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

# Detector signal characterization with a Bayesian network in XENONnT

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  S. Ahmed Maouloud
LPNHE, Sorbonne Université, CNRS/IN2P3, 75005 Paris, France  L. Althueser
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<EMAIL_ADDRESS>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<EMAIL_ADDRESS>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  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  Q.
Pellegrini  LPNHE, Sorbonne Université, CNRS/IN2P3, 75005 Paris, France  R.
Peres  Physik-Institut, University of Zürich, 8057 Zürich, Switzerland  C.
Peters<EMAIL_ADDRESS>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  T. R. Pollmann  Nikhef and the University of
Amsterdam, Science Park, 1098XG Amsterdam, Netherlands  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  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 developed a detector signal characterization model based on a Bayesian
network trained on the waveform attributes generated by a dual-phase xenon
time projection chamber. By performing inference on the model, we produced a
quantitative metric of signal characterization and demonstrate that this
metric can be used to determine whether a detector signal is sourced from a
scintillation or an ionization process. We describe the method and its
performance on electronic-recoil (ER) data taken during the first science run
of the XENONnT dark matter experiment. We demonstrate the first use of a
Bayesian network in a waveform-based analysis of detector signals. This method
resulted in a 3% increase in ER event selection efficiency with a
simultaneously effective rejection of events outside of the region of
interest. The findings of this analysis are consistent with the previous
analysis from XENONnT, namely a background-only fit of the ER data.

##  I Introduction

XENONnT is a dark matter direct detection experiment currently operating at
INFN Laboratori Nazionali del Gran Sasso (LNGS) in Italy. The experiment has a
wide range of (astro)particle physics capabilities, including the search for
weakly-interacting massive particles (WIMPs), solar axions, and coherent
electron-neutrino nucleus scattering from 8B solar neutrinos [1]. XENONnT’s
physics program aims to make substantial progress on sensitivities through
improvements in hardware, software, and analysis methods. The XENON
collaboration recently reported a search for WIMPs [2] and an analysis of
electronic-recoil (ER) data [3] using the data collected during Science Run 0
(SR0). These new results relied on XENONnT’s unprecedentedly low background
radioactivity rates and its keV-scale energy threshold. To achieve the low
intrinsic background rates in ultra-rare event search experiments, large
numbers of events not originating from the desired interactions in the target
must be rejected; to this end, robust classification and characterization of
detector signals are crucial for dark matter searches and other background-
dominant processes.

During the past decade, the incorporation of machine learning techniques,
particularly deep learning, has led to innovation within the field of
(astro)particle physics [4, 5, 6]. Advances in computer vision have made
convolutional neural networks a common approach to deep learning applications
in (astro)particle physics for classification problems; see for instance [7,
8, 9, 10, 10, 11, 12, 13, 10]. Given the success of deep learning methods,
applications of machine learning in direct dark matter searches with time
projection chambers have seen increased attention [14]. Recently, the use of
Bayesian networks has been presented for event localization [15] and for
inference in the search for dark matter [16].

Motivated by such applications, we developed a Bayesian network for a
waveform-based analysis of detector signals. With this method, we aimed to
quantify how alike a detector signal is to the understood models of
scintillation (S1 signals) and ionization (S2 signals). S1 and S2 signals
which can be explained by these understood models are defined as “canonical”
in shape. We constructed a Bayesian network to quantify the extent to which a
detector signal shape is canonical. We evaluated how the model performs in
classifying S1 and S2 signals respectively and compared the model performance
to that of the baseline method of signal classification. Then, we further
applied this quality metric beyond signal classification as the primary
detector signal quality feature in event selection. We present the first
application of a waveform-based analysis of detector signals using a Bayesian
network by analyzing the electronic-recoil data reported in [3] and obtain
results that are in agreement with the original work.

The paper is organized as follows. In Section II we provide an overview of the
XENONnT experiment. In Section III we describe the use of a Bayesian network
to study S1 and S2 signal classification. In Section IV we apply the
quantitative scores from the Bayesian network for selecting ER events, and we
further present the results of this application. And finally in Section V we
summarize the results and outline future work.

##  II The XENONnT Experiment

The XENONnT detector is a dual-phase xenon time projection chamber (TPC) with
an active target mass of 5.9 tonnes of liquid Xe (LXe). Detailed information
regarding XENONnT detector conditions, systems, and subsystems can be found in
[17, 18, 19, 20, 21, 22, 3].

