
==== 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

11952
10.1140/epjc/s10052-023-11952-7
Regular Article - Experimental Physics
A search for decays of the Higgs boson to invisible particles in events with a top-antitop quark pair or a vector boson in proton-proton collisions at s=13TeV
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CMS Collaborationcms-publication-committee-chair@cern.ch

282
1 https://ror.org/00ad27c73 grid.48507.3e 0000 0004 0482 7128 Yerevan Physics Institute, Yerevan, Armenia
2 https://ror.org/039shy520 grid.450258.e 0000 0004 0625 7405 Institut für Hochenergiephysik, Vienna, Austria
3 https://ror.org/008x57b05 grid.5284.b 0000 0001 0790 3681 Universiteit Antwerpen, Antwerpen, Belgium
4 https://ror.org/006e5kg04 grid.8767.e 0000 0001 2290 8069 Vrije Universiteit Brussel, 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.412368.a 0000 0004 0643 8839 Universidade Estadual Paulista, Universidade Federal do ABC, São Paulo, Brazil
11 grid.410344.6 0000 0001 2097 3094 Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria
12 https://ror.org/02jv3k292 grid.11355.33 0000 0001 2192 3275 University of Sofia, Sofia, Bulgaria
13 https://ror.org/04xe01d27 grid.412182.c 0000 0001 2179 0636 Instituto De Alta Investigación, Universidad de Tarapacá, Casilla 7 D, Arica, Chile
14 https://ror.org/00wk2mp56 grid.64939.31 0000 0000 9999 1211 Beihang University, Beijing, China
15 https://ror.org/03cve4549 grid.12527.33 0000 0001 0662 3178 Department of Physics, Tsinghua University, Beijing, China
16 https://ror.org/03v8tnc06 grid.418741.f 0000 0004 0632 3097 Institute of High Energy Physics, Beijing, China
17 https://ror.org/02v51f717 grid.11135.37 0000 0001 2256 9319 State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China
18 https://ror.org/0064kty71 grid.12981.33 0000 0001 2360 039X Sun Yat-Sen University, Guangzhou, China
19 https://ror.org/04c4dkn09 grid.59053.3a 0000 0001 2167 9639 University of Science and Technology of China, Hefei, China
20 https://ror.org/03x8rhq63 grid.450259.f 0000 0004 1804 2516 Institute of Modern Physics and Key Laboratory of Nuclear Physics and Ion-beam Application (MOE)-Fudan University, Shanghai, China
21 https://ror.org/00a2xv884 grid.13402.34 0000 0004 1759 700X Zhejiang University, Hangzhou, Zhejiang, China
22 https://ror.org/02mhbdp94 grid.7247.6 0000 0004 1937 0714 Universidad de Los Andes, Bogotá, Colombia
23 https://ror.org/03bp5hc83 grid.412881.6 0000 0000 8882 5269 Universidad de Antioquia, Medellin, Colombia
24 https://ror.org/00m31ft63 grid.38603.3e 0000 0004 0644 1675 University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Split, Croatia
25 https://ror.org/00m31ft63 grid.38603.3e 0000 0004 0644 1675 University of Split, Faculty of Science, Split, Croatia
26 https://ror.org/02mw21745 grid.4905.8 0000 0004 0635 7705 Institute Rudjer Boskovic, Zagreb, Croatia
27 https://ror.org/02qjrjx09 grid.6603.3 0000 0001 2116 7908 University of Cyprus, Nicosia, Cyprus
28 https://ror.org/024d6js02 grid.4491.8 0000 0004 1937 116X Charles University, Prague, Czech Republic
29 https://ror.org/01gb99w41 grid.440857.a 0000 0004 0485 2489 Escuela Politecnica Nacional, Quito, Ecuador
30 https://ror.org/01r2c3v86 grid.412251.1 0000 0000 9008 4711 Universidad San Francisco de Quito, Quito, Ecuador
31 grid.423564.2 0000 0001 2165 2866 Academy of Scientific Research and Technology of the Arab Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt
32 https://ror.org/023gzwx10 grid.411170.2 0000 0004 0412 4537 Center for High Energy Physics (CHEP-FU), Fayoum University, El-Fayoum, Egypt
33 https://ror.org/03eqd4a41 grid.177284.f 0000 0004 0410 6208 National Institute of Chemical Physics and Biophysics, Tallinn, Estonia
34 https://ror.org/040af2s02 grid.7737.4 0000 0004 0410 2071 Department of Physics, University of Helsinki, Helsinki, Finland
35 https://ror.org/01x2x1522 grid.470106.4 0000 0001 1106 2387 Helsinki Institute of Physics, Helsinki, Finland
36 https://ror.org/0208vgz68 grid.12332.31 0000 0001 0533 3048 Lappeenranta-Lahti University of Technology, Lappeenranta, Finland
37 https://ror.org/03xjwb503 grid.460789.4 0000 0004 4910 6535 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
38 grid.508893.f Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
39 https://ror.org/00pg6eq24 grid.11843.3f 0000 0001 2157 9291 CNRS, IPHC UMR 7178, Université de Strasbourg, Strasbourg, France
40 https://ror.org/02avf8f85 Institut de Physique des 2 Infinis de Lyon (IP2I ), Villeurbanne, France
41 https://ror.org/00aamz256 grid.41405.34 0000 0001 0702 1187 Georgian Technical University, Tbilisi, Georgia
42 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany
43 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany
44 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X RWTH Aachen University, III. Physikalisches Institut B, Aachen, Germany
45 https://ror.org/01js2sh04 grid.7683.a 0000 0004 0492 0453 Deutsches Elektronen-Synchrotron, Hamburg, Germany
46 https://ror.org/00g30e956 grid.9026.d 0000 0001 2287 2617 University of Hamburg, Hamburg, Germany
47 https://ror.org/04t3en479 grid.7892.4 0000 0001 0075 5874 Karlsruher Institut fuer Technologie, Karlsruhe, Germany
48 grid.6083.d 0000 0004 0635 6999 Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi, Greece
49 https://ror.org/04gnjpq42 grid.5216.0 0000 0001 2155 0800 National and Kapodistrian University of Athens, Athens, Greece
50 grid.4241.3 0000 0001 2185 9808 National Technical University of Athens, Athens, Greece
51 https://ror.org/01qg3j183 grid.9594.1 0000 0001 2108 7481 University of Ioánnina, Ioannina, Greece
52 https://ror.org/01jsq2704 grid.5591.8 0000 0001 2294 6276 MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary
53 https://ror.org/035dsb084 grid.419766.b 0000 0004 1759 8344 Wigner Research Centre for Physics, Budapest, Hungary
54 grid.418861.2 0000 0001 0674 7808 Institute of Nuclear Research ATOMKI, Debrecen, Hungary
55 https://ror.org/02xf66n48 grid.7122.6 0000 0001 1088 8582 Institute of Physics, University of Debrecen, Debrecen, Hungary
56 Karoly Robert Campus, MATE Institute of Technology, Gyongyos, Hungary
57 https://ror.org/04p2sbk06 grid.261674.0 0000 0001 2174 5640 Panjab University, Chandigarh, India
58 https://ror.org/04gzb2213 grid.8195.5 0000 0001 2109 4999 University of Delhi, Delhi, India
59 https://ror.org/0491yz035 grid.473481.d 0000 0001 0661 8707 Saha Institute of Nuclear Physics, HBNI, Kolkata, India
60 https://ror.org/03v0r5n49 grid.417969.4 0000 0001 2315 1926 Indian Institute of Technology Madras, Madras, India
61 https://ror.org/05w6wfp17 grid.418304.a 0000 0001 0674 4228 Bhabha Atomic Research Centre, Mumbai, 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 grid.4466.0 0000 0001 0578 5482 INFN Sezione di Bari, Università di Bari, Politecnico di Bari, Bari, Italy
70 grid.6292.f 0000 0004 1757 1758 INFN Sezione di Bologna, Università di Bologna, Bologna, Italy
71 grid.8158.4 0000 0004 1757 1969 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, Firenze, Italy
73 https://ror.org/049jf1a25 grid.463190.9 0000 0004 0648 0236 INFN Laboratori Nazionali di Frascati, Frascati, Italy
74 grid.5606.5 0000 0001 2151 3065 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 https://ror.org/015kcdd40 grid.470211.1 0000 0004 8343 7696 INFN Sezione di Napoli, Università di Napoli ’Federico II’, Napoli, Italy; Università della Basilicata, Potenza, Italy;Università G. Marconi, Rome, Italy
77 grid.11696.39 0000 0004 1937 0351 INFN Sezione di Padova, Università di Padova, Padova, Italy; Università di Trento, Trento, Italy
78 grid.8982.b 0000 0004 1762 5736 INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
79 grid.9027.c 0000 0004 1757 3630 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.7841.a 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, Torino, Italy; Università del Piemonte Orientale, Novara, Italy
83 grid.5133.4 0000 0001 1941 4308 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 https://ror.org/05kzjxq56 grid.14005.30 0000 0001 0356 9399 Chonnam National University, Institute for Universe and Elementary Particles, Kwangju, Korea
86 https://ror.org/046865y68 grid.49606.3d 0000 0001 1364 9317 Hanyang University, Seoul, Korea
87 https://ror.org/047dqcg40 grid.222754.4 0000 0001 0840 2678 Korea University, Seoul, Korea
88 https://ror.org/01zqcg218 grid.289247.2 0000 0001 2171 7818 Kyung Hee University, Department of Physics, Seoul, Korea
89 https://ror.org/00aft1q37 grid.263333.4 0000 0001 0727 6358 Sejong University, Seoul, Korea
90 https://ror.org/04h9pn542 grid.31501.36 0000 0004 0470 5905 Seoul National University, Seoul, Korea
91 https://ror.org/05en5nh73 grid.267134.5 0000 0000 8597 6969 University of Seoul, Seoul, Korea
92 https://ror.org/01wjejq96 grid.15444.30 0000 0004 0470 5454 Yonsei University, Department of Physics, Seoul, Korea
93 https://ror.org/04q78tk20 grid.264381.a 0000 0001 2181 989X Sungkyunkwan University, Suwon, Korea
94 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
95 https://ror.org/00twb6c09 grid.6973.b 0000 0004 0567 9729 Riga Technical University, Riga, Latvia
96 https://ror.org/03nadee84 grid.6441.7 0000 0001 2243 2806 Vilnius University, Vilnius, Lithuania
97 https://ror.org/00rzspn62 grid.10347.31 0000 0001 2308 5949 National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia
98 grid.11893.32 0000 0001 2193 1646 Universidad de Sonora (UNISON), Hermosillo, Mexico
99 grid.512574.0 Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico
100 https://ror.org/05vss7635 grid.441047.2 0000 0001 2156 4794 Universidad Iberoamericana, Mexico City, Mexico
101 https://ror.org/03p2z7827 grid.411659.e 0000 0001 2112 2750 Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
102 https://ror.org/02drrjp49 grid.12316.37 0000 0001 2182 0188 University of Montenegro, Podgorica, Montenegro
103 grid.412621.2 0000 0001 2215 1297 National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan
104 grid.9922.0 0000 0000 9174 1488 AGH University of Science and Technology Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland
105 https://ror.org/00nzsxq20 grid.450295.f 0000 0001 0941 0848 National Centre for Nuclear Research, Swierk, Poland
106 https://ror.org/039bjqg32 grid.12847.38 0000 0004 1937 1290 Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland
107 https://ror.org/01hys1667 grid.420929.4 Laboratório de Instrumentação e Física Experimental de Partículas, Lisbon, Portugal
108 grid.7149.b 0000 0001 2166 9385 VINCA Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia
109 https://ror.org/05xx77y52 grid.420019.e 0000 0001 1959 5823 Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain
110 https://ror.org/01cby8j38 grid.5515.4 0000 0001 1957 8126 Universidad Autónoma de Madrid, Madrid, Spain
111 https://ror.org/006gksa02 grid.10863.3c 0000 0001 2164 6351 Universidad de Oviedo, Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA), Oviedo, Spain
112 grid.7821.c 0000 0004 1770 272X Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain
113 https://ror.org/02phn5242 grid.8065.b 0000 0001 2182 8067 University of Colombo, Colombo, Sri Lanka
114 https://ror.org/033jvzr14 grid.412759.c 0000 0001 0103 6011 University of Ruhuna, Department of Physics, Matara, Sri Lanka
115 https://ror.org/01ggx4157 grid.9132.9 0000 0001 2156 142X CERN, European Organization for Nuclear Research, Geneva, Switzerland
116 https://ror.org/03eh3y714 grid.5991.4 0000 0001 1090 7501 Paul Scherrer Institut, Villigen, Switzerland
117 grid.5801.c 0000 0001 2156 2780 ETH Zurich-Institute for Particle Physics and Astrophysics (IPA), Zurich, Switzerland
118 https://ror.org/02crff812 grid.7400.3 0000 0004 1937 0650 Universität Zürich, Zurich, Switzerland
119 https://ror.org/00944ve71 grid.37589.30 0000 0004 0532 3167 National Central University, Chung-Li, Taiwan
120 https://ror.org/05bqach95 grid.19188.39 0000 0004 0546 0241 National Taiwan University (NTU), Taipei, Taiwan
121 https://ror.org/028wp3y58 grid.7922.e 0000 0001 0244 7875 Chulalongkorn University, Faculty of Science, Department of Physics, Bangkok, Thailand
122 https://ror.org/05wxkj555 grid.98622.37 0000 0001 2271 3229 Çukurova University, Physics Department, Science and Art Faculty, Adana, Turkey
123 https://ror.org/014weej12 grid.6935.9 0000 0001 1881 7391 Middle East Technical University, Physics Department, Ankara, Turkey
124 https://ror.org/03z9tma90 grid.11220.30 0000 0001 2253 9056 Bogazici University, Istanbul, Turkey
125 https://ror.org/059636586 grid.10516.33 0000 0001 2174 543X Istanbul Technical University, Istanbul, Turkey
126 https://ror.org/03a5qrr21 grid.9601.e 0000 0001 2166 6619 Istanbul University, Istanbul, Turkey
127 grid.466758.e Institute for Scintillation Materials of National Academy of Science of Ukraine, Kharkiv, Ukraine
128 https://ror.org/00183pc12 grid.425540.2 0000 0000 9526 3153 National Science Centre, Kharkiv Institute of Physics and Technology, Kharkiv, Ukraine
129 https://ror.org/0524sp257 grid.5337.2 0000 0004 1936 7603 University of Bristol, Bristol, United Kingdom
130 https://ror.org/03gq8fr08 grid.76978.37 0000 0001 2296 6998 Rutherford Appleton Laboratory, Didcot, UK
131 https://ror.org/041kmwe10 grid.7445.2 0000 0001 2113 8111 Imperial College, London, UK
132 grid.7728.a 0000 0001 0724 6933 Brunel University, Uxbridge, UK
133 https://ror.org/005781934 grid.252890.4 0000 0001 2111 2894 Baylor University, Waco, TX USA
134 https://ror.org/047yk3s18 grid.39936.36 0000 0001 2174 6686 Catholic University of America, Washington, DC USA
135 https://ror.org/03xrrjk67 grid.411015.0 0000 0001 0727 7545 The University of Alabama, Tuscaloosa, AL USA
136 https://ror.org/05qwgg493 grid.189504.1 0000 0004 1936 7558 Boston University, Boston, MA USA
137 https://ror.org/05gq02987 grid.40263.33 0000 0004 1936 9094 Brown University, Providence, RI USA
138 https://ror.org/05t99sp05 grid.468726.9 0000 0004 0486 2046 University of California, Davis, Davis, CA USA
139 grid.19006.3e 0000 0000 9632 6718 University of California, Los Angeles, CA USA
140 https://ror.org/05t99sp05 grid.468726.9 0000 0004 0486 2046 University of California, Riverside, Riverside, CA USA
141 https://ror.org/05t99sp05 grid.468726.9 0000 0004 0486 2046 University of California, San Diego, La Jolla, CA USA
142 grid.133342.4 0000 0004 1936 9676 Department of Physics, University of California, Santa Barbara, Santa Barbara, CA USA
143 https://ror.org/05dxps055 grid.20861.3d 0000 0001 0706 8890 California Institute of Technology, Pasadena, CA USA
144 https://ror.org/05x2bcf33 grid.147455.6 0000 0001 2097 0344 Carnegie Mellon University, Pittsburgh, PA USA
145 https://ror.org/02ttsq026 grid.266190.a 0000 0000 9621 4564 University of Colorado Boulder, Boulder, CO USA
146 https://ror.org/05bnh6r87 grid.5386.8 0000 0004 1936 877X Cornell University, Ithaca, NY USA
147 https://ror.org/020hgte69 grid.417851.e 0000 0001 0675 0679 Fermi National Accelerator Laboratory, Batavia, IL USA
148 https://ror.org/02y3ad647 grid.15276.37 0000 0004 1936 8091 University of Florida, Gainesville, FL USA
149 https://ror.org/05g3dte14 grid.255986.5 0000 0004 0472 0419 Florida State University, Tallahassee, FL USA
