https://doi.org/10.1140/epjc/s10052-023-11582-z
Regular Article - Experimental Physics
Search for dark matter produced in association with a single top quark and an energetic W boson in 
13 TeV 
collisions with the ATLAS detector
1
Department of Physics, University of Adelaide, Adelaide, Australia
2
Department of Physics, University of Alberta, Edmonton, AB, Canada
3
Department of Physics, Ankara University, Ankara, Türkiye
4
Division of Physics, TOBB University of Economics and Technology, Ankara, Türkiye
5
LAPP, Université Savoie Mont Blanc, CNRS/IN2P3, Annecy, France
6
APC, Université Paris Cité, CNRS/IN2P3, Paris, France
7
High Energy Physics Division, Argonne National Laboratory, Argonne, IL, USA
8
Department of Physics, University of Arizona, Tucson, AZ, USA
9
Department of Physics, University of Texas at Arlington, Arlington, TX, USA
10
Physics Department, National and Kapodistrian University of Athens, Athens, Greece
11
Physics Department, National Technical University of Athens, Zografou, Greece
12
Department of Physics, University of Texas at Austin, Austin, TX, USA
13
Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan
14
Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona, Spain
15
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China
16
Physics Department, Tsinghua University, Beijing, China
17
Department of Physics, Nanjing University, Nanjing, China
18
University of Chinese Academy of Science (UCAS), Beijing, China
19
Institute of Physics, University of Belgrade, Belgrade, Serbia
20
Department for Physics and Technology, University of Bergen, Bergen, Norway
21
Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
22
University of California, Berkeley, CA, USA
23
Institut für Physik, Humboldt Universität zu Berlin, Berlin, Germany
24
Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern, Switzerland
25
School of Physics and Astronomy, University of Birmingham, Birmingham, UK
26
Department of Physics, Bogazici University, Istanbul, Türkiye
27
Department of Physics Engineering, Gaziantep University, Gaziantep, Türkiye
28
Department of Physics, Istanbul University, Istanbul, Türkiye
29
Istinye University, Sariyer, Istanbul, Türkiye
30
Facultad de Ciencias y Centro de Investigaciónes, Universidad Antonio Nariño, Bogotá, Colombia
31
Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia
32
Dipartimento di Fisica e Astronomia A. Righi, Università di Bologna, Bologna, Italy
33
INFN Sezione di Bologna, Bologna, Italy
34
Physikalisches Institut, Universität Bonn, Bonn, Germany
35
Department of Physics, Boston University, Boston, MA, USA
36
Department of Physics, Brandeis University, Waltham, MA, USA
37
Transilvania University of Brasov, Brasov, Romania
38
Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania
39
Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi, Romania
40
National Institute for Research and Development of Isotopic and Molecular Technologies, Physics Department, Cluj-Napoca, Romania
41
University Politehnica Bucharest, Bucharest, Romania
42
West University in Timisoara, Timisoara, Romania
43
Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovak Republic
44
Department of Subnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice, Slovak Republic
45
Physics Department, Brookhaven National Laboratory, Upton, NY, USA
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Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, y CONICET, Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
47
California State University, CA, USA
48
Cavendish Laboratory, University of Cambridge, Cambridge, UK
49
Department of Physics, University of Cape Town, Cape Town, South Africa
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iThemba Labs, Western Cape, South Africa
51
Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg, South Africa
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National Institute of Physics, University of the Philippines, Diliman, Philippines
53
University of South Africa, Department of Physics, Pretoria, South Africa
54
University of Zululand, KwaDlangezwa, South Africa
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School of Physics, University of the Witwatersrand, Johannesburg, South Africa
56
Department of Physics, Carleton University, Ottawa, ON, Canada
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Faculté des Sciences Ain Chock, Réseau Universitaire de Physique des Hautes Energies-Université Hassan II, Casablanca, Morocco
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Faculté des Sciences, Université Ibn-Tofail, Kénitra, Morocco
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Faculté des Sciences Semlalia, Université Cadi Ayyad, LPHEA-Marrakech, Morocco
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LPMR, Faculté des Sciences, Université Mohamed Premier, Oujda, Morocco
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Faculté des sciences, Université Mohammed V, Rabat, Morocco
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Institute of Applied Physics, Mohammed VI Polytechnic University, Ben Guerir, Morocco
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CERN, Geneva, Switzerland
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Affiliated with an institute covered by a cooperation agreement with CERN, Geneva, Switzerland
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Affiliated with an international laboratory covered by a cooperation agreement with CERN, Geneva, Switzerland
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Enrico Fermi Institute, University of Chicago, Chicago, IL, USA
67
LPC, Université Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand, France