The working principle of the detector can be described as follows: when a
particle interacts within the LXe, the energy transferred to the target
excites and ionizes the atoms. The excitation of Xe atoms creates dimer
states, which then decay promptly by emitting VUV photons. These photons are
detected with photomultiplier tube (PMT) arrays at the top and bottom of the
TPC. The prompt scintillation signal of an interaction is called an S1 signal.
Simultaneously, the ionization of Xe atoms at the interaction site liberates
atomic electrons. Some of these electrons recombine with nearby ions to create
excited states, which then contribute to the S1 signal. The remaining
electrons are drifted upward to a liquid-gas interface by an applied electric
field between a cathode at the bottom of the detector and a gate electrode at
the top of the liquid. A thin gaseous Xe layer above the liquid acts as an
amplification region, where an anode accelerates the electrons into the gas,
generating a proportional electroluminescence signal. This secondary
ionization-induced signal is called an S2 signal, and its size is proportional
to the number of extracted electrons.

For any detector signal, the electronic pulses from different PMTs are
clustered in time, forming a waveform. Given the stochastic nature of the
prompt and secondary scintillation processes, each waveform will have a unique
shape and size, with a typical S1 signal having a much narrower time profile
than a typical S2 signal, owing to the nature of their production mechanisms.
An event is formed from a pair of S1 and S2 detector signals from a single-
scatter interaction. The interaction 3D position and energy deposited as
ionization and scintillation light is reconstructed for each event.

The XENONnT SR0 electric field configuration presented new low-energy analysis
opportunities due to a higher light yield and thus a lower energy threshold,
but also introduced new challenges for event reconstruction and background
mitigation, including lower electron production and longer electron drift
time. For more information on the electric field configuration in XENONnT SR0,
see [3].

Challenges to a sensitive rare-event analysis in this case include effectively
rejecting radiogenic-sourced interactions that occur in the top gas region of
the TPC, which can be mistakenly reconstructed to have occurred within the LXe
region of the TPC, requiring effective gas-event mitigation for analysis.
Additionally, the rate of accidental coincidences (ACs), which occur when two
detector signals classified as S1 and S2 signals do not originate from the
same single-scatter interaction within the TPC, increases with a longer
electron drift time and errors in detector signal classification. These
challenges require careful approaches both to classification of S1 and S2
signals and to event selection based on the characteristics of detector
signals comprising an event, to reduce events outside of the region of
interest (ROI) for a given analysis.

##  III Signal Classification

Current and previous S1 and S2 signal classification algorithms employed in
direct dark matter detection experiments with LXe TPCs rely on manually
analyzing and optimizing a decision boundary using the size (area) and the
width of the signal [23, 24, 25, 26]. In XENONnT SR0, a waveform was
classified as an S1 (S2) signal if its waveform rises sufficiently quickly
(slowly) and has at least 3 (4) contributing PMTs [3]. This classification
method lacks the ability to provide an informative classification confidence
metric, or score, owing to its being deterministic. Therefore, further
detector signal quality selections must be applied to reduce detector signal
misclassification rates. To overcome the limitations of using this detector
signal classification method, we developed a waveform-based classification
model based on a Bayesian network, which produces continuous outputs that can
be used in an informative way.

###  III.1 Input Data

The training and evaluation data for this work consists of a combination of
simulated and measured data, primarily simulated ER interactions ranging from
[0.75, 200] keV. The simulated data was generated using XENONnT’s waveform
simulator package, `WFSim` [27], and event-building software, `straxen` [28].
Light and charge yields used in `WFSim` are computed using `NEST` [29, 30].

In `WFSim`, the light yield for an interaction with a given energy is used to
generate S1 signals before computing the photons’ arrival times at the PMTs.
The light yield accounts for scintillation of the Xe atoms, electron-ion
recombination, and the singlet-to-triplet fraction of excited states. The
observed light yield probability distribution is computed for each PMT based
on an S1 light collection efficiency (LCE) map. The simulation process for S2
signals differs because electrons are drifted toward the liquid-gas interface,
during which electronegative impurities may reduce the number of electrons
arriving at the liquid-gas interface. The arrival times of the electrons at
the liquid-gas interface are computed based on electron drift and diffusion
models, followed by calculating the photon timing of the electroluminescence
of individual electrons. Then, based on the S2 LCE map, the charge yield
probability distribution is computed for each PMT.