150 https://ror.org/04atsbb87 grid.255966.b 0000 0001 2229 7296 Florida Institute of Technology, Melbourne, FL USA
151 https://ror.org/02mpq6x41 grid.185648.6 0000 0001 2175 0319 University of Illinois at Chicago (UIC), Chicago, IL USA
152 https://ror.org/036jqmy94 grid.214572.7 0000 0004 1936 8294 The University of Iowa, Iowa City, IA USA
153 https://ror.org/00za53h95 grid.21107.35 0000 0001 2171 9311 Johns Hopkins University, Baltimore, MD USA
154 https://ror.org/001tmjg57 grid.266515.3 0000 0001 2106 0692 The University of Kansas, Lawrence, KS USA
155 https://ror.org/05p1j8758 grid.36567.31 0000 0001 0737 1259 Kansas State University, Manhattan, KS USA
156 https://ror.org/041nk4h53 grid.250008.f 0000 0001 2160 9702 Lawrence Livermore National Laboratory, Livermore, CA USA
157 https://ror.org/047s2c258 grid.164295.d 0000 0001 0941 7177 University of Maryland, College Park, MD USA
158 https://ror.org/042nb2s44 grid.116068.8 0000 0001 2341 2786 Massachusetts Institute of Technology, Cambridge, MA USA
159 https://ror.org/017zqws13 grid.17635.36 0000 0004 1936 8657 University of Minnesota, Minneapolis, MN USA
160 https://ror.org/02teq1165 grid.251313.7 0000 0001 2169 2489 University of Mississippi, Oxford, MS USA
161 https://ror.org/043mer456 grid.24434.35 0000 0004 1937 0060 University of Nebraska-Lincoln, Lincoln, NE USA
162 grid.273335.3 0000 0004 1936 9887 State University of New York at Buffalo, Buffalo, NY USA
163 https://ror.org/04t5xt781 grid.261112.7 0000 0001 2173 3359 Northeastern University, Boston, MA USA
164 https://ror.org/000e0be47 grid.16753.36 0000 0001 2299 3507 Northwestern University, Evanston, IL USA
165 https://ror.org/00mkhxb43 grid.131063.6 0000 0001 2168 0066 University of Notre Dame, Notre Dame, IN USA
166 https://ror.org/00rs6vg23 grid.261331.4 0000 0001 2285 7943 The Ohio State University, Columbus, OH USA
167 https://ror.org/00hx57361 grid.16750.35 0000 0001 2097 5006 Princeton University, Princeton, NJ USA
168 https://ror.org/00wek6x04 grid.267044.3 0000 0004 0398 9176 University of Puerto Rico, Mayaguez, PR USA
169 https://ror.org/02dqehb95 grid.169077.e 0000 0004 1937 2197 Purdue University, West Lafayette, IN USA
170 https://ror.org/04keq6987 grid.504659.b 0000 0000 8864 7239 Purdue University Northwest, Hammond, IN USA
171 https://ror.org/008zs3103 grid.21940.3e 0000 0004 1936 8278 Rice University, Houston, TX USA
172 https://ror.org/022kthw22 grid.16416.34 0000 0004 1936 9174 University of Rochester, Rochester, NY USA
173 https://ror.org/0420db125 grid.134907.8 0000 0001 2166 1519 The Rockefeller University, New York, NY USA
174 https://ror.org/05vt9qd57 grid.430387.b 0000 0004 1936 8796 Rutgers, The State University of New Jersey, Piscataway, NJ USA
175 https://ror.org/020f3ap87 grid.411461.7 0000 0001 2315 1184 University of Tennessee, Knoxville, TN USA
176 https://ror.org/01f5ytq51 grid.264756.4 0000 0004 4687 2082 Texas A &M University, College Station, TX USA
177 grid.264784.b 0000 0001 2186 7496 Texas Tech University, Lubbock, TX USA
178 https://ror.org/02vm5rt34 grid.152326.1 0000 0001 2264 7217 Vanderbilt University, Nashville, TN USA
179 https://ror.org/0153tk833 grid.27755.32 0000 0000 9136 933X University of Virginia, Charlottesville, VA USA
180 https://ror.org/01070mq45 grid.254444.7 0000 0001 1456 7807 Wayne State University, Detroit, MI USA
181 https://ror.org/01y2jtd41 grid.14003.36 0000 0001 2167 3675 University of Wisconsin-Madison, Madison, WI USA
182 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
183 https://ror.org/00s8vne50 grid.21072.36 0000 0004 0640 687X Yerevan State University, Yerevan, Armenia
184 https://ror.org/04d836q62 grid.5329.d 0000 0004 1937 0669 TU Wien, Vienna, Austria
185 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
186 https://ror.org/01r9htc13 grid.4989.c 0000 0001 2348 6355 Université Libre de Bruxelles, Brussels, Belgium
187 https://ror.org/04wffgt70 grid.411087.b 0000 0001 0723 2494 Universidade Estadual de Campinas, Campinas, Brazil
188 https://ror.org/041yk2d64 grid.8532.c 0000 0001 2200 7498 Federal University of Rio Grande do Sul, Porto Alegre, Brazil
189 grid.412352.3 0000 0001 2163 5978 UFMS, Nova Andradina, Brazil
190 https://ror.org/05qbk4x57 grid.410726.6 0000 0004 1797 8419 University of Chinese Academy of Sciences, Beijing, China
191 https://ror.org/036trcv74 grid.260474.3 0000 0001 0089 5711 Nanjing Normal University, Nanjing, China
192 https://ror.org/036jqmy94 grid.214572.7 0000 0004 1936 8294 The University of Iowa, Iowa City, IA USA
193 https://ror.org/05qbk4x57 grid.410726.6 0000 0004 1797 8419 University of Chinese Academy of Sciences, Beijing, China
194 grid.9132.9 0000 0001 2156 142X an Institute or an International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
195 https://ror.org/00h55v928 grid.412093.d 0000 0000 9853 2750 Helwan University, Cairo, Egypt
196 https://ror.org/04w5f4y88 grid.440881.1 0000 0004 0576 5483 Zewail City of Science and Technology, Zewail, Egypt
197 https://ror.org/0066fxv63 grid.440862.c 0000 0004 0377 5514 British University in Egypt, Cairo, Egypt
198 https://ror.org/00cb9w016 grid.7269.a 0000 0004 0621 1570 Ain Shams University, Cairo, Egypt
199 https://ror.org/02dqehb95 grid.169077.e 0000 0004 1937 2197 Purdue University, West Lafayette, IN USA
200 https://ror.org/04k8k6n84 grid.9156.b 0000 0004 0473 5039 Université de Haute Alsace, Mulhouse, France
201 https://ror.org/03cve4549 grid.12527.33 0000 0001 0662 3178 Department of Physics, Tsinghua University, Beijing, China
202 https://ror.org/04j5z3x06 grid.412290.c 0000 0000 8024 0602 The University of the State of Amazonas, Manaus, Brazil
203 grid.412176.7 0000 0001 1498 7262 Erzincan Binali Yildirim University, Erzincan, Turkey
204 https://ror.org/00g30e956 grid.9026.d 0000 0001 2287 2617 University of Hamburg, Hamburg, Germany
205 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany
206 grid.411751.7 0000 0000 9908 3264 Isfahan University of Technology, Isfahan, Iran
207 grid.7787.f 0000 0001 2364 5811 Bergische University Wuppertal (BUW), Wuppertal, Germany
208 https://ror.org/02wxx3e24 grid.8842.6 0000 0001 2188 0404 Brandenburg University of Technology, Cottbus, Germany
209 https://ror.org/02nv7yv05 grid.8385.6 0000 0001 2297 375X Forschungszentrum Jülich, Juelich, Germany
210 https://ror.org/01ggx4157 grid.9132.9 0000 0001 2156 142X CERN, European Organization for Nuclear Research, Geneva, Switzerland
211 https://ror.org/01jaj8n65 grid.252487.e 0000 0000 8632 679X Physics Department, Faculty of Science, Assiut University, Assiut, Egypt
212 https://ror.org/035dsb084 grid.419766.b 0000 0004 1759 8344 Wigner Research Centre for Physics, Budapest, Hungary
213 https://ror.org/02xf66n48 grid.7122.6 0000 0001 1088 8582 Institute of Physics, University of Debrecen, Debrecen, Hungary
214 grid.418861.2 0000 0001 0674 7808 Institute of Nuclear Research ATOMKI, Debrecen, Hungary
215 grid.7399.4 0000 0004 1937 1397 Universitatea Babes-Bolyai-Facultatea de Fizica, Cluj-Napoca, Romania
216 https://ror.org/02xf66n48 grid.7122.6 0000 0001 1088 8582 Faculty of Informatics, University of Debrecen, Debrecen, Hungary
217 https://ror.org/02qbzdk74 grid.412577.2 0000 0001 2176 2352 Punjab Agricultural University, Ludhiana, India
218 https://ror.org/04q2jes40 grid.444415.4 0000 0004 1759 0860 UPES-University of Petroleum and Energy Studies, Dehradun, India
219 https://ror.org/02y28sc20 grid.440987.6 0000 0001 2259 7889 University of Visva-Bharati, Santiniketan, India
220 https://ror.org/04a7rxb17 grid.18048.35 0000 0000 9951 5557 University of Hyderabad, Hyderabad, India
221 grid.34980.36 0000 0001 0482 5067 Indian Institute of Science (IISc), Bangalore, India
222 grid.417971.d 0000 0001 2198 7527 Indian Institute of Technology (IIT), Mumbai, India
223 https://ror.org/04gx72j20 grid.459611.e 0000 0004 1774 3038 IIT Bhubaneswar, Bhubaneswar, India
224 https://ror.org/01741jv66 grid.418915.0 0000 0004 0504 1311 Institute of Physics, Bhubaneswar, India
225 https://ror.org/01js2sh04 grid.7683.a 0000 0004 0492 0453 Deutsches Elektronen-Synchrotron, Hamburg, Germany
226 https://ror.org/00af3sa43 grid.411751.7 0000 0000 9908 3264 Department of Physics, Isfahan University of Technology, Isfahan, Iran
227 https://ror.org/024c2fq17 grid.412553.4 0000 0001 0740 9747 Sharif University of Technology, Tehran, Iran
228 https://ror.org/04jf6jw55 grid.510412.3 Department of Physics, University of Science and Technology of Mazandaran, Behshahr, Iran
229 https://ror.org/02an8es95 grid.5196.b 0000 0000 9864 2490 Italian National Agency for New Technologies, Energy and Sustainable Economic Development, Bologna, Italy
230 https://ror.org/02wdzfm91 grid.510931.f Centro Siciliano di Fisica Nucleare e di Struttura Della Materia, Catania, Italy
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232 https://ror.org/04swxte59 grid.508348.2 Scuola Superiore Meridionale, Università di Napoli ’Federico II’, Naples, Italy
233 https://ror.org/020hgte69 grid.417851.e 0000 0001 0675 0679 Fermi National Accelerator Laboratory, Batavia, IL USA
234 grid.4691.a 0000 0001 0790 385X Università di Napoli ’Federico II’, Naples, Italy
235 grid.466875.e 0000 0004 1757 5572 Laboratori Nazionali di Legnaro dell’INFN, Legnaro, Italy
236 grid.5326.2 0000 0001 1940 4177 Consiglio Nazionale delle Ricerche-Istituto Officina dei Materiali, Perugia, Italy
237 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
238 https://ror.org/059ex5q34 grid.418270.8 0000 0004 0428 7635 Consejo Nacional de Ciencia y Tecnología, Mexico City, Mexico
239 https://ror.org/03xjwb503 grid.460789.4 0000 0004 4910 6535 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
240 https://ror.org/02qsmb048 grid.7149.b 0000 0001 2166 9385 Faculty of Physics, University of Belgrade, Belgrade, Serbia
241 grid.443373.4 0000 0001 0438 3334 Trincomalee Campus, Eastern University, Sri Lanka, Nilaveli, Sri Lanka
242 grid.8982.b 0000 0004 1762 5736 INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
243 https://ror.org/04gnjpq42 grid.5216.0 0000 0001 2155 0800 National and Kapodistrian University of Athens, Athens, Greece
244 https://ror.org/02s376052 grid.5333.6 0000 0001 2183 9049 Ecole Polytechnique Fédérale Lausanne, Lausanne, Switzerland
245 https://ror.org/02crff812 grid.7400.3 0000 0004 1937 0650 Universität Zürich, Zurich, Switzerland
246 https://ror.org/05kdjqf72 grid.475784.d 0000 0000 9532 5705 Stefan Meyer Institute for Subatomic Physics, Vienna, Austria
247 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
248 Near East University, Research Center of Experimental Health Science, Mersin, Turkey
249 https://ror.org/02s82rs08 grid.505922.9 Konya Technical University, Konya, Turkey
250 https://ror.org/017v96566 0000 0004 6412 5697 Izmir Bakircay University, Izmir, Turkey
251 https://ror.org/02s4gkg68 grid.411126.1 0000 0004 0369 5557 Adiyaman University, Adiyaman, Turkey
252 https://ror.org/05msvfx67 grid.465940.a 0000 0004 0520 0861 Istanbul Gedik University, Istanbul, Turkey
253 https://ror.org/013s3zh21 grid.411124.3 0000 0004 1769 6008 Necmettin Erbakan University, Konya, Turkey
254 grid.411743.4 0000 0004 0369 8360 Bozok Universitetesi Rektörlügü, Yozgat, Turkey
255 https://ror.org/02kswqa67 grid.16477.33 0000 0001 0668 8422 Marmara University, Istanbul, Turkey
256 https://ror.org/010t24d82 grid.510982.7 Milli Savunma University, Istanbul, Turkey
257 https://ror.org/04v302n28 grid.16487.3c 0000 0000 9216 0511 Kafkas University, Kars, Turkey
258 https://ror.org/04kwvgz42 grid.14442.37 0000 0001 2342 7339 Hacettepe University, Ankara, Turkey
259 grid.506076.2 0000 0004 1797 5496 Istanbul University-Cerrahpasa, Faculty of Engineering, Istanbul, Turkey
260 https://ror.org/01jjhfr75 grid.28009.33 0000 0004 0391 6022 Ozyegin University, Istanbul, Turkey
261 https://ror.org/006e5kg04 grid.8767.e 0000 0001 2290 8069 Vrije Universiteit Brussel, Brussel, Belgium
262 https://ror.org/01ryk1543 grid.5491.9 0000 0004 1936 9297 School of Physics and Astronomy, University of Southampton, Southampton, UK
263 https://ror.org/0524sp257 grid.5337.2 0000 0004 1936 7603 University of Bristol, Bristol, UK
264 https://ror.org/01v29qb04 grid.8250.f 0000 0000 8700 0572 IPPP Durham University, Durham, UK
265 https://ror.org/02bfwt286 grid.1002.3 0000 0004 1936 7857 Faculty of Science, Monash University, Clayton, Australia
266 grid.7605.4 0000 0001 2336 6580 Università di Torino, Turin, Italy
267 https://ror.org/02faxbd19 grid.418297.1 0000 0000 8888 5173 Bethel University, St. Paul, MN USA
268 https://ror.org/037vvf096 grid.440455.4 0000 0004 1755 486X Karamanoğlu Mehmetbey University, Karaman, Turkey
269 https://ror.org/05dxps055 grid.20861.3d 0000 0001 0706 8890 California Institute of Technology, Pasadena, CA USA
270 https://ror.org/00znex860 grid.265465.6 0000 0001 2296 3025 United States Naval Academy, Annapolis, MD USA
271 https://ror.org/03hx84x94 grid.448543.a 0000 0004 0369 6517 Bingol University, Bingol, Turkey
272 https://ror.org/00aamz256 grid.41405.34 0000 0001 0702 1187 Georgian Technical University, Tbilisi, Georgia
273 https://ror.org/004ah3r71 grid.449244.b 0000 0004 0408 6032 Sinop University, Sinop, Turkey
274 https://ror.org/047g8vk19 grid.411739.9 0000 0001 2331 2603 Erciyes University, Kayseri, Turkey
275 https://ror.org/03vb4dm14 grid.412392.f 0000 0004 0413 3978 Texas A &M University at Qatar, Doha, Qatar
276 https://ror.org/040c17130 grid.258803.4 0000 0001 0661 1556 Kyungpook National University, Daegu, Korea
277 grid.9132.9 0000 0001 2156 142X Another Institute or International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
278 https://ror.org/00ad27c73 grid.48507.3e 0000 0004 0482 7128 Yerevan Physics Institute, Yerevan, Armenia
279 grid.9132.9 0000 0001 2156 142X Another Institute or International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
280 https://ror.org/041kmwe10 grid.7445.2 0000 0001 2113 8111 Imperial College, London, UK
281 grid.443859.7 0000 0004 0477 2171 Institute of Nuclear Physics of the Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
282 grid.9132.9 0000 0001 2156 142X CERN, 1211 Geneva 23, Switzerland
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© CERN for the benefit of the CMS Collaboration 2023
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Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development.
A search for decays to invisible particles of Higgs bosons produced in association with a top-antitop quark pair or a vector boson, which both decay to a fully hadronic final state, has been performed using proton-proton collision data collected at s=13TeV by the CMS experiment at the LHC, corresponding to an integrated luminosity of 138fb-1. The 95% confidence level upper limit set on the branching fraction of the 125GeV Higgs boson to invisible particles, B(H→inv), is 0.54 (0.39 expected), assuming standard model production cross sections. The results of this analysis are combined with previous B(H→inv) searches carried out at s=7, 8, and 13TeV in complementary production modes. The combined upper limit at 95% confidence level on B(H→inv) is 0.15 (0.08 expected).

