92 https://ror.org/05en5nh73 grid.267134.5 0000 0000 8597 6969 University of Seoul, Seoul, Korea
93 https://ror.org/01wjejq96 grid.15444.30 0000 0004 0470 5454 Department of Physics, Yonsei University, Seoul, Korea
94 https://ror.org/04q78tk20 grid.264381.a 0000 0001 2181 989X Sungkyunkwan University, Suwon, Korea
95 https://ror.org/02gqgne03 grid.472279.d 0000 0004 0418 1945 College of Engineering and Technology, American University of the Middle East (AUM), Dasman, Kuwait
96 https://ror.org/00twb6c09 grid.6973.b 0000 0004 0567 9729 Riga Technical University, Riga, Latvia
97 https://ror.org/05g3mes96 grid.9845.0 0000 0001 0775 3222 University of Latvia (LU), Riga, Latvia
98 https://ror.org/03nadee84 grid.6441.7 0000 0001 2243 2806 Vilnius University, Vilnius, Lithuania
99 https://ror.org/00rzspn62 grid.10347.31 0000 0001 2308 5949 National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia
100 grid.11893.32 0000 0001 2193 1646 Universidad de Sonora (UNISON), Hermosillo, Mexico
101 grid.512574.0 Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico
102 https://ror.org/05vss7635 grid.441047.2 0000 0001 2156 4794 Universidad Iberoamericana, Mexico City, Mexico
103 https://ror.org/03p2z7827 grid.411659.e 0000 0001 2112 2750 Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
104 https://ror.org/02drrjp49 grid.12316.37 0000 0001 2182 0188 University of Montenegro, Podgorica, Montenegro
105 https://ror.org/03y7q9t39 grid.21006.35 0000 0001 2179 4063 University of Canterbury, Christchurch, New Zealand
106 grid.412621.2 0000 0001 2215 1297 National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan
107 grid.9922.0 0000 0000 9174 1488 Faculty of Computer Science, Electronics and Telecommunications, AGH University of Krakow, Kraków, Poland
108 https://ror.org/00nzsxq20 grid.450295.f 0000 0001 0941 0848 National Centre for Nuclear Research, Swierk, Poland
109 https://ror.org/039bjqg32 grid.12847.38 0000 0004 1937 1290 Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland
110 grid.1035.7 0000000099214842 Warsaw University of Technology, Warsaw, Poland
111 https://ror.org/01hys1667 grid.420929.4 Laboratório de Instrumentação e Física Experimental de Partículas, Lisbon, Portugal
112 https://ror.org/02qsmb048 grid.7149.b 0000 0001 2166 9385 Faculty of Physics, University of Belgrade, Belgrade, Serbia
113 grid.7149.b 0000 0001 2166 9385 VINCA Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia
114 https://ror.org/05xx77y52 grid.420019.e 0000 0001 1959 5823 Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain
115 https://ror.org/01cby8j38 grid.5515.4 0000 0001 1957 8126 Universidad Autónoma de Madrid, Madrid, Spain
116 https://ror.org/006gksa02 grid.10863.3c 0000 0001 2164 6351 Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA), Universidad de Oviedo, Oviedo, Spain
117 grid.7821.c 0000 0004 1770 272X Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain
118 https://ror.org/02phn5242 grid.8065.b 0000 0001 2182 8067 University of Colombo, Colombo, Sri Lanka
119 https://ror.org/033jvzr14 grid.412759.c 0000 0001 0103 6011 Department of Physics, University of Ruhuna, Matara, Sri Lanka
120 https://ror.org/01ggx4157 grid.9132.9 0000 0001 2156 142X CERN, European Organization for Nuclear Research, Geneva, Switzerland
121 https://ror.org/03eh3y714 grid.5991.4 0000 0001 1090 7501 Paul Scherrer Institut, Villigen, Switzerland
122 grid.5801.c 0000 0001 2156 2780 ETH Zurich-Institute for Particle Physics and Astrophysics (IPA), Zurich, Switzerland
123 https://ror.org/02crff812 grid.7400.3 0000 0004 1937 0650 Universität Zürich, Zurich, Switzerland
124 https://ror.org/00944ve71 grid.37589.30 0000 0004 0532 3167 National Central University, Chung-Li, Taiwan
125 https://ror.org/05bqach95 grid.19188.39 0000 0004 0546 0241 National Taiwan University (NTU), Taipei, Taiwan
126 https://ror.org/028wp3y58 grid.7922.e 0000 0001 0244 7875 High Energy Physics Research Unit, Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand
127 https://ror.org/05wxkj555 grid.98622.37 0000 0001 2271 3229 Physics Department, Science and Art Faculty, Çukurova University, Adana, Turkey
128 https://ror.org/014weej12 grid.6935.9 0000 0001 1881 7391 Physics Department, Middle East Technical University, Ankara, Turkey
129 https://ror.org/03z9tma90 grid.11220.30 0000 0001 2253 9056 Bogazici University, Istanbul, Turkey
130 https://ror.org/059636586 grid.10516.33 0000 0001 2174 543X Istanbul Technical University, Istanbul, Turkey
131 https://ror.org/03a5qrr21 grid.9601.e 0000 0001 2166 6619 Istanbul University, Istanbul, Turkey
132 https://ror.org/0547yzj13 grid.38575.3c 0000 0001 2337 3561 Yildiz Technical University, Istanbul, Turkey
133 grid.466758.e Institute for Scintillation Materials of National Academy of Science of Ukraine, Kharkiv, Ukraine
134 https://ror.org/00183pc12 grid.425540.2 0000 0000 9526 3153 National Science Centre, Kharkiv Institute of Physics and Technology, Kharkiv, Ukraine
135 https://ror.org/0524sp257 grid.5337.2 0000 0004 1936 7603 University of Bristol, Bristol, UK
136 https://ror.org/03gq8fr08 grid.76978.37 0000 0001 2296 6998 Rutherford Appleton Laboratory, Didcot, UK
137 https://ror.org/041kmwe10 grid.7445.2 0000 0001 2113 8111 Imperial College, London, UK
138 grid.7728.a 0000 0001 0724 6933 Brunel University, Uxbridge, UK
139 https://ror.org/005781934 grid.252890.4 0000 0001 2111 2894 Baylor University, Waco, TX USA
140 https://ror.org/047yk3s18 grid.39936.36 0000 0001 2174 6686 Catholic University of America, Washington, DC USA
141 https://ror.org/03xrrjk67 grid.411015.0 0000 0001 0727 7545 The University of Alabama, Tuscaloosa, AL USA
142 https://ror.org/05qwgg493 grid.189504.1 0000 0004 1936 7558 Boston University, Boston, MA USA
143 https://ror.org/05gq02987 grid.40263.33 0000 0004 1936 9094 Brown University, Providence, RI USA
144 https://ror.org/05t99sp05 grid.468726.9 0000 0004 0486 2046 University of California, Davis, Davis, CA USA
145 grid.19006.3e 0000 0000 9632 6718 University of California, Los Angeles, CA USA
146 https://ror.org/05t99sp05 grid.468726.9 0000 0004 0486 2046 University of California, Riverside, Riverside, CA USA
147 https://ror.org/05t99sp05 grid.468726.9 0000 0004 0486 2046 University of California, San Diego, La Jolla, CA USA
148 grid.133342.4 0000 0004 1936 9676 Department of Physics, University of California, Santa Barbara, Santa Barbara, CA USA
149 https://ror.org/05dxps055 grid.20861.3d 0000 0001 0706 8890 California Institute of Technology, Pasadena, CA USA
150 https://ror.org/05x2bcf33 grid.147455.6 0000 0001 2097 0344 Carnegie Mellon University, Pittsburgh, PA USA
151 https://ror.org/02ttsq026 grid.266190.a 0000 0000 9621 4564 University of Colorado Boulder, Boulder, CO USA
152 https://ror.org/05bnh6r87 grid.5386.8 0000 0004 1936 877X Cornell University, Ithaca, NY USA
153 https://ror.org/020hgte69 grid.417851.e 0000 0001 0675 0679 Fermi National Accelerator Laboratory, Batavia, IL USA
154 https://ror.org/02y3ad647 grid.15276.37 0000 0004 1936 8091 University of Florida, Gainesville, FL USA
155 https://ror.org/05g3dte14 grid.255986.5 0000 0004 0472 0419 Florida State University, Tallahassee, FL USA
156 https://ror.org/04atsbb87 grid.255966.b 0000 0001 2229 7296 Florida Institute of Technology, Melbourne, FL USA
157 https://ror.org/02mpq6x41 grid.185648.6 0000 0001 2175 0319 University of Illinois Chicago, Chicago, USA
158 https://ror.org/036jqmy94 grid.214572.7 0000 0004 1936 8294 The University of Iowa, Iowa City, IA USA
159 https://ror.org/00za53h95 grid.21107.35 0000 0001 2171 9311 Johns Hopkins University, Baltimore, MD USA
160 https://ror.org/001tmjg57 grid.266515.3 0000 0001 2106 0692 The University of Kansas, Lawrence, KS USA
161 https://ror.org/05p1j8758 grid.36567.31 0000 0001 0737 1259 Kansas State University, Manhattan, KS USA
162 https://ror.org/041nk4h53 grid.250008.f 0000 0001 2160 9702 Lawrence Livermore National Laboratory, Livermore, CA USA
163 https://ror.org/047s2c258 grid.164295.d 0000 0001 0941 7177 University of Maryland, College Park, MD USA
164 https://ror.org/042nb2s44 grid.116068.8 0000 0001 2341 2786 Massachusetts Institute of Technology, Cambridge, MA USA
165 https://ror.org/017zqws13 grid.17635.36 0000 0004 1936 8657 University of Minnesota, Minneapolis, MN USA
166 https://ror.org/02teq1165 grid.251313.7 0000 0001 2169 2489 University of Mississippi, Oxford, MS USA
167 https://ror.org/043mer456 grid.24434.35 0000 0004 1937 0060 University of Nebraska-Lincoln, Lincoln, NE USA
168 grid.273335.3 0000 0004 1936 9887 State University of New York at Buffalo, Buffalo, NY USA
169 https://ror.org/04t5xt781 grid.261112.7 0000 0001 2173 3359 Northeastern University, Boston, MA USA
170 https://ror.org/000e0be47 grid.16753.36 0000 0001 2299 3507 Northwestern University, Evanston, IL USA
171 https://ror.org/00mkhxb43 grid.131063.6 0000 0001 2168 0066 University of Notre Dame, Notre Dame, IN USA
172 https://ror.org/00rs6vg23 grid.261331.4 0000 0001 2285 7943 The Ohio State University, Columbus, OH USA
173 https://ror.org/00hx57361 grid.16750.35 0000 0001 2097 5006 Princeton University, Princeton, NJ USA
174 https://ror.org/00wek6x04 grid.267044.3 0000 0004 0398 9176 University of Puerto Rico, Mayagüez, PR USA
175 https://ror.org/02dqehb95 grid.169077.e 0000 0004 1937 2197 Purdue University, West Lafayette, IN USA
176 https://ror.org/04keq6987 grid.504659.b 0000 0000 8864 7239 Purdue University Northwest, Hammond, IN USA
177 https://ror.org/008zs3103 grid.21940.3e 0000 0004 1936 8278 Rice University, Houston, TX USA
178 https://ror.org/022kthw22 grid.16416.34 0000 0004 1936 9174 University of Rochester, Rochester, NY USA
179 https://ror.org/0420db125 grid.134907.8 0000 0001 2166 1519 The Rockefeller University, New York, NY USA
180 https://ror.org/05vt9qd57 grid.430387.b 0000 0004 1936 8796 Rutgers, The State University of New Jersey, Piscataway, NJ USA
181 https://ror.org/020f3ap87 grid.411461.7 0000 0001 2315 1184 University of Tennessee, Knoxville, TN USA
182 https://ror.org/01f5ytq51 grid.264756.4 0000 0004 4687 2082 Texas A &M University, College Station, TX USA
183 grid.264784.b 0000 0001 2186 7496 Texas Tech University, Lubbock, TX USA
184 https://ror.org/02vm5rt34 grid.152326.1 0000 0001 2264 7217 Vanderbilt University, Nashville, TN USA
185 https://ror.org/0153tk833 grid.27755.32 0000 0000 9136 933X University of Virginia, Charlottesville, VA USA
186 https://ror.org/01070mq45 grid.254444.7 0000 0001 1456 7807 Wayne State University, Detroit, MI USA
187 https://ror.org/01y2jtd41 grid.14003.36 0000 0001 2167 3675 University of Wisconsin-Madison, Madison, WI USA
188 grid.9132.9 0000 0001 2156 142X Authors Affiliated with an Institute or an International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
189 https://ror.org/00s8vne50 grid.21072.36 0000 0004 0640 687X Yerevan State University, Yerevan, Armenia
190 https://ror.org/04d836q62 grid.5329.d 0000 0004 1937 0669 TU Wien, Vienna, Austria
191 grid.442567.6 0000 0000 9015 5153 Institute of Basic and Applied Sciences, Faculty of Engineering, Arab Academy for Science, Technology and Maritime Transport, Alexandria, Egypt
192 https://ror.org/00cv9y106 grid.5342.0 0000 0001 2069 7798 Ghent University, Ghent, Belgium
193 https://ror.org/04wffgt70 grid.411087.b 0000 0001 0723 2494 Universidade Estadual de Campinas, Campinas, Brazil
194 https://ror.org/041yk2d64 grid.8532.c 0000 0001 2200 7498 Federal University of Rio Grande do Sul, Porto Alegre, Brazil
195 grid.412352.3 0000 0001 2163 5978 UFMS, Nova Andradina, Brazil
196 https://ror.org/036trcv74 grid.260474.3 0000 0001 0089 5711 Nanjing Normal University, Nanjing, China
197 https://ror.org/036jqmy94 grid.214572.7 0000 0004 1936 8294 The University of Iowa, Iowa City, IA USA
198 https://ror.org/05qbk4x57 grid.410726.6 0000 0004 1797 8419 University of Chinese Academy of Sciences, Beijing, China
199 https://ror.org/02egfyg20 grid.464262.0 0000 0001 0318 1175 China Center of Advanced Science and Technology, Beijing, China
200 https://ror.org/05qbk4x57 grid.410726.6 0000 0004 1797 8419 University of Chinese Academy of Sciences, Beijing, China
201 https://ror.org/01g140v14 grid.495581.4 China Spallation Neutron Source, Dongguan, Guangdong China
202 https://ror.org/00s13br28 grid.462338.8 0000 0004 0605 6769 Henan Normal University, Xinxiang, China
203 https://ror.org/01r9htc13 grid.4989.c 0000 0001 2348 6355 Université Libre de Bruxelles, Brussels, Belgium
204 grid.9132.9 0000 0001 2156 142X an Institute or an International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
205 https://ror.org/0066fxv63 grid.440862.c 0000 0004 0377 5514 British University in Egypt, Cairo, Egypt
206 https://ror.org/03q21mh05 grid.7776.1 0000 0004 0639 9286 Cairo University, Cairo, Egypt
207 https://ror.org/02dqehb95 grid.169077.e 0000 0004 1937 2197 Purdue University, West Lafayette, IN USA
208 https://ror.org/04k8k6n84 grid.9156.b 0000 0004 0473 5039 Université de Haute Alsace, Mulhouse, France
209 https://ror.org/03cve4549 grid.12527.33 0000 0001 0662 3178 Department of Physics, Tsinghua University, Beijing, China
210 https://ror.org/04j5z3x06 grid.412290.c 0000 0000 8024 0602 The University of the State of Amazonas, Manaus, Brazil
211 grid.412176.7 0000 0001 1498 7262 Erzincan Binali Yildirim University, Erzincan, Turkey
212 https://ror.org/00g30e956 grid.9026.d 0000 0001 2287 2617 University of Hamburg, Hamburg, Germany
213 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany
214 grid.411751.7 0000 0000 9908 3264 Isfahan University of Technology, Isfahan, Iran
215 grid.7787.f 0000 0001 2364 5811 Bergische University Wuppertal (BUW), Wuppertal, Germany
216 https://ror.org/02wxx3e24 grid.8842.6 0000 0001 2188 0404 Brandenburg University of Technology, Cottbus, Germany
217 https://ror.org/02nv7yv05 grid.8385.6 0000 0001 2297 375X Forschungszentrum Jülich, Jülich, Germany
218 https://ror.org/01ggx4157 grid.9132.9 0000 0001 2156 142X CERN, European Organization for Nuclear Research, Geneva, Switzerland
219 https://ror.org/02xf66n48 grid.7122.6 0000 0001 1088 8582 Institute of Physics, University of Debrecen, Debrecen, Hungary
220 grid.418861.2 0000 0001 0674 7808 Institute of Nuclear Research ATOMKI, Debrecen, Hungary
221 grid.7399.4 0000 0004 1937 1397 Universitatea Babes-Bolyai-Facultatea de Fizica, Cluj-Napoca, Romania
222 https://ror.org/01jaj8n65 grid.252487.e 0000 0000 8632 679X Physics Department, Faculty of Science, Assiut University, Asyût, Egypt
223 grid.419766.b 0000 0004 1759 8344 HUN-REN Wigner Research Centre for Physics, Budapest, Hungary
224 https://ror.org/02qbzdk74 grid.412577.2 0000 0001 2176 2352 Punjab Agricultural University, Ludhiana, India
225 https://ror.org/02y28sc20 grid.440987.6 0000 0001 2259 7889 University of Visva-Bharati, Santiniketan, India
226 grid.34980.36 0000 0001 0482 5067 Indian Institute of Science (IISc), Bangalore, India
227 https://ror.org/028vtqb15 grid.462084.c 0000 0001 2216 7125 Birla Institute of Technology, Mesra, Mesra, India
228 https://ror.org/04gx72j20 grid.459611.e 0000 0004 1774 3038 IIT Bhubaneswar, Bhubaneswar, India
229 https://ror.org/01741jv66 grid.418915.0 0000 0004 0504 1311 Institute of Physics, Bhubaneswar, India
230 https://ror.org/04a7rxb17 grid.18048.35 0000 0000 9951 5557 University of Hyderabad, Hyderabad, India
231 https://ror.org/01js2sh04 grid.7683.a 0000 0004 0492 0453 Deutsches Elektronen-Synchrotron, Hamburg, Germany
232 https://ror.org/00af3sa43 grid.411751.7 0000 0000 9908 3264 Department of Physics, Isfahan University of Technology, Isfahan, Iran
233 https://ror.org/024c2fq17 grid.412553.4 0000 0001 0740 9747 Sharif University of Technology, Tehran, Iran
234 https://ror.org/04jf6jw55 grid.510412.3 Department of Physics, University of Science and Technology of Mazandaran, Behshahr, Iran
235 https://ror.org/00h55v928 grid.412093.d 0000 0000 9853 2750 Helwan University, Cairo, Egypt
236 https://ror.org/02an8es95 grid.5196.b 0000 0000 9864 2490 Italian National Agency for New Technologies, Energy and Sustainable Economic Development, Bologna, Italy
237 https://ror.org/02wdzfm91 grid.510931.f Centro Siciliano di Fisica Nucleare e di Struttura Della Materia, Catania, Italy
238 https://ror.org/00j0rk173 grid.440899.8 0000 0004 1780 761X Università degli Studi Guglielmo Marconi, Rome, Italy
239 https://ror.org/04swxte59 grid.508348.2 Scuola Superiore Meridionale, Università di Napoli ‘Federico II’, Naples, Italy
240 https://ror.org/020hgte69 grid.417851.e 0000 0001 0675 0679 Fermi National Accelerator Laboratory, Batavia, IL USA
241 https://ror.org/00cb9w016 grid.7269.a 0000 0004 0621 1570 Ain Shams University, Cairo, Egypt
242 grid.5326.2 0000 0001 1940 4177 Consiglio Nazionale delle Ricerche-Istituto Officina dei Materiali, Perugia, Italy
243 https://ror.org/00twb6c09 grid.6973.b 0000 0004 0567 9729 Riga Technical University, Riga, Latvia
244 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
245 https://ror.org/059ex5q34 grid.418270.8 0000 0004 0428 7635 Consejo Nacional de Ciencia y Tecnología, Mexico City, Mexico
246 grid.443373.4 0000 0001 0438 3334 Trincomalee Campus, Eastern University, Sri Lanka, Nilaveli, Sri Lanka
247 Saegis Campus, Nugegoda, Sri Lanka
248 https://ror.org/04gnjpq42 grid.5216.0 0000 0001 2155 0800 National and Kapodistrian University of Athens, Athens, Greece
249 https://ror.org/02s376052 grid.5333.6 0000 0001 2183 9049 Ecole Polytechnique Fédérale Lausanne, Lausanne, Switzerland
250 https://ror.org/02crff812 grid.7400.3 0000 0004 1937 0650 Universität Zürich, Zurich, Switzerland
251 https://ror.org/05kdjqf72 grid.475784.d 0000 0000 9532 5705 Stefan Meyer Institute for Subatomic Physics, Vienna, Austria
252 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
253 Near East University, Research Center of Experimental Health Science, Mersin, Turkey
254 https://ror.org/02s82rs08 grid.505922.9 Konya Technical University, Konya, Turkey
255 https://ror.org/017v96566 0000 0004 6412 5697 Izmir Bakircay University, Izmir, Turkey
256 https://ror.org/02s4gkg68 grid.411126.1 0000 0004 0369 5557 Adiyaman University, Adiyaman, Turkey
257 grid.411743.4 0000 0004 0369 8360 Bozok Universitetesi Rektörlügü, Yozgat, Turkey
258 https://ror.org/02kswqa67 grid.16477.33 0000 0001 0668 8422 Marmara University, Istanbul, Turkey
259 https://ror.org/010t24d82 grid.510982.7 Milli Savunma University, Istanbul, Turkey
260 https://ror.org/04v302n28 grid.16487.3c 0000 0000 9216 0511 Kafkas University, Kars, Turkey
261 grid.444283.d 0000 0004 0371 5255 Istanbul Okan University, Istanbul, Turkey
262 https://ror.org/04kwvgz42 grid.14442.37 0000 0001 2342 7339 Hacettepe University, Ankara, Turkey
263 grid.506076.2 0000 0004 1797 5496 Faculty of Engineering, Istanbul University-Cerrahpasa, Istanbul, Turkey
264 https://ror.org/0547yzj13 grid.38575.3c 0000 0001 2337 3561 Yildiz Technical University, Istanbul, Turkey
265 https://ror.org/006e5kg04 grid.8767.e 0000 0001 2290 8069 Vrije Universiteit Brussel, Brussels, Belgium
266 https://ror.org/01ryk1543 grid.5491.9 0000 0004 1936 9297 School of Physics and Astronomy, University of Southampton, Southampton, UK
267 https://ror.org/0524sp257 grid.5337.2 0000 0004 1936 7603 University of Bristol, Bristol, UK
268 https://ror.org/01v29qb04 grid.8250.f 0000 0000 8700 0572 IPPP Durham University, Durham, UK
269 https://ror.org/02bfwt286 grid.1002.3 0000 0004 1936 7857 Faculty of Science, Monash University, Clayton, Australia
270 grid.7605.4 0000 0001 2336 6580 Università di Torino, Turin, Italy
271 https://ror.org/05wnc7373 grid.446604.4 0000 0004 0583 4952 Bethel University, St. Paul, MN USA
272 https://ror.org/037vvf096 grid.440455.4 0000 0004 1755 486X Karamanoğlu Mehmetbey University, Karaman, Turkey
273 https://ror.org/05dxps055 grid.20861.3d 0000 0001 0706 8890 California Institute of Technology, Pasadena, CA USA
274 https://ror.org/00znex860 grid.265465.6 0000 0001 2296 3025 United States Naval Academy, Annapolis, MD USA
275 https://ror.org/03hx84x94 grid.448543.a 0000 0004 0369 6517 Bingol University, Bingol, Turkey
276 https://ror.org/00aamz256 grid.41405.34 0000 0001 0702 1187 Georgian Technical University, Tbilisi, Georgia
277 https://ror.org/004ah3r71 grid.449244.b 0000 0004 0408 6032 Sinop University, Sinop, Turkey
278 https://ror.org/047g8vk19 grid.411739.9 0000 0001 2331 2603 Erciyes University, Kayseri, Turkey
279 https://ror.org/00d3pnh21 grid.443874.8 0000 0000 9463 5349 Horia Hulubei National Institute of Physics and Nuclear Engineering (IFIN-HH), Bucharest, Romania
280 grid.9132.9 0000 0001 2156 142X an Institute or an International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
281 https://ror.org/03vb4dm14 grid.412392.f 0000 0004 0413 3978 Texas A &M University at Qatar, Doha, Qatar
282 https://ror.org/040c17130 grid.258803.4 0000 0001 0661 1556 Kyungpook National University, Daegu, Korea
283 grid.9132.9 0000 0001 2156 142X Another Institute or International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
284 https://ror.org/008x57b05 grid.5284.b 0000 0001 0790 3681 Universiteit Antwerpen, Antwerp, Belgium
285 https://ror.org/00ad27c73 grid.48507.3e 0000 0004 0482 7128 Yerevan Physics Institute, Yerevan, Armenia
286 https://ror.org/04t5xt781 grid.261112.7 0000 0001 2173 3359 Northeastern University, Boston, MA USA
287 https://ror.org/041kmwe10 grid.7445.2 0000 0001 2113 8111 Imperial College, London, UK
288 grid.443859.7 0000 0004 0477 2171 Institute of Nuclear Physics of the Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
289 grid.9132.9 0000 0001 2156 142X CERN, 1211 Geneva 23, Switzerland
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Funded by SCOAP3.
A study of the anomalous couplings of the Higgs boson to vector bosons, including CP-violation effects, has been conducted using its production and decay in the WW channel. This analysis is performed on proton–proton collision data collected with the CMS detector at the CERN LHC during 2016–2018 at a center-of-mass energy of 13 TeV, and corresponds to an integrated luminosity of 138fb-1. The different-flavor dilepton (eμ) final state is analyzed, with dedicated categories targeting gluon fusion, electroweak vector boson fusion, and associated production with a W or Z boson. Kinematic information from associated jets is combined using matrix element techniques to increase the sensitivity to anomalous effects at the production vertex. A simultaneous measurement of four Higgs boson couplings to electroweak vector bosons is performed in the framework of a standard model effective field theory. All measurements are consistent with the expectations for the standard model Higgs boson and constraints are set on the fractional contribution of the anomalous couplings to the Higgs boson production cross section.