Subsequently, for both S1 and S2 signal simulations, once the arrival times of
photons are computed, the currents in the PMTs are simulated using a model of
the PMT and digitizer response with sampling time resolution of 10 ns [31].
Then, using `straxen`, PMT signals are scanned for PMT “hits” above a
threshold. PMT hits are grouped iteratively into clusters with adjacent hits
within a 700 ns time window, forming a waveform that can subsequently be
classified as an S1, S2, or “unknown” by `straxen`. In XENONnT simulations and
SR0 data-taking, every waveform is saved with a fixed number of 200 samples.
Sample duration in XENONnT can vary from a few tens of ns for an S1 signal and
up to few hundreds of ns for an S2 signal, to accommodate the full waveform
within the fixed 200-sample interval.

We augmented the training data in the low-area range where signal
classification is particularly challenging in SR0. To this end, we simulated a
set of S2-only signals with [1, 10] electrons (at very low ER interaction
energies, S1 signals are rarely able to be observed). Additionally, a very
pure ($>$99.9%) measured sample of single-electron S2 signals, produced from a
highly-emitting electron source near the gas region, was added to ensure that
experimental effects at these low areas were represented in the training
sample despite any limitations in modeling at these low areas. In total, the
simulation and measured data used in training and evaluation consisted of 106
waveforms with ground-truth labels.

The training dataset was composed of true S1 or S2 waveforms from single-
scatter interactions within the detector’s 4 tonne fiducial volume, which is
defined in [3]. In this work, we define out-of-distribution detector signals
as any types of waveforms which were not included in the training set for the
model. This includes S1 or S2 signals with non-canonical shapes and
interactions in gas, where both can be vetoed during analysis based on their
characteristics, like waveform shape, as will be demonstrated later.

The top panels of Fig. 1 show simulated S1 and S2 waveforms downsampled to 50
samples, with an absolute amplitude in units of [PE/ns]. The waveform samples
represent the light collected in a certain window of time. The bottom panels
of Fig. 1 show the second component of the input to the algorithm, quantiles
with 50 elements. The quantiles represent the amount of time elapsed for a
given fraction of the total waveform area to be observed — for instance, if
considering 50 quantiles, each quantile is the duration of time elapsed for an
additional 2% of the total waveform area to be observed. The waveforms and
quantiles are transformations of each other, where the quantiles explicitly
contain time profile information, and the waveforms explicitly contain signal
size information. These discretized samples of the data are treated as
individual attributes, as explained in Section III.2.

Figure 1: Individual examples of an S1 signal (green) and S2 signal (purple)
from simulated data used as input for training. The S1 signal example has a
total area of 18 PE and duration of 2000 ns; the S2 signal area is 1766 PE and
duration is 12000 ns. Top: waveforms, downsampled to 50 samples total, with
the elapsed time of the signal in the secondary x-axis, illustrating the
different temporal profiles between a typical S1 and S2 signal. Bottom:
quantiles, 50 total, with relative total observed area in the secondary
x-axis.

###  III.2 Classification with a naive Bayes classifier

A naive Bayes classifier (NBC) is a type of Bayesian network that uses a
simple graph-based representation to compactly encode a complex, high-
dimensional distribution [32, 33]. For a comprehensive explanation of Bayesian
networks, see e.g. [34].

The graph structure of an NBC is shown in Fig. 2, where each circle in the
graph is called a node, which represents a variable, discrete or continuous,
that depends on a stochastic process. This is known as a random variable. The
arrows between nodes denote dependence between random variables, and the
direction denotes causality. To avoid a variable depending upon itself, there
can be no cyclic paths in the graph. The class node, $C$, is the parent node
of the set of attribute nodes, $\vec{A}=\\{A_{1},\ A_{2},\ \dots,\ A_{n}\\}$.

Figure 2: Graph structure of a naive Bayes classifier. Class node ($C$, either
S1 or S2) is assumed to directly influence the value of each attribute node
($A_{i}$). Each attribute node is conditionally independent from all other
attribute nodes, given the class node.

The graph structure of an NBC implies that all attributes are directly
dependent on the class, and conditionally independent from each other, given
the class. In this work, the attributes denote quantiles and waveform elements
of time-series data, as depicted in Fig. 1. The independence assumption is
naive in this case because the attributes, being time-series data, are not
truly independent. The class node maps each attribute to the signal
classification, either S1 or S2. In practice, the set of possible values that
the random variable $C$ can take is $\\{0,\ 1\\}$, which are indices
corresponding to the discrete classes.

