]DeceasedAlso at ]INFN - Roma Tre, 00146 Roma, ItalyAlso at ]Coimbra
Polytechnic - ISEC, 3030-199 Coimbra, PortugalAlso at ]Physikalisches
Institut, Universität Heidelberg, Heidelberg, Germany XENON Collaboration

# First Dark Matter Search with Nuclear Recoils from the XENONnT Experiment

E. Aprile  Physics Department, Columbia University, New York, NY 10027, USA
K. Abe  Kamioka Observatory, Institute for Cosmic Ray Research, and Kavli
Institute for the Physics and Mathematics of the Universe (WPI), University of
Tokyo, Higashi-Mozumi, Kamioka, Hida, Gifu 506-1205, Japan  F. Agostini
Department of Physics and Astronomy, University of Bologna and INFN-Bologna,
40126 Bologna, Italy  S. Ahmed Maouloud  LPNHE, Sorbonne Université,
CNRS/IN2P3, 75005 Paris, France  L. Althueser<EMAIL_ADDRESS>Institut für Kernphysik, Westfälische Wilhelms-Universität Münster, 48149
Münster, Germany  B. Andrieu  LPNHE, Sorbonne Université, CNRS/IN2P3, 75005
Paris, France  E. Angelino  INAF-Astrophysical Observatory of Torino,
Department of Physics, University of Torino and INFN-Torino, 10125 Torino,
Italy  J. R. Angevaare  Nikhef and the University of Amsterdam, Science Park,
1098XG Amsterdam, Netherlands  V. C. Antochi  Oskar Klein Centre, Department
of Physics, Stockholm University, AlbaNova, Stockholm SE-10691, Sweden  D.
Antón Martin  Department of Physics & Kavli Institute for Cosmological
Physics, University of Chicago, Chicago, IL 60637, USA  F. Arneodo  New York
University Abu Dhabi - Center for Astro, Particle and Planetary Physics, Abu
Dhabi, United Arab Emirates  L. Baudis  Physik-Institut, University of Zürich,
8057 Zürich, Switzerland  A. L. Baxter  Department of Physics and Astronomy,
Purdue University, West Lafayette, IN 47907, USA  M. Bazyk  SUBATECH, IMT
Atlantique, CNRS/IN2P3, Université de Nantes, Nantes 44307, France  L.
Bellagamba  Department of Physics and Astronomy, University of Bologna and
INFN-Bologna, 40126 Bologna, Italy  R. Biondi  Max-Planck-Institut für
Kernphysik, 69117 Heidelberg, Germany  A. Bismark  Physik-Institut, University
of Zürich, 8057 Zürich, Switzerland  E. J. Brookes  Nikhef and the University
of Amsterdam, Science Park, 1098XG Amsterdam, Netherlands  A. Brown
Physikalisches Institut, Universität Freiburg, 79104 Freiburg, Germany  S.
Bruenner  Nikhef and the University of Amsterdam, Science Park, 1098XG
Amsterdam, Netherlands  G. Bruno  SUBATECH, IMT Atlantique, CNRS/IN2P3,
Université de Nantes, Nantes 44307, France  R. Budnik  Department of Particle
Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001,
Israel  T. K. Bui  Kamioka Observatory, Institute for Cosmic Ray Research, and
Kavli Institute for the Physics and Mathematics of the Universe (WPI),
University of Tokyo, Higashi-Mozumi, Kamioka, Hida, Gifu 506-1205, Japan  C.
Cai  Department of Physics & Center for High Energy Physics, Tsinghua
University, Beijing 100084, China  J. M. R. Cardoso  LIBPhys, Department of
Physics, University of Coimbra, 3004-516 Coimbra, Portugal  D. Cichon  Max-
Planck-Institut für Kernphysik, 69117 Heidelberg, Germany  A. P. Cimental
Chavez  Physik-Institut, University of Zürich, 8057 Zürich, Switzerland  A. P.
Colijn  Nikhef and the University of Amsterdam, Science Park, 1098XG
Amsterdam, Netherlands  J. Conrad  Oskar Klein Centre, Department of Physics,
Stockholm University, AlbaNova, Stockholm SE-10691, Sweden  J. J. Cuenca-
García  Physik-Institut, University of Zürich, 8057 Zürich, Switzerland  J. P.
Cussonneau  [  SUBATECH, IMT Atlantique, CNRS/IN2P3, Université de Nantes,
Nantes 44307, France  V. D’Andrea  [  INFN-Laboratori Nazionali del Gran Sasso
and Gran Sasso Science Institute, 67100 L’Aquila, Italy  M. P. Decowski
Nikhef and the University of Amsterdam, Science Park, 1098XG Amsterdam,
Netherlands  P. Di Gangi  Department of Physics and Astronomy, University of
Bologna and INFN-Bologna, 40126 Bologna, Italy  S. Di Pede  Nikhef and the
University of Amsterdam, Science Park, 1098XG Amsterdam, Netherlands  S.
Diglio  SUBATECH, IMT Atlantique, CNRS/IN2P3, Université de Nantes, Nantes
44307, France  K. Eitel  Institute for Astroparticle Physics, Karlsruhe
Institute of Technology, 76021 Karlsruhe, Germany  A. Elykov  Institute for
Astroparticle Physics, Karlsruhe Institute of Technology, 76021 Karlsruhe,
Germany  S. Farrell  Department of Physics and Astronomy, Rice University,
Houston, TX 77005, USA  A. D. Ferella  Department of Physics and Chemistry,
University of L’Aquila, 67100 L’Aquila, Italy  INFN-Laboratori Nazionali del
Gran Sasso and Gran Sasso Science Institute, 67100 L’Aquila, Italy  C. Ferrari
INFN-Laboratori Nazionali del Gran Sasso and Gran Sasso Science Institute,
67100 L’Aquila, Italy  H. Fischer  Physikalisches Institut, Universität
Freiburg, 79104 Freiburg, Germany  M. Flierman  Nikhef and the University of
Amsterdam, Science Park, 1098XG Amsterdam, Netherlands  W. Fulgione  INAF-
Astrophysical Observatory of Torino, Department of Physics, University of
Torino and INFN-Torino, 10125 Torino, Italy  INFN-Laboratori Nazionali del
Gran Sasso and Gran Sasso Science Institute, 67100 L’Aquila, Italy  C. Fuselli
Nikhef and the University of Amsterdam, Science Park, 1098XG Amsterdam,
Netherlands  P. Gaemers  Nikhef and the University of Amsterdam, Science Park,
1098XG Amsterdam, Netherlands  R. Gaior  LPNHE, Sorbonne Université,
CNRS/IN2P3, 75005 Paris, France  A. Gallo Rosso  Oskar Klein Centre,
Department of Physics, Stockholm University, AlbaNova, Stockholm SE-10691,
Sweden  M. Galloway  Physik-Institut, University of Zürich, 8057 Zürich,
Switzerland  F. Gao  Department of Physics & Center for High Energy Physics,
Tsinghua University, Beijing 100084, China  R. Glade-Beucke  Physikalisches
Institut, Universität Freiburg, 79104 Freiburg, Germany  L. Grandi  Department
of Physics & Kavli Institute for Cosmological Physics, University of Chicago,
Chicago, IL 60637, USA  J. Grigat  Physikalisches Institut, Universität
Freiburg, 79104 Freiburg, Germany  H. Guan  Department of Physics and
Astronomy, Purdue University, West Lafayette, IN 47907, USA  M. Guida  Max-
Planck-Institut für Kernphysik, 69117 Heidelberg, Germany  R. Hammann  Max-
Planck-Institut für Kernphysik, 69117 Heidelberg, Germany  A. Higuera
Department of Physics and Astronomy, Rice University, Houston, TX 77005, USA
C. Hils  Institut für Physik & Exzellenzcluster PRISMA+, Johannes Gutenberg-
Universität Mainz, 55099 Mainz, Germany  L. Hoetzsch  Max-Planck-Institut für
Kernphysik, 69117 Heidelberg, Germany  N. F. Hood  Department of Physics,
University of California San Diego, La Jolla, CA 92093, USA  J. Howlett
Physics Department, Columbia University, New York, NY 10027, USA  M. Iacovacci
Department of Physics “Ettore Pancini”, University of Napoli and INFN-Napoli,
80126 Napoli, Italy  Y. Itow  Kobayashi-Maskawa Institute for the Origin of
Particles and the Universe, and Institute for Space-Earth Environmental
Research, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602,
Japan  J. Jakob  Institut für Kernphysik, Westfälische Wilhelms-Universität
Münster, 48149 Münster, Germany  F. Joerg  Max-Planck-Institut für Kernphysik,
69117 Heidelberg, Germany  A. Joy  Oskar Klein Centre, Department of Physics,
Stockholm University, AlbaNova, Stockholm SE-10691, Sweden  N. Kato  Kamioka
Observatory, Institute for Cosmic Ray Research, and Kavli Institute for the
Physics and Mathematics of the Universe (WPI), University of Tokyo, Higashi-
Mozumi, Kamioka, Hida, Gifu 506-1205, Japan  M. Kara  Institute for
Astroparticle Physics, Karlsruhe Institute of Technology, 76021 Karlsruhe,
Germany  P. Kavrigin  Department of Particle Physics and Astrophysics,
Weizmann Institute of Science, Rehovot 7610001, Israel  S. Kazama  Kobayashi-
Maskawa Institute for the Origin of Particles and the Universe, and Institute
for Space-Earth Environmental Research, Nagoya University, Furo-cho, Chikusa-
ku, Nagoya, Aichi 464-8602, Japan  M. Kobayashi  Kobayashi-Maskawa Institute
for the Origin of Particles and the Universe, and Institute for Space-Earth
Environmental Research, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi
464-8602, Japan  G. Koltman  Department of Particle Physics and Astrophysics,
Weizmann Institute of Science, Rehovot 7610001, Israel  A. Kopec  Department
of Physics, University of California San Diego, La Jolla, CA 92093, USA  F.
Kuger  Physikalisches Institut, Universität Freiburg, 79104 Freiburg, Germany
H. Landsman  Department of Particle Physics and Astrophysics, Weizmann
Institute of Science, Rehovot 7610001, Israel  R. F. Lang  Department of
Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA  L.
Levinson  Department of Particle Physics and Astrophysics, Weizmann Institute
of Science, Rehovot 7610001, Israel  I. Li  Department of Physics and
Astronomy, Rice University, Houston, TX 77005, USA  S. Li  Department of
Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA  S.