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] Hayrapetyan A. http://dx.doi.org/10.13039/501100002428 Austrian Science Fund FWF Tumasyan A. http://dx.doi.org/10.13039/501100002661 Belgian Fonds de la Recherche Scientifique FRS – FNRS Adam W. http://dx.doi.org/10.13039/501100003130 Belgian Fonds voor Wetenschappelijk Onderzoek FWO Andrejkovic J. W. http://dx.doi.org/10.13039/501100003593 CNPq Conselho Nacional de Desenvolvimento Cientifico e Tecnelógica Bergauer T. http://dx.doi.org/10.13039/501100002322 CAPES Coordenação de Aperfeiçoamento de Pessoal de Nível Superior Chatterjee S. http://dx.doi.org/10.13039/501100004586 FAPERJ Fundação de Amparo à Pesquisa do Estado de Rio de Janeiro Damanakis K. http://dx.doi.org/10.13039/501100004263 FAPERGS Fundação de Amparo À Pesquisa do Estado do Rio Grande do Sul Dragicevic M. http://dx.doi.org/10.13039/501100001807 FAPESP Fundação de Amparo à Pesquisa do Estado de São Paulo Hussain P. 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Helsinki Institute of PhysicsHIP D’Hondt J. http://dx.doi.org/10.13039/501100004794 Institut National de Physique Nucléaire et de Physique des Particules IN2P3 Dansana S. http://dx.doi.org/10.13039/501100004794 Centre National de la Recherche Scientifique CNRS De Moor A. http://dx.doi.org/10.13039/501100006489 Commissariat à l’Énergie Atomique et aux Énergies Alternatives CEA Delcourt M. http://dx.doi.org/10.13039/501100002347 Bundesministerium für Bildung und Forschung BMBF El Faham H. http://dx.doi.org/10.13039/501100001659 Deutsche Forschungsgemeinschaft DFG Lowette S. http://dx.doi.org/10.13039/501100001656 Helmholtz-Gemeinschaft Deutscher Forschungszentren HGF Makarenko I. 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. 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K. http://dx.doi.org/10.13039/501100001864 MES Ministry of Education and Science De Lentdecker G. http://dx.doi.org/10.13039/501100008523 Lithuanian Academy of Sciences LAS or Lietuvos Mokslu Akademija Favart L. http://dx.doi.org/10.13039/501100003093 Ministry of Education ?Ministry of Higher Education, Malaysia Gianneios P. http://dx.doi.org/10.13039/501100004386 University of Malaya http://dx.doi.org/10.13039/501100006348 BUAP Benemérita Universidad Autónoma de Puebla Jaramillo J. http://dx.doi.org/10.13039/501100008688 CINVESTAV Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional Khalilzadeh A. http://dx.doi.org/10.13039/501100003141 CONACYT Consejo Nacional de Ciencia y Tecnología Lee K. LNSLaboratorio Nacional de Supercómputo del Sureste Mahdavikhorrami M. http://dx.doi.org/10.13039/100010096 SEP Secretaría de Educación Pública Malara A. http://dx.doi.org/10.13039/501100005324 UASLP Universidad Autónoma de San Luis Potosí Paredes S. MOSMinistry of Science Pétré L. http://dx.doi.org/10.13039/501100003524 Ministry of Business, Innovation and Employment MBIE Postiau N. http://dx.doi.org/10.13039/501100008689 Pakistan Atomic Energy Commission PAEC Thomas L. http://dx.doi.org/10.13039/501100004569 Ministry of Educaton and Science Ministerstwo Edukacji I Nauki; MES [was MSHE, Ministerstwo Nauki i Szkolnictwa Wyzszego] Vanden Bemden M. http://dx.doi.org/10.13039/501100004442 National Science Centre Narodowe Centrum Nauki; NSC Vander Velde C. 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 Vanlaer P. http://dx.doi.org/10.13039/501100004564 Ministry of Education, Science and Technological Development of Serbia MESTD Mota Amarilo K. 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) Rendón C. http://dx.doi.org/10.13039/501100008530 Fondo Europeo de Desarrollo Regional, Spain FEDER (ERDF) Samalan A. https://doi.org/10.13039/100011941 Plan de Ciencia, Tecnología e Innovación del Principado de Asturias PCTI Skovpen K. http://dx.doi.org/10.13039/501100008981 MOSTR Ministry of Science, Technology, and Research Van Den Bossche N. ETH BoardEidgenössische Technische Hochschule (ETH) Zürich van der Linden J. http://dx.doi.org/10.13039/501100003006 ETH Zurich Eidgenössische Technische Hochschule (ETH) Zürich Wezenbeek L. http://dx.doi.org/10.13039/501100004219 PSI Paul Scherrer Institut Benecke A. http://dx.doi.org/10.13039/501100001711 SNF Swiss National Science Foundation (Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung) Bethani A. UniZHUniversität Zürich Bruno G. 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Sloan Foundation http://dx.doi.org/10.13039/100005156 Alexander von Humboldt Foundation Alexander von Humboldt-Stiftung Damanakis K. 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pmcIntroduction