The quantiles and waveform elements are continuous values. Therefore, the
range of possible values each attribute can take on must be either
parameterized or discretized. For this work, we discretize the attribute’s
values by binning and assigning indices corresponding to the bin. The Bayesian
blocks method performs discretized, non-uniform binning of a continuous
variable based on the observed values for that random variable attribute, as
described in Section 3.1 of [35]. The set of possible values that an attribute
can take is $\\{0,\ \dots,\ m\\}$, where $m$ is the number of bins defined by
the Bayesian blocks method.

It follows that each entry in the full joint distribution over all of the
random variables in this graph structure is defined as:

$P(C,\ A_{1},\ \dots,\ A_{n})\ \propto\ P(C)\prod_{i=1}^{n}P(A_{i}\ |\ C),$
(1)

where $P(C)$ is the prior distribution over the signal classes and $P(A_{i}\
|\ C)$ is the local joint probability distribution of the $i^{\text{th}}$
attribute conditioned on the signal class. For this work, we chose to use a
flat prior on the class distribution, $P(C)$, meaning a 50/50 split of S1 and
S2 signals. This is a logical choice of prior for the ER physics analysis
presented here, which requires both an S1 signal and an S2 signal for an event
to be considered. Regardless, the choice of prior was not found to
significantly affect the performance of the classifier.

The probability distribution of the attributes conditioned upon the signal
class is learned from the training data for each attribute. Once the
conditional probability distributions are learned, the probability of a
waveform belonging to each class can be inferred using Bayes’ rule. This is
known as a probability query and is defined as:

$P(C\ |\ A_{1}=a_{1},\ \dots,\ A_{n}=a_{n})=\\\
\frac{P(C)\prod\limits_{i=1}^{n}P(A_{i}=a_{i}\ |\ C)}{P(A_{1}=a_{1},\ \dots,\
A_{n}=a_{n})}\ ,$ (2)

where the result of the query is the posterior probability distribution over
the values of $C$, conditioned on the observed values of the attribute nodes,
$\vec{a}=\\{a_{1},\ a_{2},\ \dots,\ a_{n}\\}$. Note that the denominator does
not depend on the value of $C$. In practice, the natural logarithm of the
posterior probability is calculated to avoid computational loss of precision.

The number of attributes used in evaluation and subsequently in Section IV was
chosen by training for S1/S2 signal classification using multiple attribute
options and selecting the choice of attributes with optimal classification
performance. In this work, we found that 100 attributes comprised of 50
waveform samples and 50 quantiles, as shown in Fig. 1, had the highest
classification performance of those studied.

We found the benefits of using an NBC for signal classification to be three-
fold. First, the Bayesian classification approach is intuitive and
interpretable. Second, the NBC structure has been shown to be effective for
classification even in cases where there are strong dependencies between the
attribute nodes [36], with the advantages of being faster to learn, faster to
query, and smaller to store in memory than a graphical model that includes
complex dependencies among attributes. Finally, the output of a probability
query of the network is informative about the network’s confidence in a signal
belonging to each class; this capability is not present in current and
previous S1 and S2 signal classification algorithms [23, 24, 25, 26].

###  III.3 Naive Bayes classifier performance

The NBC was constructed and trained by building upon the scientific `Python`
software stack [37, 38, 39]. The trained model was evaluated using 50% of the
labeled data, which was not used in training. For each signal, the most
probable class, S1 or S2, can be decided by performing a probability query for
each class and choosing the most probable class.

The NBC can be evaluated as a deterministic classifier by taking a static
decision boundary on the posterior distribution, in this case
$P(C=S1|\vec{A})=P(C=S2|\vec{A})=0.5$. The classification performance of the
NBC is shown in Table 1. The NBC, even given the independence assumptions
described in Section III.2, outperformed the `straxen` classification, which
correctly classified 99.974% of S1 signals and 99.907% of S2 signals. We
ascribe this improvement to the NBC having sufficient parameters to describe
the conditional probability distributions encoded in the attributes.

Naive Bayes Classifier
---
| True S1 | True S2
Predicted S1 | 99.999 $\pm~{}0.001~{}\%$ | 0.003 $\pm~{}0.001~{}\%$
Predicted S2 | 0.001 $\pm~{}0.001~{}\%$ | 99.997 $\pm~{}0.001~{}\%$
Table 1: Performance results on evaluation data of the naive Bayes classifier
described in Section III.2 for detector signal classification. True S1 (S2)
denotes the labeled S1 (S2) signal populations in the validation dataset.