Liang  Department of Physics and Astronomy, Rice University, Houston, TX
77005, USA  S. Lindemann  Physikalisches Institut, Universität Freiburg, 79104
Freiburg, Germany  M. Lindner  Max-Planck-Institut für Kernphysik, 69117
Heidelberg, Germany  K. Liu  Department of Physics & Center for High Energy
Physics, Tsinghua University, Beijing 100084, China  J. Loizeau  SUBATECH, IMT
Atlantique, CNRS/IN2P3, Université de Nantes, Nantes 44307, France  F.
Lombardi  Institut für Physik & Exzellenzcluster PRISMA+, Johannes Gutenberg-
Universität Mainz, 55099 Mainz, Germany  J. Long  Department of Physics &
Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL
60637, USA  J. A. M. Lopes  [  LIBPhys, Department of Physics, University of
Coimbra, 3004-516 Coimbra, Portugal  Y. Ma  Department of Physics, University
of California San Diego, La Jolla, CA 92093, USA  C. Macolino  Department of
Physics and Chemistry, University of L’Aquila, 67100 L’Aquila, Italy  INFN-
Laboratori Nazionali del Gran Sasso and Gran Sasso Science Institute, 67100
L’Aquila, Italy  J. Mahlstedt  Oskar Klein Centre, Department of Physics,
Stockholm University, AlbaNova, Stockholm SE-10691, Sweden  A. Mancuso
Department of Physics and Astronomy, University of Bologna and INFN-Bologna,
40126 Bologna, Italy  L. Manenti  New York University Abu Dhabi - Center for
Astro, Particle and Planetary Physics, Abu Dhabi, United Arab Emirates  F.
Marignetti  Department of Physics “Ettore Pancini”, University of Napoli and
INFN-Napoli, 80126 Napoli, Italy  T. Marrodán Undagoitia  Max-Planck-Institut
für Kernphysik, 69117 Heidelberg, Germany  K. Martens  Kamioka Observatory,
Institute for Cosmic Ray Research, and Kavli Institute for the Physics and
Mathematics of the Universe (WPI), University of Tokyo, Higashi-Mozumi,
Kamioka, Hida, Gifu 506-1205, Japan  J. Masbou  SUBATECH, IMT Atlantique,
CNRS/IN2P3, Université de Nantes, Nantes 44307, France  D. Masson
Physikalisches Institut, Universität Freiburg, 79104 Freiburg, Germany  E.
Masson  LPNHE, Sorbonne Université, CNRS/IN2P3, 75005 Paris, France  S.
Mastroianni  Department of Physics “Ettore Pancini”, University of Napoli and
INFN-Napoli, 80126 Napoli, Italy  M. Messina  INFN-Laboratori Nazionali del
Gran Sasso and Gran Sasso Science Institute, 67100 L’Aquila, Italy  K. Miuchi
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan  K.
Mizukoshi  Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan
A. Molinario  INAF-Astrophysical Observatory of Torino, Department of Physics,
University of Torino and INFN-Torino, 10125 Torino, Italy  S. Moriyama
Kamioka Observatory, Institute for Cosmic Ray Research, and Kavli Institute
for the Physics and Mathematics of the Universe (WPI), University of Tokyo,
Higashi-Mozumi, Kamioka, Hida, Gifu 506-1205, Japan  K. Morå
<EMAIL_ADDRESS>Physics Department, Columbia University, New
York, NY 10027, USA  Y. Mosbacher  Department of Particle Physics and
Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel  M. Murra
Physics Department, Columbia University, New York, NY 10027, USA  J. Müller
Physikalisches Institut, Universität Freiburg, 79104 Freiburg, Germany  K. Ni
Department of Physics, University of California San Diego, La Jolla, CA 92093,
USA  U. Oberlack  Institut für Physik & Exzellenzcluster PRISMA+, Johannes
Gutenberg-Universität Mainz, 55099 Mainz, Germany  B. Paetsch  Department of
Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot
7610001, Israel  J. Palacio  Max-Planck-Institut für Kernphysik, 69117
Heidelberg, Germany  R. Peres  Physik-Institut, University of Zürich, 8057
Zürich, Switzerland  C. Peters  Department of Physics and Astronomy, Rice
University, Houston, TX 77005, USA  J. Pienaar  Department of Physics & Kavli
Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637,
USA  M. Pierre  Nikhef and the University of Amsterdam, Science Park, 1098XG
Amsterdam, Netherlands  SUBATECH, IMT Atlantique, CNRS/IN2P3, Université de
Nantes, Nantes 44307, France  V. Pizzella  Max-Planck-Institut für Kernphysik,
69117 Heidelberg, Germany  G. Plante  Physics Department, Columbia University,
New York, NY 10027, USA  J. Qi  Department of Physics, University of
California San Diego, La Jolla, CA 92093, USA  J. Qin  Department of Physics
and Astronomy, Purdue University, West Lafayette, IN 47907, USA  D. Ramírez
García  Physik-Institut, University of Zürich, 8057 Zürich, Switzerland  R.
Singh  Department of Physics and Astronomy, Purdue University, West Lafayette,
IN 47907, USA  L. Sanchez  Department of Physics and Astronomy, Rice
University, Houston, TX 77005, USA  J. M. F. dos Santos  LIBPhys, Department
of Physics, University of Coimbra, 3004-516 Coimbra, Portugal  I. Sarnoff  New
York University Abu Dhabi - Center for Astro, Particle and Planetary Physics,
Abu Dhabi, United Arab Emirates  G. Sartorelli  Department of Physics and
Astronomy, University of Bologna and INFN-Bologna, 40126 Bologna, Italy  J.
Schreiner  Max-Planck-Institut für Kernphysik, 69117 Heidelberg, Germany  D.
Schulte  Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
48149 Münster, Germany  P. Schulte  Institut für Kernphysik, Westfälische
Wilhelms-Universität Münster, 48149 Münster, Germany  H. Schulze Eißing
Institut für Kernphysik, Westfälische Wilhelms-Universität Münster, 48149
Münster, Germany  M. Schumann  Physikalisches Institut, Universität Freiburg,
79104 Freiburg, Germany  L. Scotto Lavina  LPNHE, Sorbonne Université,
CNRS/IN2P3, 75005 Paris, France  M. Selvi  Department of Physics and
Astronomy, University of Bologna and INFN-Bologna, 40126 Bologna, Italy  F.
Semeria  Department of Physics and Astronomy, University of Bologna and INFN-
Bologna, 40126 Bologna, Italy  P. Shagin  Institut für Physik &
Exzellenzcluster PRISMA+, Johannes Gutenberg-Universität Mainz, 55099 Mainz,
Germany  S. Shi  Physics Department, Columbia University, New York, NY 10027,
USA  E. Shockley  Department of Physics, University of California San Diego,
La Jolla, CA 92093, USA  M. Silva  LIBPhys, Department of Physics, University
of Coimbra, 3004-516 Coimbra, Portugal  H. Simgen  Max-Planck-Institut für
Kernphysik, 69117 Heidelberg, Germany  A. Takeda  Kamioka Observatory,
Institute for Cosmic Ray Research, and Kavli Institute for the Physics and
Mathematics of the Universe (WPI), University of Tokyo, Higashi-Mozumi,
Kamioka, Hida, Gifu 506-1205, Japan  P.-L. Tan  Oskar Klein Centre, Department
of Physics, Stockholm University, AlbaNova, Stockholm SE-10691, Sweden  A.
Terliuk  [  Max-Planck-Institut für Kernphysik, 69117 Heidelberg, Germany  D.
Thers  SUBATECH, IMT Atlantique, CNRS/IN2P3, Université de Nantes, Nantes
44307, France  F. Toschi  Institute for Astroparticle Physics, Karlsruhe
Institute of Technology, 76021 Karlsruhe, Germany  Physikalisches Institut,
Universität Freiburg, 79104 Freiburg, Germany  G. Trinchero  INAF-
Astrophysical Observatory of Torino, Department of Physics, University of
Torino and INFN-Torino, 10125 Torino, Italy  C. Tunnell  Department of Physics
and Astronomy, Rice University, Houston, TX 77005, USA  F. Tönnies
Physikalisches Institut, Universität Freiburg, 79104 Freiburg, Germany  K.
Valerius  Institute for Astroparticle Physics, Karlsruhe Institute of
Technology, 76021 Karlsruhe, Germany  G. Volta  Physik-Institut, University of
Zürich, 8057 Zürich, Switzerland  C. Weinheimer  Institut für Kernphysik,
Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany  M. Weiss
Department of Particle Physics and Astrophysics, Weizmann Institute of
Science, Rehovot 7610001, Israel  D. Wenz<EMAIL_ADDRESS>Institut für
Physik & Exzellenzcluster PRISMA+, Johannes Gutenberg-Universität Mainz, 55099
Mainz, Germany  C. Wittweg  Physik-Institut, University of Zürich, 8057
Zürich, Switzerland  T. Wolf  Max-Planck-Institut für Kernphysik, 69117
Heidelberg, Germany  V. H. S. Wu  Institute for Astroparticle Physics,
Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany  Y. Xing
SUBATECH, IMT Atlantique, CNRS/IN2P3, Université de Nantes, Nantes 44307,
France  D. Xu  Physics Department, Columbia University, New York, NY 10027,
USA  Z. Xu  Physics Department, Columbia University, New York, NY 10027, USA
M. Yamashita  Kamioka Observatory, Institute for Cosmic Ray Research, and
Kavli Institute for the Physics and Mathematics of the Universe (WPI),
University of Tokyo, Higashi-Mozumi, Kamioka, Hida, Gifu 506-1205, Japan  L.
Yang  Department of Physics, University of California San Diego, La Jolla, CA
92093, USA  J. Ye  Physics Department, Columbia University, New York, NY
10027, USA  L. Yuan  Department of Physics & Kavli Institute for Cosmological
Physics, University of Chicago, Chicago, IL 60637, USA  G. Zavattini  INFN -
Ferrara and Dip. di Fisica e Scienze della Terra, Università di Ferrara, 44122
Ferrara, Italy  M. Zhong  Department of Physics, University of California San
Diego, La Jolla, CA 92093, USA  T. Zhu  Physics Department, Columbia
University, New York, NY 10027, USA<EMAIL_ADDRESS>
###### Abstract