After the discovery of the Higgs boson (H) by the ATLAS and CMS Collaborations in 2012 [1–3], the CMS [4–11] and ATLAS [12–18] experiments set constraints on the spin-parity properties of the Higgs boson and its couplings with gluons and electroweak (EW) gauge bosons, denoted here as Hgg and HVV, respectively. The Higgs boson quantum numbers are consistent with the standard model (SM) expectation JPC=0++, but the possibility of small, anomalous couplings is not yet ruled out. In beyond-the-SM (BSM) theories, interactions with the Higgs boson may occur through several anomalous couplings, which lead to new tensor structures in the interaction terms that can be both CP-even or CP-odd. The CP-odd anomalous couplings between the Higgs boson and BSM particles may generate CP violation in the interactions of the Higgs boson.

In this paper, we study the tensor structure of the Hgg and HVV couplings, and we search for several anomalous effects, including CP violation, using the different-flavor dilepton (eμ) final state from H→WW decays. The Higgs boson production processes include gluon fusion (ggH), EW vector boson fusion (VBF), and associated production with a W or Z boson (VH). Higgs boson production and decay processes are sensitive to certain anomalous contributions, which can be described by higher-dimensional operators in an effective field theory (EFT) [19] that can modify the kinematic distributions of the Higgs boson decay products and the particles from associated production.

Each production process of the Higgs boson is identified using its kinematic features, and events are assigned to corresponding production categories. The matrix element likelihood approach (MELA) [20–24] is employed to construct observables that are optimal for the measurement of anomalous couplings, or EFT operators, at the production vertex. These and other decay-based variables are used to explore all kinematic features of the events, giving the analysis sensitivity to simultaneous anomalous effects at the Higgs boson production and decay vertices. Fully simulated signal samples that include anomalous couplings incorporate the detector response into the analysis.

The analysis is based on the proton–proton (pp) collision data collected at the CERN LHC from 2016 to 2018, at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138fb-1. This paper builds on a previous analysis conducted by the CMS Collaboration in the H→WW channel [25], which focused on measuring the Higgs boson production cross sections and coupling parameters in the so-called κ framework [26]. We follow a formalism used in previous CMS analyses of anomalous couplings in Run 1 and Run 2 [4–11, 27, 28], focusing on the case where the Higgs boson is produced on-shell. The coupling parameters are extracted using the signal strength and the fractional contributions of the couplings to the cross section. A general study of the HVV interaction is performed with four anomalous couplings analyzed individually. Through SU(2) x U(1) symmetry considerations, the anomalous HVV couplings are reduced in number to three and analyzed simultaneously. The primary HVV coupling measurements are performed in terms of cross section fractions with additional interpretations in terms of EFT couplings included. A study of the Hgg interaction is also performed in terms of a CP-odd anomalous coupling cross section fraction.

This paper is organized as follows. The phenomenology of anomalous couplings is discussed in Sect. 2. Section 3 gives a brief overview of the CMS apparatus. Data sets and Monte Carlo (MC) simulation samples are discussed in Sect. 4. The event reconstruction and selection are outlined in Sects. 5 and 6, respectively. Methods to estimate backgrounds are given in Sect. 7. In Sect. 8, we discuss the kinematic variables associated with Higgs boson production and decay. Sources of systematic uncertainties are presented in Sect. 9. The results are presented and discussed in Sect. 10. Finally, a summary is given in Sect. 11. Tabulated results are provided in the HEPData record for this analysis [29].

Phenomenology

In this analysis, we investigate anomalous coupling effects in gluon fusion or electroweak Higgs boson production, as well as in its decay to WW pairs. A detailed discussion of the theoretical considerations can be found in Refs. [22, 24, 28]. The interaction of the spin-zero Higgs boson with two spin-one gauge bosons such as WW, ZZ, Zγ, γγ, or gg, can be parametrized by the scattering amplitude1

where and are the spin-one gauge boson four-momentum and polarization vectors, mV1 is the pole mass of the boson, and f~μν(i)=12ϵμνρσf(i),ρσ (with ϵμνρσ the Levi-Civita symbol), is the scale of BSM physics, and v is the Higgs field vacuum expectation value.

The only leading tree-level contributions in the scattering amplitude are a1ZZ≠0 and a1WW≠0; other a1 coupling parameters (Zγ, γγ, gg) do not contribute because the pole mass vanishes. Additional ZZ and WW couplings are considered anomalous contributions. Anomalous terms arising in the SM via loop effects are typically small and are not yet accessible experimentally. The BSM contributions, however, could yield larger coupling parameters. Among the anomalous contributions, considerations of symmetry and gauge invariance require κ1ZZ=κ2ZZ, κ1γγ=κ2γγ=0, κ1gg=κ2gg=0, and κ1Zγ=0 [24]. The presence of CP-odd couplings together with any of the other couplings (all of them CP-even), will result in CP violation. We reduce the number of independent parameters by assuming that a2γγ, a3γγ, a2Zγ and a3Zγ are constrained in direct decays of H→γγ and Zγ, therefore fixing them to be zero. The a2gg term results from loop effects in the SM.