###  III.4 Naive Bayes classifier score as a signal characterization metric

In addition to the NBC being an effective deterministic classifier, the values
output from the probability queries were found to be informative about the
characteristics of the S1 or S2 signal’s shape. Due to violation of the
independence assumptions implied by the NBC structure, as well as the use of
an uninformative prior, in this case the probability query returns a “score”
rather than a reliable probability. Nevertheless, the scores from the NBC can
be used to characterize each signal beyond the task of deterministic S1/S2
signal classification. We define the NBC score as the natural logarithm of the
ratio of the calculated probability queries of the class, $C$, having the
value S1 or S2, given the values of the attributes:

$\text{NBC score}=\ln{(P(C=\text{S}1\ |\ A_{1}=a_{1},\ \dots,\
A_{n}=a_{n})})\\\ -\ln{(P(C=\text{S}2\ |\ A_{1}=a_{1},\ \dots,\
A_{n}=a_{n}))}\ .$ (3)

This NBC score quantifies the extent to which the model favors the signal
being of either canonical scintillation-origin (S1-like) or canonical
ionization-origin (S2-like). A detector signal with a large positive value for
NBC score has an S1-like shape, while a large negative value for NBC score
would imply an S2-like shape. Detector signals with NBC scores near 0 are
neither S1-like nor S2-like. Each event, which consists of a S1 and S2 signal
pair, will have an S1 NBC score, referring to the NBC score of the S1 signal,
and an S2 NBC score, referring to the NBC score of the S2 signal.

To illustrate the utility of the NBC score beyond deterministic
classification, we considered the calibration source ${}^{83\text{m}}$Kr,
which decays via two ER-inducing internal conversion steps, first depositing
32.1 keV and then 9.4 keV, with a half-life of the latter decay of 154 ns
[40]. ${}^{83\text{m}}$Kr is used as a standard candle for calibration in
XENONnT and other xenon TPCs due to its distinct properties, including this
prompt two-step decay. In practice, the two decays are often merged into a
single S1 signal due to the intermediate state’s short half-life being on the
same order of magnitude as an S1 signal’s total width, with the much wider S2
signals almost always being merged into a single S2 signal. Therefore,
correctly distinguishing the separated S1 signals from the merged S1 signals
in ${}^{83\text{m}}$Kr data is critical for energy response studies, which
rely on properly characterizing S1 signals as being merged or separated.

Fig. 3 demonstrates a case where NBC scores can be used to isolate detector
signals which are non-canonical in shape, i.e. not truly isolated S1 signals
produced within the fiducial volume of the detector. Based on the results of
this test case, the NBC scores were concluded to be a useful metric for
reducing temporal overlap of signals. Furthermore, in the following section,
we demonstrate that, due to its robustness against out-of-distribution
samples, applying the NBC scores in event selection is suitable for physics
analyses where one wishes to reject S1 and S2 signals of non-canonical shapes.

Figure 3: ${}^{83\text{m}}$Kr calibration data corrected S2 area vs. corrected
S1 area (cS2, cS1). Corrections on area are calculated to normalize detector
effects that vary across time and space, see [3] for details. The color scale
indicates the S1 signal’s NBC score (Eq. 3). The rightmost population contains
the merged (41.5 keV) S1 signals, and thus is shown to have an NBC score that
is less canonically S1-like, owing to the true underlying physical process
being a merging of two S1 signals. The 32.1 keV (middle) and 9.4 keV (left)
populations have S1 NBC scores which are more canonically S1-like. The S2
signals for the 32.1 keV and 9.4 keV are merged into a single S2 signal; thus
all three populations of S1 signals shown have equivalent-sized S2 signals.

##  IV Event selection using the NBC scores

In this section we describe the application of signal characterization in
event selection based on NBC scores to the XENONnT SR0 ER dataset.

Most recorded signals in a dark matter detector science run, as in XENONnT’s
SR0 campaign, are not derived from single-scatter recoil interactions in the
fiducial volume. They are primarily due to mislabeled detector signals,
detector signals from interactions in the gas which are misplaced within the
fiducial volume, multiple detector signals which are merged together in
processing, and detector signals grouped from lone hits from multiple PMTs,
such as dark counts. These signals can contribute to events that are defined
as being outside of the ER region of interest (ROI). Conversely, events within
the ER ROI are defined as single-scatter ER events within the energy range of
interest and occurring within the fiducial volume.