We report on the first search for nuclear recoils from dark matter in the form
of weakly interacting massive particles (WIMPs) with the XENONnT experiment
which is based on a two-phase time projection chamber with a sensitive liquid
xenon mass of $5.9\text{\,}\mathrm{t}\text{/}$. During the $1.09\pm
0.03\text{\,}\mathrm{t}\text{${}\cdot{}$}\mathrm{y}\text{/}$ exposure used for
this search, the intrinsic [85]Kr and [222]Rn concentrations in the liquid
target were reduced to unprecedentedly low levels, giving an electronic recoil
background rate of $15.8\pm
1.3\text{\,}\mathrm{events}\text{/}\text{(}\mathrm{t}\text{${}\cdot{}$}\mathrm{y}\text{${}\cdot{}$}\mathrm{keV}\text{)}$
in the region of interest. A blind analysis of nuclear recoil events with
energies between $3.3\text{\,}\mathrm{keV}\text{/}$ and
$60.5\text{\,}\mathrm{keV}\text{/}$ finds no significant excess. This leads to
a minimum upper limit on the spin-independent WIMP-nucleon cross section of
$2.58\text{\times}{10}^{-47}\text{\,}{\mathrm{cm}}^{2}\text{/}$ for a WIMP
mass of $28\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$ at
$90\text{\,}\mathrm{\char 37\relax}\text{/}$ confidence level. Limits for
spin-dependent interactions are also provided. Both the limit and the
sensitivity for the full range of WIMP masses analyzed here improve on
previous results obtained with the XENON1T experiment for the same exposure.

Astrophysical and cosmological observations indicate the existence of a
massive, non-luminous, non-relativistic and non-baryonic dark matter (DM)
component of the Universe [1]. One well-motivated class of DM candidates is
weakly interacting massive particles (WIMPs), which arise naturally in several
beyond-Standard-Model theories [2]. Direct detection searches for WIMPs with
masses of a few $\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$ to tens of
$\mathrm{TeV}\text{/}{\mathrm{\text{$c$}}}^{2}$ using liquid xenon (LXe) time
projection chambers (TPCs) have produced the most stringent limits to date on
elastic spin-independent WIMP-nucleon cross sections [3, 4, 5].

The XENON Dark Matter project currently operates the XENONnT experiment at the
INFN Laboratori Nazionali del Gran Sasso (LNGS) underground laboratory. It is
an upgrade of its predecessor, XENON1T [6], with a new, larger dual-phase TPC
featuring a sensitive LXe mass of $5.9\text{\,}\mathrm{t}\text{/}$. The
XENON1T cryogenics, gaseous purification and krypton distillation systems, as
well as the $700\text{\,}\mathrm{t}\text{/}$ water Cherenkov muon veto (MV)
tank [7, 8] are reused to operate XENONnT. Inside the water tank, a new
neutron veto (NV) detector encloses the TPC cryostat. For the exposure used in
this analysis, the NV was operated as a water Cherenkov detector, tagging
neutrons through their capture on hydrogen which releases a
$2.22\text{\,}\mathrm{MeV}\text{/}$ $\upgamma$-ray.

The senstive LXe detector volume, enclosed by a polytetrafluoroethylene (PTFE)
cylinder with a height of $1.49\text{\,}\mathrm{m}\text{/}$ and a diameter of
$1.33\text{\,}\mathrm{m}\text{/}$, is viewed by 494 Hamamatsu R11410-21 3-inch
photomultiplier tubes (PMTs) [9] distributed in a top and a bottom array. To
fill the vessel housing the TPC, a total of $8.5\text{\,}\mathrm{t}\text{/}$
liquified xenon is required which is continuously purified by a new liquid-
phase purification system [10]. Together with a high flow radon distillation
system [11], a careful selection of detector construction materials [12] and a
specialized assembly procedure, this led to an unprecedentedly low electronic
recoil (ER) background of $15.8\pm
1.3\text{\,}\mathrm{events}\text{/}\text{(}\mathrm{t}\text{${}\cdot{}$}\mathrm{y}\text{${}\cdot{}$}\mathrm{keV}\text{)}$
below recoil energies of $30\text{\,}\mathrm{keV}\text{/}$ [13].

Particles depositing energy in the LXe produce a prompt scintillation signal
(S1) as well as ionization electrons which drift upwards and are extracted
into the gas above the liquid due to applied electric fields. Here a second
scintillation signal (S2), proportional to the number of extracted electrons,
is produced. WIMPs are expected to primarily produce nuclear recoils (NRs),
where a xenon nucleus recoils, while the background is dominated by ER
interactions where an electron recoils. A higher scintillation-to-ionisation
ratio is expected for NRs, but unlike ERs, a fraction of the total recoil
energy is also lost as unobservable heat.

Three parallel-wire electrodes (cathode, gate and anode) are used to establish
the drift and extraction fields. The gate and anode electrodes are reinforced
with two and four transverse wires, respectively, to minimize wire sagging.
Two additional parallel-wire screening electrodes are used to shield the PMT
arrays from the electric fields. After two months of commissioning at a drift
field of ~$100\text{\,}\mathrm{V}\text{/}\mathrm{cm}$, a short between the
bottom screening and cathode electrodes limited the applied drift field to
$23\text{\,}\mathrm{V}\mathrm{/}\mathrm{c}\mathrm{m}$, corresponding to a
maximum drift time of $2.2\text{\,}\mathrm{ms}\text{/}$. The extraction field
was set to $2.9\text{\,}\mathrm{kV}\text{/}\mathrm{cm}$ in LXe to reduce
localized, intermittent bursts of single electron S2 signals. Despite the
lower-than-designed drift and extraction fields, the energy and position
resolution, as well as the energy threshold, are comparable to those achieved
with XENON1T.

The TPC and veto detectors are integrated into a single data aquisition system
[14]. The data acquired by the MV uses the same hardware event trigger as in
XENON1T [15], whereas data from the TPC and NV are acquired in a “triggerless”
mode, with each individual PMT channel recording all signals above a channel-
specific threshold of ~$0.13\text{\,}\text{/}$ photoelectrons
($\mathrm{\mathrm{PE}}\text{/}$).

The recorded signals are processed using custom-developed open source software
packages [16, 17]. Each PMT signal is scanned for PMT “hits” above threshold,
and hits found in the TPC channels are clustered and classified into S1, S2 or
“unclassified” peaks based on pulse shape and PMT hit-pattern. At least three
PMTs must contribute to an S1 within $\pm 50\text{\,}\mathrm{ns}\text{/}$
around the center of the integrated peak waveform. Events are built in time
intervals between $2.45\text{\,}\mathrm{ms}\text{/}$ before and
$0.25\text{\,}\mathrm{ms}\text{/}$ after S2s, and overlapping events are
merged. The event S2 is required to be greater than
$100\text{\,}\mathrm{\mathrm{PE}}\text{/}$, and have fewer than eight other
peaks larger than half of the S2 peak area within $\pm
10\text{\,}\mathrm{ms}\text{/}$.