The relationship between the ZZ and WW couplings is mostly relevant for VBF production. There are no kinematic differences between the ZZ and WW fusion processes; therefore, it is not possible to disentangle the couplings. One possibility is to set the ZZ and WW couplings to be equal, ai=aiZZ=aiWW, leaving four HVV anomalous couplings to be measured: a2, a3, κ1/(Λ1)2, and κ2Zγ/(Λ1Zγ)2. The a1ZZ=a1WW relationship also appears under custodial symmetry. This approach provides a general test of the Higgs boson Lagrangian tensor structure and a search for CP violation in HVV interactions. In an alternative approach, the SU(2) × U(1) symmetry reduces the number of independent HVV anomalous couplings to three (a2, a3, and κ1/(Λ1)2) through the introduction of the following coupling parameter relationships [19] :2 a1WW=a1ZZ,

3 a2WW=cw2a2ZZ,

4 a3WW=cw2a3ZZ,

5 κ1WW(Λ1WW)2=1cw2-sw2κ1ZZ(Λ1ZZ)2-2sw2a2ZZmZ2,

6 κ2Zγ(Λ1Zγ)2=2swcwcw2-sw2κ1ZZ(Λ1ZZ)2-a2ZZmZ2,

where cw and sw are the cosine and sine of the weak mixing angle, respectively, and mZ is the Z boson mass. With this approach, there is a linear relationship between the scattering amplitude couplings and the SM EFT (SMEFT) couplings in the Higgs basis [19]:7 δcz=12a1ZZ-1,

8 czz=-2sw2cw2e2a2ZZ,

9 c~zz=-2sw2cw2e2a3ZZ,

10 cz□=mZ2sw2e2κ1ZZ(Λ1ZZ)2,

where e is the electron charge. The amplitude couplings may also be related to the SMEFT Warsaw basis [19, 30] couplings through the following translation [28, 31] :11 δa1ZZ=v2Λ22cH□+6e2sw2cHWB+3cw22sw2-12cHD,

12 κ1ZZ=v2Λ2-2e2sw2cHWB+1-12sw2cHD,

13 a2ZZ=-2v2Λ2sw2cHB+cw2cHW+swcwcHWB,

14 a3ZZ=-2v2Λ2sw2cHB~+cw2cHW~+swcwcHW~B,

where Λ is the UV cutoff of the theory (set to 1 TeV), and δa1ZZ is a correction to the SM value of a1ZZ. Further discussion on the EFT operators corresponding to the couplings considered here may be found in Chapter 2.2 of Ref. [19]. The assumed constraints on a2γγ, a3γγ, a2Zγ and a3Zγ imply that only one of the three coupling parameters cHW, cHWB, and cHB is independent; the same is also true for their CP-odd counterparts cHW~, cHW~B, and cHB~. Therefore, we have four independent HVV couplings in both the Higgs and Warsaw basis. All the EFT couplings are expected to be zero in the SM.

We thus adopt two approaches to the HVV coupling study. In Approach 1, we use the aiZZ=aiWW relationship and individually analyze each of the four anomalous couplings. In Approach 2, we enforce the SU(2) x U(1) relationships from Eqs. (2–6) and analyze the three independent anomalous couplings both individually and simultaneously. Approach 1 may be considered to follow the relationships from Eqs. (2–5) in the limiting case cw=1.

It is convenient to measure the fractional contribution of the anomalous couplings to the Higgs boson cross section rather than the anomalous couplings themselves. For the anomalous HVV couplings, the effective fractional cross sections fai are defined as15

where ∑j sums over all the coupling parameters considered, including a1, and σi is the cross section for the process corresponding to ai=1 and aj≠i=0. Many systematic uncertainties cancel out in the ratio, and the physical range is conveniently bounded between -1 and +1. Our primary measurements are performed in terms of cross section fractions, with additional interpretations in terms of the SMEFT Higgs and Warsaw basis couplings also included. For consistency with previous CMS measurements, the σi coefficients used to define the fractional cross sections correspond to the gg→H→VV→2e2μ process [28]. The numerical values are given in Table 1 as calculated using the JHUGen simulation [20–23]. Two sets of values are shown corresponding to the different coupling relationships adopted in Approach 1 and 2.

It has been shown that the angular correlations of the associated jets in the ggH + 2 jets process are sensitive to anomalous Hgg coupling effects at the production vertex [32]. The quark-quark initiated process, qq→qqH, corresponds to the gluon scattering topology sensitive to anomalous effects. For the anomalous Hgg coupling, the effective fractional cross section can be defined as16

The σ3gg and σ2gg cross sections correspond to a3gg=1,a2gg=0 and a2gg=1,a3gg=0, respectively, and are equal. With this analysis it is not possible to distinguish the top quark, bottom quark, and heavy BSM particle contributions in the gluon fusion loop. As such, the Hgg coupling is treated as an effective coupling with heavy degrees of freedom integrated out.Table 1 The cross sections (σi) of the anomalous contributions (ai) relative to the SM value (σ1) used to define the fractional cross sections fai for the Approach 1 and 2 coupling relationships. For the κ1 and κ2Zγ couplings, the numerical values Λ1=Λ1Zγ=100GeV are chosen to keep all coefficients of similar order of magnitude

fai	ai	Approach 1 σi/σ1	Approach 2 σi/σ1	
fa2	a2	0.361	6.376	
fa3	a3	0.153	0.153	
fΛ1	κ1	0.682	5.241	
fΛ1Zγ	κ2Zγ	1.746	-	

The CMS detector

The CMS apparatus [33] is a multipurpose, nearly hermetic detector, designed to identify electrons, muons, photons, and (charged and neutral) hadrons [34–37]. A global reconstruction “particle-flow” (PF) algorithm [38] combines the information provided by the all-silicon inner tracker and by the crystal electromagnetic and brass-scintillator hadron calorimeters, operating inside a 3.8T superconducting solenoid, with data from gas-ionization muon detectors interleaved with the solenoid return yoke, to build τleptons, jets, missing transverse momentum, and other physics objects [39–41].

Events of interest are selected using a two-tiered trigger system [42, 43]. The first level (L1), composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of around 100kHz within a fixed latency of about 4μs [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 1kHz before data storage [43]. A more detailed description of the CMS detector, together with a definition of the coordinate system and kinematic variables, can be found in Ref. [33].

Data sets and simulation

The data sets included in this analysis were recorded with the CMS detector in 2016, 2017, and 2018, and correspond to integrated luminosities of 36.3, 41.5, and 59.7fb-1, respectively [44–46]. The collision events must fulfill HLT selection criteria that require the presence of one or two leptons satisfying isolation and identification requirements. For the 2016 data set, the single-electron trigger has a transverse momentum (pT) threshold of 25GeV for electrons with pseudorapidity η<2.1 and 27GeV for 2.1<η<2.5, whereas the single-muon trigger has a pT threshold of 24GeV for η<2.4. For the 2017 (2018) data set, the pT threshold is 35 (32)GeV for the single-electron trigger (covering η<2.5) and 27 (24)GeV for the single-muon trigger (η<2.4). The dilepton eμ trigger has pT thresholds of 23 and 12GeV for the leading and subleading leptons, respectively, with the same coverage in pseudorapidity for electrons and muons as above. During the first part of data taking in 2016, a lower pT threshold of 8GeV for the subleading muon was used.

Monte Carlo event generators are used to model the signal and background processes. For each process, three independent sets of simulated events, corresponding to the three years of data taking, are used. This approach includes year-dependent effects in the CMS detector, data taking, and event reconstruction. All simulated events corresponding to a given data set share the same set of parton distribution functions (PDFs), underlying event (UE) tune, and parton shower (PS) configuration. The PDF sets used are NNPDF 3.0 [47, 48] for 2016 and NNPDF 3.1 [49] for 2017 and 2018. The CUETP8M1 [50] tune is used to describe the UE in 2016 simulations, whereas the CP5 [51] tune is adopted in 2017 and 2018 simulated events. The MC samples are interfaced with pythia 8.226 [52] in 2016, and 8.230 in 2017 and 2018, for the modeling of UE, PS, and hadronization. Standard Model Higgs boson production through ggH, VBF, and VH is simulated at next-to-leading order (NLO) accuracy in quantum chromodynamics (QCD), including finite quark mass effects, using powheg v2 [53–59]. The minlo hvj [58] extension of powheg v2 is used for the simulation of WH and quark-induced ZH production, providing NLO accuracy for the VH+0- and 1-jet processes. For ggH production, the simulated events are weighted to match the NNLOPS [60, 61] prediction in the hadronic jet multiplicity (Njet) and Higgs boson pT distributions. The weighting is based on pT and Njet as computed in the simplified template cross section scheme 1.0 [62]. The minlo hjj [63] generator, which provides NLO accuracy for Njet≥2, is also used for ggH production. The associated production processes with top quarks (tt¯H) and bottom quarks (bb¯H) are simulated with powheg v2 and MadGraph 5_amc@nlo v2.2.2 [64], respectively, and have a negligible contribution in the analysis phase space. All SM Higgs boson samples are normalized to the cross sections recommended in Ref. [19]. The Higgs boson mass in the event generation is assumed to be 125GeV, while a value of 125.38GeV [65] is used for the calculation of cross sections and branching fractions. The decay to a pair of W bosons and subsequently to leptons or hadrons is performed using the JHUGen v5.2.5 generator in 2016, and v7.1.4 in 2017 and 2018, for ggH, VBF, and quark-induced ZH samples. The Higgs boson and W boson decays are performed using pythia 8.212 for the other signal simulations.

The ggH, VBF, and VH Higgs boson events with HVV anomalous couplings are generated with JHUGen at LO accuracy. With respect to the κ2Zγ/(Λ1Zγ)2 coupling parameter discussed in Sect. 2, the sign convention of the photon field is determined by the sign in front of the gauge fields in the covariant derivative. In this analysis, we define the covariant derivative Dμ=∂μ-ieσiWμi/(2sw)+ieBμ/(2cw) following the convention in JHUGen [31]. The JHUGen and powheg SM Higgs boson simulations were compared after parton showering and no significant differences in the distributions of kinematic observables were found. We adopt the JHUGen simulation to describe the kinematic features in all production modes with HVV anomalous couplings. The expected yields are scaled to match the SM theoretical predictions [19] for inclusive cross sections and the powheg SM prediction of relative event yields in the event categorization based on associated particles. Simulation of the ggH + 2 jets process with Hgg anomalous couplings is done using minlo X0jj [66] at NLO in QCD. A large number of signal samples with various anomalous couplings were generated. The MELA package [20–24] contains a library of matrix elements from JHUGen for different Higgs boson signal hypotheses. Matrix elements from different coupling signal hypotheses, but with the same production mechanism, are used to reweight the generated signal events. This procedure is used in the construction of the predictions for the different coupling components and their interference, allowing us to cover all points in the signal model phase space with sufficient statistical precision.

Background events are produced using several simulations. The quark-initiated nonresonant WW process is simulated with powheg v2 [67] at NLO accuracy for inclusive production. A reweighting is performed to match the diboson pT spectrum computed at NNLO+NNLL QCD accuracy [68, 69]. The mcfm v7.0 [70–72] generator is used to simulate gluon-induced WW production at LO accuracy, with the normalization chosen to match the NLO cross section [73]. Nonresonant EW production of WW pairs with two additional jets is simulated at LO accuracy with MadGraph 5_amc@nlo v2.4.2 using the MLM matching and merging scheme [74]. Top quark pair production (tt¯) and single top quark processes, including tW, s- and t-channel contributions, are simulated with powheg v2 [75–77]. A reweighting of the top quark and antiquark pT spectrum at parton level is performed for the tt¯simulation in order to match the NNLO and next-to-next-to-leading logarithm (NNLL) QCD predictions, including also the NLO EW contribution [78].

The Drell–Yan (DY) production of a charged-lepton pair is simulated with MadGraph 5_amc@nlo v2.4.2 at NLO accuracy with up to two additional partons, using the FxFx matching and merging scheme [79]. Production of a W boson associated with an initial state radiation photon (Wγ) is simulated with MadGraph 5_amc@nlo v2.4.2 at NLO accuracy with up to 1 additional parton, using the FxFx jet merging. Diboson processes containing at least one Z boson or a virtual photon (γ∗) with a mass as low as 100MeV are generated with powheg v2 [67] at NLO accuracy. Production of a W boson in association with a γ∗ (Wγ∗) for masses below 100MeV is simulated by pythia 8.212 in the parton showering of Wγ events. Triboson processes with inclusive decays are also simulated at NLO accuracy with MadGraph 5_amc@nlo v2.4.2.

For all processes, the detector response is simulated using a detailed description of the CMS detector, based on the Geant4 toolkit [80]. The distribution of additional pp interactions within the same or nearby bunch crossings (pileup) in the simulation is reweighted to match that observed in data. The efficiency of the trigger system is evaluated in data on a per lepton basis using dilepton events consistent with the Z boson decay. The overall efficiencies of the trigger selections used in the analysis are obtained as the average of the per-lepton efficiencies weighted by their probability. The resulting efficiencies are applied directly on simulated events.