Because the NBC was trained on S1 and S2 signals generated from ER
interactions within the fiducial volume, events outside of the ER ROI,
relative to ER events within the ROI, will have neither strongly S1-like or
S2-like NBC scores for their S1 and S2 signals, respectively. The NBC score is
a single metric that represents the characteristic of the full waveform shape.
Given this feature of the NBC scores, we evaluated their ability to be used in
place of several low-dimensional quality selection parameters that were used
in the SR0 analysis in XENONnT as signal quality selection criteria [3].

We calculated the efficiency of applying the NBC scores to select ER events
and the effectiveness of removing events outside the ER ROI using calibration
data from 220Rn and 37Ar injections in XENONnT. The 220Rn decay chain produces
212Pb, a uniform $\beta$-emitting source of ER events across the [1-140] keV
energy region in this analysis. The 220Rn data was used to define signal
selection efficiency across the ER energy spectrum [41]. 37Ar decays by
electron capture into 37Cl, producing an electron vacancy in either the K, L,
or M-shell. In particular, the K-shell vacancy (90.2% branching ratio) being
filled by an electron rearrangement deposits a total energy of 2.82 keV [42],
which was useful in this study for calibrating ER event acceptance near the
threshold of detection with high statistics and minimal contamination.

We calculated NBC scores for both the S1 signal and S2 signal of each event in
the calibration data. Each event’s S1 (S2) signal selection depends upon a
decision boundary between the NBC score of S1 (S2) signals and the S1 (S2)
observed signal area. The optimal decision boundaries used in this selection
were determined using the 220Rn calibration dataset and chosen to isolate non-
canonical detector signals. It is noteworthy that the selection can be made
more strict or loose depending on the analysis application. We then evaluated
both the efficiency of accepting ER-like events, and the effectiveness at
rejecting events outside of the ER ROI, using the NBC score boundaries that
were imposed on S1 and S2 signals contributing to events reconstructed within
the fiducial volume.

The selection of ER events in this Bayesian network-based method differs from
the previous work in [3] by reducing several signal quality selection criteria
applied in [3] to only two: one selection on the S1 signal’s NBC score, and
one selection on the S2 signal’s NBC score. Both methods further apply
identical additional selection criteria to remove remaining multiple scatter
events, mis-paired S1 and S2 signals, and accidental coincidence events.

Fig. 4 shows the S1 and S2 NBC selection performance on 220Rn calibration
data. The bulk of the events removed from the 220Rn calibration data contain
gas-like S2 signals and predominantly lie above the band of ER events in Fig.
4. In addition, events containing single electrons misclassified as S1 signals
(cS1$<$25 PE) are removed. The remaining events outside of the ER ROI were
removed by the additional selection criteria mentioned above.

Figure 4: Performance of the S1 NBC and S2 NBC selection criteria on 220Rn
calibration data, within the fiducial volume. A bin colored black indicates
the fraction of remaining events to be exactly 0. Adjacent panels show the
fraction of remaining events per bin, projected along the cS1 and cS2 axes.
Events outside of the region of interest (ROI) are effectively targeted by the
S1 and S2 NBC selection criteria. Above the ER band, gaseous S2 signals are
mis-reconstructed into events within the fiducial volume, becoming the primary
source of background events. Following the S1 and S2 NBC selection criteria,
selections to target multiple scatter events, mis-paired S1 and S2 signals,
and accidental coincidences are applied, which remove the remaining events
outside of the ER ROI.

The ER event acceptance was calculated using both 37Ar monoenergetic data
within the fiducial volume, and clean 212Pb data within the fiducial volume
from 220Rn calibration. The same procedure as in [3] was used for the
acceptance calculation, but using solely the S1 and S2 NBC event selection
criteria for detector signal quality selection. The results of these
efficiency calculations are shown in Fig. 5. The results of this analysis are
shown in combined energy scale, which is a linear combination of cS1 and cS2
values from an event, the calculation of which is described in [3]. For ER
events, the combined energy is a reconstructed value of the energy deposited
by the interaction in the detector. The overall efficiency is the product of
the individual efficiencies from the S1 signal detection (dominant at low
energies), the S2 signal detection, the S1 and S2 NBC selection criteria, the
AC selection criteria applied in [3], and the pairing/single scatter selection
criteria applied in [3].

The increase in total efficiency relative to the previous work is 3%. The
improvement arises from fewer ER events being removed from the data than in
the previous method, which relied on several more sequential selection
criteria.