The PMT hit patterns of S2 signals are used to reconstruct the horizontal
position ($\mathrm{X},\mathrm{Y}$) of an event using neural network models
[18, 19]. Each model was trained by the S2 light distribution on the top PMT
array generated through optical simulations with Geant4 [8], corrected for the
number of exlcuded PMTs and electronics per-PMT response with the XENONnT
waveform simulator (WFSim) [20]. The horizontal interaction position
resolution for simulated events close to the PTFE detector walls is
~$1\text{\,}\mathrm{cm}\text{/}$, and ~$0.75\text{\,}\mathrm{cm}\text{/}$
within the fiducial volume (FV), for a $1000\text{\,}\mathrm{P}\mathrm{E}$ S2
(~$30\text{\,}\mathrm{e}\mathrm{x}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}\
\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{n}\mathrm{s}$).
The depth, 0pt, of an interaction is reconstructed from the measured drift
time between S1 and S2 and the electron drift velocity with a resolution
$<$1\text{\,}\%$$. The $50\text{\,}\mathrm{\char 37\relax}\text{/}$ S2 width
of a single electron signal is about $600\text{\,}\mathrm{ns}\text{/}$ and the
width of S2s within the FV of the detector typically range from
$2\text{\,}\mathrm{\SIUnitSymbolMicro s}\text{/}$ to
$9\text{\,}\mathrm{\SIUnitSymbolMicro s}\text{/}$. The drift field has a
radial component that shifts ionization electrons originating deeper in the
detector inwards when they are observed at the liquid surface. This inward
shift is corrected with a data-driven approach, assuming a uniform
distribution of [83m]Kr calibration events in radius squared ($\mathrm{R}$2)
as in [18].

The position and time information of the detected S1 and S2 signals is used to
correct for the inhomogeneous detector response due to quanta generation and
collection effects, and corresponds to corrections of up to $30\text{\,}\%$
for either signal. Scintillation photons are affected by a position-dependent
optical light collection efficiency which reduces the S1 peak area. A light
yield (LY) map normalized to the mean response in the (FV) is generated using
[83m]Kr signals. The electric field dependence of the LY is removed using a
drift field map constructed by matching the spatial distribution of [83m]Kr to
a COMSOL [21] simulation, accounting for potential charge accumulations on the
PTFE surfaces. This drift field map was validated with data using the measured
S1 ratio of the two [83m]Kr decays [22]. The resulting LY map is valid over
the full energy range of this analysis and is used to correct S1 signals,
referred to as cS1.

The S2 peak area reduces exponentially for signals deeper in the detector, as
drifting electrons can be captured by electronegative impurities. This effect
leads to a time-dependent lifetime of the free electrons which is corrected
using data from [83m]Kr and [222]Rn decays, and monitored with a new purity
monitor system [23]. The charge yield of the respective sources was corrected
by the drift field map using low-field data from [24]. An electron lifetime
better than $10\text{\,}\mathrm{ms}\text{/}$ was reached throughout the
science run with a liquid purification flow of
$8.3\text{\,}\mathrm{t}\text{/}\mathrm{d}$ [10]. The spatial variation in the
S2 response is dominated by the position-dependent optical light collection
efficiency and inhomogeneous electroluminescence amplification. [83m]Kr events
are used to obtain a normalized horizontal S2 peak area correction map. Time-
dependent variations of the single electron gain and extraction efficiency
following each ramping up of the electric field are corrected by their
respective data-driven trends. S2 signals summed over the top and bottom
array, and corrected for the above effects are referred to as cS2.

The method to convert the cS1 and cS2 signals of NRs and ERs into a combined
energy scale is described in [25]. The photon and electron gains are found to
be $g_{1}=$0.151\pm
0.001\text{\,}\mathrm{\mathrm{PE}}\mathrm{/}\mathrm{photon}$$ and
$g_{2}=$16.5\pm 0.6\text{\,}\mathrm{\mathrm{PE}}\mathrm{/}\mathrm{electron}$$,
assuming the mean energy to produce a charge or light quantum to
$13.7\text{\,}\mathrm{eV}\mathrm{/}\mathrm{quantum}$ [26]. Reconstructed
energies using this scale directly give the ER-equivalent energy
($\mathrm{$\mathrm{keV}\text{/}${}_{\mathrm{ER}}}\text{/}$), while the NR-
equivalent energy ($\mathrm{$\mathrm{keV}\text{/}${}_{\mathrm{NR}}}\text{/}$)
requires a model for energy lost to heat, and uses the full NR detector model,
described later.

The science search data was collected from July 6${}^{\text{th}}$ to November
10${}^{\text{th}}$ 2021\. This period, named Science Run 0 (SR0), contains a
total of $97.1\text{\,}\mathrm{d}\text{/}$ of data which corresponds to a
deadtime- and veto-corrected livetime of $95.1\text{\,}\mathrm{d}\text{/}$.
The length of SR0 was primarily chosen to investigate the XENON1T ER excess
[25], leading to a WIMP search exposure of $1.09\pm
0.03\text{\,}\mathrm{t}\text{${}\cdot{}$}\mathrm{y}\text{/}$. The detector
conditions were stable throughout SR0 with an average LXe temperature of
$(176.8\pm 0.4)$ $\mathrm{K}\text{/}$ and pressure of $(1.890\pm 0.004)$
$\mathrm{bar}\text{/}$, where the uncertainties represent the corresponding
RMS over SR0. PMT gains were monitored by weekly calibrations with a pulsed
low-intensity light source and voltages were adjusted at the beginning of SR0
to achieve ~$2\text{\times}{10}^{6}$ gains for all PMTs. The time dependence
of the PMT gains was modeled and the signals were corrected, resulting in a
gain variation $<{$3\text{\,}\mathrm{\char 37\relax}\text{/}$}$. In total $17$
PMTs were excluded from analysis due to internal vacuum degradation,
instability, light emission or noise. Five of these PMTs are distributed
evenly in the top PMT array. Periods of data taken with an intermittent and
localized high rate of S2 emission from single or few electrons are not
included in calibration and search data. Calibrations with [83m]Kr were
performed every second week to correct the detector response for position- and
time-dependent effects, and to monitor the stability of cS1 and cS2.

The NR response of XENONnT and the NV tagging efficiency were calibrated using
an external [241]AmBe source which was placed in three positions close to the
TPC cryostat. [241]AmBe emits neutrons via the alpha-capture reaction
$\isotope[9]{Be}(\upalpha,n)\isotope[12]{C}$ which has a chance of about
$60\text{\,}\mathrm{\char 37\relax}\text{/}$ to emit an additional
$4.44\text{\,}\mathrm{MeV}\text{/}$ $\upgamma$-ray [27]. This $\upgamma$-ray,
well above the NV threshold, is used to select NR S1 signals in a
~$400\text{\,}\mathrm{ns}\text{/}$ window. After applying the same data-
quality cuts as used in the main analysis, 1986 events remain in the region of
interest (ROI), shown in Figure 1. Only $1.8\pm 0.6\text{\,}\text{/}$ events
are expected from random coincidences between the two detectors, determined
through a sideband study. The tagging efficiency of the NV is estimated from
the number of delayed neutron capture signals following the NR S1 signals.
This data-driven tagging efficiency is corrected for position-dependent
effects using Geant4 [28] simulations which account for the full spatial
distribution of neutrons emitted by detector materials [8]. The length of the
veto window was set to $250\text{\,}\mathrm{\SIUnitSymbolMicro s}\text{/}$
with a 5-fold PMT coincidence and a $5\text{\,}\mathrm{\mathrm{PE}}\text{/}$
event area threshold in the NV. This gives a neutron tagging efficiency of
$53\pm 3\text{\,}\mathrm{\char 37\relax}\text{/}$, and a livetime reduction of
$1.6\text{\,}\mathrm{\char 37\relax}\text{/}$.

The ER response model is calibrated with $2051$ [212]Pb $\upbeta$ events from
a [220]Rn calibration source [29], before SR0 and with events from an [37]Ar
source [30] collected after SR0, as discussed in [13]. NR and ER calibration
datasets were fitted using the LXe response model and fast detector simulation
described in [31]. For both datasets, a Markov-Chain Monte Carlo (MCMC)
sampling of the parameter space gives the best-fit point and posterior
distribution. The goodness-of-fit (GOF) was assessed by partitioning the cS1,
cS2 space into equiprobable bins according to both best-fit models and then
computing a Poisson $\chi^{2}$ likelihood, as well as one-dimensional
projections on cS2. Neither tests reject the best-fit model, with two-
dimensional p-values of $0.18$ and $0.39$ for ER and NR, respectively, and no
significant p-values for the one-dimensional projections. The calibration data
and contours of the best-fit model are shown in Figure 1. The leakage fraction
of the [220]Rn ER events below the NR median is $1.1^{+0.2}_{-0.3}\,\%$.

The full ER model has too many parameters to be tractable in the inference toy
MC simulations. Using linear combinations of the original parameters
identified with a principal component analysis reduces parameter redundancies,
and these parameter directions are then ranked according to their impact on
the background expectation in a signal-like region in cS1 and cS2. The two
parameters with the highest impact are included as nuisance parameters in the
ER model used in the WIMP search likelihood.

Figure 1: NR and ER calibration data from [241]AmBe (orange), [220]Rn (blue)
and [37]Ar (black). The median and the $\pm 2\text{\,}\sigma$ contours of the
NR and ER model are shown in blue and red respectively. The gray dash-dotted
contour lines show the reconstructed NR energy
($\mathrm{$\mathrm{keV}\text{/}${}_{\mathrm{NR}}}\text{/}$). Only not shaded
events up to a cS1 of $100\text{\,}\mathrm{\mathrm{PE}}\text{/}$ are
considered in the response model fits.