http://dx.doi.org/10.13039/501100013699 Austrian Federal Ministry of Education, Science and Research BMBWF (Bundesministerium für Bildung, Wissenschaft, Forschung) [name change from BMWFW] Tumasyan A. http://dx.doi.org/10.13039/501100002428 Austrian Science Fund FWF Adam W. http://dx.doi.org/10.13039/501100002661 Belgian Fonds de la Recherche Scientifique FRS – FNRS Andrejkovic J. 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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 Skovpen 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) Tytgat M. http://dx.doi.org/10.13039/501100008530 Fondo Europeo de Desarrollo Regional, Spain FEDER (ERDF) Van Den Bossche N. https://doi.org/10.13039/100011941 Plan de Ciencia, Tecnología e Innovación del Principado de Asturias PCTI Vermassen B. http://dx.doi.org/10.13039/501100008981 MOSTR Ministry of Science, Technology, and Research Wezenbeek L. 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Council of Scientific and Industrial Research, Indiahttp://dx.doi.org/10.13039/501100005375 Latvian Council of Science Latvijas Zinatnes Padome Waltenberger W. http://dx.doi.org/10.13039/501100004569 Ministy of Education and Science, project no. 2022/WK/14 Ministerstwo Edukacji I Nauki; MES Wulz C.-E. http://dx.doi.org/10.13039/501100004281 National Science Center, Opus 2021/41/B/ST2/01369 and 2021/43/B/ST2/01552 Narodowe Centrum Nauki Darwish M. R. http://dx.doi.org/10.13039/501100001871 Fundação para a Ciência e a Tecnologia, CEECIND/01334/2018 http://dx.doi.org/10.13039/100008982 National Priorities Research Program by Qatar National Research Fund Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia María de Maeztu, grant MDM-2017-0765 and projects PID2020-113705RB, PID2020-113304RB, PID2020-116262RB and PID2020-113341RB-I00https://doi.org/10.13039/100011941 Programa Severo Ochoa del Principado de Asturias http://dx.doi.org/10.13039/501100002873 Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chulalongkorn University (Thailand) http://dx.doi.org/10.13039/501100002873 CUAASC Chulalongkorn Academic into Its 2nd Century Project Advancement Project De Moor A. http://dx.doi.org/10.13039/100001201 Kavli Foundation http://dx.doi.org/10.13039/100007065 Nvidia Corporation hardware contribution: Titan Xp GPUs Faham H. El http://dx.doi.org/10.13039/100000928 Welch Foundation, contract C-1845 http://dx.doi.org/10.13039/100011223 Weston Havens Foundation Institut für Hochenergiephysik (HEPHY) using the Cloud Infrastructure Platform (CLIP), ViennaInter-University Institute for High Energies, Brusselshttp://dx.doi.org/10.13039/501100005041 Université Catholique de Louvain, Louvain-la-Neuve http://dx.doi.org/10.13039/501100009568 São Paulo Research and Analysis Center, São Paulo http://dx.doi.org/10.13039/501100006702 Universidade do Estado do Rio de Janeiro, Rio de Janeiro University of Sofia, Sofiahttp://dx.doi.org/10.13039/501100011181 Institute of High Energy Physics of the Chinese Academy of Sciences, Beijing http://dx.doi.org/10.13039/501100005789 National Institute of Chemical Physics and Biophysics, Tallinn Helsinki Institute of Physics, HelsinkiGrille de Recherche d’Ile de France (GRIF), Institut de recherche sur les lois fondamentales de l’Univers, CEA, Université Paris-Saclay, Gif-sur-Yvette, France and Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de ParisInstitut de recherche sur les lois fondamentales de l’Univers, CEA, Université Paris-Saclay, Gif-sur-YvetteInstitut national de physique nucléaire et de physique des particules, IN2P3, VilleurbanneInstitut Pluridisciplinaire Hubert Curien (IPHC), StrasbourgLaboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseauhttp://dx.doi.org/10.13039/501100001647 Deutsches Elektronen-Synchrotron, Hamburg http://dx.doi.org/10.13039/100009133 Karlsruher Institut für Technologie, Karlsruhe http://dx.doi.org/10.13039/501100007210 RWTH Aachen University, Aachen University of Ioánnina, Ioánninahttp://dx.doi.org/10.13039/501100014549 Wigner Research Centre for Physics, Budapest http://dx.doi.org/10.13039/501100001405 Tata Institute of Fundamental Research, Mumbai http://dx.doi.org/10.13039/501100004007 INFN CNAF, Bologna INFN Sezione di Bari, Università di Bari, Politecnico di Bari, Barihttp://dx.doi.org/10.13039/100009093 INFN Sezione di Pisa, Università di Pisa, Scuola Normale Superiore di Pisa, Pisa http://dx.doi.org/10.13039/501100004271 INFN Sezione di Roma, Sapienza Università di Roma, Rome INFN Sezione di Trieste, Università di Trieste, TriesteLaboratori Nazionali di Legnaro, Legnarohttp://dx.doi.org/10.13039/501100002531 Kyungpook National University, Daegu http://dx.doi.org/10.13039/501100004253 National Centre for Physics, Quaid-I-Azam University, Islamabad Akademickie Centrum Komputerowe Cyfronet AGH, KrakowNational Centre for Nuclear Research, SwierkLaboratório de Instrumentação e Física Experimental de Partículas, Lisboahttp://dx.doi.org/10.13039/501100003693 Korea Institute of Science and Technology Information (KISTI), Daejeon http://dx.doi.org/10.13039/501100009613 Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, SantanderPort d’Informació Científica, Bellaterrahttp://dx.doi.org/10.13039/100012470 CERN, European Organization for Nuclear Research, Geneva CSCS - Swiss National Supercomputing Centre, LuganoNational Center for High-performance Computing (NCHC), Hsinchu Cityhttp://dx.doi.org/10.13039/501100004175 Middle East Technical University, Physics Department, Ankara National Scientific Center, Kharkov Institute of Physics and Technology, Kharkovhttp://dx.doi.org/10.13039/100008475 GridPP, Brunel University, Uxbridge http://dx.doi.org/10.13039/501100000761 GridPP, Imperial College, London http://dx.doi.org/10.13039/501100000851 GridPP, Queen Mary University of London, London GridPP, Royal Holloway, University of London, Londonhttp://dx.doi.org/10.13039/100014570 GridPP, Rutherford Appleton Laboratory, Didcot http://dx.doi.org/10.13039/501100005618 GridPP, University of Bristol, Bristol GridPP, University of Glasgow, Glasgowhttp://dx.doi.org/10.13039/100007492 Baylor University, Waco http://dx.doi.org/10.13039/100006961 California Institute of Technology, Pasadena http://dx.doi.org/10.13039/100006230 Fermi National Accelerator Laboratory, Batavia http://dx.doi.org/10.13039/100006919 Massachusetts Institute of Technology, Cambridge http://dx.doi.org/10.13039/100017223 National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility, Berkeley Open Science Grid (OSG) ConsortiumPittsburgh Supercomputing Center (PSC), Pittsburghhttp://dx.doi.org/10.13039/100006377 Purdue University, West Lafayette Texas Advanced Computing Center (TACC), Austinhttp://dx.doi.org/10.13039/100007911 University of California, San Diego, La Jolla http://dx.doi.org/10.13039/100007493 University of Colorado Boulder, Boulder http://dx.doi.org/10.13039/100009406 University of Florida, Gainesville http://dx.doi.org/10.13039/100008114 University of Nebraska-Lincoln, Lincoln http://dx.doi.org/10.13039/100007015 University of Wisconsin-Madison, Madison http://dx.doi.org/10.13039/100006537 Vanderbilt University, Nashville issue-copyright-statement© EDP Sciences, Societa Italiana di Fisica (SIF) and Springer-Verlag GmbH, DE, part of Springer Nature 2023
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pmcIntroduction

The Higgs boson (H) [1–6] of mass 125GeV was discovered by the ATLAS and CMS Collaborations in 2012 [7–9]. Since then its properties, including its coupling to other standard model (SM) particles, have been extensively studied using proton-proton (pp) collision data from the CERN LHC collected at s=7, 8, and 13TeV with the ATLAS [10] and CMS [11] detectors. Properties of the Higgs boson can be exploited to probe for signs of behaviour beyond the SM (BSM). In the SM, the decay of the Higgs boson to an invisible final state (H→inv) is only possible via H→ZZ∗→4ν, with a branching fraction of 0.1% [12]. Several BSM theories predict a larger branching fraction to invisible final states, B(H→inv)  [13–16], namely in Ref. [17] and references therein. For example, in a scenario where the Higgs boson connects the SM and dark matter (DM) sectors [18–23], B(H→inv) is enhanced as the Higgs boson can decay to a pair of DM particles of mass mDM<mH/2.

Direct searches for H→inv have been performed by the ATLAS [24–29] and CMS [30–36] Collaborations using data collected during Run 1 (2011–2012) and Run 2 (2015–2018). These target channels in which the Higgs boson is produced via vector boson fusion (VBF), gluon-gluon fusion (ggH), and in association with either a vector boson (VH, where V stands for either a W or Z boson) or with a t t¯ quark pair (tt¯H). The current most stringent constraint on B(H→inv) set by the CMS experiment is via the VBF channel using Run 1 and Run 2 data, which reports a 95% confidence level (CL) upper limit of 0.18 (0.10 expected) [36].

In this paper, a search for an invisibly decaying Higgs boson, produced in association with a t t¯ quark pair or a V boson, where the associated particles decay to a fully hadronic final state, is reported. Representative leading order (LO) Feynman diagrams for tt¯H and VH are presented in Fig. 1. The search in the VH channel looks only at topologies in which the presence of the V boson is inferred from well separated decay products, complementing the previous VH search with merged decay products arising from boosted V bosons [35]. The search uses LHC pp collision data collected during the years 2016–2018, corresponding to a total integrated luminosity of 138fb-1 at s=13TeV. This is the first time that these final states have been used by the CMS experiment to search for the H→inv process using data from 2016–2018.