The effectiveness of this method at removing events outside of the ER ROI was
calculated using the SR0 ER dataset. Events outside of the ER ROI were tagged
using the set of signal quality selection criteria developed in [3]. These
tagged populations were then used to evaluate the relative effectiveness of
the S1 and S2 NBC selections at removing events outside of the ER ROI. The
population overlap between events rejected by the previous sequential quality
selection criteria and the S1 and S2 NBC selection criteria of this analysis
was was 96%. This can be interpreted to mean that the NBC selection criteria
are successful at removing events originating from gas-like S1 and S2 signals,
misclassified S1 or S2 signals, and mis-reconstructed signals due to
misclustering of individual PMT signals such as dark counts, lone hits, or
multiple signals from multiple interactions merged together, populations
similarly observed in the 220Rn calibration dataset. The non-unitary overlap
between populations removed by the selection methods can be attributed to the
increase in ER event selection efficiency.

Figure 5: Comparison of total event selection efficiency between this work and
the previous work reported from XENONnT SR0 [3]. The step increase at 10 keV
in efficiency is due to the nuclear-recoil region of data being blinded below
10 keV during both analyses. On average, this method is 3% more efficient,
with the greatest relative improvement in efficiency being in the 2-20 keV
energy region.

###  IV.1 Analysis of electronic-recoil spectrum

The low-energy electronic-recoil spectrum of XENONnT SR0 was measured in a
total exposure of 1.16 tonne-years; it mainly consists of radiogenic ER events
from 222Rn contamination in the LXe target. The spectrum is shown in Fig. 6
and was fit by a detailed background model, with all components as described
in [3], with a step-function approximation to account for the electron binding
energies in the solar neutrino spectrum as suggested in [43], and by using an
unbinned maximum likelihood framework. The goodness-of-fit measurement for the
spectrum is $\chi^{2}/N_{\text{dof}}\ =128.64/128=1.004$ (p-value of 0.467).
As in [3], the ER data is consistent with the background-only hypothesis.

The individual background components contributing to the SR0 ER dataset are
summarized in Table 2. It should be noted that the uncertainties on each
component in Table 2, while valid for each study individually, are strongly
correlated between this work and the previous work. The dominant source of ER
events at low energies is the $\beta$-decay of 214Pb. The activity
concentration of 214Pb in SR0 from this analysis was estimated to be $(1.39\pm
0.08)$ µBq/kg, which agrees with the best-fit activity concentration of 214Pb
reported in [3]. The higher number of observed events in this work can be
attributed to the higher average selection efficiency. The lower-fitted
contribution of 133Xe to the total number of events, which is a second-order
contribution to the event rate above 80 keV, can be attributed to the decrease
in relative efficiency gain above 80 keV seen in Fig. 5. The remaining
components’ best-fit number of observed events are within the expected
uncertainty ranges of the reported values in [3].

Figure 6: Top panel: SR0 ER data (black) selected using the Bayesian network-based approach with the best-fit background-only model $B_{0}$ (red). The subdominant AC contribution is not visible. Bottom panel: $\Delta$Events/bin corresponds to the difference in observed data in Events/(t$\cdot$y$\cdot$keV) between those selected using the Bayesian network-based approach and those selected using the previous method described in [3]. The increase of observed events particularly at energies below 20 keV is consistent with the increase in efficiency of this work relative to [3]. Component | Fit (this work) | Fit (prev. work)
---|---|---
214Pb | 1050 $\pm$ 130 | 960 $\pm$ 120
85Kr | 100 $\pm$ 60 | 90 $\pm$ 60
Materials | 280 $\pm$ 50 | 270 $\pm$ 50
136Xe | 1580 $\pm$ 60 | 1550 $\pm$ 50
Solar $\nu$ | 310 $\pm$ 30 | 300 $\pm$ 30
124Xe | 250 $\pm$ 30 | 250 $\pm$ 30
AC | 0.71 $\pm$ 0.03 | 0.71 $\pm$ 0.03
133Xe | 80 $\pm$ 60 | 150 $\pm$ 60
${}^{83\text{m}}$Kr | 101 $\pm$ 17 | 80 $\pm$ 16
Table 2: Best-fit background model, $B_{0}$ components, with number of events
observed for each component in SR0 within the energy range of (1, 140) keV.
The right column has the number of events reported from [3].

Additional potential sources of systematic uncertainty in the results of this
analysis include any introduced by the NBC method and variations in signal
shapes between training and experimental data. We found that the choice of
number of attributes used in the NBC did not cause a statistically significant
difference in the deterministic classification results shown in Table 1. For
the signal size, the most significant systematic effects in this work would
arise from nonuniformities in the drift field within the fiducial volume,
which were already accounted for in the reconstructed combined energy
resolution. Thus, to avoid double counting, the systematic uncertainties are
calculated using a method identical to that in [3].