The ROI is defined by cS1 between $0\text{\,}\mathrm{\mathrm{PE}}\text{/}$ and
$100\text{\,}\mathrm{\mathrm{PE}}\text{/}$ and cS2 between
$126\text{\,}\mathrm{\mathrm{PE}}\text{/}$ and
$12\,589\text{\,}\mathrm{\mathrm{PE}}\text{/}$. Together with detection and
selection efficiencies, this gives an energy range with at least
$10\text{\,}\mathrm{\char 37\relax}\text{/}$ total efficiency from
$3.3\text{\,}\mathrm{$\mathrm{keV}\text{/}${}_{\mathrm{NR}}}\text{/}$-$60.5\text{\,}\mathrm{$\mathrm{keV}\text{/}${}_{\mathrm{NR}}}\text{/}$.
All events reconstructed with an ER energy below
$20\text{\,}\mathrm{$\mathrm{keV}\text{/}${}_{\mathrm{ER}}}\text{/}$ and found
in the cS1 and cS2 contours of the ER and NR band were blinded. For the study
of the ER data presented in [13] all events above the $-2\text{\,}\sigma$
quantile of the ER band or with a reconstructed ER energy larger than
$10\text{\,}\mathrm{$\mathrm{keV}\text{/}${}_{\mathrm{ER}}}\text{/}$ were
unblinded. The remaining region was unblinded only after finalizing the
analysis procedure presented here.

The event selection criteria from [18] were optimized for the ROI in this
analysis. Data quality cuts are applied in order to include only well-
reconstructed events and to suppress backgrounds. All cuts were optimized
based on calibration data and simulations using WFSim. Each valid event is
required to have a valid S1-S2 pair. Events tagged by the MV or NV are removed
from the data selection as are multiple-scatter (MS) events since WIMPs are
expected to induce only single-scatter (SS) NRs. The MV uses a veto window of
$1\text{\,}\mathrm{ms}\text{/}$ with a 5-fold PMT coincidence and a
$10\text{\,}\mathrm{\mathrm{PE}}\text{/}$ MV event area threshold.

A dedicated cut similar to that in [32] using a gradient boosted decision tree
(GBDT) was developed to reduce the background due to randomly paired S1-S2
signals called accidental coincidences (ACs). This cut uses S2 area and shape,
as well as interaction depth, and reduces the AC background by $65\text{\,}\%$
at $95\text{\,}\%$ signal acceptance. Due to an insufficient model of the S2
pulse shape near the transverse wires, caused by local variations of the drift
and extraction field with respect to the rest of the TPC, an optimization of
the GBDT and other S2 shape-based cuts was not possible with WFSim.
Consequently, the LXe target is split into two parts in the modeling for the
WIMP search. A less strict data-driven model for the S2 width cut and no GBDT
selection is used in an $8.9\text{\,}\mathrm{cm}\text{/}$ wide band around the
transverse wires, leading to a lower signal-to-background ratio, but with a
$10\text{\,}\mathrm{\char 37\relax}\text{/}$ higher selection efficiency. The
total selection efficiency for these “near”- and “far”-wire regions is
estimated following the procedure in [25, 18]. Efficiency losses due to the
event building are also taken into account in the selection efficiency.

The detection efficiency of the TPC, dominated by the S1 detection efficiency,
is evaluated using WFSim and validated with a data-driven method [31, 33].
Both methods agree within $1\text{\,}\mathrm{\char 37\relax}\text{/}$.
Efficiency losses at small energies are dominated by the 3-fold PMT
coincidence requirement. The upper cS1 ROI edge, chosen to include the full
WIMP spectrum, determines the upper edge of this analysis. The combined
selection efficiency of the near and far wire regions, the detection and the
total efficiencies of the analysis are shown together with the normalized
recoil spectra of three different WIMP masses in Figure 2.

Figure 2: Detection and selection efficiency for NR events in this search as a
function of the NR recoil energy. The total efficiency in the WIMP search
region (black) is dominated by the detection efficiency (green) at low
energies and event selections (blue) at higher energies until the edge of the
ROI. Normalized recoil spectra for WIMPs with masses of
$10\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$,
$50\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$, and
$200\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$ are shown with
orange dashed lines for reference.

In order to mitigate background events from detector radioactivity as well as
“surface events” produced by ERs from [210]Pb plate-out [3], only events
reconstructed in a central FV (illustrated in Figure A.2 in the supplementary
material) are considered in the analysis. The FV shape is optimised based on
the background distributions, as well as constrained to not include regions
where the detector is not sensitive or models are incomplete. The total LXe
mass of the FV after considering the systematic uncertainty of the field
distortion correction is $4.18\pm 0.13\text{\,}\mathrm{t}\text{/}$.

Five different background components make up the total background model:
radiogenic neutrons, coherent elastic neutrino-nucleus scattering
($\mathrm{CE}\nu\mathrm{NS}$), ERs, surface events and ACs. The expectation
values for each are summarized in Table 1. In addition to the full expectation
values, we include for illustration expectation values in a signal-like region
defined to contain half of a
$200\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$ WIMP signal with
the lowest signal-to-background ratio.

The NR background in XENONnT is dominated by radiogenic neutrons from
spontaneous fission and ($\upalpha$, $n$)-reactions. Neutron yields and
energies originating from various detector materials are evaluated as in [31,
8]. A custom interface based on the fitted NR model accepts Geant4 simulation
inputs, and provides observable quanta processed by WFSim to construct the
neutron background model [34]. The neutron rate was estimated based on this
full detector simulation and compared against a data-driven method. The data-
driven estimate uses a combined Poisson likelihood for MS and SS events tagged
by the NV, together with a simulation-driven MS/SS ratio which was validated
with [241]AmBe data. The maximum deviation of the MS/SS ratio estimated as a
function of radius between data and simulation was found to be less than
$20\text{\,}\mathrm{\char 37\relax}\text{/}$. However, a wrong sign in the NV
tagging window, discovered only after unblinding of the main data, meant that
the simulation and data-driven estimates found before were no longer in
agreement. This error arose from the premise that the tagging efficiency was
determined in a forward coincidence, counting the number NV tags for a given
set of NR SS events, while the tagging is done by a backwards veto triggered
when a NV event satisfies the threshold criteria. In accordance with the
analysis plan, the data-driven rate estimate is used. Four events in the WIMP
blinding region are tagged by the NV and cut, three of them also fail the SS
cut, compatible with the MS/SS ratio from simulations. This gives a total
neutron expectation of $1.1^{+0.6}_{-0.5}$ events which is a factor
~$6\text{\,}\text{/}$ higher than predicted by simulations. Analysis choices
such as the NV tagging window and the FV were not re-optimized after this
correction.

Table 1:  Expected number of events for each model component and observed events. The “nominal” column shows expectation values and uncertainties, if applicable, before unblinding. The nominal ER value is the observed number of ER events before unblinding. Other columns show best-fit expectation values and uncertainties for a free fit including a $200\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$ WIMP signal component. The best-fit signal cross-section is $3.22\text{\times}{10}^{-47}\text{\,}{\mathrm{cm}}^{2}\text{/}$. In addition to the expectation values in the full ROI, we include the expectation values in a signal-like cS1,cS2 region containing the $50\%$ of signal in with the best signal-to-background ratio. This region is indicated in Figure 3 with an orange dashed contour. The best-fit and pre-unblinding values agree within uncertainties for all components which include an ancillary constraint term.  | Nominal | Best Fit
---|---|---
| ROI | Signal-like
ER | $134$ | $135_{-11}^{+12}$ | $0.92\pm 0.08$
Neutrons | $1.1^{+0.6}_{-0.5}$ | $1.1\pm 0.4$ | $0.42\pm 0.16$
$\mathrm{CE}\nu\mathrm{NS}$ | $0.23\pm 0.06$ | $0.23\pm 0.06$ | $0.022\pm 0.006$
AC | $4.3\pm 0.9$ | $4.4_{-0.8}^{+0.9}$ | $0.32\pm 0.06$
Surface | $14\pm 3$ | $12\pm 2$ | $0.35\pm 0.07$
Total Background | 154 | $152\pm 12$ | $2.03_{-0.15}^{+0.17}$
WIMP | - | $2.6$ | $1.3$
Observed | - | $152$ | $3$

The remaining contribution to the NR background is predominately due to
$\mathrm{CE}\nu\mathrm{NS}$ from [8]B solar neutrinos. The rate is constrained
by measurements of the [8]B flux [35], but the total uncertainty of the
expectation value is dominated by the detector response model uncertainties.
The number of cosmogenic neutrons is conservatively estimated to be less than
$0.01$ events after MV tagging [7], not including the additional suppression
by the NV. Thus, this background is considered to be negligible.

The ER background is dominated by $\upbeta$-decays of [214]Pb originating from
the decay of [222]Rn in the LXe. Solar neutrino-electron scattering, [85]Kr
and $\upgamma$-rays emitted by detector materials also contribute to the ER
background [13]. The ER response model fit was updated after unblinding of the
main data to use the same data quality selections as of this study, compared
to [13]. Prior to unblinding, $134$ events are found in the ER band of the
ROI.

Data-driven models are constructed for AC events and surface background
events. The AC background is concentrated at low S1 and S2, and is therefore a
particular challenge for low-mass WIMP searches. The model is constructed from
a synthetic dataset made from isolated S1s and S2s using the method in [32].
Looser cuts in the near-wire region give a ~$6$ times larger AC rate for this
region compared to the rest of the TPC. Background sidebands and [220]Rn and
[37]Ar calibration data were used to validate the AC model, and the rate is
estimated with an uncertainty of better than $5\text{\,}\%$. The surface
background model is constructed from [210]Po events originating from the TPC
walls, using a similar method as in [31]. The data is described in radius
using a parametric likelihood fit based on events found below the blinded
region. cS1 and cS2 are modeled using a kernel density estimation derived from
events reconstructed outside of the TPC. The wall model is validated using the
unblinded WIMP region outside of the FV as a sideband. The expected values for
both backgrounds are summarized in Table 1 and their distributions in the
(cS1, cS2) space are shown in Figure 3. In addition, an extended version of
Table 1 differentiating the near and far wire region can be found in Table 2
in the supplemental materials.