Event reconstruction

The identification and measurement of the properties of individual particles (PF candidates) in an event is achieved in the PF algorithm by combining information from various subdetectors. Electrons are identified and their momenta are measured in the pseudorapidity interval η<2.5 by combining tracks in the silicon tracker with spatially compatible energy deposits in the electromagnetic calorimeter. Muons are identified and their momenta are measured in the pseudorapidity range η<2.4 by matching tracks in the muon system and the silicon tracker. For better rejection of nonprompt leptons, increasing the sensitivity of the analysis, leptons are required to be isolated and well reconstructed using a set of criteria based on the quality of the track reconstruction, shape of calorimetric deposits, and energy flux in the vicinity of the particle’s trajectory [34, 35]. In addition, a selection based on a dedicated multivariate analysis (MVA) tagger developed for the CMS tt¯H analysis [81] is added in all channels for muon candidates.

Multiple pp interaction vertices are identified from tracking information by use of the adaptive vertex fitting algorithm [82]. The primary pp interaction vertex is taken to be the vertex corresponding to the hardest scattering in the event, evaluated using tracking information alone, as described in Section 9.4.1 of Ref. [83]. Leptons are required to be associated to the primary vertex using transverse and longitudinal impact parameter criteria [34, 35].

Hadronic jets are clustered from PF candidates using the infrared- and collinear-safe anti-kT algorithm with distance parameters of 0.4 (AK4) and 0.8 (AK8). The jet momentum is determined as the vectorial sum of all particle momenta in the jet. The AK8 jets considered are required to be reconstructed within the silicon tracker acceptance (η<2.4), whereas AK4 jets are reconstructed in the range η<4.7. For AK4 jets, contamination from pileup is suppressed using charged-hadron subtraction which removes charged PF candidates originating from vertices other than the primary interaction vertex. The residual contribution from neutral particles originating from pileup vertices is removed by means of an event-by-event jet-area-based correction to the jet four-momentum [84]. For AK8 jets, the pileup-per-particle identification algorithm (PUPPI) [85] is used to mitigate the effect of pileup at the reconstructed-particle level, making use of local shape information, event pileup properties, and tracking information. Additional selection criteria are applied to remove jets potentially dominated by instrumental effects or reconstruction failures [84].

The AK8 jets are used to reconstruct hadronic Vboson decays in a single merged jet when the decay products are highly collimated. This approach targets boosted W or Z bosons originating from the VH production mode. Such Lorentz-boosted Vdecays are identified using the ratio of the 2- to 1-subjettiness [86], τ2/τ1, and the groomed jet mass mJ. The groomed mass is calculated after applying a modified mass drop algorithm [87, 88], known as the soft-drop algorithm [89], with parameters β=0, zcut=0.1, and R0=0.8. The algorithm also identifies two hard subjets within the AK8 jet.

We refer to the identification of jets likely originating from bottom quarks as b tagging [90, 91]. For each AK4 jet in the event, a score is calculated through a multivariate combination of different jet properties, making use of boosted decision trees and deep neural networks. A jet is considered b-tagged if its associated score exceeds a threshold, tuned to achieve a certain tagging efficiency as measured in tt¯events. The chosen working point corresponds to about 90% efficiency for bottom quark jets and to a mistagging rate of about 10% for light-flavor or gluon jets and of about 50% for charm quark jets.

The missing transverse momentum vector p→Tmiss is computed as the negative vector sum of the transverse momenta of all the PF candidates in an event, and its magnitude is denoted as pTmiss [41]. The PUPPI algorithm is applied to reduce the pileup dependence of the p→Tmiss observable by computing the p→Tmiss from the PF candidates weighted by their probability to originate from the primary interaction vertex [41].

Event selection

The analysis is performed using H→WW candidate events in the eμ final state. For an event to be selected, the transverse momenta of the leading lepton pTℓ1 and the subleading lepton pTℓ2 must be greater than 25 and 13GeV, respectively. The pTℓ2 threshold in the case of a muon is lowered to 10GeV for the 2016 data set because of the lower threshold in the corresponding HLT algorithm. Events containing additional leptons with pT>10GeV are discarded. The dilepton system is required to have an invariant mass mℓℓ greater than 12GeV and transverse momentum pTℓℓ above 30GeV. A requirement on the missing transverse momentum of pTmiss>20GeV is implemented. We define transverse mass discriminating variables mTH and mTℓ2 as17 mTH=2pTℓℓpTmiss[1-cosΔΦ(p→Tℓℓ,p→Tmiss)],

18 mTℓ2=2pTℓ2pTmiss[1-cosΔΦ(p→Tℓ2,p→Tmiss)],

and select events with mTH>60GeV and mTℓ2>30GeV. The mTH requirement suppresses the DY→ττ background process and avoids overlap with the H→ττ analysis [11]. To ensure orthogonality with a future off-shell H→WW analysis we require mTH<125GeV. In addition, the region 76.2<mℓℓ<106.2GeV is excluded to avoid overlap with the off-shell H→ZZ→2ℓ2ν analysis [10]. These requirements will simplify a future combination of Higgs boson decay final states. Finally, events with any b-tagged jets with pT>20GeV are vetoed. These base selection criteria are summarized in Table 2.Table 2 Summary of the base selection criteria

Variable	Selection	
Number of leptons	2 (eμ of opposite charge)	
pTℓ1	>25 GeV	
pTℓ2	>13 GeV (10GeV for 2016 data)	
mℓℓ	12–76.2GeV or >106.2GeV	
pTℓℓ	>30 GeV	
pTmiss	>20 GeV	
mTℓ2	>30 GeV	
mTH	60–125GeV	
Njet(bjets)	0	

For the HVV coupling analysis, exclusive selection criteria, which are based on the associated jet activity in the event, are applied that target the ggH, VBF, and VH production processes. The AK4 (AK8) jets considered are required to have pT>30(200)GeV. In the ggH channel, zero or one AK4 jet is required in the event. For the VBF and Resolved VH channels, we require two AK4 jets with dijet masses of mjj>120GeV and 60<mjj<120GeV, respectively. The Boosted VH channel requires the presence of a V-tagged AK8 jet (Vjet); such jets have a groomed mass in the region 65<mJ<105GeV and satisfy the requirement τ2/τ1<0.4. In the other channels, a Vjet veto is implemented to ensure orthogonality. These production channels for the HVV coupling study are summarized in Table 3.Table 3 Summary of the ggH, VBF, and VH production channels used for the HVV coupling study

Variable	ggH	VBF	Resolved VH	Boosted VH	
Njet(Vjets)	0	0	0	>0	
Njet(AK4 jets)	0 and 1	2	2	-	
mjj	-	>120 GeV	60–120GeV	-	

As the production vertex of the ggH + 2 jets process is sensitive to anomalous Hgg coupling effects, we use a 2-jet ggH channel that follows the VBF selection described above for the Hgg coupling analysis. The HWWdecay vertex is not sensitive to anomalous Hgg effects, and so decay-based variables are not studied in this channel. This permits a relatively tight selection of mℓℓ<55GeV which is beneficial for background suppression. The 0- and 1-jet ggH channels are also included to constrain the ggH signal strength. All channels included for the Hgg coupling study are summarized in Table 4.Table 4 Summary of ggH channel selections used for the Hgg coupling study

Variable	ggH	2-jet ggH	
Njet (AK4 jets)	0 and 1	2	
mjj	-	>120 GeV	
mℓℓ	-	<55 GeV	

Control regions (CRs) are defined using the base selection criteria together with a set of alternative requirements summarized in Table 5. They are used to validate the background description and to estimate the number of background events in the signal region (SR). A dedicated ττ CR targets events from the DY process Z→ττ with τ leptons decaying leptonically to produce the eμ final state. Also a top quark CR is defined to enhance events with one or more top quarks decaying to a W boson and bottom quark. Splitting events according to the number of associated jets, separate ττ and top quark CRs are defined for the 0-, 1- and 2-jet SRs. An additional CR with an enhanced contribution from the nonresonant WW background is used in the 2-jet SR. All CRs are used in the final data fit to constrain the DY, top quark, and WW background normalizations.Table 5 Summary of the ττ, top quark, and WW control region requirements

Variable	ττ	Top quark	WW	
mℓℓ	40–80GeV	>50 GeV	>106.2 GeV	
mTH	<60 GeV	-	60–125GeV	
mTℓ2	-	>30 GeV	>30 GeV	
	0	>0	0	

Additional ττ, top quark, and WWCRs are defined requiring a Vjet. These CRs are used to validate the background description in the Boosted VH channel. However, they generally do not have a sufficient number of events to significantly constrain the background normalizations in the final fit to the data. As such, we rely on the 2-jet CRs to determine the normalizations to be used in the Boosted VH channel. Agreement between data and the background prediction in the Vjet CRs is observed when using normalizations determined in the 2-jet CRs.

Background estimation

The nonprompt-lepton backgrounds originating from leptonic decays of heavy quarks, hadrons misidentified as leptons, and electrons from photon conversions are suppressed by identification and isolation requirements imposed on electrons and muons. In this analysis, the nonprompt-lepton background primarily originates from W+jets events and is estimated from data, as described in detail in Ref. [92]. The procedure involves measuring the rate at which a nonprompt lepton passing a loose selection further passes a tight selection (misidentification rate) and the corresponding rate for a prompt lepton to pass this selection (prompt rate). The misidentification rate is measured in a data sample enriched in multijet events, whereas the prompt rate is measured using a tag-and-probe method [93] in a data sample enriched in DY events. The nonprompt-lepton background estimation is validated with data in a CR enriched with W+jets events, in which a pair of same-sign leptons is required.

The backgrounds from top quark processes and nonresonant WW production are estimated using a combination of MC simulations and the dedicated CRs described in the previous section. The normalisations of these backgrounds are left as free parameters in the fit, keeping different parameters for each jet multiplicity region. The top quark background normalization is measured from the observed data in the top quark enriched CRs. A separate normalization parameter is included for the quark-induced and gluon-induced WW backgrounds. For the 2-jet regions, the WW enriched CR is used to constrain the WW background normalisation parameters. In the 0- and 1-jet channels, these parameters are constrained directly in the signal regions, which span the high mℓℓ phase space enriched in WW events.

The DY→ττ background process is estimated with a data-embedding technique [94]. As for the top quark and WW backgrounds, the DY normalization is left unconstrained in the data fit. The DY→ττ enriched CR described in Sect. 6 is used to constrain the free normalization parameters in the 0-, 1-, 2-jet regions. The data-embedded samples cover the events that pass the eμ triggers, which represent the vast majority of the selected events. The remaining DY→ττ events, which enter the analysis through the single-lepton triggers (≈5% of the total), are estimated using MC simulation.Fig. 1 Topologies of the Higgs boson production and decay for vector boson fusion qq′→qq′H (left), qq¯′→VH (center), and gluon fusion with decay gg→H→2ℓ2ν (right). For the electroweak production topologies, the intermediate vector bosons and their decays are shown in green and the H→WW decay is marked in red. For the gg→H→2ℓ2ν topology, the W boson leptonic decays are shown in green. In all cases, the incoming particles are depicted in brown and the angles characterizing kinematic distributions are marked in blue. Five angles fully characterize the orientation of the production and decay chain and are defined in the suitable rest frames

The WZ and Wγ∗ background contributions are simulated as described in Sect. 4, and a data-to-simulation scale factor is derived in a three-lepton CR, as described in Ref. [92]. The contribution of the Wγ process may also be a background because of photon conversions in the detector material. This process is estimated using MC simulation and validated using data in a CR requiring events with a leading μ and a trailing e with same sign and a separation in ΔR=Δϕ2+Δη2 (where ϕ is the azimuthal angle in radians) smaller than 0.5. Triple vector boson production is a minor background in all channels and is estimated using MC simulation.

Observables and kinematic discriminants

In this paper, we search for anomalous HVV and Hgg coupling effects by studying: the two quark jets from VBF and VH production (HVV coupling);

the H→WW decay products (HVV coupling); and

the two quark jets from ggH + 2 jets production (Hgg coupling).

The VBF, VH, and ggH production and decay topologies relevant for the HVV coupling are illustrated in Fig. 1.