The missing transverse momentum, p→Tmiss, is the transverse component of the negative vector sum of all reconstructed particle momenta in an event, and has a magnitude pTmiss. There are two main sources of background events resulting in p→Tmiss measurement. The first is events with invisible Z boson decays and visible jets (Z→inv). The second is referred to as the lost lepton background, ℓlost, where ℓ stands for either an e or μ. This includes events from tt¯+jets and W+jets processes where one or more leptons are misreconstructed, excluded by the phase space selection, or fall outside the detector acceptance. Control regions (CRs) enriched in these background sources, requiring either one lepton, one photon, or two same-flavour opposite-sign leptons, are used to constrain these backgrounds from data. The hadronic recoil is defined as the vectorial sum of the p→Tmiss and the pT of any selected charged lepton(s) or photon in an event, and its magnitude is used as the discriminating variable to separate the H→inv signal from backgrounds. The 95% CL upper limit on B(H→inv) is extracted from a fit to the hadronic recoil distribution of selected events, performed across the signal regions (SRs) and CRs. In the SRs, the hadronic recoil is equivalent to the pTmiss, while in the CRs it effectively measures the pT of the V boson or photon. The exclusion of leptons and photons ensures good correspondence between SRs and CRs.Fig. 1 Representative LO Feynman diagrams for the SM Higgs boson production channels tt¯H and VH

This paper is organised as follows: Section 2 is a brief description of the CMS detector. The simulated samples used in this analysis are summarised in Sect. 3. Section 4 describes the event reconstruction and object definitions used in this analysis, while the event selection and event categorisation are detailed in Sect. 5. The data CRs used for estimating the SM backgrounds are introduced in Sect. 6. Section 7 describes the statistical procedure used to constrain the backgrounds and extract the signal. The results of the search are presented in Sect. 8. The results of combining this search with other CMS searches for invisibly decaying Higgs bosons are described in Sect. 9, and the results are summarised in Sect. 10.

The CMS detector

The CMS apparatus is a multipurpose, nearly hermetic detector, designed to trigger on [37, 38] and identify electrons, muons, photons, and (charged and neutral) hadrons [39–41]. The central feature of the CMS apparatus is a superconducting solenoid, of 6m internal diameter. Within the field volume are the silicon pixel and strip tracker, the crystal electromagnetic calorimeter (ECAL), and the brass-scintillator hadron calorimeter (HCAL). Muons are measured in gas-ionisation chambers embedded in the steel flux-return yoke of the magnet. Besides the barrel and endcap detectors, CMS has extensive forward calorimetry, performed on high η objects in the HCAL forward calorimeter, which is located 11.2m from the interaction region along the beam axis. A global “particle-flow” (PF) algorithm [42] aims to reconstruct all individual particles in an event, combining information provided by all subdetectors. The reconstructed particles are used to build τ leptons, jets, and pTmiss  [43–45].

The first level of the CMS trigger system, composed of custom hardware processors, uses information from the calorimeters and muon detectors to select the most interesting events, at a rate of roughly 100kHz. The high-level trigger (HLT) processor farm performs event reconstruction similar to that of the full CMS reconstruction, but optimised for speed. This decreases the event rate from around 100\,kHz to around 1\,kHz, before data storage [38].

The procedures for calculating the integrated luminosity recorded by the CMS detector for each data-taking year are documented in Refs. [46–48] for 2016–2018, respectively.

A more detailed description of the CMS experiment can be found in Ref. [49].

Simulated samples

Monte Carlo (MC) simulated events are used to model signal and background contributions in all analysis regions, except for quantum chromodynamics (QCD) multijet production processes, which are estimated from data using a dedicated control sample and simulation-based transfer factors. The method for estimating QCD multijet production is detailed in Sect. 6.2. In all cases, MC samples are produced using either powheg version 1.0 or higher [50] or MadGraph 5_amc@nlo version 2.4.2 or higher [51] matrix element (ME) generators. The ME is encoded with the maximum amount of information available for a hard scattering event. The parton-level simulation provided by the ME generators is interfaced with pythia version 8 [52] to model the shower and hadronisation of partons in the initial and final states, along with the underlying event description, using the tune CUETP8M1 (CP5) when simulating events for the 2016 (2017 and 2018) data-taking periods [53]. The propagation of all final state particles through the CMS detector is simulated using the Geant4  [54] toolkit. Samples for 2016 make use of the NNPDF3.0 LO or next-to-LO (NLO) parton distribution functions (PDFs) [55], whereas samples for the years 2017 and 2018 use the NNPDF3.1 next-to-NLO (NNLO) PDFs.

Processes featuring H→inv occurring in tt¯H, VH, VBF, and ggH channels are modelled by powheg version 2.0 [56–59] at NLO in QCD. These samples require the SM Higgs boson to decay to four neutrinos (H→ZZ∗→4ν) resulting in B(H→inv) =1. The cross sections are appropriately normalised to the corresponding SM predictions computed at NLO (tt¯H), NNLO (VH, VBF), and next-to-NNLO (ggH) accuracy in QCD, and to NLO accuracy in electroweak (EW) corrections [60]. Background ZH processes with the Higgs boson decaying to bb¯ and the associated Z boson decaying to bb¯, ℓℓ, and qq¯ (where q represents a light or charm quark) are generated at NLO using MadGraph 5_amc@nlo with the FxFx [61] matching scheme for 2016 samples, and with powheg version 2.0 [62] for 2017 and 2018 samples.

The V+jets processes are generated at LO in QCD using MadGraph 5_amc@nlo with up to four partons in the final state using the MLM [63] matching scheme between hard scatters and parton showers. These processes are generated in bins of hadronic transverse energy, HT, which is the magnitude of the p→T sum of all jets reconstructed at generator level. The LO simulation of V+jets processes is corrected to account for missing higher-order diagrams with K-factors derived from MadGraph 5_amc@nlo-generated NLO QCD V+jets processes with up to two partons. These K-factors are extracted as a function of boson pT and the pT of the leading jet in the event. These K-factors are extracted as a function of boson pT and the pT of the leading jet in the event, and typically vary between 0.5 and 1.5 depending on the boson pT.

The γ+jets processes are generated at NLO in QCD with MadGraph 5_amc@nlo, using a binning based on the pT of the photon. The binning scheme for this sample is defined at the ME level to increase the statistical precision in the phase space regions probed by this analysis.

Processes including t-channel single t quarks, and t t¯ pairs with up to two additional partons in ME computation are generated at NLO with powheg version 2.0 [64, 65]. Single t quarks produced in the s channel are modelled using MadGraph 5_amc@nlo, and also in the tW channel using powheg version 1.0 [66]. The t quark pT spectrum in t t¯ processes is corrected to match the spectrum obtained from the NNLO QCD + NLO EW simulation, following Ref. [67]. Rare tt¯X + jets backgrounds cover processes where t t¯ is produced in association with a boson X (γ, V, or a visibly decaying H), generated at NLO. The tt¯γ + jets, tt¯W + jets, and tt¯Z + jets samples are generated using MadGraph 5_amc@nlo, with subsequent decays generated using MadSpin [68] to account for spin correlations in the former two cases. The tt¯H  + jets sample, where the H decays to visible states, is generated using powheg.

Diboson ZZ and WZ production processes are generated at LO using pythia, while the WW process is simulated at NLO in QCD using the powheg version 2.0 [69]. The QCD multijet samples are generated at LO using MadGraph 5_amc@nlo in exclusive ranges of HT in order to increase the statistical precision in the phase-space probed by this analysis.

Event reconstruction

During LHC runs, each beam crossing results in several pp collisions in the detector. Additional pp interactions within the same or nearby bunch crossing, known as pileup, make PF object reconstruction more challenging. The reduction of the effect of pileup relies on mitigation techniques [70] that filter energy deposits associated with pileup vertices and remove objects not associated with the primary interaction vertex (PV). The PV is the vertex associated with the hardest scattering in the event, according to tracking information, as described in Ref. [71]. All simulated samples from Section 3 are reweighted to match the pileup distribution observed in data. In the SR, the final state is required to contain jets, a sizeable hadronic recoil, and no isolated leptons or photons. Candidate leptons and photons are selected with pT>10GeV and pseudorapidity |η|<2.4 for muons [40], pT>10GeV and either |η|<1.44 or 1.57<|η|<2.5 for electrons [39], pT>20GeV and |η|<2.3 for hadronically decaying tau leptons [43], and pT>15GeV and either |η|<1.44 or 1.57<|η|<2.5 for photons [39]. These selection criteria are optimised to reject background contributions, mainly from QCD processes. Other selection criteria depend on the isolation of the lepton or photon from hadronic interactions in the detector within a cone of small (tight isolation) or large (loose isolation) radius. Loose identification and isolation criteria are used to veto candidate events in the SR that contain leptons or photons. The veto efficiencies are > 99, ≃ 95, and ≃ 90% for loose muons, electrons, and photons, respectively. The SR background contributions are estimated using μ+jets, e+jets, μμ+ jets, ee + jets, and γ+jets CRs. Tight and loose identification and isolation criteria are used to select and count muons, electrons, and photons in the CRs, enhancing the purity at little expense to the efficiency. These achieve typical selection efficiencies of ≃ 95, 70, and 70 (≃ 98, 95 and 90)%, for tight (loose) muons, electrons, and photons, respectively.

Jets are reconstructed by clustering all PF candidates originating from the PV with the anti-kT jet clustering algorithm [72, 73], using a distance parameter R=0.4 (AK4). Jet momentum is determined as the vectorial sum of all particle momenta in the jet, and is found from simulation to be, on average, within 5–10% of the true momentum over the whole pT spectrum and detector acceptance. Charged-hadron subtraction [44] is then applied to remove charged particles from pileup vertices [74]. To ensure the measured jet energy matches that of the particle level jets, jet energy corrections (JEC) derived from simulation as functions of pT and η are applied. Further corrections are applied due to residual discrepancies in the jet energy scale (JES) between data and simulated samples [44]. Additionally, each jet must pass selection criteria to remove jets adversely affected by instrumentation or reconstruction failure. The jet energy resolution (JER) in simulated samples is smeared to match the measured resolution, which is typically 15–20% at 30GeV, 10% at 100GeV, and 5% at 1TeV  [44]. The AK4 jets are required to have pT>30GeV and |η|<5.0, and those with loose leptons and photons located within a cone of ΔR<0.4 of the jet direction are removed.

The AK4 jets that originate from the hadronisation of a bottom quark (b-tagged jets) are identified using the DeepCSV algorithm, which correctly identifies b jets with pT>20GeV with a probability of 80% and has a charm or light jet mistag probability of 10% [75]. Simulated events containing b jets are corrected to be in agreement with the data by deriving corrections from data control samples that contain b jets.

Pileup effects are mitigated at the reconstructed particle level using the pileup per particle identification algorithm (PUPPI) [76, 77] by defining a local shape variable that can discriminate between particles originating from the PV and from pileup. Charged particles originating from pileup are discarded. For neutral particles, a local shape variable is computed based on the information from charged particles in their vicinity that originate from the PV within the tracker acceptance, and information from both charged and neutral particles outside this acceptance. The momenta of neutral particles are then rescaled based on the probability that they originated from the PV as deduced from the local shape variable [76].

When a high pT t quark or V boson decays hadronically, a large set of collimated particles cross the detector. These can be clustered within a single jet of radius R=0.8 (AK8) using the anti-kT algorithm. In order to reduce pileup effects, PUPPI PF candidates are used to seed the AK8 jet finder. The main feature that distinguishes hadronically decaying t quarks or V bosons from the quark or gluon fragmentation is the jet mass. To improve the resolution, the modified mass-drop tagger algorithm [78–80] (also known as the soft-drop algorithm, SD) with the angular exponent β=0, soft cutoff threshold zcut<0.1, and characteristic radius R0=0.8 [81] is applied to each AK8 jet to remove soft and wide-angle radiation. In addition, a deep neural network (DNN) classifier called the DeepAK8 [82] algorithm is employed by assigning a set of numerical scores to each reconstructed AK8 jet corresponding to the probabilities that it originates from particular final states of V boson decays, for example Z→bb¯, Z→qq¯, W→cs, rather than from QCD multijet processes. For this analysis, reconstructed AK8 jets originating from t quarks (W bosons) are selected by requiring pT>400(200)GeV, SD mass mSD between 120 and 210 (65 and 120)GeV, and a DeepAK8 probability score for t quarks (W bosons) larger than between 72.5 and 83.4 (91.8 and 92.5)% depending on the year of data-taking. The resulting t quark (W boson) tagging efficiency at the pT>400(200)GeV threshold limit is estimated from simulation as 28 (25)% with a 1% mistag rate from QCD jets. Simulated events containing AK8 jets are corrected to agree with the data using data-derived correction factors, and dedicated JEC are also applied [82].

The calculation of energy sums such as the hadronic recoil, p→Tmiss, and H→Tmiss, which is the negative p→T sum of jets reconstructed at the HLT level with a pTmiss threshold of 20GeV applied, are based on AK4 jets, therefore JEC are propagated through the use of the p→T-corrected jets.

Event selection and categorisation

In this analysis the signal is extracted from a combined fit to the hadronic recoil distribution of events in SRs and CRs as defined for the tt¯H and VH categories. The CRs are used to estimate the contributions of different SM processes in each SR. Where possible, the CRs have kinematic requirements identical to the SR, and leptons or a photon are used in the CR definition, but otherwise ignored in the calculation of event observables. The e+jets and μ+jets CRs, enriched in W+jets and t quark background processes, are used to derive corrections to ℓlost contributions predicted by simulation. The ee + jets, μμ+ jets, and, in the case of the VH category, γ+jets CR samples are used to derive corrections to the expected contribution from Z+jets production, where the Z boson decays to a pair of neutrinos. A QCD multijet enriched CR (hadronic sideband) is also used to estimate hadronic backgrounds in the SR.

Trigger requirements

Events of interest are collected via a suite of triggers that are applied to variables calculated using PF candidates reconstructed at the level of the HLT. The trigger requirements vary amongst analysis regions and data-taking periods. Events in the SR, hadronic sideband, and muon CRs are collected using HLT selection criteria on pTmiss and the missing HT, HTmiss, which is the magnitude of H→Tmiss. Muons are not considered in the calculation of PF pTmiss and PF HTmiss to allow the same trigger to be used in the SR and the muon CRs, with a typical efficiency of >90% for pTmiss >250GeV. The use of the combined pTmiss and HTmiss triggers in the muon CRs instead of single-muon triggers corresponds more closely to the selection in the SR and minimises selection biases. Trigger thresholds increase with time due to the increase in instantaneous luminosity during Run 2. In 2016, the pTmiss and HTmiss thresholds vary between 90 and 120GeV. In 2017 and 2018, these thresholds are 120GeV. During data-taking in 2017, additional corrections were applied to account for the effect of ECAL endcap noise at high |η| on PF pTmiss measurements. Additionally, for 2016 and 2017 data-taking periods, there was an inefficiency arising from a gradual shift in the timing of the ECAL trigger inputs in the region |η|>2.0 [37]. This resulted in events containing an electron or photon (jet) with pT>50(100)GeV having an efficiency loss of up to 20%, depending on pT and η. Correction factors for this trigger inefficiency are obtained from 2016 and 2017 data and applied to simulation samples as a function of η.