Figure 3: DM search data in the cS1-cS2 space. Each event is represented with
a pie-chart, showing the fraction of the best-fit model, including the
expected number of $200\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$
WIMPs (orange) evaluated at the position of the event. The size of the pie-
charts is proportional to the signal model at that position. Background
probability density distributions are shown as $1\text{\,}\sigma$ (dark) and
$2\text{\,}\sigma$ (light) regions as indicated in the legend for ER (blue),
AC (purple) and surface (green, “wall”). The neutron background (yellow in
pies) has a similar distribution to the WIMP (orange filled area showing the
$2\text{\,}\sigma$ region). The orange dashed contour contains a signal-like
region which is constructed to contain 50% of a
$200\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$ WIMP signal with
the highest possible signal-to-noise ratio.

The statistical analysis of the WIMP search data uses toy MC simulations of
the experiment to calibrate the distribution of a log-likelihood-ratio test
statistic as in [31, 36]. Four terms make up the likelihood: two search-data
terms for events near and far from the transverse wires, an ER calibration
term and a term representing ancillary measurements of parameters. The first
three are extended unbinned likelihoods in cS1, cS2, as well as $\mathrm{R}$
for the first term. All three terms have the same form as equation (21) in
[31]. The two search-data likelihoods include components for the ER, AC,
surface, $\mathrm{CE}\nu\mathrm{NS}$ and radiogenic neutron backgrounds, as
well as the WIMP signal. The [220]Rn calibration term includes the ER model as
well as an AC component. The expected number of events for each component is a
nuisance parameter in the likelihood. In addition, two shape parameters for
the ER model are included, and a parameter representing the uncertainty of the
expected number of signal events given the NR response model. The ER shape
parameters mainly modify the signal-like ER tail below
$S1=$10\text{\,}\mathrm{\mathrm{PE}}\text{/}$$, where they allow the signal-
like ER tail below the median S2 expected from a
$200\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$ WIMP to vary
between $0.009$ and $0.017$ at $60\%$ confidence level. The signal shape is
fixed, as even a large signal excess would be small enough that the
calibration constraints would dominate. The signal expectation value for a
certain cross-section is included as a nuisance parameter. The ancillary
measurement term includes Gaussians representing the measurements constraining
the AC, radiogenic, surface and $\mathrm{CE}\nu\mathrm{NS}$ rates, and the
uncertain signal expectation.

The signal NR spectrum is modeled with the Helm form factor for the nuclear
cross section [37], and a standard halo model with parameters fixed to the
recommendations of [36]. The main change from previous XENON publications is
an updated local standard of rest velocity of
$238\text{\,}\mathrm{km}\text{/}\mathrm{s}$ [38, 39]. The NR model fit to
calibration data is used to construct a model for the signal in cS1 and cS2.

Figure 4: Upper limit on spin-independent WIMP-nucleon cross section at
$90\text{\,}\mathrm{\char 37\relax}\text{/}$ confidence level (full black
line) as a function of the WIMP mass. A power-constraint is applied to the
limit to restrict it at or above the median unconstrained upper limit. The
dashed lines show the upper limit without a power-constraint applied. The
$1\text{\,}\sigma$ (green) and $2\text{\,}\sigma$ (yellow) sensitivity bands
are shown as shaded regions, with lighter colors indicating the range of
possible downwards fluctuations. The result from XENON1T [3] is shown in blue
with the same power-constraint applied. At masses above
~$100\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$, the limit scales
with mass as indicated with the extrapolation formula.

After unblinding, the ROI contains $152$ events, $16$ of which were in the
blinded WIMP region. The data is shown in Figure 3, and the best-fit
expectation values are in Table 1. The binned GOF test indicates no large-
scale mismodelling ($\textrm{p}=$0.63$$). At high cS1,
$\gtrapprox$50\text{\,}\mathrm{\mathrm{PE}}\text{/}$$, we observe more events
which are consistent with ER events than our model or calibration data
predicts, in particular between cS1s of
$50\text{\,}\mathrm{\mathrm{PE}}\text{/}$ and
$75\text{\,}\mathrm{\mathrm{PE}}\text{/}$. Of the $16$ former blinded events,
$13$ are found in the upper right half of the horizontal event distribution,
with no correlation with the transverse wires observed (see Figure A.3). The
[220]Rn, [83m]Kr and [37]Ar calibration datasets do not exhibit any asymmetry,
nor is any seen in the acceptances evaluated in the $\mathrm{X},\mathrm{Y}$
plane for any of the applied cuts.

The WIMP discovery p-value indicates no significant excess ($\textrm{p}\geq
0.20$, with the minimum for masses above
~$100\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$), and the
resulting limits on spin-independent interactions are shown in Figure 4, with
spin-dependent limits included in Figures A.1a and A.1b of the supplementary
material. To constrain large downwards fluctuations, the limit is subjected to
a power-constraint following [40]. We choose a very conservative power
threshold of $50\%$, higher than that advocated in [36], as that paper
mistakenly defined the power-constraint in terms of discovery power when
settling on a threshold of $15\%$. See the supplementary materials for further
discussion. For spin-independent interactions the lowest upper limit is
$2.58\text{\times}{10}^{-47}\text{\,}{\mathrm{cm}}^{2}\text{/}$ at
$28\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$ and 90% confidence
level (CL). At masses above
~$100\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$, the limit is
$$6.08\text{\times}{10}^{-47}\text{\,}{\mathrm{cm}}^{2}\text{/}$\times(M_{\mathrm{DM}}/($100\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$))$.
For spin-independent interactions the lowest upper limit is
$2.58\text{\times}{10}^{-47}\text{\,}{\mathrm{cm}}^{2}\text{/}$ at
$28\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$ and 90% CL. At
masses above ~$100\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$, the
limit is
$$6.08\text{\times}{10}^{-47}\text{\,}{\mathrm{cm}}^{2}\text{/}$\times(M_{\mathrm{DM}}/($100\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$))$.

In conclusion, a blind analysis of $95.1\text{\,}\mathrm{d}\text{/}$ of
science data with a total exposure of $1.09\pm
0.03\text{\,}\mathrm{t}\text{${}\cdot{}$}\mathrm{y}\text{/}$ has been
performed. The best fit to the data is compatible with the background-only
hypothesis. The experiment achieved an ER background level of $15.8\pm
1.3\text{\,}\mathrm{events}\text{/}\text{(}\mathrm{t}\text{${}\cdot{}$}\mathrm{y}\text{${}\cdot{}$}\mathrm{keV}\text{)}$,
$\raisebox{2.15277pt}{\texttildelow}5$ times lower than XENON1T, with
comparable detector resolutions, and energy threshold. This results in a
sensitivity improvement with respect to XENON1T by a factor of $1.7$ at a WIMP
mass of $100\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$.

Currently, XENONnT continues to take data, with a further reduced [222]Rn ER
background, using the radon distillation system with combined gaseous and
liquid xenon flow. Subsequent data-taking is planned with the NV operating as
designed, with Gd-sulphate-octahydrate loaded into the water [41, 42] to
increase the neutron tagging efficiency to ~$87\text{\,}\mathrm{\char
37\relax}\text{/}$ with a lower overall lifetime reduction [8].

We gratefully acknowledge support from the National Science Foundation, Swiss
National Science Foundation, German Ministry for Education and Research, Max
Planck Gesellschaft, Deutsche Forschungsgemeinschaft, Helmholtz Association,
Dutch Research Council (NWO), Weizmann Institute of Science, Israeli Science
Foundation, Binational Science Foundation, Fundacao para a Ciencia e a
Tecnologia, Région des Pays de la Loire, Knut and Alice Wallenberg Foundation,
Kavli Foundation, JSPS Kakenhi and JST FOREST Program in Japan, Tsinghua
University Initiative Scientific Research Program and Istituto Nazionale di
Fisica Nucleare. This project has received funding/support from the European
Union’s Horizon 2020 research and innovation programme under the Marie
Skłodowska-Curie grant agreement No 860881-HIDDeN. Data processing is
performed using infrastructures from the Open Science Grid, the European Grid
Initiative and the Dutch national e-infrastructure with the support of SURF
Cooperative. We are grateful to Laboratori Nazionali del Gran Sasso for
hosting and supporting the XENON project.