When combined with the momentum transfer of the vector bosons, the five angles illustrated for VBF/VH production provide complete kinematic information for production and decay of the Higgs boson. The illustration for Higgs boson production via ggH in association with two jets is identical to the VBF diagram, except for replacing the intermediate vector bosons by gluons. Full production kinematic information is extracted for VBF, VH, and ggH + 2 jets candidate events using discriminants built from the matrix element calculations of the MELA package. The MELA approach is designed to reduce the number of observables to a minimum, while retaining all essential information. To form the production-based MELA kinematic discriminants, we use jets to reconstruct the four-momentum of the associated production particles. The presence of two neutrinos in the final state means it is not possible to reconstruct the four-momentum of all the Higgs boson decay products. Therefore, decay-based kinematic discriminants built from matrix elements are not used in this analysis. Instead, we rely on kinematic variables related to the measured final state of the Higgs boson decay. The strategies used for each of the topologies listed above are now discussed in more detail.

Kinematic features of two quark jets in VBF and VH channels

Kinematic distributions of associated particles in VBF and VH production are sensitive to the anomalous HVV couplings of the Higgs boson.

As illustrated in Fig. 1, a set of seven observables can be defined for the VBF and VH production topologies: Ω={θ1(′),θ2(′),θ∗,Φ,Φ1,q12,q22}, with q12 and q22 the squared four-momenta of the vector bosons [22]. Three types of discriminants are defined using the full kinematic description characterized by Ω. The first type of discriminant is designed to separate signal and background Higgs boson production processes:19 Dsig=Psig(Ω)Psig(Ω)+Pbkg(Ω),

where the probability density P for a specific process is calculated from the matrix elements provided by the MELA package. The second type of discriminant separates the anomalous coupling BSM process from that of the SM:20 DBSM=PBSM(Ω)PBSM(Ω)+PSM(Ω).

Throughout this document the generic BSM label is generally replaced by the specific anomalous coupling state targeted. For the a3 CP-odd and a2 CP-even coupling parameters, we use, respectively, D0- and D0+, whereas for the Λ1 coupling parameters we use DΛ1 and DΛ1Zγ. The third type of discriminant isolates the interference contribution:21 Dint=PSM-BSMint(Ω)PSM(Ω)+PBSM(Ω),

where PSM-BSMint is the interference part of the probability distribution for a process with a mixture of the SM and BSM contributions. The CP label is generally used for the a3 coupling parameter, as the BSM signal in this case is a pseudoscalar and the interference discriminant is a CP-sensitive observable. The P values are normalized to give the same integrated cross sections in the relevant phase space of each process. Such normalization leads to a balanced distribution of events in the range between 0 and 1 for Dsig and DBSM, and between -1 and +1 for Dint.

The selected events are split into three main production channels: VBF, Resolved VH, and Boosted VH. In the first two channels, the four-momenta of the two AK4 jets assigned as the associated particles are used in the MELA probability calculation. For the Boosted VH category, we use the four-momentum of the two subjets of the V-tagged AK8 jet. An estimate of the Higgs boson four-momentum is also required for the probability calculation. This can not be measured directly since the final state contains two neutrinos. As such, we construct a proxy Higgs boson four-momentum in the following manner. The px and py of the dineutrino system are estimated from the p→Tmiss in a given event. The corresponding pz is then set to equal that of the dilepton system, which is based on the observed correlation between these variables at the generator level for simulated signals. Finally, the mass of the dineutrino system is set equal to the mean value of the generator-level dineutrino mass. The resulting four-momentum can then be combined with that of the measured dilepton system to create a proxy Higgs boson four-momentum. We note that the MELA probability calculation for the production vertices is largely based on the kinematic features of the associated particles, so the reconstruction of the proxy Higgs boson has a relatively small effect on the final discriminants. As an illustrative example of the MELA based discriminants used in this analysis, Fig. 2 shows the D0- discriminant in the VBF and Resolved VH production channels for a number of different signal hypotheses. The discriminants are designed to target the dominant signal production process in a given channel.Fig. 2 The D0- discriminant in the VBF (upper) and Resolved VH (lower) production channels for a number of VBF (upper) and VH (lower) signal hypotheses. Pure a1 (fa3=0) and a3 (fa3=1) HVV signal hypotheses are shown along with two mixed coupling hypotheses (fa3=0.005 and fa3=0.01). All distributions are normalized to unity

In the VBF channel, a DVBF discriminant is constructed, following Eq. (19), where Psig corresponds to the probability for the VBF production hypothesis, and Pbkg corresponds to that of gluon fusion production in association with two jets. The discriminant is also suitable for separating SM backgrounds from the VBF signal process. In the Resolved and Boosted VH channels, the corresponding discriminants do not give a significant level of separation with respect to ggH production or SM backgrounds. This is due to the relatively tight selection criteria, which limit the phase space to VH-like events. Hence, these discriminants are not included in the VH channels.

The DCP discriminant is sensitive to the sign of the interference between the CP-even SM and CP-odd BSM states. An asymmetry between the number of events detected with positive and negative DCP values is expected for mixed CP states. Therefore, a forward-backward categorization (forward defined as DCP>0 and backward as DCP<0) is used to analyze the CP-odd couplings. Similarly, Dint gives sensitivity to the sign of the interference between the SM and a2 HVV BSM states. A forward-backward Dint categorization is also included. The value of Dint used to define the categories is chosen to symmetrize the SM Higgs boson expectation. In the case of the Λ1 measurements, the interference discriminants were shown to be highly correlated with the DBSM discriminants and so are not considered.

We now discuss the categorization and construction of the final multidimensional discriminants used for the two HVV coupling approaches defined in Sect. 2. The binning of the final discriminants was optimized to ensure sufficient statistical precision in the predictions of all bins, while retaining the kinematic information required to discriminate between the SM and anomalous coupling signal hypotheses.

VBF/ VH analysis strategy for Approach 1

In Approach 1, each of the four anomalous HVV coupling parameters (a2, a3, κ1/(Λ1)2, and κ2Zγ/(Λ1Zγ)2) are analyzed separately. For this purpose, we construct a multidimensional discriminant for each of the four anomalous couplings in the VBF, Resolved VH, and Boosted VH channels.

In the VBF channel, we use two bins of the production discriminant DVBF, corresponding to low and high purity, using a bin boundary of 0.75. The mℓℓ variable, which is sensitive to anomalous effects at the H→WW decay vertex, is included with two bins in the range 12–76.2GeV. A bin boundary of 45GeV is chosen based on the expected signal shape changes induced by anomalous effects. Finally, one of the DBSM discriminants is included with ten equally sized bins. Depending on the anomalous coupling under study this discriminant may be D0+, D0-, DΛ1 or DΛ1Zγ.

For the VH channels, the mℓℓ and DBSM observables are used to build 2D kinematic discriminants. The mℓℓ bins are the same as for the VBF channel. In the Resolved VH channel, we use four DBSM bins of equal size. For the Boosted VH case, three variable bins with boundaries of 0.6 and 0.8 are used, a large first bin is chosen because relatively little signal is expected at low values of DBSM. A distinct multidimensional discriminant is constructed for each anomalous coupling hypothesis in the VH channels.

For the a3 coupling parameter, a forward-backward categorization of events based on DCP is implemented. In the case of the a2 coupling parameter, Dint is largely correlated with D0+ in the VH channels. Therefore, a forward-backward Dint categorization is implemented only in the VBF channel. Figures 3, 4 and 5 show the discriminants used in the final fit to the data for the a2, a3, κ1/(Λ1)2, and κ2Zγ/(Λ1Zγ)2 Approach 1 coupling studies in the VBF and VH channels. A summary of the observables used in the HVV Approach 1 analysis may be found in Table 6.

VBF/ VH analysis strategy for Approach 2

In Approach 2, we use one categorization strategy and build one multidimensional discriminant in each channel to target all the HVV coupling parameters (a2, a3, κ1/(Λ1)2) simultaneously. In the VBF channel, the DCP and Dint discriminants are used to create four interference categories. Both DVBF and mℓℓ are used as for Approach 1. All three DBSM discriminants that target the a2,a3 and κ1/(Λ1)2 coupling parameters are included. However, the number of bins we implement is limited by the number of simulated events. Also the DBSM discriminants are significantly correlated and so have similar performance for all couplings. Therefore, we use the CP-odd discriminant D0- and just one of the CP-even discriminants, D0+, both with three bins and bin boundaries of 0.1 and 0.9. A dedicated rebinning strategy is applied to the [D0-,D0+] distribution merging bins dominated by the SM Higgs boson prediction or with low precision in the background prediction. In the VH channels, just two categories using DCP are defined and the discriminant is built using mℓℓ as for Approach 1. Again, both D0- and D0+ are chosen for the final discriminant. For the Resolved VH channel, we use three bins with boundaries of 0.25 and 0.75, whereas for the Boosted VH case we use two bins with a boundary of 0.8. The same rebinning strategy described for the VBF channel is applied to both Resolved and Boosted VH multidimensional discriminants. Table 6 includes a summary of the observables used in the HVV Approach 2 analysis.Fig. 3 Observed and predicted distributions after fitting the data for [DVBF,mℓℓ,D0+] in the VBF channel (upper), and for [mℓℓ,D0+] in the Resolved VH (lower left) and Boosted VH (lower right) channels. For the VBF channel, the Dint<0.4 (left) and Dint>0.4 (right) categories are shown. The predicted Higgs boson signal is shown stacked on top of the background distributions. For the fit, the a1 and a2 HVV coupling contributions are included. The corresponding pure a1 (fa2=0) and a2 (fa2=1) signal hypotheses are also shown superimposed, their yields correspond to the predicted number of SM signal events scaled by an arbitrary factor to improve visibility. The uncertainty band corresponds to the total systematic uncertainty. The lower panel in each figure shows the ratio of the number of events observed to the total prediction

Fig. 4 Observed and predicted distributions after fitting the data for [DVBF,mℓℓ,D0-] in the VBF channel (upper), and for [mℓℓ,D0-] in the Resolved VH (middle) and Boosted VH (lower) channels. For each channel, the DCP<0 (left) and DCP>0 (right) categories are shown. For the fit, the a1 and a3 HVV coupling contributions are included. More details are given in the caption of Fig. 3

Fig. 5 Observed and predicted distributions after fitting the data for [DVBF,mℓℓ,DΛ1] (upper left) and [DVBF,mℓℓ,DΛ1Zγ] (upper right) in the VBF channel, and for [mℓℓ,DΛ1] (left) and [mℓℓ,DΛ1Zγ] (right) in the Resolved VH (middle) and Boosted VH (lower) channels. For the fits, the a1 and κ1/(Λ1)2 (left) or a1 and κ2Zγ/(Λ1Zγ)2 (right) HVV coupling contributions are included. More details are given in the caption of Fig. 3

Kinematic features of H→WW decay products in 0- and 1-jet ggH channels

Similar to the SM H→WW analysis [25], we use mℓℓ and mT to build 2D discriminants in the 0- and 1-jet ggH channels. The distributions have nine bins for mℓℓ in the range 12–200GeV and six bins for mT in the range 60–125GeV. The bin widths vary and are optimized to achieve good separation between the SM Higgs boson signal and backgrounds, as well as between the different anomalous coupling signal hypotheses. In particular, a finer binning with respect to the SM H→WW analysis is implemented in regions where anomalous effects are most significant. Figure 6 shows the [mT,mℓℓ] distributions in the 0- and 1-jet ggH channels. The same [mT,mℓℓ] discriminant is used to study all HVV anomalous couplings for both Approach 1 and 2.