Events in the e+jets and ee + jets CRs from the 2016, 2017, and 2018 data sets are required to pass a tight (loose) single-electron trigger with pT thresholds of 27, 35, and 32 (105, 115, and 115)GeV, respectively. The low-threshold single-electron triggers require the electron candidate to pass a tight isolation condition, while the high-threshold trigger imposes a looser selection on the isolation to improve the efficiency at high pT. Photon events are required to pass a single-photon trigger with a pT threshold of 175 (200)GeV without any isolation condition for the 2016 (2017 and 2018) data sets. Simulated electron or photon events are accepted if they pass exactly one of the above trigger requirements, and the efficiency of this selection is corrected with data-derived efficiency correction factors.

Offline selection

In order to select events with a large amount of jet activity and sizeable hadronic recoil, a further offline selection is applied to all regions. To improve the purity of the signal, large missing energy is desirable, therefore events require the hadronic recoil, HTmiss, and HT to be greater than 200GeV. Furthermore, the largest pT of an AK4 jet in an event, p→T,1j, is required to be greater than 80GeV. To ensure consistency amongst different estimators of the hadronic recoil, the recoil as calculated from PF candidates in pTmiss and from PF jets in HTmiss must satisfy HTmiss/recoil<1.2 and azimuthal separation |Δϕ(recoil→,H→Tmiss)|<0.5. To further improve the quality of events, a selection is made on pT,trackmiss, which is equivalent to pTmiss but calculated using only charged PF particles, and therefore is expected to be well-aligned with the hadronic recoil direction. Requirements of pT,trackmiss>60GeV and azimuthal separation |Δϕ(recoil→,p→T,trackmiss)|<1 are applied in the SR and hadronic sideband. The kinematic selection for all regions is optimised according to the Asimov significance between signal (S) and background (B) yields assuming a background systematic uncertainty ΔB of 5% or 10% [83]. The peaks of the distribution for a given variable corresponds to its selection threshold.

In order to facilitate the combination of this analysis with the results from other H→inv searches, additional selections are introduced to reduce the potential event overlap. A veto is implemented to ensure orthogonality with the VBF phase space, through a veto on events with leading (subleading) AK4 jets with |η1|(|η2|)>2.4, and an inversion of the kinematic selection employed by the VBF H→inv analysis [36]. This removes events containing two AK4 jets with p→T,1j>80GeV and the subleading jet pT, p→T,2j, to be greater than 40GeV, where the jets are from opposite detector hemispheres (η1η2<0), have a large mjj (>200GeV), small azimuthal separation (Δϕjj<1.5), and a large η gap (|ηmjj|>1.0). Moreover, orthogonality to leptonic tt¯H decays is ensured in the single-lepton CRs by requiring the transverse mass of the combined single-lepton and hadronic recoil system, defined as1 mTℓ=2pTℓ(recoil)[1-cos(ϕ(p→Tℓ)-ϕ(recoil→))],

to be lower than 110GeV. Orthogonality between leptonic tt¯H decays in the dilepton CRs is ensured by requiring the invariant mass of the charged lepton pair, mℓℓ, to be lower than 120GeV in these CRs. Selecting on the invariant masses of lepton pairs also suppresses the tt¯H signal contamination in the CRs. Overlap between the ggH/boosted VH H→inv analysis and the resolved VH category of this analysis is rendered negligible by explicitly removing events from the low-purity boosted VH category defined in Ref. [35] if they contain exactly two AK4 jets with an invariant mass, mjj, forming a dijet candidate with 65<mjj<120GeV. No corresponding selection is necessary for the resolved VH category as a result, while there is negligible change to the sensitivity of the boosted VH category.

During significant periods of data-taking in 2018, the HCAL portion corresponding to the region -1.57<ϕ<-0.87, -3.0<η<-1.39 was not functional. Events from 2018 with -1.8<ϕ(recoil→)<-0.6 are vetoed if they contain jets within the affected region, which removes ≈65% of the total data from the affected region. To ensure good correspondence between data and simulation, the simulation is reweighted to account for the efficiency loss. A summary of the offline requirements are provided in Table 1.Table 1 Offline selection applied to all categories and regions in this analysis to improve signal purity and reduce overlap with the phase space of other H→inv searches

Variable	Selection	Purpose	
recoil	>200GeV	Signal purity	
HTmiss	>200GeV	
p→T,1j	>80GeV	
HTmiss/recoil	<1.2	Event quality	
|Δϕ(recoil→,H→Tmiss)|	<0.5	
|η1|, |η2|	<2.4	Analysis orthogonalisation	
VBF signal	Veto (inversion on signal selection)	
mTℓ	<110GeV	
mℓℓ	<120GeV	

Signal regions

The search focuses on three types of hadronic final states: those with boosted t quarks and/or boosted W bosons reconstructed with dedicated merged jet algorithms; those with one or more b jets and no boosted t quark or W boson, targetting the bulk of hadronic tt¯H events; and those with two resolved jets with the mjj compatible with that of a W or Z boson. The latter complements the boosted VH channel analysed in Ref. [35].

Events are categorised into boosted and resolved tt¯H, and resolved VH topologies. The tt¯H category requires that at least five AK4 jets and one b jet are present. The boosted tt¯H topology requires that at least one AK8 jet is reconstructed and either t- or W-tagged, and is subcategorised by the AK8 jet and b jet multiplicities. Events without such t- or W-tagged jets are categorised as belonging to a resolved tt¯H topology, with further selections on the leading AK4 jet (leading or subleading b jet) p→T and the hadronic recoil, |Δϕ(recoil→,p→T,1j)| (|Δϕ(recoil→,p→T,1b)| or |Δϕ(recoil→,p→T,2b)|) applied to discriminate between tt¯H and tt¯+jets processes. Finally, the remaining events are allocated to the resolved VH topology category if they have exactly two AK4 jets with mjj between 65 and 120GeV, compatible with a W or Z boson decay. The resolved VH subcategories are separated according to the b jet multiplicity. Subcategories are also defined based on p→T,2j to suppress QCD multijet background. The subcategory definitions are summarised in Table 2. The intended outcome of this categorisation is a set of event samples with high purity for a given production mode, and minimal background contamination or signal cross-contamination.Table 2 Categorisation of the tt¯H and VH production modes in the analysis. No additional selections are applied to the boosted tt¯H subcategories

Category	Subcategory	nj	nb	nt	nW	p→T,2j (GeV)	Other	
	2Boosted1b	≥5	1	2			
	2Boosted2b	≥5	≥2	2			
Boosted tt¯H	1t1b	≥5	1	1	0	>80	–	
	1t2b	≥5	≥2	1	0			
	1W1b	≥5	1	0	1			
	1W2b	≥5	≥2	0	1			
	5j1b	5	1	0	0		|Δϕ(recoil→,p→T,1b)|>1.0,	
Resolved tt¯H	6j1b	≥6	1	0	0	>80	|Δϕ(recoil→,p→T,1j)|>π/2	
	5j2b	5	≥2	0	0		|Δϕ(recoil→,p→T,1b)|>1.0,	
	6j2b	≥6	≥2	0	0		|Δϕ(recoil→,p→T,2b)|>π/2	
	2j0b	2	0	0	0			
VH	2j1b	2	1	0	0	>30	65<mjj<120GeV	
	2j2b	2	2	0	0			

A requirement on |Δϕmin(p→Tmiss,p→T,1234)|, defined as the minimum azimuthal separation between the hadronic recoil and the momentum direction of any of the four highest pT jets, of >0.5 is applied to suppress QCD multijet events where the hadronic recoil is aligned with a jet. A parameter ω~min is designed to suppress events where missing energy is the result of a jet pT mismeasurement, and is especially effective in categories with no b jets. For the ith jet in the event, ωi is defined as arctan(HT,minmiss/pT,i), where pT,i is the pT of jet i, and HT,minmiss is the minimum value of HTmiss that can be obtained by changing the value of pT,i. The value of ωi minimised over i is ω~min. A detailed derivation of this variable is given in Ref. [84]. QCD multijet events in the SR are further suppressed by requiring ω~min>0.3. Requirements to suppress QCD events are applied in the SR only for tt¯H categories, and to both SR and CRs in the VH categories in order to ensure good correspondence amongst the regions. The selections applied to ω~min and |Δϕmin(p→Tmiss,p→T,1234)| are not applied in the CRs used for background estimation of the tt¯H categories, where the hadronic recoil does not stem from jet mismeasurement. This is to increase event counts in the CRs, particularly in the boosted tt¯H categories.

The hadronic recoil in tt¯H production is closely aligned with the direction of the Higgs boson typically. In t t¯ events, the p→Tmiss is usually parallel or antiparallel to the direction of the leading b jet, as the t quarks are produced back-to-back. Therefore, the angles between the direction of the hadronic recoil and the leading or subleading jet or b jet p→T directions provide additional features for t t¯ background suppression in the resolved tt¯H categories. The angular variables |Δϕ(recoil→,p→T,1j)|, |Δϕ(recoil→,p→T,1b)|, and |Δϕ(recoil→,p→T,2b)| are the most sensitive discriminators between tt¯H and t t¯. The selection based on these angular variables has been optimised by maximising the combined expected sensitivity of the tt¯H analysis and is summarised in Table 2.

Control regions and background estimation

The analysis makes use of the μ+jets and e+jets CRs to estimate ℓlost background contributions, which are mainly from tt¯+jets, single t quark, and W+jets events. The background contributions from Z→inv, which include ZZ, tt¯Z, and Drell-Yan (DY) contributions, are estimated from the μμ+ jets, ee + jets, and γ+jets CRs. Hadronic backgrounds in the SR such as QCD multijet contributions are estimated using a transfer factor method applied to a QCD enriched sideband CR.

Estimation of ℓlost and Z→inv backgrounds

The μ+jets (e+jets) CR is defined by requiring exactly one tightly-isolated muon (electron) with pT>20(40)GeV. Both CRs require 50<mTℓ<110GeV. The single-lepton CRs are used to constrain the ℓlost background, which is the main source of background in the tt¯H and VH  2j2b categories. In the tt¯H category, the ℓlost contribution arises mainly from t t¯, single t quark, and tt¯V processes, while in the VH category it is from W  + jet events.

In the μμ+ jets (ee + jets) CR, one tightly-isolated muon (electron) with pT>20(40)GeV, and one loose muon (electron) with the opposite charge and pT>10(10)GeV are required with invariant mass, mμμ (mee), compatible with a Z boson. For the tt¯H (VH) category, the invariant mass is required to be between 75 and 105 (60 and 120)GeV. The processes Z→νν and Z→ℓℓ are kinematically nearly identical, largely due to lepton universality, hence the dilepton regions can be used to constrain the Z→inv background and minimise theoretical uncertainties. This is important for the Z→inv background, which dominates the VH category and contributes to the tt¯H category especially at high hadronic recoil. In the tt¯H category, events are selected for which Δϕ(recoil→,p→T,trackmiss)>π/2, which reduces the tt¯+jets background and favours DY production in the dilepton CRs.

The γ+jets CR is used for background estimation in the VH category only, and requires exactly one loose photon with pT>230GeV. This region is used to constrain the Z→inv background as the event kinematics and topologies are similar for Z+jets and γ+jets events, improving the sensitivity to the VH signal primarily at high hadronic recoil compared to the dilepton CRs because of the larger number of events.

Photons can usually be discriminated from other sources of ECAL deposits using the properties of the deposits themselves, such as isolation in ECAL and HCAL, or the shape of the electromagnetic showers. However, occasionally other particles will be incorrectly identified as photons, for example where a jet is misidentified as a photon in QCD multijet events. In order to estimate the contribution from misidentified photons in the γ+jets CR, a purity measurement is performed. The purity is defined as the fraction of reconstructed photon candidates that correspond to genuine isolated photons originating from the PV in the event. The photon purity is measured in data based on the lateral width σηη [85], which parametrises the shape of the energy deposit associated with the photon in the ECAL. The characteristic σηη distribution from genuine photons peaks at σηη<1, while the distribution due to misidentified photons possesses a less pronounced peak with a much broader decline for σηη>1. A template fit to the σηη distribution is performed, where for genuine photons simulated γ+jets events are used to build the signal templates, while for misidentified photons a data sample enriched in misidentified photon events is obtained by inverting the isolation requirements in the γ+jets CR. The purity is defined as the fraction of genuine photons extracted from the fit that pass the σηη selection. The photon purity is measured separately in bins of pTγ and for each data-taking period and varies between 1.5 and 4.5%. The contamination is the fraction of misidentified photons in the γ+jets CR, and is estimated at around 4% for pTγ>200GeV. The QCD multijet contribution in the γ+jets CR is then estimated by weighting events in data for each pTγ bin by the corresponding contamination. A 25% systematic uncertainty is attributed to the QCD multijet background normalisation, and is estimated by performing the procedure for different σηη binning in the template fit, which accounts for any mismodelling of the simulated σηη distribution. The statistical uncertainty in the photon purity estimate in each pTγ bin is found to be much smaller than the systematic one. The full requirements for the analysis CRs are shown in Table 3.Table 3 Summary of all CR requirements, excluding selections suppressing the QCD multijet background, and excluding the requirement of Δϕ(recoil→,p→T,trackmiss)>π/2 applied to the tt¯H category in the dilepton CRs. No mass requirements are imposed in the γ+jets

Control region	Category	nobject reqs.	Mass reqs. (GeV)	pT reqs. (GeV)	
μ+jets	tt¯H	nμ=1	50<mTμ<110	pT,1μ>20	
VH	
e+jets	tt¯H	ne=1	50<mTe<110	pT,1e>40	
VH	
μμ+ jets	tt¯H	nμ=2	75<mμμ<105	pT,1μ>20, pT,2μ>10	
VH	60<mμμ<120	
ee + jets	tt¯H	ne=2	75<mee<105	pT,1e>40, pT,2e>10	
VH	60<mee<120	
γ+jets	VH	nγ=1	–	pTγ>230	

Residual backgrounds from QCD multijet production

The event selection aims to reduce background contributions from QCD multijet production as much as possible by requiring |Δϕmin(p→Tmiss,p→T,1234)|>0.5 and ω~min>0.3, although a QCD multijet background enriched sideband is used to estimate any remaining background contribution with the help of a transfer factor between sideband and SR, which is derived from simulation. The sideband is defined with an identical selection to that of the SR, but with an inversion on the requirements on |Δϕmin(p→Tmiss,p→T,1234)| and ω~min, such that |Δϕmin(p→Tmiss,p→T,1234)|<0.5 and more stringently ω~min<0.2. The criteria for ω~min is determined by optimising the sideband to be as QCD multijet-enriched as possible while ensuring the SR has negligible QCD multijet background. For the VH category, the mjj requirement is also inverted in order to have the sideband sufficiently populated.