## References

  * Bertone  _et al._ [2005] G. Bertone, D. Hooper, and J. Silk, Particle dark matter: Evidence, candidates and constraints, Phys. Rept. 405, 279 (2005), arXiv:hep-ph/0404175 .
  * Roszkowski  _et al._ [2018] L. Roszkowski, E. M. Sessolo, and S. Trojanowski, WIMP dark matter candidates and searches – current status and future prospects, Rept. Prog. Phys. 81, 066201 (2018), arXiv:1707.06277 [hep-ph] .
  * Aprile  _et al._ [2018] E. Aprile _et al._ (XENON), Dark Matter Search Results from a One Ton-Year Exposure of XENON1T, Phys. Rev. Lett. 121, 111302 (2018), arXiv:1805.12562 [astro-ph.CO] .
  * Meng  _et al._ [2021] Y. Meng _et al._ (PandaX), Dark Matter Search Results from the PandaX-4T Commissioning Run, Phys. Rev. Lett 127, 261802 (2021), arXiv:2107.13438 [hep-ex] .
  * Aalbers  _et al._ [2022] J. Aalbers _et al._ (LZ), First Dark Matter Search Results from the LUX-ZEPLIN (LZ) Experiment, (2022), arXiv:2207.03764 [astro-ex] .
  * Aprile  _et al._ [2017] E. Aprile _et al._ (XENON), The XENON1T Dark Matter Experiment, Eur. Phys. J. C 77, 881 (2017), arXiv:1708.07051 [astro-ph.IM] .
  * Aprile  _et al._ [2014] E. Aprile _et al._ (XENON), Conceptual design and simulation of a water Cherenkov muon veto for the XENON1T experiment, JINST 9 (11), P11006 (2014), arXiv:1406.2374 [astro-ph.IM] .
  * Aprile  _et al._ [2020a] E. Aprile _et al._ (XENON), Projected WIMP sensitivity of the XENONnT dark matter experiment, JCAP 2020 (11), 031, arXiv:2007.08796 [physics.ins-det] .
  * Antochi  _et al._ [2021] A. Antochi _et al._ , Improved quality tests of R11410-21 photomultiplier tubes for the XENONnT experiment, JINST 16 (08), P08033 (2021), arXiv:2104.15051 [physics.ins-det] .
  * Plante  _et al._ [2022] G. Plante, E. Aprile, J. Howlett, and Y. Zhang, Liquid-phase purification for multi-tonne xenon detectors, Eur. Phys. J. C 82, 860 (2022), arXiv:2205.07336 [physics.ins-det] .
  * Murra  _et al._ [2022] M. Murra, D. Schulte, C. Huhmann, and C. Weinheimer, Design, construction and commissioning of a high-flow radon removal system for XENONnT, Eur. Phys. J. C 82, 10.1140/epjc/s10052-022-11001-9 (2022), arXiv:2205.11492 [physics.ins-det] .
  * Aprile  _et al._ [2021a] E. Aprile _et al._ (XENON), Material radiopurity control in the XENONnT experiment, Eur. Phys. J. C 82, 10.1140/epjc/s10052-022-10345-6 (2021a), arXiv:2112.05629 [physics.ins-det] .
  * Aprile  _et al._ [2022a] E. Aprile _et al._ (XENON), Search for new physics in electronic recoil data from XENONnT, Phys. Rev. Lett. 129, 161805 (2022a), arXiv:2207.11330 .
  * Aprile  _et al._ [2022b] E. Aprile _et al._ (XENON), The Triggerless Data Acquisition System of the XENONnT Experiment, accepted by JINST (2022b), arXiv:2212.11032 [physics.ins-det] .
  * Aprile  _et al._ [2019a] E. Aprile _et al._ (XENON), The XENON1T Data Acquisition System, JINST 14 (07), P07016, arXiv:1906.00819 [physics.ins-det] .
  * Aalbers  _et al._ [2023] J. Aalbers _et al._ , AxFoundation/strax: Streaming analysis for xenon experiments (2023).
  * XENON Collaboration [2022a] XENON Collaboration, XENONnT/straxen: Streaming analysis for XENON(nT) (2022a).
  * Aprile  _et al._ [2019b] E. Aprile _et al._ (XENON), XENON1T Dark Matter Data Analysis: Signal Reconstruction, Calibration and Event Selection, Phys. Rev. D 100, 052014 (2019b), arXiv:1906.04717 [physics.ins-det] .
  * Liang  _et al._ [2022] S. Liang, A. Higuera, C. Peters, V. Roy, W. U. Bajwa, H. Shatkay, and C. D. Tunnell, Domain-Informed Neural Networks for Interaction Localization Within Astroparticle Experiments, Front. Artif. Intell. 5, 832909 (2022), arXiv:2112.07995 [hep-ex] .
  * XENON Collaboration [2022b] XENON Collaboration, Xenonnt/wfsim: v1.0.2 (2022b).
  * [21] COMSOL AB, Stockholm, Sweden, COMSOL Multiphysics.
  * Akerib  _et al._ [2017] D. Akerib _et al._ (LUX), 83mKr calibration of the 2013 LUX dark matter search, Phys. Rev. D 96, 112009 (2017), arXiv:1708.02566 [physics.ins-det] .
  * Carugno  _et al._ [1990] G. Carugno, B. Dainese, F. Pietropaolo, and F. Ptohos, Electron lifetime detector for liquid argon, Nucl. Instrum. Meth. A 292, 580 (1990).
  * Jörg  _et al._ [2022] F. Jörg, D. Cichon, G. Eurin, L. Hötzsch, T. Marrodán Undagoitia, and N. Rupp, Characterization of alpha and beta interactions in liquid xenon, Eur. Phys. J. C 82, 361 (2022), arXiv:2109.13735 [physics.ins-det] .
  * Aprile  _et al._ [2020b] E. Aprile _et al._ (XENON), Excess electronic recoil events in XENON1T, Phys. Rev. D 102, 072004 (2020b), arXiv:2006.09721 [hep-ex] .
  * Dahl [2009] C. E. Dahl,  _The physics of background discrimination in liquid xenon, and first results from Xenon10 in the hunt for WIMP dark matter_ , Ph.D. thesis, Princeton U. (2009).
  * Scherzinger  _et al._ [2015] J. Scherzinger, J. Annand, G. Davatz, K. Fissum, U. Gendotti, R. Hall-Wilton, E. Håkansson, R. Jebali, K. Kanaki, M. Lundin, B. Nilsson, A. Rosborge, and H. Svensson, Tagging fast neutrons from an 241Am/9Be source, Appl. Radiat. Isot. 98, 74 (2015).
  * Agostinelli  _et al._ [2003] S. Agostinelli _et al._ (GEANT4), GEANT4 – a simulation toolkit, Nucl. Instrum. Meth. A 506, 250 (2003).
  * Lang  _et al._ [2016] R. F. Lang, A. Brown, E. Brown, M. Cervantes, S. Macmullin, D. Masson, J. Schreiner, and H. Simgen, A Rn-220 source for the calibration of low-background experiments, JINST, Volume 11, P04004 (April 2016) 11, P04004 (2016), arXiv:1602.01138 [physics.ins-det] .
  * Aprile  _et al._ [2023] E. Aprile _et al._ (XENON), Low-energy Calibration of XENON1T with an Internal 37Ar Source, Eur. Phys. J. C 83, 542 (2023), arXiv:2211.14191 [physics.ins-det] .
  * Aprile  _et al._ [2019c] E. Aprile _et al._ (XENON), XENON1T dark matter data analysis: Signal and background models and statistical inference, Phys. Rev. D 99, 112009 (2019c).
  * Aprile  _et al._ [2021b] E. Aprile _et al._ (XENON), Search for Coherent Elastic Scattering of Solar 8B Neutrinos in the XENON1T Dark Matter Experiment, Phys. Rev. Lett. 126, 091301 (2021b), arXiv:2012.02846 [hep-ex] .
  * XENON Collaboration [2022c] XENON Collaboration, Xenonnt/pema (2022c).
  * XENON Collaboration [2023] XENON Collaboration, XENONnT/epix: Electron and photon instructions generator for XENON (2023).
  * Aharmim  _et al._ [2013] B. Aharmim _et al._ (SNO Collaboration), Combined analysis of all three phases of solar neutrino data from the sudbury neutrino observatory, Phys. Rev. C 88, 025501 (2013).
  * Baxter  _et al._ [2021] D. Baxter _et al._ , Recommended conventions for reporting results from direct dark matter searches, Eur. Phys. J. C 81, 907 (2021), arXiv:2105.00599 [hep-ex] .
  * Lewin and Smith [1996] J. D. Lewin and P. F. Smith, Review of mathematics, numerical factors, and corrections for dark matter experiments based on elastic nuclear recoil, Astroparticle Physics 6, 87 (1996).
  * Bland-Hawthorn and Gerhard [2016] J. Bland-Hawthorn and O. Gerhard, The Galaxy in Context: Structural, Kinematic, and Integrated Properties, Annual Review of Astronomy and Astrophysics 54, 529 (2016).
  * Abuter  _et al._ [2021] R. Abuter _et al._ (GRAVITY), Improved GRAVITY astrometric accuracy from modeling optical aberrations, Astron. Astrophys. 647, A59 (2021).
  * Cowan  _et al._ [2011] G. Cowan, K. Cranmer, E. Gross, and O. Vitells, Power-Constrained Limits, (2011), arXiv:1105.3166 [physics.data-an] .
  * Marti  _et al._ [2020] L. Marti _et al._ , Evaluation of gadolinium’s action on water cherenkov detector systems with EGADS, Nucl. Instrum. Methods. Phys. Res. A 959, 163549 (2020).
  * Abe  _et al._ [2022] K. Abe _et al._ (Super-Kamiokande), First gadolinium loading to Super-Kamiokande, NIM-A 1027, 166248 (2022).
  * Aprile  _et al._ [2019d] E. Aprile _et al._ (XENON), Constraining the spin-dependent WIMP-nucleon cross sections with XENON1T, Phys. Rev. Lett. 122, 141301 (2019d), arXiv:1902.03234 [astro-ph.CO] .
  * Klos  _et al._ [2013] P. Klos, J. Menéndez, D. Gazit, and A. Schwenk, Large-scale nuclear structure calculations for spin-dependent WIMP scattering with chiral effective field theory currents, Phys. Rev. D 88, 083516 (2013), [Erratum: Phys.Rev.D 89, 029901 (2014)], arXiv:1304.7684 [nucl-th] .
  * Hoferichter  _et al._ [2016] M. Hoferichter, P. Klos, J. Menéndez, and A. Schwenk, Analysis strategies for general spin-independent WIMP-nucleus scattering, Phys. Rev. D 94, 063505 (2016), arXiv:1605.08043 [hep-ph] .