Kinematic features of two quark jets in 2-jet ggH channel

For the Hgg coupling, we adopt a similar approach to the VBF CP study, where the CP-odd a3 HVV coupling parameter is included. In this case, the optimal observables are D0-ggH and DCPggH, targeting the CP-odd a3 Hgg coupling parameter. A forward-backward categorization is implemented using DCPggH, and the DVBF and D0-ggH observables are used to build 2D discriminants. The mℓℓ variable is not considered in this case because it is not sensitive to anomalous Hgg effects. For DVBF, the bin boundary is relaxed to 0.5 to ensure sufficient ggH events are accepted in the more VBF-like bin. For D0-, eight (five) bins are used in the more (less) VBF-like bin with larger bin sizes at the extremes of the distribution to ensure sufficient precision in the background and signal predictions. The 0- and 1-jet channels discussed previously are also included in this study to constrain the ggH signal strength. The [DVBF, D0-ggH] distributions used to analyze the Hgg a3 anomalous coupling in the 2-jet ggH channel are shown in Fig. 7. A summary of the observables used in the Hgg analysis is given in Table 6.Table 6 The kinematic observables used for the interference based categorization and for the final discriminants used in the fits to data to study the HVV and Hgg couplings. For each of the anomalous HVV couplings in Approach 1, we have a dedicated analysis in the VBF and VH channels. In Approach 2, we use one analysis to target all anomalous HVV couplings simultaneously

Analysis	Channel	Categorization	Final discriminant	
HVV	VBF (a2)	Dint	[DVBF, mℓℓ, D0+]	
Approach 1	VBF (a3)	DCP	[DVBF, mℓℓ, D0-]	
VBF (κ1)	-	[DVBF, mℓℓ, DΛ1]	
VBF (κ2Zγ)	-	[DVBF, mℓℓ, DΛ1Zγ]	
VH (a2)	-	[mℓℓ, D0+]	
VH (a3)	DCP	[mℓℓ, D0-]	
VH (κ1)	-	[mℓℓ, DΛ1]	
VH (κ2Zγ)	-	[mℓℓ, DΛ1Zγ]	
0- and 1-jet ggH	-	[mT, mℓℓ]	
HVV	VBF	DCP, Dint	[DVBF, mℓℓ, D0-, D0+]	
Approach 2	VH	DCP	[mℓℓ, D0-, D0+]	
0- and 1-jet ggH	-	[mT, mℓℓ]	
Hgg	2-jet ggH	DCPggH	[DVBF, D0-ggH]	
0- and 1-jet ggH	-	[mT, mℓℓ]	

Fig. 6 Observed and predicted distributions after fitting the data for [mT,mℓℓ] in the 0- (upper) and 1-jet (lower) ggH channels. For the fit, the a1 and a3 HVV coupling contributions are included. More details are given in the caption of Fig. 3

Fig. 7 Observed and predicted distributions after fitting the data for [DVBF, D0-ggH] in the 2-jet ggH channel. Both the DCPggH<0 (upper) and DCPggH>0 (lower) categories are shown. In this case, the VBF and ggH signals are shown separately. For the fit, the a2gg and a3gg coupling contributions are included. The corresponding pure a2gg (fa3ggH=0) and a3gg (fa3ggH=1) signal hypotheses are also shown superimposed, their yields correspond to the predicted number of SM signal events. More details are given in the caption of Fig. 3

Systematic uncertainties

The signal extraction is performed using binned templates to describe the various signal and background processes. Systematic uncertainties that change the normalization or shape of the templates are included. All the uncertainties are modeled as nuisance parameters that are profiled in the maximum likelihood fit described in Sect. 10. The systematic uncertainties arise from both experimental or theoretical sources.

Experimental uncertainties

The following experimental systematic uncertainties are included in the final fit to data:The total uncertainty associated with the measurement of the integrated luminosity for 2016, 2017, and 2018 is 1.2% [44], 2.3% [45], and 2.5% [46], respectively. This uncertainty is partially correlated among the three data sets, resulting in an overall uncertainty of 1.6%.

The systematic uncertainty in the trigger efficiency is determined by varying the tag lepton selection criteria and the Z boson mass window used in the tag-and-probe method. It affects both the normalization and the shape of the signal and background distributions, and is kept uncorrelated among data sets. The total normalization uncertainty is less than 1%.

The tag-and-probe method is also used to determine the lepton identification and isolation efficiency. Corrections are applied to account for any discrepancy in the efficiencies measured in data and simulation. The corresponding systematic uncertainty is about 1% for electrons and 2% for muons.

The uncertainties in the determination of the lepton momentum scale mainly arise from the limited data sample used for their estimation. The impact on the normalization of the signal and background templates ranges between 0.6–1.0% for the electron momentum scale and is about 0.2% for the muon momentum scale. They are treated as uncorrelated among the three data-taking years.

The jet energy scale uncertainty is modeled by implementing eleven independent nuisance parameters corresponding to different jet energy correction sources, six of which are correlated among the three data sets. Their effects vary in the range of 1–10%, mainly depending on the jet multiplicity in the analysis phase space. Another source of uncertainty arises from the jet energy resolution smearing applied to simulated samples to match the pT resolution measured in data. The effect varies in a range of 1–5%, depending on the jet multiplicity and is uncorrelated among the data sets. These uncertainties are included for both AK4 and AK8 jets. In addition, the mJ scale and resolution, and Vtagging corrections with their corresponding uncertainties are included for V-tagged AK8 jets. These variables are calibrated in a top quark–antiquark sample enriched in hadronically decaying W bosons [95].

The effects of the unclustered energy scale, jet energy scale, and lepton pT scales are included for the calculation of the missing transverse momentum. The resulting normalization systematic uncertainty is 1–10% and is treated as uncorrelated among the years.

Both the normalization and shape of the signal and background templates are affected by the jet pileup identification uncertainty. The effect is below 1%.

The uncertainty associated with the b tagging efficiency is modeled by seventeen nuisance parameters out of which five are of a theoretical origin and are correlated among the three data sets. The remaining set of four parameters per data set are treated as uncorrelated as they arise from the statistical accuracy of the efficiency measurement [90].

Estimation of the nonprompt-lepton background is affected by the limited size of the data sets used for the misidentification rate measurements. It is also affected by the difference in the flavor composition of jets misidentified as leptons between the misidentification rate measurement region (enriched in multijet events) and the signal phase space. The effects on the nonprompt-lepton background estimation range between a few percent to about 10% depending on the SR and are treated as nuisance parameters uncorrelated between electrons and muons and among the three data sets. A normalization uncertainty of 30% [92] is assigned to fully cover for any discrepancies with respect to data in a W+jets CR and is treated as uncorrelated among data sets.

The statistical uncertainties due to the limited number of simulated events are also included for all bins of the background distributions used to extract the results [96].

Theoretical uncertainties

Multiple theoretical uncertainties are considered and are correlated among data sets, unless stated otherwise:The uncertainties related to the choice of PDF and αS have a minor effect on the shape of the distributions. Therefore, only normalization effects related to the event acceptance and to the cross section are included. However, these uncertainties are not considered for the backgrounds that have their normalization constrained through data in dedicated CRs. For the Higgs boson signal processes, these uncertainties are calculated by the LHC Higgs cross section working group [19].

The theoretical uncertainties arising from missing higher-order corrections in the cross section calculations are also included. Background simulations are reweighted to the alternative scenarios corresponding to renormalization μR and factorization μF scales varied by factors 0.5 or 2 and the envelopes of the varied templates are taken as the one standard deviations. For background processes that have their normalization constrained through data in dedicated CRs, we consider only the shape effect of the uncertainties coming from the missing higher-order corrections. The WWnonresonant background has the uncertainties derived by varying μR, μF, and the resummation scale. For the ggH and VBF signal processes, the effects of the missing higher-order corrections on the overall cross section are decoupled into multiple sources according to the recipes described in Ref. [19].

The uncertainty due to the pileup modeling was included for the main simulated background processes (DY, WW, top quark) as well as the ggH and VBF signals. The effect is determined by varying the total inelastic pp cross section (69.2mb [97, 98]) within the assigned 5% uncertainty.

The PS modeling mainly affects the jet multiplicity, causing migration of events between categories that results in template shape changes. Associated uncertainties are evaluated by reweighting events with varied PS weights computed with pythia 8.212. The effect on the signal strength is found to be below 1%.

Uncertainties associated with UE modeling are evaluated by varying the UE tune parameters used in the MC sample generation. Systematic uncertainties are correlated between the 2017 and 2018 data sets since they share the same UE tunes, whereas for 2016 the uncertainty is considered uncorrelated. The UE uncertainty has a minimal effect on the template shapes and affects the normalization by about 1.5%.

A 15% uncertainty is applied to the relative fraction of the gg-induced component in nonresonant WW production [99]. The relative fraction between single top quark and tt¯processes is assigned a systematic uncertainty of 8% [100]. Additional process-specific (DY, ) uncertainties, related to corrections to account for possible discrepancies between data and simulation, are assigned and are correlated among data sets.

Results

Fig. 8 Expected (dashed) and observed (solid) profiled likelihood on fa2 (upper left), fΛ1 (upper right), fa3 (lower left), and fΛ1Zγ (lower right) using Approach 1. In each case, the signal strength modifiers are treated as free parameters. The dashed horizontal lines show the 68 and 95% CL regions. Axis scales are varied for fa2 and fΛ1 to improve the visibility of important features

Fig. 9 Expected (dashed) and observed (solid) profiled likelihood on fa2 (upper left), fΛ1 (upper right) and fa3 (bottom) using Approach 2. The other two anomalous coupling cross section fractions are either fixed to zero (blue) or left floating in the fit (red). In each case, the signal strength modifiers are treated as free parameters. The dashed horizontal lines show the 68 and 95% CL regions. Axis scales are varied for fa2 and fΛ1 to improve the visibility of important features

Table 7 Summary of constraints on the anomalous HVV and Hgg coupling parameters with the best fit values and allowed 68 and 95% CL (in square brackets) intervals. For Approach 1, each fai is studied independently. For Approach 2, each fai is shown separately with the other two cross section fractions either fixed to zero or left floating in the fit. In each case, the signal strength modifiers are treated as free parameters

Analysis	fai		Observed (×10-3)	Expected (×10-3)	
HVV	fa2	Best fit	0.5	0.0	
Approach 1	68% CL	[− 0.8, 3.5]	[− 1.4, 1.3]	
95% CL	[− 5.7, 12.0]	[− 5.2, 6.1]	
fa3	Best fit	0.9	0.0	
68% CL	[− 2.7, 4.1]	[− 0.7, 0.7]	
95% CL	[− 553.0, 561.0]	[− 2.8, 2.9]	
fΛ1	Best fit	− 0.2	0.0	
68% CL	[− 0.5, 0.0]	[− 0.2, 0.5]	
95% CL	[− 1.4, 0.7]	[− 0.6,1.4]	
fΛ1Zγ	Best fit	3.0	0.0	
68% CL	[− 11.0, 9.1]	[− 5.0, 3.8]	
95% CL	[− 55.0, 42.0]	[− 14.0, 11.0]	
HVV	fa2	Best fit	38.0	0.0	
Approach 2	68% CL	[− 112.2, 129.3]	[− 30.9, 37.5]	
(Fix others)	95% CL	[− 376.6, 430.0]∪[− 989.2, − 826.3]	[− 126.1, 136.8]	
fa3	Best fit	0.8	0.0	
68% CL	[− 0.8, 3.5]	[− 0.8, 1.1]	
95% CL	[− 7.6, 58.8]	[− 3.4, 4.3]	
fΛ1	Best fit	− 0.15	0.0	
68% CL	[− 1.21, 0.16]	[− 0.4, 0.4]	
95% CL	[− 19.5, 118.5]∪[909.9, 964.1]	[− 1.7, 18.9]	
HVV	fa2	Best fit	− 1.0	0.0	
Approach 2	68% CL	[− 104.1, 139.9]	[− 31.1, 39.8]	
(Float others)	95% CL	[− 986.4, 981.2]	[− 127.5, 148.7]	
fa3	Best fit	0.34	0.0	
68% CL	[− 0.69, 3.4]	[− 1.0, 1.2]	
95% CL	[− 201.3, 361.5]	[− 4.3, 5.3]	
fΛ1	Best fit	− 0.1	0.0	
68% CL	[− 1.08, 3.78]∪[7.2, 20.7]	[− 0.4, 0.9]	
95% CL	[− 994.8, 993.9]	[− 1.9, 21.4]	
Hgg	fa3ggH	Best fit	− 34	0	
68% CL	[− 721, 383]	[− 1000, 1000]	
95% CL	[− 1000, 1000]	[− 1000, 1000]	

Fig. 10 The observed correlation coefficients between HVV anomalous coupling cross section fractions and signal strength modifiers (left) and between SMEFT Higgs basis coupling parameters (right)

Fig. 11 Expected (dashed) and observed (solid) profiled likelihood on the δcz (upper left), cz□ (upper right), czz (lower left), and c~zz (lower right) couplings of the SMEFT Higgs basis. All four couplings are studied simultaneously. The dashed horizontal lines show the 68 and 95% CL regions

The optimization and validation of the analysis were performed using simulation and data in CRs. The data in the SRs were examined once all details of the analysis were finalized. For the final results, we perform a binned maximum likelihood fit to the data combining all channels and data-taking periods. The statistical approach was developed by the ATLAS and CMS Collaborations in the context of the LHC Higgs Combination Group [101]. The likelihood function is defined for candidate events as:22 L(data|μggH,μEW,fai,θ)=∏jPoisson(nj|sj(μggH,μEW,fai,θ)+bj(θ))p(θ~|θ),

where j runs over all bins and nj is the observed number of data events in each bin. Total signal and background expectations in each bin are represented by sj and bj, respectively. The individual signal and background processes considered in each category are described using binned templates of multidimensional discriminants as described in Sect. 8. Each signal process is parametrized as a linear combination of terms originating from the SM, and anomalous couplings and their interference. The signal expectation depends on the parameters μggH, μEW, and fai, and is constrained by the data fit. Both the signal and background expectations are functions of θ, which represents the full set of nuisance parameters corresponding to the systematic uncertainties. The CRs described in Sect. 6 are included in the fit in the form of single bins, representing the number of events in each CR.