The SRs in both the tt¯H and VH categories suffer from limited simulated QCD multijet event counts, so it is not possible to reliably define a transfer factor for each SR bin in individual subcategories. Within the statistical precision of the simulated QCD multijet samples, the shape of the hadronic recoil and relative population of the tt¯H subcategories are observed not to depend on ω~min and |Δϕmin(p→Tmiss,p→T,1234)|. Therefore, the expected QCD sideband yields are integrated over all tt¯H subcategories and hadronic recoil intervals, and over hadronic recoil intervals for each VH category, in the sideband and SR, to construct the transfer factors. The resulting hadronic recoil distributions are used to predict the relative QCD multijet background in each subcategory and hadronic recoil interval.

The estimated QCD multijet background yield in the tt¯H SR for subcategory i and hadronic recoil interval j, Ni,jQCD,SRtt¯H, is given by2 Ni,jQCD,SRtt¯H=∑p∑q(Np,qdata,CRtt¯H-Np,qEW,CRtt¯H)TFQCDtt¯Hfcitt¯Hfmjtt¯H,

where EW refers to processes that are not QCD multijet, summation indices p and q are the subcategory and hadronic recoil bins, respectively, TFQCDtt¯H is the QCD multijet simulation transfer factor defined as the ratio between the expected QCD multijet background contribution in the SR and the sideband, and fcitt¯H and fmjtt¯H are the fractions of simulated QCD multijet events in each subcategory and hadronic recoil bin, respectively.

In the VH category, the sideband regions are defined for each subcategory, as the number of simulated QCD multijet events is sufficient to derive the hadronic recoil fractions fmj separately for each subcategory. The method is otherwise analogous to that of tt¯H, given by Eq. 2.

The results of the QCD prediction aggregated over data sets from the 2016–2018 period are found to be small in comparison to background contributions from ℓlost and Z→inv processes. In addition to the statistical uncertainties, a 100% systematic uncertainty is assigned to the predicted background yields from QCD multijet production. The actual uncertainty in the QCD prediction is measured at around 50%, derived by calculating the QCD contribution in the entire tt¯H category for a signal-depleted validation region analogous to the SR but requiring 0.2<ω~min<0.3 and |Δϕmin(p→Tmiss,p→T,1234)|>0.5, and comparing the estimate to data. It is inflated to 100% to be more conservative when handling the individual tt¯H subcategories that are limited by event counts at larger hadronic recoil, which was found to have negligible impact on the final fit.

Statistical interpretation

A maximum likelihood fit method is used to obtain an upper limit on B(H→inv). The fit is performed simultaneously across each year, region, category, and hadronic recoil interval, with systematic uncertainties acting as nuisance parameters in the fit correlated to varying degrees across year and category.

Likelihood model

The limits on B(H→inv) are extracted via a simultaneous binned maximum likelihood fit to the hadronic recoil distributions obtained in the SR and CRs. The likelihood can be written as3 L=LSRLμLeLμμLeeLγ,

where LSR is the likelihood function for the SR (boosted tt¯H, resolved tt¯H, VH), and Lμ, Le, Lμμ, Lee, and Lγ designate the likelihood functions for the μ+jets, e+jets, μμ+ jets, ee + jets, and γ+jets CRs, respectively. The likelihood function for the SR is defined as4 LSR=∏cat=incat∏recoil=j(i)nξ(i)Poissonnobsi,j∣npredi,j,

with5 npredi,j=μ^si,jρsi,j+bℓlosti,jIi,jρℓlosti,j+bZ→invi,jLi,jρZ→invi,j+bQCDi,jρQCDi,j,

where the symbols are defined in Table 4. The signal strength, μ^, is interpreted as the maximum likelihood estimator for B(H→inv), where the signal prediction assumes that B(H→inv)=1. The fit also includes additional free parameters Ii,j and Li,j, which depend on category i, hadronic recoil bin j, and the number of recoil bins in each category nξ(i). The first of these parameters, Ii,j, simultaneously scales the normalisation of the ℓlost background in the SR and the sum of the W+jets, t t¯  + jets, and single t quark backgrounds, Xt,Wi,j, in the μ+jets and e+jets CRs. The second of these parameters, Li,j, simultaneously scales the normalisation of the Z→inv background in the SR (Z(νν) + jets and tt¯Z(νν)) and the sum of the γ  + jets, DY + jets, tt¯Z + jets, and multiboson backgrounds, XZ/γi,j, in the μμ+ jets, ee + jets, and γ+jets CRs.Table 4 Meaning of the symbols used in Eqs. 4 and 5 that define the likelihood function

Symbol	Meaning	
μ^	Signal strength estimator of B(H→inv)	
si,j	Simulation predicted number of signal events in bin i, j of the SR	
ρsi,j	Systematic uncertainties affecting signal prediction in bin i, j of the SR	
bℓlosti,j	Simulation predicted number of ℓlost events in bin i, j of the SR	
Ii,j	Normalisation parameter for the ℓlost estimation in bin i, j	
ρℓlosti,j	Systematic uncertainties affecting the ℓlost background in bin i, j of the SR	
bZ→invi,j	Simulation predicted number of Z→inv events in bin i, j of the SR	
Li,j	Normalisation parameter for the Z→inv estimation in bin i, j	
ρZ→invi,j	Systematic uncertainties affecting the Z→inv background in bin i, j of the SR	
bQCDi,j	Predicted number of QCD events in bin i, j of the SR	
ρQCDi,j	Systematic uncertainties of the QCD component in bin i, j of the SR	

The likelihood for the μ+jets and e+jets CRs is given by6

and for the μμ+ jets, ee + jets, and γ+jets CRs is given by7 Lμμ,ee,γ=∏cat=incat∏recoil=j(i)nξ(i)×Poissonnobsi,j∣XZ/γi,jLi,jρZ/γi,j+Xotheri,jρotheri,j,

where Xi,j is the sum of background yields, and ρi,j refers to the associated systematic uncertainty.

Because of the low event counts in the dilepton CRs, the subcategory yields are summed into the boosted and resolved tt¯H categories. For the boosted tt¯H category, the μμ+ jets and ee + jets CR yields are summed together to form a single ℓℓ+jets CR. Furthermore, in the boosted and resolved tt¯H subcategories, Ii,j are shared across subcategories, therefore i takes only two values corresponding to the boosted and resolved tt¯H classes.

Systematic uncertainties

The model on which the maximum likelihood fit is based is inclusive of experimental and theoretical uncertainties. These are modelled as nuisance parameters, which are typically constrained by a template fit where there is a dependence on the hadronic recoil distribution, but are otherwise constrained by a log-normal distribution for those that affect the overall normalisation of a given process.

Theoretical uncertainties related to the PDF parameters and missing higher order corrections in the QCD and EW perturbative expansions are estimated by following the procedure outlined in Ref. [60] for tt¯H and VH processes, and in Ref. [86] for V+jets and γ+jets processes. Systematic uncertainties related to the PDF, and the renormalisation and factorisation scales, are treated as independent nuisance parameters but are correlated across years in the fit.

A photon normalisation uncertainty of 40% is included in the γ+jets CR, to cover uncertainties in the translation between the γ+jets and Z→ℓℓ yields, and is only correlated between 2017 and 2018 samples given the γ+jets sample for 2016 is generated with a different tune.

Data-derived correction factors are applied to simulated events containing b, t, and W jets, and therefore the systematic uncertainties due to the limited precision in these corrections are propagated to the simulated samples. These are referred to as tagging uncertainties, and also account for the uncertainties in the tagging efficiencies and misidentification probabilities. The tagging methods and uncertainty propagation are consistent between years, and therefore are correlated across years in the fit.

The uncertainty in the combined PF pTmiss and HTmiss trigger efficiency is computed using the μ+jets and μμ+ jets CRs. These are independent of the pTmiss and HTmiss data sets in the SR, ensuring an unbiased measurement of the uncertainty. This uncertainty is measured at 2%, and is applied independently in each year of data-taking due to variations in the trigger performance. The same uncertainty is measured in the electron and photon trigger efficiency, and is similarly uncorrelated between years. An additional trigger inefficiency uncertainty due to the mistiming of ECAL trigger inputs detailed in Sect. 5.1 is applied to the data-taking years 2016 and 2017.

The uncertainty in the integrated luminosity varies between 1.2–2.5% depending on the data-taking year, with an overall uncertainty of 1.6% for the 2016–2018 period [46–48]. The uncertainty is applied with correlated and uncorrelated components across years.

The uncertainties considered in the analysis are presented in Table 5 with the pre-fit ranges corresponding to the maximum and minimum deviations of the event yields from their nominal values across each region, year of data-taking, category, recoil bin, and all SM background processes, when the respective systematic uncertainty is changed within ±1 standard deviation. Systematic uncertainties not specified above are typically assumed to be uncorrelated from year to year when performing the fit. Those for which the source of the systematic uncertainty is identical for each year are treated as correlated. All systematic uncertainties are correlated across regions.

The overall experimental uncertainty is found to be dominated by W tagging for the tt¯H and b tagging for the VH categories in the SR. The lepton and photon candidate efficiencies for identification, isolation, and reconstruction, and uncertainties in the JER, JES, and trigger efficiencies also make significant contributions. The theoretical uncertainty is dominated by variations in the renormalisation scale, factorisation scale, and PDF for V+jets processes, although these are particularly sensitive to the high exclusive jet multiplicity characterising the tt¯H and VH categories.Table 5 The ranges corresponding to the maximum and minimum deviations of the event yields from their nominal values, provided where applicable across each region, year of data-taking, category, recoil bin, and all SM background processes, when the respective systematic uncertainty is changed within ±1 standard deviation

Systematic uncertainties on background yields (pre-fit)	Signal region	ℓ+jets	ℓℓ+jets	γ+jets	
	tt¯H cat.	VH cat.	tt¯H cat.	VH cat.	tt¯H cat.	VH cat.	VH cat.	
Theoretical uncertainties								
Fact. scale V+jets (QCD)	<1.0-7.7 %	<1.0-19 %	<1.0-2.6 %	<1.0-11 %	<1.0-20 %	<1.0-22 %	6.0 %	
Ren. scale V+jets (QCD)	<1.0-7.2 %	<1.0-8.6 %	<1.0-3.6 %	<1.0-10 %	<1.0-14 %	2.0-11 %	12 %	
PDF V+jets	<1.0-9.1 %	2.0-23 %	<1.0-3.1 %	<1.0-15 %	<1.0-23 %	<1.0-26 %	8.0 %	
Ren. & Fact. scale tt¯H (QCD)	<1.0-1.7 %	<1.0 %	<1.0-1.4 %	<1.0-1.4 %	<1.0 %	<1.0 %	–	
Ren. & Fact. scale t t¯ (QCD)	7.8-15 %	2.5-9.3 %	6.4-17 %	<1.0-6.3 %	<1.0-5.8 %	<1.0-5.8 %	–	
NNLO QCD & NLO EW t quark pT reweighting (inc. PDF)	<1.0-3.1 %	<1.0-1.2 %	<1.0-4.0 %	<1.0-3.9 %	<1.0 %	<1.0 %	–	
Ren. & Fact. scale VV (QCD)	<1.0 %	<1.0 %	<1.0 %	<1.0 %	<1.0 %	<1.0 %	<1.0 %	
tt¯H & VH cat. cross section (QCD)	5.8-9.2 %	<1.0-3.8 %	–	–	–	–	–	
tt¯H & VH cat. cross section (PDF & αs)	3.6 %	1.6-1.8 %	–	–	–	–	–	
Initial-state radiation	2.0 %	3.0-6.0 %	2.0 %	<1.0-4.2 %	2.0 %	6.0 %	<1.0-4.0 %	
Final-state radiation	5.0 %	3.0-5.0 %	2.0-2.2 %	<1.0-3.1 %	4.6-5.0 %	5.0 %	2.0-3.0 %	
Photon normalisation	–	–	–	–	–	–	40 %	
Experimental uncertainties								
Integrated luminosity	1.2-2.5 %	1.2-2.5 %	1.2-2.5 %	1.2-2.5 %	1.2-2.5 %	1.2-2.5 %	1.2-2.5 %	
t-tagging	3.2-6.5 %	–	2.1-5.7 %	–	–	–	–	
W-tagging	7.8-18 %	–	7.1-18 %	–	–	–	–	
b-tagging	8.2-12 %	8.2-22 %	6.5-11 %	2.4-11 %	5.6-8.7 %	1.6-9.6 %	6.6-9.0 %	
Electron identification & isolation	–	–	3.7-11 %	4.7-9.6 %	<1.0-15 %	<1.0-20 %	–	
Electron reconstruction	–	–	<1.0-1.8 %	<1.0 %	1.0-1.5 %	<1.0-1.4 %	–	
Muon identification	–	–	<1.0-1.0 %	<1.0-1.0 %	<1.0-1.8 %	<1.0-1.9 %	–	
Muon isolation	–	–	<1.0 %	<1.0 %	<1.0 %	<1.0 %	–	
Lepton veto	<1.0 %	<1.0 %	–	–	–	–	–	
Photon identification & isolation	–	–	–	–	–	–	2.4-12 %	
Photon reconstruction	–	–	–	–	–	–	<1.0 %	
Pileup	1.4-8.8 %	<1.0-4.5 %	<1.0-4.8 %	<1.0-4.7 %	<1.0-2.1 %	<1.0-7.9 %	<1.0-3.3 %	
Trigger inefficiency	<1.0-12 %	<1.0-1.4 %	<1.0-3.4 %	<1.0-2.4 %	<1.0-1.6 %	<1.0-1.5 %	<1.0-0.3 %	
Trigger	2.0 %	2.0 %	2.0 %	2.0 %	2.0 %	2.0 %	2.0 %	
Tau lepton veto	<1.0 %	<1.0 %	<1.0-1.0 %	<1.0-2.4 %	<1.0 %	<1.0 %	<1.0 %	
JER	2.4-3.6 %	<1.0-1.1 %	1.7-3.0 %	<1.0-1.5 %	<1.0-3.5 %	<1.0-1.4 %	<1.0-2.9 %	
JES	<1.0-6.3 %	<1.0-2.9 %	<1.0-5.0 %	<1.0-2.2 %	<1.0-6.7 %	<1.0-2.8 %	<1.0-3.8 %	
QCD prediction	100 %	100 %	–	–	–	–	–	