##  Appendix A Supplementary Material

### Limits on spin-dependent WIMP interactions

In addition to spin-independent WIMP-nucleon interactions, WIMPs may couple to
the nuclear spin. Following the procedure of [43], and using the form factors
of [44], we place upper limits on this interaction assuming couplings to
either only protons or only neutrons in the nucleus,
$\sigma^{\mathrm{SD}}_{\chi p}$ and $\sigma^{\mathrm{SD}}_{\chi n}$,
respectively. Unlike the spin-independent case, where detailed nuclear form
factors fit the Helm form factor well, the form factors for spin-dependent
interactions are subject to larger uncertainties [45]. We consider a detailed
exploration of the range of this uncertainty for spin-dependent responses
beyond the scope of this work, as the uncertainty predominately changes the
expected recoil rate, so that the results presented here can be re-scaled.
However, we note that in e.g. [5], the range of recoil rates for these fluxes
span approximately one order of magnitude.

(a)  (b)

Figure A.1: Upper limit on spin-dependent WIMP-proton (a) and WIMP-neutron (b)
interactions at $90\text{\,}\mathrm{\char 37\relax}\text{/}$ confidence level
(full black line) as a function of the WIMP mass. The limit is constrained by
a power-constraint restricting upper limits to lie at or above the median
unconstrained upper limit. The $1\text{\,}\sigma$ (green) and
$2\text{\,}\sigma$ (yellow) sensitivity bands are shown as shaded regions,
with lighter colors indicating the range of possible downwards fluctuations.
The dashed line shows the upper limit without a power-constraint applied.
Results from XENON1T [43] are shown in blue with the same power-constraint
applied. At masses above
~$100\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$, the limit scales
with mass as indicated with the extrapolation formula.

### Spatial event distribution

The distribution of events in the horizontal plane enters the likelihood only
as radius $\mathrm{R}$ or in the near-wire/far-wire partition. Therefore, no
dedicated GOF tests were defined in this plane prior to unblinding, and
results are expected to be robust against a potential mismodelling that does
not affect these variables.

Figure A.2 and A.3 show the spatial distribution of all events found in the
ROI after unblinding. The lower number of events next to the TPC wall for low
z in Figure A.2 is due to a charge insensitive region caused by an
inhomogeneity of the drift field. Field inhomogeneities also cause a variation
in drift speed as function of $R$ leading to a small bias in the reconstructed
z-position as it can be seen from the slight bending of the near cathode
events in Figure A.2. The bias is accounted for in the estimation of the
fiducial volume and mass. The reconstruction bias is about
$2\text{\,}\mathrm{cm}\text{/}$ at the bottom outer edge of the fiducial
volume and changes to roughly $-0.4\text{\,}\mathrm{cm}\text{/}$ at a radius
of $40\text{\,}\mathrm{cm}\text{/}$.

Figure A.3 shows clusters with a higher density of events near the transverse
wires as well as localised over densities in a periodic pattern close to the
TPC wall outside of the fiducial volume. The former is caused by the higher
rate of AC events and overall less strict requirements on the S2 width near
the transverse wires as explained in the main body of the paper. The latter is
an artefact due to the structure of the TPC PTFE cylinder which is composed of
pillars and panels. The over densities are localised near the TPC pillars.

In total 13 of the 16 former blinded events are found in the upper right half
of the horizontal event distribution. The events are neither found near the
transverse wires nor the position of the single to few electron S2s burst
which were localized in a $10\text{\,}\mathrm{cm}\text{/}$ radius around
($5\text{\,}\mathrm{cm}\text{/}$,$-20\text{\,}\mathrm{cm}\text{/}$) in $X$ and
$Y$. Additional test were carried out after unblinding to check if any
systematic bias was overlooked during the development of corrections or data
quality selections. The [220]Rn ER band calibration data taken before SR0 was
tested for a similar asymmetry for all calibration data points found in the
lowest $5\text{\,}\mathrm{\char 37\relax}\text{/}$ of the ER band in cS2. Only
a weak correlation with the transverse wires was found, as expected due to the
$10\text{\,}\mathrm{\char 37\relax}\text{/}$ higher relative selection
efficiency, but no asymmetry in the horizontal event distribution. The [37]Ar
calibration data taken after SR0 and [83m]Kr taken every second week during
SR0 were also tested for non-uniformity. In both cases no indication is found
of an asymmetric bias in the event reconstruction. The impact of each data
quality cut on the unblinded data was tested in several parameter spaces. The
selections showed only expected correlations, e.g. the impact of the radius of
the FV on the surface background, but none of the selections showed any
behavior which could explain the observed asymmetry.

Figure A.2: Spatial distribution of the search data in the
$4.18\text{\,}\mathrm{t}\text{/}$ fiducial volume (blue line). Each event is
represented with a pie-chart, showing the fraction of the best-fit PDF
including a $200\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$ WIMP
evaluated at the position of the event, color-coded as in Figure 3. Events
reconstructed outside of the fiducial volume are colored in gray. Black dashed
lines depict the boundaries of the sensitive volume given by the cathode and
gate positions. The TPC radius is indicated by a vertical black line. Figure
A.3: Distribution of the search data in the horizontal plane. Each event is
represented with a pie-chart, showing the fraction of the best-fit PDF
including a $200\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$ WIMP
evaluated at the position of the event, color-coded as in Figure 3. Events
with a reconstructed radius outside of the fiducial volume are shown in gray.
The inner (outer) circle indicates the FV selection (TPC radius), and dashed
lines show the transverse wire positions.

### Comparison of upper limits

Figure A.4 compares this work to other recent results, both with and without a
power-constraint applied consistent with the original PCL recommendation. In
order to not place limits on models for which an experiment has low
sensitivity, a set of recommendations adopted by LXe dark matter experiments
[36] recommends using a power-constraint [40]. The set of recommendations
erroneously defines sensitivity in terms of discovery power, while it should
be in terms of “rejection power”; the probability for a certain signal to be
excluded given the no-signal hypothesis. This rejection power corresponds to
the quantile of upper limits for that signal, as used to produce the
conventional sensitivity bands. The power-constrained limit is defined by
setting a signal size threshold corresponding to a certain rejection power,
and only placing upper limits at or above this threshold. This aims both to
limit arbitrarily low limits being set by a systematic fluctuations, and
moderates the effect on the upper limit of mis-modelling, in particular
overestimated backgrounds. The choice of threshold rejection power is a
fiducial one, and previous publications and the community recommendations
(using discovery rather than rejection power) set it to correspond to the
$-1\text{\,}\sigma$ quantile of the limit distribution. Given the need to
amend the recommendations, we choose a very conservative rejection power
threshold of 0.5 for this work, corresponding to the median unconstrained
limit.

Figure A.4: Upper limits on spin-independent WIMP-nucleon cross section at $90\text{\,}\mathrm{\char 37\relax}\text{/}$ confidence level for this work (black lines), LZ [5] (purple lines, preprint), PandaX-4T [4] (red lines) and XENON1T [3] (blue lines). For PandaX and LZ, dashed lines represent their published result, for XENON results the dashed lines represent limits without a power-constraint applied. Full lines for each experiment represent a limit that is power-constrained to always lie at or above the median un-constrained limit.  Table 2: Extended table from table 1, including expectation values computed separately for the wire region.  | Nominal | Best Fit
---|---|---
| ROI | Signal like
| Full Volume | off wire | on wire | Full Volume | off wire | on wire
ER | $134$ | $135_{-11}^{+12}$ | $110_{-9}^{+10}$ | $24\pm 2$ | $0.92\pm 0.08$ | $0.76_{-0.06}^{+0.07}$ | $0.167_{-0.014}^{+0.015}$
Neutrons | $1.1^{+0.6}_{-0.5}$ | $1.1\pm 0.4$ | $0.9\pm 0.4$ | $0.18\pm 0.07$ | $0.42\pm 0.16$ | $0.35\pm 0.14$ | $0.07\pm 0.03$
$\mathrm{CE}\nu\mathrm{NS}$ | $0.23\pm 0.06$ | $0.23\pm 0.06$ | $0.19\pm 0.05$ | $0.041\pm 0.011$ | $0.022\pm 0.006$ | $0.019\pm 0.005$ | $0.0038\pm 0.0010$
AC | $4.3\pm 0.9$ | $4.4_{-0.8}^{+0.9}$ | $2.1\pm 0.4$ | $2.3_{-0.4}^{+0.5}$ | $0.32\pm 0.06$ | $0.16\pm 0.04$ | $0.16\pm 0.04$
Surface | $14\pm 3$ | $12\pm 2$ | $11\pm 2$ | $0.90_{-0.17}^{+0.18}$ | $0.35\pm 0.07$ | $0.32\pm 0.06$ | $0.026\pm 0.005$
Total Background | 154 | $152\pm 12$ | $124_{-9}^{+10}$ | $28\pm 2$ | $2.03_{-0.15}^{+0.17}$ | $1.61_{-0.12}^{+0.13}$ | $0.42_{-0.03}^{+0.04}$
WIMP | - | $2.6$ | $2.1$ | $0.5$ | $1.3$ | $1.1$ | $0.2$
Observed | - | $152$ | $124$ | $28$ | $3$ | $2$ | $1$