The μggH and μEW parameters correspond to the Higgs boson signal strength modifiers for the ggH and VBF/VH signals, respectively. Signal yields for the VBF and VH processes are related to each other because the same HVV couplings enter both in production and decay of the Higgs boson. The ggH signal is initiated predominantly by the top fermion couplings and is unrelated to the VBF and VH production mechanisms. As the signal strength modifiers are free parameters in the fit, the overall signal event yield is not used to discriminate between alternative signal hypotheses. The fai parameter corresponds to the anomalous coupling cross section fraction and determines the shape of the signal expectation. The cross section fraction for the SM coupling is simply taken as 1-fai. In Approach 1, the SM and just one anomalous HVV coupling are included, and each fai is thus studied independently. Depending on the particular anomalous coupling under investigation, fai may represent fa2, fa3, fΛ1, or fΛ1Zγ. For Approach 2, the SM and three anomalous HVV couplings are included. In this case, fai represents fa2, fa3 and fΛ1, which are studied simultaneously. It is explicitly required that fa2+fa3+fΛ1≤1 to avoid probing an unphysical parameter space. Finally, there is just one anomalous coupling corresponding to fa3ggH to consider for the Hgg vertex. For this study, we also include the effect of the CP-odd HVV anomalous coupling on the VBF process. This is achieved by including fa3 as a free parameter in the fit. The p(θ~|θ) are the probability density functions (PDFs) for the observed values of the nuisance parameters, θ~, obtained from calibration measurements. The systematic uncertainties that affect only the normalizations of the signal and background processes are treated as PDFs following a log-normal distribution, whereas shape-altering systematic uncertainties are treated as Gaussian PDFs [101].

Additional interpretations in terms of the SMEFT Higgs and Warsaw basis coupling parameters are also considered using Eqs. (7–10) and Eqs. (11–14), respectively. In each case, four independent couplings are studied simultaneously and the effect of the couplings on the total width of the Higgs boson is taken into account. For the fai measurements, this effect is absorbed by the signal strength modifiers. A parameterization of the partial widths of the main Higgs boson decay modes as a function of the couplings is used to determine the effect on the Higgs boson width [24, 28].

The likelihood is maximized with respect to the signal modifier parameters and with respect to the nuisance parameters. Confidence level (CL) intervals are determined from profile likelihood scans of the respective parameters. The allowed 68% and 95% CL intervals are defined using the set of parameter values at which the profile likelihood function -2ΔlnL=1.00 and 3.84 [102], respectively, for which exact coverage is expected in the asymptotic limit [103]. The likelihood value at a given fai is determined by the shape of the signal hypothesis and the relative signal event yields between categories. Expected results are obtained using the Asimov data set [104] constructed using the SM values of the signal modifier parameters.

For Approach 1, where we assume aiZZ=aiWW, the expected and observed fa2, fa3, fΛ1, and fΛ1Zγ likelihood scans are shown in Fig. 8. Significant interference effects for negative values of fa2, around -0.25, and positive values of fΛ1, around 0.5, are evident. Relatively large changes in the signal shape with respect to the SM are predicted at these values. Also evident are narrow minima around fai  = 0. The anomalous coupling terms in Eq. (1) have a qi2 dependence, which can be larger at the VBF/VH production vertex than at the Higgs decay vertex. This causes the cross section and the shape of the VBF/VH signal hypothesis to change rapidly with fai. For fΛ1Zγ, there are no anomalous effects at the Higgs decay vertex and so the only structure present is the narrow minimum related to the VBF/VH production vertex. The axis scales are varied to improve the visibility of important features for fa2 and fΛ1. For Approach 2, where the SU(2) x U(1) coupling relationships from Eqs. (2–6) are adopted, the expected and observed fa2, fa3 and fΛ1 likelihood scans are shown in Fig. 9. The results are shown for each fai separately with the other two fai either fixed to zero or left floating in the fit. The measured values of the signal strength parameters correspond to μEW=0.9-0.24+0.19 and μggH=0.9-0.20+0.38 when all parameters float simultaneously. It is notable that the observed -2ΔlnL profile values are generally lower than expected. This is consistent with a downward statistical fluctuation in the number of VBF and VH events. The lowest μEW value measured is 0.82 for the Approach 1 fa3 fit which can be compared with the highest value of 0.97 for the corresponding fΛ1 fit. In each case, the uncertainty in μEW is about 20% and as such all fitted values are consistent with both the SM and each other. More generally, all anomalous HVV coupling parameter measurements are consistent with the expectations for the SM Higgs boson. The p-value compatibility of the full Approach 2 fit, where all signal parameters float simultaneously, with the SM is 91%. A summary of constraints on the anomalous HVV coupling parameters with the best fit values and allowed 68% and 95% CL intervals are shown in Table 7. The most stringent constraints on the HVV anomalous coupling cross section fractions are at the per mille level. Some constraints are less stringent than expected due to the fitted values of μEW being lower than the SM expectation. The observed correlation coefficients between HVV anomalous coupling cross section fractions and signal strength modifiers are displayed in Fig. 10.

For the SMEFT Higgs basis interpretation, the expected and observed constraints on the δcz, cz□, czz, and c~zz coupling parameters are shown in Fig. 11. Table 8 presents a summary of the constraints on the couplings whereas Fig. 10 reports the observed correlation coefficients between them. For the Warsaw basis interpretation, the expected and observed constraints on the cH□, cHD, cHW, cHWB, cHB, cHW~, cHW~B, and cHB~ coupling parameters are presented in Table 9. To cover all the Warsaw basis coupling parameters, three independent fits to the data were performed with a different choice of four independent couplings in each. A summary of the constraints on the SMEFT Higgs and Warsaw basis coupling parameters is presented in Fig. 12.Table 8 Summary of constraints on the SMEFT Higgs basis coupling parameters with the best fit values and 68% CL uncertainties. All four couplings are studied simultaneously

Coupling	Observed	Expected	
δcz	-0.06-0.16+0.09	0.00-0.10+0.08	
cz□	0.01-0.06+0.02	0.00-0.02+0.02	
czz	0.03-0.52+0.30	0.00-0.29+0.23	
c~zz	-0.17-0.30+0.42	0.00-0.32+0.29	

Finally, the expected and observed fa3ggH likelihood scans are shown in Fig. 13. The result is consistent with the expectation for a SM Higgs boson. Excluding the effect of the CP-odd HVV anomalous coupling, by fixing fa3 to zero, has a negligible effect. For fa3ggH approaching unity, the observed -2ΔlnL profile values are larger than expected. This is consistent with downward statistical fluctuations in the data for a couple of bins where sensitivity to the a3 Hgg coupling contribution is enhanced (Fig. 7 upper). The constraint on the anomalous Hgg coupling parameter with the best fit value and allowed 68% CL interval is shown in Table 7.Table 9 Summary of constraints on the SMEFT Warsaw basis coupling parameters with the best fit values and 68% CL uncertainties. Only one of cHW, cHWB, and cHB is independent, the same is also true for cHW~, cHW~B, and cHB~. Three independent fits to the data were performed with a different choice of four independent couplings in each

Coupling	Observed	Expected	
cH□	-0.76-3.43+1.43	0.00-1.84+1.37	
cHD	-0.12-0.32+0.93	0.00-0.30+0.43	
cHW	0.08-0.87+0.43	0.00-0.48+0.37	
cHWB	0.17-1.79+0.88	0.00-0.96+0.77	
cHB	0.03-0.26+0.13	0.00-0.14+0.11	
cHW~	-0.26-0.50+0.67	0.00-0.52+0.48	
cHW~B	-0.54-1.03+1.37	0.00-1.07+0.99	
cHB~	-0.08-0.15+0.20	0.00-0.16+0.15	

Fig. 12 Summary of constraints on the SMEFT Higgs (upper) and Warsaw (lower) basis coupling parameters with the best fit values and 68% CL uncertainties. For the Warsaw basis, only one of cHW , cHWB, and cHB is independent, the same is also true for cHW~, cHW~B, and cHB~

Fig. 13 Expected (dashed) and observed (solid) profiled likelihood on fa3ggH. The signal strength modifiers and the CP-odd HVV anomalous coupling cross section fraction are treated as free parameters. The crossing of the observed likelihood with the dashed horizontal line shows the observed 68% CL region

Summary

This paper presents a study of the anomalous couplings of the Higgs boson (H) with vector bosons, including CP violating effects, using its associated production with hadronic jets in gluon fusion, electroweak vector boson fusion, and associated production with a W or Z boson, and its subsequent decay to a pair of W bosons. The results are based on the proton–proton collision data set collected by the CMS detector at the LHC during 2016–2018, corresponding to an integrated luminosity of 138fb-1 at a center-of-mass energy of 13TeV. The analysis targets the different-flavor dilepton (eμ) final state, with kinematic information from associated jets combined using matrix element techniques to increase sensitivity to anomalous effects at the production vertex. Dedicated Monte Carlo simulation and matrix element reweighting provide modeling of all kinematic features in the production and decay of the Higgs boson with full simulation of detector effects. A simultaneous measurement of four Higgs boson

couplings to electroweak vector bosons has been performed in the framework of a standard model effective field theory. All measurements are consistent with the expectations for the standard model Higgs boson and constraints are set on the fractional contribution of the anomalous couplings to the Higgs boson cross section. The most stringent constraints on the HVV anomalous coupling cross section fractions are at the per mille level. These results are in agreement with those obtained in the H→ZZ and H→ττ channels, and also significantly surpass those of the previous H→WW anomalous coupling analysis from the CMS experiment in both scope and precision.

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); ERC PRG, RVTT3 and MoER TK202 (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); SRNSF (Georgia); BMBF, DFG, and HGF (Germany); GSRI (Greece); NKFIH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Republic of Korea); MES (Latvia); LMTLT (Lithuania); MOE and UM (Malaysia); BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MOS (Montenegro); MBIE (New Zealand); PAEC (Pakistan); MES and NSC (Poland); FCT (Portugal); MESTD (Serbia); MCIN/AEI and PCTI (Spain); MOSTR (Sri Lanka); Swiss Funding Agencies (Switzerland); MST (Taipei); MHESI and NSTDA (Thailand); TUBITAK and TENMAK (Turkey); NASU (Ukraine); STFC (United Kingdom); DOE and NSF (USA). Rachada-pisek 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, 101115353, 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 and 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; ICSC – National Research Center for High Performance Computing, Big Data and Quantum Computing, funded by the NextGenerationEU program (Italy); the Latvian Council of Science; the Ministry of Education and Science, project no. 2022/WK/14, and the National Science Center, contracts Opus 2021/41/B/ST2/01369 and 2021/43/B/ST2/01552 (Poland); the Fundação para a Ciência e a Tecnologia, grant CEECIND/01334/2018 (Portugal); the National Priorities Research Program by Qatar National Research Fund; MCIN/AEI/10.13039/501100011033, ERDF “a way of making Europe”, and the Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia María de Maeztu, grant MDM-2017-0765 and Programa Severo Ochoa del Principado de Asturias (Spain); the Chulalongkorn Academic into Its 2nd Century Project Advancement Project, and the National Science, Research and Innovation Fund via the Program Management Unit for Human Resources and Institutional Development, Research and Innovation, grant B37G660013 (Thailand); the Kavli Foundation; the Nvidia Corporation; the SuperMicro Corporation; the Welch Foundation, contract C-1845; and the Weston Havens Foundation (USA).

Data Availability Statement

Data cannot be made available for reasons disclosed in the data availability statement. [Author’s 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 the “CMS data preservation, re-use and open access policy.]

Code Availability Statement

This manuscript has no associated code/software. [Author’s comment: There is no code availability statement.]

Declarations

Conflict of interest

The authors declare that they have no conflict of interest.

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