Results

The hadronic recoil distributions across all tt¯H and VH subcategories are shown in Figs. 2, 3, 4 and 5. The predicted background yield from the fit to the CRs only is shown with the result of a fit including the data in the SR. The agreement between the data and simulation is presented below each distribution, with the uncertainty in the predicted background uncertainty (Bkg. unc.) accounting for both systematic and simulated statistical contributions. Figures 2 (3) shows the μ+jets (e+jets) CR yields for the tt¯H and VH categories, respectively, aggregated over 2016–2018. In these CRs, ℓlost background from t t¯, W→ℓν, and single t quark production dominates, with smaller contributions from multiboson and tt¯X processes. The μμ+ jets, ee + jets, ℓℓ+jets (only for tt¯H), and γ+jets (only for VH) CR distributions used for the prediction of backgrounds stemming from Z→inv decays are shown in Fig. 4 for 2016–2018. In addition, the total SM background prediction in the SR, consisting of ℓlost, Z→inv, and QCD backgrounds, is shown for the tt¯H and VH category in Fig. 5. The SR distributions contain all the Higgs boson production modes in the fitted B(H→inv) signal, including the ggH and VBF contamination in the tt¯H and VH categories, with the prevalence of the ggH process due to its high production cross section. The post-fit event yields for each subcategory and recoil bin in the SR are tabulated in Table 6. For these results, a fit assuming B(H→inv) =0 such that only SM background contributions are considered (B-only) is performed simultaneously using only the CRs (CR only), which are independent of the SR, or across both SR and CRs (CR+SR). A fit across all regions, including signal and background contributions (S+B fit), is also performed, in which the signal contribution is weighted by the best-fit signal strength, B(H→inv). In all cases, uncertainties are inclusive of statistical and systematic contributions.Fig. 2 Distributions of hadronic recoil in the tt¯H (upper plot) and VH (lower plot) categories for the μ+jets CR. The black histogram shows the total background (bkg.) prediction from a CR only, B-only fit, while the red histogram shows the yields from a CR + SR S + B fit. The uncertainty in the predicted background (Bkg. unc.) accounts for both systematic and simulated statistical contributions

Fig. 3 Distributions of hadronic recoil in the tt¯H (upper plot) and VH (lower plot) categories for the e+jets CR. The black histogram shows the total background (bkg.) prediction from a CR only, B-only fit, while the red histogram shows the yields from a CR + SR S + B fit. The uncertainty in the predicted background (Bkg. unc.) accounts for both systematic and simulated statistical contributions

Fig. 4 Distributions of hadronic recoil in the tt¯H category for the μμ+ jets, ee + jets, and ℓℓ+jets CRs (upper plot), and the VH category for the μμ+ jets, ee + jets, and γ+jets CRs (lower plot). The black histogram shows the total background (bkg.) prediction from a CR only, B-only fit, while the red histogram shows the yields from a CR + SR S + B fit. The uncertainty in the predicted background (Bkg. unc.) accounts for both systematic and simulated statistical contributions

Fig. 5 Distributions of hadronic recoil in the tt¯H (upper plot) and VH (lower plot) categories for the SR, showing the signal contributions from tt¯H, VH, ggH, and VBF weighted by B(H→inv)=0.07. The black histogram shows the total background (bkg.) prediction from a CR only, B-only fit, while the red histogram shows the yields from a CR + SR S + B fit. The uncertainty in the predicted background (Bkg. unc.) accounts for both systematic and simulated statistical contributions

Table 6 Total post-fit yields in the SRs in each recoil bin and analysis category obtained by summing the contributions from the individual data-taking periods. B-only fits are performed for either CR+SR or CR only cases. The extracted signal yields from an S+B fit are also reported, where the signal strength is weighted by B(H→inv)=0.07

Subcategory	Hadronic recoil	ℓlost	Z→inv	QCD	Total background	Data	Signal	
		CR only	CR only	CR only	CR only	CR + SR		B(H→inv)=0.07	
		B-only fit	B-only fit	B-only fit	B-only fit	B-only fit		S+B fit	
tt¯H 1t1b	[200, 300)	251.1 ± 9.5	35.2 ± 4.1	23.1 ± 16.8	309.4 ± 19.8	295.5 ± 11.6	288.0 ± 17.0	1.0 ± 0.8	
	[300, 400)	235.2 ± 9.5	35.7 ± 5.0	5.2 ± 4.2	276.1 ± 11.5	268.1 ± 9.1	257.0 ± 16.0	1.3 ± 1.0	
	[400, 500)	97.5 ± 5.3	27.6 ± 4.9	0.9 ± 0.6	126.1 ± 7.2	135.5 ± 6.7	145.0 ± 12.0	1.0 ± 0.8	
	[500, ∞)	37.5 ± 2.9	26.1 ± 4.9	0.3 ± 0.3	63.9 ± 5.7	70.1 ± 5.1	66.0 ± 8.1	0.9 ± 0.7	
tt¯H 1t2b	[200, 300)	312.5 ± 12.0	19.0 ± 2.2	10.9 ± 8.6	342.4 ± 14.9	328.1 ± 10.5	298.0 ± 17.3	1.4 ± 1.2	
	[300, 400)	265.9 ± 10.7	20.2 ± 2.7	2.5 ± 1.7	288.6 ± 11.2	287.1 ± 9.3	299.0 ± 17.3	1.6 ± 1.3	
	[400, 500)	93.6 ± 5.1	15.4 ± 2.6	0.4 ± 0.3	109.5 ± 5.7	116.5 ± 5.2	136.0 ± 11.7	1.2 ± 0.9	
	[500, ∞)	35.4 ± 2.9	13.8 ± 2.5	0.2 ± <0.1	49.4 ± 3.9	52.8 ± 3.5	53.0 ± 7.3	1.0 ± 0.8	
tt¯H 1W1b	[200, 300)	1704.6 ± 49.9	190.7 ± 21.2	18.8 ± 16.8	1914.1 ± 56.8	1855.7 ± 41.2	1819.0 ± 42.6	5.7 ± 4.0	
	[300, 400)	395.6 ± 15.1	90.2 ± 12.7	4.3 ± 2.9	490.0 ± 19.9	485.0 ± 16.2	486.0 ± 22.0	2.9 ± 1.9	
	[400, 500)	56.2 ± 3.9	35.8 ± 6.5	0.8 ± 0.5	92.7 ± 7.7	103.7 ± 7.1	111.0 ± 10.5	0.9 ± 0.6	
	[500, ∞)	9.9 ± 1.3	13.9 ± 2.9	0.3 ± <0.1	24.1 ± 3.2	29.5 ± 3.0	37.0 ± 6.1	0.4 ± 0.3	
tt¯H 1W2b	[200, 300)	1295.8 ± 40.7	53.1 ± 5.7	5.6 ± 3.8	1354.5 ± 41.3	1311.6 ± 29.4	1276.0 ± 35.7	3.9 ± 3.2	
	[300, 400)	266.2 ± 11.8	27.2 ± 3.8	1.3 ± 0.9	294.7 ± 12.4	291.3 ± 9.9	298.0 ± 17.3	1.9 ± 1.6	
	[400, 500)	38.3 ± 3.3	8.1 ± 1.5	0.2 ± <0.1	46.6 ± 3.7	47.6 ± 3.1	47.0 ± 6.9	0.6 ± 0.4	
	[500, ∞)	6.0 ± 1.0	3.7 ± 0.7	0.1 ± <0.1	9.9 ± 1.2	11.3 ± 1.1	17.0 ± 4.1	0.2 ± <0.1	
tt¯H 2Boosted1b	[200, 300)	20.2 ± 3.6	3.8 ± 0.4	0.3 ± 0.3	24.3 ± 3.6	20.4 ± 2.6	14.0 ± 3.7	0.5 ± 0.3	
	[300, ∞)	6.3 ± 1.4	6.1 ± 0.9	0.1 ± <0.1	12.5 ± 1.7	12.9 ± 1.6	15.0 ± 3.9	0.5 ± 0.4	
tt¯H 2Boosted2b	[200, 300)	15.8 ± 2.9	3.9 ± 0.9	0.3 ± <0.1	20.0 ± 3.1	18.0 ± 2.4	15.0 ± 3.9	0.4 ± 0.3	
	[300, ∞)	5.4 ± 1.3	3.8 ± 0.5	0.1 ± <0.1	9.3 ± 1.4	8.6 ± 1.1	6.0 ± 2.4	0.5 ± 0.4	
tt¯H 5j1b	[200, 300)	5279.7 ± 114.4	1703.7 ± 82.8	99.1 ± 78.5	7082.4 ± 161.6	7122.6 ± 127.6	7207.0 ± 84.9	14.4 ± 7.7	
	[300, 400)	1135.0 ± 31.8	836.4 ± 50.0	22.5 ± 17.3	1994.0 ± 61.7	1960.9 ± 43.2	1907.0 ± 43.7	7.4 ± 3.8	
	[400, 500)	182.2 ± 9.0	267.5 ± 24.9	4.0 ± 2.8	453.6 ± 26.6	438.8 ± 16.2	427.0 ± 20.7	2.7 ± 1.4	
	[500, ∞)	54.2 ± 3.7	146.0 ± 20.3	1.5 ± 1.0	201.7 ± 20.6	226.2 ± 11.5	221.0 ± 14.9	1.5 ± 0.8	
tt¯H 5j2b	[200, 300)	1317.8 ± 47.3	350.0 ± 16.6	11.8 ± 8.5	1679.6 ± 50.9	1635.4 ± 33.9	1602.0 ± 40.0	6.3 ± 4.2	
	[300, 400)	188.7 ± 9.2	174.1 ± 10.4	2.7 ± 2.0	365.5 ± 14.1	363.3 ± 10.7	367.0 ± 19.2	2.9 ± 1.8	
	[400, 500)	33.6 ± 3.5	53.8 ± 5.1	0.5 ± 0.3	87.9 ± 6.2	86.3 ± 4.5	91.0 ± 9.5	0.9 ± 0.5	
	[500, ∞)	8.2 ± 1.4	24.6 ± 3.5	0.2 ± <0.1	33.0 ± 3.8	36.8 ± 2.5	36.0 ± 6.0	0.5 ± 0.3	
tt¯H 6j1b	[200, 300)	3851.5 ± 87.9	805.5 ± 38.8	85.9 ± 66.3	4742.9 ± 116.7	4672.6 ± 87.1	4632.0 ± 68.1	12.3 ± 8.1	
	[300, 400)	876.0 ± 27.5	438.8 ± 26.1	19.5 ± 13.4	1334.2 ± 40.2	1332.5 ± 30.4	1371.0 ± 37.0	6.7 ± 4.0	
	[400, 500)	179.6 ± 8.5	162.8 ± 15.4	3.4 ± 2.5	345.9 ± 17.8	330.9 ± 11.4	312.0 ± 17.7	2.4 ± 1.4	
	[500, ∞)	61.0 ± 4.0	98.2 ± 13.6	1.3 ± 1.0	160.5 ± 14.3	179.1 ± 8.4	197.0 ± 14.0	1.6 ± 0.8	
tt¯H 6j2b	[200, 300)	1214.0 ± 38.7	237.2 ± 11.4	15.6 ± 12.0	1466.8 ± 42.1	1433.1 ± 29.9	1404.0 ± 37.5	7.8 ± 6.1	
	[300, 400)	237.9 ± 12.0	118.8 ± 7.1	3.6 ± 2.9	360.3 ± 14.2	351.9 ± 10.8	341.0 ± 18.5	3.8 ± 2.9	
	[400, 500)	38.8 ± 3.8	40.9 ± 4.0	0.6 ± 0.4	80.3 ± 5.6	79.9 ± 4.3	91.0 ± 9.5	1.4 ± 1.0	
	[500, ∞)	12.9 ± 1.7	21.6 ± 3.0	0.2 ± <0.1	34.7 ± 3.5	38.1 ± 2.4	41.0 ± 6.4	0.7 ± 0.4	
VH 2j0b	[200, 300)	17753.9 ± 373.6	29102.3 ± 655.5	105.8 ± 68.3	46962.1 ± 757.6	47499.1 ± 460.7	47559.0 ± 218.1	185.6 ± 92.5	
	[300, 400)	2535.2 ± 69.4	5505.3 ± 155.0	16.8 ± 12.0	8057.3 ± 170.3	8075.7 ± 106.8	8106.0 ± 90.0	44.3 ± 23.0	
	[400, 500)	278.9 ± 16.1	684.1 ± 34.7	2.8 ± 1.8	965.8 ± 38.3	944.5 ± 26.7	938.0 ± 30.6	6.6 ± 3.4	
	[500, ∞)	19.2 ± 3.1	76.9 ± 8.1	0.9 ± 0.5	97.1 ± 8.7	95.7 ± 6.6	98.0 ± 9.9	0.6 ± 0.3	
VH 2j1b	[200, 300)	3020.1 ± 84.0	2490.4 ± 114.7	26.2 ± 24.5	5536.8 ± 144.3	5808.6 ± 111.1	5883.0 ± 76.7	20.3 ± 10.0	
	[300, 400)	360.1 ± 17.3	609.0 ± 44.1	3.6 ± 3.0	972.7 ± 47.5	962.3 ± 30.1	949.0 ± 30.8	5.2 ± 2.8	
	[400, ∞)	36.3 ± 4.5	66.7 ± 7.3	0.6 ± 0.5	103.7 ± 8.6	111.3 ± 7.7	120.0 ± 11.0	0.7 ± 0.4	
VH 2j2b	[200, 300)	209.4 ± 14.0	422.3 ± 46.6	2.0 ± 1.2	633.7 ± 48.6	620.1 ± 26.8	617.0 ± 24.8	10.8 ± 7.9	
	[300, ∞)	30.7 ± 3.5	102.6 ± 15.4	0.2 ± <0.1	133.6 ± 15.8	131.1 ± 9.8	128.0 ± 11.3	3.5 ± 2.5	

Fig. 6 Left: observed and expected limits at 95% CL for the tt¯H and VH categories using 2016–2018 data. Right: the profile likelihood scan corresponding to observed and expected (where B(H→inv)=0) limits in the fit to the tt¯H and VH categories

The best-fit value for μ^ and corresponding 68 and 95% CL confidence intervals are extracted following the procedure outlined in Refs. [87, 88]. The computing of upper limits adheres to the CLs criterion [89, 90] under the asymptotic approximation [83]. The upper limits on B(H→inv) as extracted from the likelihood fit presented in Sect. 7.1 are found to be 0.43 (0.52 expected) and 0.74 (0.53 expected) at 95% CL for the tt¯H and VH categories, respectively, with a combined upper limit of 0.54 (0.39 expected). These results are shown in Fig. 6 together with the observed and expected profile likelihood distribution. The expected distribution assumes B(H→inv)=0. The results are compatible with the background expectation. The best-fit B(H→inv) for the tt¯H and VH categories is μ^=0.07-0.10+0.10(stat.) -0.17+0.18(syst.) (0.00-0.10+0.10(stat.) -0.16+0.17(syst.) expected), where the pre-fit normalisation assumes that B(H→inv) =1. The systematic uncertainty with the largest impact on the B(H→inv) measurement for the tt¯H and VH categories using 2016–2018 data are those associated with the JES, while the statistical uncertainty contributes significantly to the overall uncertainty on B(H→inv). The breakdown of the impacts into uncertainty groups are presented in Table 7, together with the expectation assuming B(H→inv) =0. The best-fit estimate for the tt¯H (VH) category is μ^=-0.16-0.26+0.26 (0.00-0.25+0.26) (μ^=0.28-0.27+0.27 (0.00-0.26+0.27)).