68
Nevis Laboratory, Columbia University, Irvington, NY, USA
69
Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
70
Dipartimento di Fisica, Università della Calabria, Rende, Italy
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INFN Gruppo Collegato di Cosenza, Laboratori Nazionali di Frascati, Frascati, Italy
72
Physics Department, Southern Methodist University, Dallas, TX, USA
73
Physics Department, University of Texas at Dallas, Richardson, TX, USA
74
National Centre for Scientific Research “Demokritos”, Agia Paraskevi, Greece
75
Department of Physics, Stockholm University, Stockholm, Sweden
76
Oskar Klein Centre, Stockholm, Sweden
77
Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen, Germany
78
Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
79
Institut für Kern- und Teilchenphysik, Technische Universität Dresden, Dresden, Germany
80
Department of Physics, Duke University, Durham, NC, USA
81
SUPA-School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK
82
INFN e Laboratori Nazionali di Frascati, Frascati, Italy
83
Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany
84
II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany
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Département de Physique Nucléaire et Corpusculaire, Université de Genève, Geneva, Switzerland
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Dipartimento di Fisica, Università di Genova, Genoa, Italy
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INFN Sezione di Genova, Genoa, Italy
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II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany
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SUPA-School of Physics and Astronomy, University of Glasgow, Glasgow, UK
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LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble, France
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Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA, USA
92
Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei, China
93
Institute of Frontier and Interdisciplinary Science and Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University, Qingdao, China
94
School of Physics and Astronomy, Shanghai Jiao Tong University, Key Laboratory for Particle Astrophysics and Cosmology (MOE), SKLPPC, Shanghai, China
95
Tsung-Dao Lee Institute, Shanghai, China
96
Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
97
Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
98
Department of Physics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong
99
Department of Physics, University of Hong Kong, Hong Kong, China
100
Department of Physics and Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
101
Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
102
IJCLab, Université Paris-Saclay, CNRS/IN2P3, 91405, Orsay, France
103
Department of Physics, Indiana University, Bloomington, IN, USA
104
INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy
105
ICTP, Trieste, Italy
106
Dipartimento Politecnico di Ingegneria e Architettura, Università di Udine, Udine, Italy
107
INFN Sezione di Lecce, Lecce, Italy
108
Dipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy
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INFN Sezione di Milano, Milan, Italy
110
Dipartimento di Fisica, Università di Milano, Milan, Italy
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INFN Sezione di Napoli, Naples, Italy
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Dipartimento di Fisica, Università di Napoli, Naples, Italy
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INFN Sezione di Pavia, Pavia, Italy
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Dipartimento di Fisica, Università di Pavia, Pavia, Italy
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INFN Sezione di Pisa, Pisa, Italy
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Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy
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INFN Sezione di Roma, Rome, Italy
118
Dipartimento di Fisica, Sapienza Università di Roma, Rome, Italy
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INFN Sezione di Roma Tor Vergata, Rome, Italy
120
Dipartimento di Fisica, Università di Roma Tor Vergata, Rome, Italy
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INFN Sezione di Roma Tre, Rome, Italy
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Dipartimento di Matematica e Fisica, Università Roma Tre, Rome, Italy
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INFN-TIFPA, Povo, Italy
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Università degli Studi di Trento, Trento, Italy
125
Department of Astro and Particle Physics, Universität Innsbruck, Innsbruck, Austria
126
University of Iowa, Iowa City, IA, USA
127
Department of Physics and Astronomy, Iowa State University, Ames, IA, USA
128
Departamento de Engenharia Elétrica, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil
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Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil
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Instituto de Física, Universidade de São Paulo, São Paulo, Brazil
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Rio de Janeiro State University, Rio de Janeiro, Brazil
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KEK, High Energy Accelerator Research Organization, Tsukuba, Japan
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Graduate School of Science, Kobe University, Kobe, Japan
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Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland
135
Marian Smoluchowski Institute of Physics, Jagiellonian University, Krakow, Poland
136
Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland
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Faculty of Science, Kyoto University, Kyoto, Japan
138
Kyoto University of Education, Kyoto, Japan
139
Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka, Japan
140
Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina
141
Physics Department, Lancaster University, Lancaster, UK
142
Oliver Lodge Laboratory, University of Liverpool, Liverpool, UK
143
Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics, University of Ljubljana, Ljubljana, Slovenia
144
School of Physics and Astronomy, Queen Mary University of London, London, UK
145
Department of Physics, Royal Holloway University of London, Egham, UK
146
Department of Physics and Astronomy, University College London, London, UK
147
Louisiana Tech University, Ruston, LA, USA
148
Fysiska institutionen, Lunds universitet, Lund, Sweden
149
Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid, Spain
150
Institut für Physik, Universität Mainz, Mainz, Germany
151
School of Physics and Astronomy, University of Manchester, Manchester, UK
152
CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
153
Department of Physics, University of Massachusetts, Amherst, MA, USA
154
Department of Physics, McGill University, Montreal, QC, Canada
155
School of Physics, University of Melbourne, Victoria, Australia
156
Department of Physics, University of Michigan, Ann Arbor, MI, USA
157
Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA
158
Group of Particle Physics, University of Montreal, Montreal, QC, Canada
159
Fakultät für Physik, Ludwig-Maximilians-Universität München, Munich, Germany
160
Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Munich, Germany
161
Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan
162
Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA
163
Institute for Mathematics, Astrophysics and Particle Physics, Radboud University/Nikhef, Nijmegen, The Netherlands
164
Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, The Netherlands
165
Department of Physics, Northern Illinois University, DeKalb, IL, USA
166
New York University Abu Dhabi, Abu Dhabi, United Arab Emirates
167
University of Sharjah, Sharjah, United Arab Emirates
168
Department of Physics, New York University, New York, NY, USA
169
Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo, Japan
170
Ohio State University, Columbus, OH, USA
171
Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK, USA
172
Department of Physics, Oklahoma State University, Stillwater, OK, USA
173
Palacký University, Joint Laboratory of Optics, Olomouc, Czech Republic
174
Institute for Fundamental Science, University of Oregon, Eugene, OR, USA
175
Graduate School of Science, Osaka University, Osaka, Japan
176
Department of Physics, University of Oslo, Oslo, Norway
177
Department of Physics, Oxford University, Oxford, UK
178
LPNHE, Sorbonne Université, Université Paris Cité, CNRS/IN2P3, Paris, France
179
Department of Physics, University of Pennsylvania, Philadelphia, PA, USA
180
Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA
181
Laboratório de Instrumentação e Física Experimental de Partículas-LIP, Lisbon, Portugal
182
Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisbon, Portugal
183
Departamento de Física, Universidade de Coimbra, Coimbra, Portugal
184
Centro de Física Nuclear da Universidade de Lisboa, Lisbon, Portugal
185
Departamento de Física, Universidade do Minho, Braga, Portugal
186
Departamento de Física Teórica y del Cosmos, Universidad de Granada, Granada, Spain
187
Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal
188
Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic
189
Czech Technical University in Prague, Prague, Czech Republic
190
Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic
191
Particle Physics Department, Rutherford Appleton Laboratory, Didcot, UK
192
IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
193
Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, CA, USA
194
Departamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile
195
Millennium Institute for Subatomic Physics at High Energy Frontier (SAPHIR), Santiago, Chile
196
Instituto de Investigación Multidisciplinario en Ciencia y Tecnología y Departamento de Física, Universidad de La Serena, La Serena, Chile
197
Department of Physics, Universidad Andres Bello, Santiago, Chile
198
Instituto de Alta Investigación, Universidad de Tarapacá, Arica, Chile
199
Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile
200
Department of Physics, University of Washington, Seattle, WA, USA
201
Department of Physics and Astronomy, University of Sheffield, Sheffield, UK
202
Department of Physics, Shinshu University, Nagano, Japan
203
Department Physik, Universität Siegen, Siegen, Germany
204
Department of Physics, Simon Fraser University, Burnaby, BC, Canada
205
SLAC National Accelerator Laboratory, Stanford, CA, USA
206
Department of Physics, Royal Institute of Technology, Stockholm, Sweden
207
Departments of Physics and Astronomy, Stony Brook University, Stony Brook, NY, USA
208
Department of Physics and Astronomy, University of Sussex, Brighton, UK
209
School of Physics, University of Sydney, Sydney, Australia
210
Institute of Physics, Academia Sinica, Taipei, Taiwan
211
E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia
212
High Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia
213
University of Georgia, Tbilisi, Georgia
214
Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel
215
Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel
216
Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece
217
International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo, Japan
218
Department of Physics, Tokyo Institute of Technology, Tokyo, Japan
219
Department of Physics, University of Toronto, Toronto, ON, Canada
220
TRIUMF, Vancouver, BC, Canada
221
Department of Physics and Astronomy, York University, Toronto, ON, Canada
222
Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan
223
Department of Physics and Astronomy, Tufts University, Medford, MA, USA
224
United Arab Emirates University, Al Ain, United Arab Emirates
225
Department of Physics and Astronomy, University of California Irvine, Irvine, CA, USA
226
Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden
227
Department of Physics, University of Illinois, Urbana, IL, USA
228
Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia-CSIC, Valencia, Spain
229
Department of Physics, University of British Columbia, Vancouver, BC, Canada
230
Department of Physics and Astronomy, University of Victoria, Victoria, BC, Canada
231
Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg, Germany
232
Department of Physics, University of Warwick, Coventry, UK
233
Waseda University, Tokyo, Japan
234
Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, Israel
235
Department of Physics, University of Wisconsin, Madison, WI, USA
236
Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal, Germany
237
Department of Physics, Yale University, New Haven, CT, USA
238
Affiliated with an institute covered by a cooperation agreement with CERN, Geneva, Switzerland
239
Borough of Manhattan Community College, City University of New York, New York, NY, USA
240
Bruno Kessler Foundation, Trento, Italy
241
Center for High Energy Physics, Peking University, Beijing, China
242
Centro Studi e Ricerche Enrico Fermi, Rome, Italy
243
CERN, Geneva, Switzerland
244
Département de Physique Nucléaire et Corpusculaire, Université de Genève, Geneva, Switzerland
245
Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spain
246
Department of Financial and Management Engineering, University of the Aegean, Chios, Greece
247
Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA
248
Department of Physics and Astronomy, University of Louisville, Louisville, KY, USA
249
Department of Physics, Ben Gurion University of the Negev, Beer Sheva, Israel
250
Department of Physics, California State University, East Bay, USA
251
Department of Physics, California State University, Sacramento, USA
252
Department of Physics, King’s College London, London, UK
253
Department of Physics, University of Fribourg, Fribourg, Switzerland
254
Department of Physics, University of Thessaly, Thessaly, Greece
255
Department of Physics, Westmont College, Santa Barbara, USA
256
Hellenic Open University, Patras, Greece
257
Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain
258
Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germany
259
Institute of Particle Physics (IPP), Toronto, Canada
260
Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan
261
Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia
262
Lawrence Livermore National Laboratory, Livermore, USA
263
Physics Department, An-Najah National University, Nablus, Palestine
264
The City College of New York, New York, NY, USA
265
The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing, China
266
TRIUMF, Vancouver, BC, Canada
267
Università di Napoli Parthenope, Naples, Italy
268
University of Chinese Academy of Sciences (UCAS), Beijing, China
269
Department of Physics, University of Colorado Boulder, Colorado, USA
270
Physics Department, Yeditepe University, Istanbul, Türkiye
271
National Institute of Physics, University of the Philippines Diliman (Philippines), Diliman, Philippines
272
Department of Physics, Stanford University, Stanford, CA, USA
273
L2IT, Université de Toulouse, CNRS/IN2P3, UPS, Toulouse, France
274
CERN, 1211, Geneva 23, Switzerland
Received:
23
November
2022
Accepted:
28
February
2023
Published online:
12
July
2023
This paper presents a search for dark matter, 
, using events with a single top quark and an energetic W boson. The analysis is based on proton–proton collision data collected with the ATLAS experiment at 13 TeV during LHC Run 2 (2015–2018), corresponding to an integrated luminosity of 139 fb
. The search considers final states with zero or one charged lepton (electron or muon), at least one b-jet and large missing transverse momentum. In addition, a result from a previous search considering two-charged-lepton final states is included in the interpretation of the results. The data are found to be in good agreement with the Standard Model predictions and the results are interpreted in terms of 95% confidence-level exclusion limits in the context of a class of dark matter models involving an extended two-Higgs-doublet sector together with a pseudoscalar mediator particle. The search is particularly sensitive to on-shell production of the charged Higgs boson state, 
, arising from the two-Higgs-doublet mixing, and its semi-invisible decays via the mediator particle, a: 
. Signal models with masses up to 1.5 TeV and a masses up to 350 GeV are excluded assuming a 
value of 1. For masses of a of 150 (250) GeV, values up to 2 are excluded for masses between 200 (400) GeV and 1.5 TeV. Signals with values between 20 and 30 are excluded for masses between 500 and 800 GeV.
D. Bruncko, I.A. Budagov, E. Fullana Torregrosa, V. Gratchev, J. Olszowska, L. Perini, S.Yu. Sivoklokov: Deceased.
© The Author(s) 2023
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