Combined H→inv limits

A variety of production modes of the Higgs boson can be used for searches for H→inv decays. A combination of the results of this analysis, analyses covering the years 2016–2018, and earlier published CMS combination results using Run 1 (years 2011–2012) and 2015 data [30] at s=7,8,and 13TeV, detailed in Table 8, is performed by means of a combined likelihood fit in which systematic uncertainties are correlated across search regions where appropriate. Unless explicitly specified below, parameters of the individual likelihood functions are treated as independent.Table 7 The observed and expected impacts on B(H→inv) for different groups of uncertainties, where the expected results are produced with B(H→inv) =0

Uncertainty group	Impact on B(H→inv)	
Observed	Expected	
Jet energy calibration	±0.11	±0.11	
Lepton veto	±0.05	-0.04+0.05	
Lepton/photon identification	±0.06	±0.06	
Theory	-0.06+0.07	-0.05+0.06	
Integrated luminosity/pileup	±0.02	-0.03+0.02	
QCD prediction	±0.02	±0.02	
Boosted object/b jet tagging	±0.02	±0.02	
Triggers	±0.04	±0.03	
Stat. uncertainty of simulation	±0.08	±0.08	
Stat. uncertainty in data	±0.10	±0.10	

Table 8 Data sets and their respective integrated luminosities used for each production mode across Run 1 and Run 2. For some data-taking periods, no H→inv search have been performed for the given production mode, and are not included in the combination

Analysis tag	Production mode	Integrated luminosity (fb-1)	
		7TeV	8TeV	13TeV (Run 2)	
VBF-tagged	VBF	–	19.2 [91]	140 [30, 36]	
VH-tagged	Z(ℓℓ)H	4.9 [91]	19.7 [91]	140 [30, 34]	
Z(bb¯)H	–	18.9 [91]	–	
V(jj)H	–	19.7 [92]	140 [30], [this paper]	
Boosted VH	–	–	138 [35]	
tt¯H-tagged	tt¯H (hadronic)	–	–	138 [this paper]	
tt¯H (leptonic)	–	–	138 [31, 32]	
ggH-tagged	ggH	–	19.7 [92]	140 [30, 35]	

For the tt¯H analysis with fully leptonic final states, a reinterpretation of the supersymmetry searches in the semileptonic and dileptonic t t¯ decay channels in Refs. [31, 32] in the context of the t t¯  + DM model studied in Ref. [33] has been performed. Another leptonic channel included in this combination is from the Z(ℓℓ)H analysis [34] using 2016–2018 data.

Analyses with hadronic final states partially overlap in their phase space selection, and this must be accounted for in the statistical combination. Those affected by overlap are the VBF analysis [36], the analysis targetting hadronic ggH and boosted VH final states [35], and the resolved VH channel described in this paper.

To remove the overlap between the VBF analysis and ggH/boosted VH analysis, events are considered for rejection in the ggH/boosted VH analysis if they have at least two AK4 jets each with |η|<4.7. Specifically, an inversion of the VBF kinematic selection is applied similarly to the tt¯H and resolved VH analysis as described in Sect. 5.2. These requirements mirror the selection used to enhance the characteristic VBF phase space in Ref. [36], with negligible effect on the sensitivity of the ggH/boosted VH analysis to B(H→inv).

The overlap between the ggH/boosted VH analysis and the VH 2j0b category of this analysis is driven by the low-purity VH category of the boosted analysis. By removing events from the low-purity boosted VH category that contain exactly two AK4 jets forming a dijet candidate with 65<mjj<120GeV, there is negligible reduction in the exclusion sensitivity of that analysis. The overlap meanwhile is reduced from 30-40% in the CR phase spaces to about 1%.

The uncertainties in the overall cross section for the signal processes are treated as correlated amongst analysis channels, and amongst data sets with the same centre-of-mass energy. The uncertainties related to missing higher-order corrections, as well as PDF variations, are obtained from Ref. [60]. In some of the channels, additional uncertainty contributions relating to signal acceptance modelling are considered. These are treated as uncorrelated amongst the different analysis channels.

The main sources of theoretical modelling uncertainties in the background estimate vary for the different analysis channels. The analyses preferentially select different phase space regions, and employ different assumptions for the modelling of theoretical uncertainties in transfer factors amongst different analysis regions. The resulting uncertainties are therefore treated as uncorrelated.

Significant correlations appear in the treatment of experimental uncertainties. The determination of the integrated luminosity estimate is affected by a number of sources of uncertainty, which are assumed to be correlated amongst all channels, and partially correlated amongst data sets. Some of the analysis channels share trigger requirements, and the uncertainties in the efficiencies of these common triggers are assumed to be correlated amongst channels and uncorrelated amongst data sets. Furthermore, analysis channels often share criteria used for identifying b-tagged jets, as well as the hadronic decay products of tau leptons. The uncertainties in the efficiencies of these identification criteria are assumed to be correlated amongst channels using the same criteria in the same data set. Finally, uncertainties in the calibration of the JER and JES are treated as correlated amongst this analysis, the VBF, and the ggH/boosted VH channels. All other experimental uncertainties are assumed to be uncorrelated amongst channels. For earlier analyses using Run 1 and 2015 data, the correlation scheme established in Ref. [30] is used.

Exclusion limits on B(H→inv) are calculated assuming SM production cross sections. The 2016–2018 data yields an overall limit of 0.16 (0.09 expected). If the Run 1 and 2015 data-taking periods are included, values larger than 0.15 (0.08 expected) are excluded at 95% CL. This value is dominated by the VBF channel, which yields a limit for B(H→inv) of 0.18 (0.10 expected). The limits for Run 1 and Run 2, separated by the Higgs boson production mode as tagged by the input analyses, are presented in Fig. 7. The integrated luminosities of the Run 1 and Run 2 data sets [30, 33–36] are described in Table 8. The final combination represents an improvement in sensitivity of approximately 20% relative to the most sensitive single channel (VBF).

Maximum likelihood fits to the individual production channels are performed, as well as to the combination of all channels. The dependence of the profile negative log-likelihood functions on the signal strength parameter μ^ is shown in Fig. 7 (right). The best-fit values of μ^ for the individual production channels are compatible with one another and with the combined value of 0.08-0.04+0.04, and the observed signal strength is compatible with the absence of a H→inv signal within two standard deviations. A breakdown of the best-fit values of μ^ for each channel are presented in Table 9. A saturated goodness-of-fit test is performed using the final combined likelihood function [93], yielding a probability of 12% that the S+B model is consistent with the observed results from the CMS experiment. Tabulated yields and fit results are provided in HEPData [94].Table 9 The observed best-fit estimates of B(H→inv), for each analysis channel in the combination, and the 95% CL observed and expected (exp) upper limits on B(H→inv)

Channel	Best-fit B(H→inv)	B(H→inv)	
Combined	0.08-0.04+0.04	0.15 (0.08 exp)	
VBF-tag	0.09-0.05+0.05	0.18 (0.10 exp)	
VH-tag	0.07-0.09+0.09	0.24 (0.18 exp)	
tt¯H-tag	-0.11-0.15+0.15	0.25 (0.30 exp)	
ggH-tag	0.22-0.16+0.16	0.49 (0.32 exp)	

Fig. 7 Top: exclusion limits at 95% CL on B(H→inv). The results are shown separately for each Higgs boson production mode as tagged by the input analyses for Run 1 and Run 2, as well as combined across modes. Bottom: scan of the profile negative log-likelihood as a function of B(H→inv) broken down by the Higgs boson production mode as tagged by the input analyses for Run 1 and Run 2

The upper limit on B(H→inv) is interpreted in the context of a set of Higgs portal models of DM interactions, where a stable weakly interacting massive particle (WIMP), such as a singlet scalar, fermion, or vector, has a substantial coupling to a Higgs boson of mass 125GeV  [19, 20]. The interaction of a WIMP with an atomic nucleus can occur via the exchange of a Higgs boson, and the resulting nuclear recoil is measured to obtain an upper bound on the spin-independent DM-nucleon scattering cross section, σDM-nucleonSI. An effective field theory (EFT) approach is considered for scalar and fermionic WIMPs, while in the vectorial case two UV-complete DM models are considered, given the EFT appraoch violates unitarity [23, 95]. The vector-spin WIMP model (Vector DMUV-comp) described in Ref. [20], and its radiative portal analogue (Vector DMm2radiative) introduced in Ref. [23] for dark Higgs boson masses m2=65 and 100GeV, and with a mixing angle between the SM and dark Higgs bosons θ=0.2, are presented. The results are compared to direct-detection searches, where in these experiments it is assumed DM particles interact with atomic nuclei. Direct-detection limits are reported by the XENON1T-Migdal [96], DarkSide-50 [97], Panda-X 4T [98], and LUX-ZEPLIN [99] experiments. Upper limits on σDM-nucleonSI for DM masses ranging from 0.1GeV to mH/2 are presented in Fig. 8 at the 90% CL using the full CMS data set. The uncertainties in σDM-nucleonSI are obtained from the extrema of a coupling parametrisation factor as derived from lattice theory [19, 100, 101]. Results of the Higgs portal interpretation and direct-detection comparison are also provided in HEPData [94].Fig. 8 Upper limits on σDM-nucleonSI as a function of DM candidate mass mDM. Results are presented for a fermion (red) and scalar (yellow) DM candidate. In addition, a vector DM candidate is studied using two UV-complete approaches, the first denoted Vector DMUV-complete [20] (burgundy), and the second a radiative portal version denoted Vector DMm2radiative [23] (orange) with a dark Higgs boson mass of m2=65 and 100GeV. Uncertainties are derived from Refs. [19, 100, 101]. Results are compared to direct-detection searches from XENON1T-Migdal [96], DarkSide-50 [97], PandaX-4T [98], and LUX-ZEPLIN [99]

The sensitivity of the Run 1 and Run 2 combination depends on the cross sections assumed for the different Higgs boson production modes: VBF, VH, ggH, and tt¯H. Cross sections can be parameterised by the coupling strength of the Higgs boson to V bosons and fermions. The cross sections can be directly scaled by coupling strength modifiers κV and κF to investigate BSM scenarios [102]. In this context, the observed 95% CL upper limits on B(H→inv) are evaluated as a function of κV and κF and shown in Fig. 9. Best estimates of κV and κF from CMS [11] are presented with the 68 and 95% CL contours. For the best estimate of κV and κF by CMS, the 95% CL limit on B(H→inv) is found to be 0.15 and varies between 0.13 and 0.17 inside the 95% CL contour.Fig. 9 Observed 95% CL upper limit on B(H→inv) as a function of coupling strength modifiers, κV and κF, for a Higgs boson of mass 125GeV. Best estimates for κV and κF from Ref. [11] are shown as a black cross, together with 68 and 95% CL contours

Summary

The results of a search for invisible decays of the Higgs boson produced in association with a top-antitop quark pair (tt¯H) or a vector boson (VH, where V stands for either a W or Z boson), which decays to a fully hadronic final state, are presented. The analysis is based on proton-proton collision data collected at s=13TeV during the 2016–2018 data-taking period by the CMS experiment at the LHC, corresponding to an integrated luminosity of 138fb-1. The tt¯H production mechanism is investigated using final states containing b jets, or boosted t quarks or W bosons. The VH production channel focuses on resolving a dijet pair with an invariant mass that is compatible with that of a W or Z boson. No significant excess of events is observed above the predicted SM background. A 95% confidence level upper limit of 0.54 (0.39 expected) is set on the branching fraction of the decay of the Higgs boson to an invisible final state, B(H→inv), assuming SM production cross sections.

The results are combined with previous B(H→inv) searches carried out at s=7, 8, and 13TeV in complementary production modes. The combined 95% confidence level upper limit on B(H→inv) of 0.15 (0.08 expected) is obtained using Run 1 (2011–2012) and Run 2 (2015–2018) data. The combination represents an improvement in sensitivity of 20% relative to the most sensitive single channel. The results are interpreted in the context of a set of Higgs portal models of dark matter interactions for dark matter masses in the range 0.1GeV and mH/2. Model-dependent exclusion limits are found to complement direct-detection experiments for light mass dark matter candidates.

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 centres and personnel of the Worldwide LHC Computing Grid and other centres 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: BMBWF and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, FAPERGS, and FAPESP (Brazil); MES and BNSF (Bulgaria); CERN; CAS, MoST, and NSFC (China); MINCIENCIAS (Colombia); MSES and CSF (Croatia); RIF (Cyprus); SENESCYT (Ecuador); MoER, ERC PUT and ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRI (Greece); NKFIH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Republic of Korea); MES (Latvia); LAS (Lithuania); MOE and UM (Malaysia); BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MOS (Montenegro); MBIE (New Zealand); PAEC (Pakistan); MES and NSC (Poland); FCT (Portugal); MESTD (Serbia); MCIN/AEI and PCTI (Spain); MOSTR (Sri Lanka); Swiss Funding Agencies (Switzerland); MST (Taipei); MHESI and NSTDA (Thailand); TUBITAK and TENMAK (Turkey); NASU (Ukraine); STFC (United Kingdom); DOE and NSF (USA). Individuals have received support from the Marie-Curie programme and the European Research Council and Horizon 2020 Grant, contract Nos. 675440, 724704, 752730, 758316, 765710, 824093, 884104, and COST Action CA16108 (European Union); the Leventis Foundation; the Alfred P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the F.R.S.-FNRS and FWO (Belgium) under the “Excellence of Science – EOS” – be.h project n. 30820817; the Beijing Municipal Science & Technology Commission, No. Z191100007219010; the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Hellenic Foundation for Research and Innovation (HFRI), Project Number 2288 (Greece); the Deutsche Forschungsgemeinschaft (DFG), under Germany’s Excellence Strategy – EXC 2121 “Quantum Universe” – 390833306, and under project number 400140256 - GRK2497; the Hungarian Academy of Sciences, the New National Excellence Program - ÚNKP, the NKFIH research grants K 124845, K 124850, K 128713, K 128786, K 129058, K 131991, K 133046, K 138136, K 143460, K 143477, 2020-2.2.1-ED-2021-00181, and TKP2021-NKTA-64 (Hungary); the Council of Science and Industrial Research, India; the Latvian Council of Science; the Ministry of Education and Science, project no. 2022/WK/14, and the National Science Center, contracts Opus 2021/41/B/ST2/01369 and 2021/43/B/ST2/01552 (Poland); the Fundação para a Ciência e a Tecnologia, grant CEECIND/01334/2018 (Portugal); the National Priorities Research Program by Qatar National Research Fund; MCIN/AEI/10.13039/501100011033, ERDF “a way of making Europe”, and the Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia María de Maeztu, grant MDM-2017-0765 and Programa Severo Ochoa del Principado de Asturias (Spain); the Chulalongkorn Academic into Its 2nd Century Project Advancement Project, and the National Science, Research and Innovation Fund via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation, grant B05F650021 (Thailand); the Kavli Foundation; the Nvidia Corporation; the SuperMicro Corporation; the Welch Foundation, contract C-1845; and the Weston Havens Foundation (USA).

Data Availability

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

Declarations

Conflict of interest

The authors declare that they have no conflict of interest.

T. Tuuva, N. Tonon, P. Baillon, G.R. Snow, A. Vorobyev: Deceased.
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