##  V Conclusion and future work

We demonstrated the first use of a Bayesian network to perform detector signal
classification, waveform-based event selection, and subsequent analysis in a
full-scale dual-phase Xe TPC. Applying the naive Bayes classifier (NBC) based
metric in event selection reduces significantly detector signals outside of
the region of interest and solves the need for additional selection criteria
based on detector signal quality. The method can be used both as an
independent analysis framework and as a valuable cross-check for analyses that
use lower-dimensional features in subsequent event selection steps. The
development of this method relies on simulated data, and the selection
criteria rely on calibration data, without optimizing on ER search data.
Therefore, due to the NBC being developed blinded to the ER dataset, it is
agnostic to any new interactions present in the XENONnT SR0 ER search data,
allowing us to demonstrate that the Bayesian network-based method of signal
selection corroborates the radiogenic ER background-only hypothesis of the
low-energy ER data from XENONnT SR0 [3].

In the future, developing data selection criteria primarily using Bayesian
network-based methods could help to increase signal-to-background ratios in
dark matter detector experiments, thereby increasing experimental sensitivity
to new physical processes. Relaxing the three-fold PMT coincidence requirement
for a valid S1 signal, which is the primary reason for efficiency loss below 2
keV, could be viable without a significant increase in the accidental
coincidence rate by using a Bayesian network specially trained for classifying
these events. With this additional improvement on efficiency in a future study
dedicated to reducing accidental coincidence background rates, low-energy
physics phenomena could be probed to new sensitivities.

Other future directions of this work in XENONnT’s physics program include the
use of dynamic Bayesian networks [44], which incorporate temporal dependencies
between the attribute nodes. If the use of dynamic Bayesian networks
adequately accounts for the temporal dependencies, then the output of the
probability queries of the model will be suitable for use in an end-to-end
probabilistic analysis. One such meritable analysis would be to define the
fiducial volume based not upon event localization algorithms, but on the
posterior probabilities from a Bayesian network.

## Acknowledgments

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

  * Aprile  _et al._ [2020] E. Aprile _et al._ (XENON Collaboration), Projected WIMP sensitivity of the XENONnT dark matter experiment, JCAP 2020 (11), 031.
  * Aprile  _et al._ [2023] E. Aprile _et al._ (XENON Collaboration), First dark matter search with nuclear recoils from the XENONnT experiment (2023), arXiv:2303.14729 .
  * Aprile  _et al._ [2022a] E. Aprile _et al._ (XENON Collaboration), Search for new physics in electronic recoil data from xenonnt, Phys. Rev. Lett. 129, 161805 (2022a).
  * Radovic  _et al._ [2018] A. Radovic, M. Williams, D. Rousseau, M. Kagan, D. Bonacorsi, A. Himmel, A. Aurisano, K. Terao, and T. Wongjirad, Machine learning at the energy and intensity frontiers of particle physics, Nature 560, 41 (2018).
  * Psihas  _et al._ [2020] F. Psihas, M. Groh, C. D. Tunnell, and K. Warburton, A review on machine learning for neutrino experiments, Int. J. Mod. Phys. A 35, 2043005 (2020).
  * Karagiorgi  _et al._ [2022] G. Karagiorgi, G. Kasieczka, S. Kravitz, B. Nachman, and D. Shih, Machine learning in the search for new fundamental physics, Nat. Rev. Phys. 4, 399 (2022).
  * de Oliveira  _et al._ [2016] L. de Oliveira, M. Kagan, L. Mackey, B. Nachman, and A. Schwartzman, Jet-images — deep learning edition, JHEP 2016 (7), 69 (2016).
  * Komiske  _et al._ [2017] P. T. Komiske, E. M. Metodiev, and M. D. Schwartz, Deep learning in color: towards automated quark/gluon jet discrimination, JHEP 2017 (1), 110 (2017).
  * Macaluso and Shih [2018] S. Macaluso and D. Shih, Pulling out all the tops with computer vision and deep learning, JHEP 2018 (10), 121.
  * Abbasi  _et al._ [2021] R. Abbasi _et al._ , A convolutional neural network based cascade reconstruction for the IceCube neutrino observatory, JINST 16 (07), P07041 (2021).
  * Abratenko  _et al._ [2021] P. Abratenko _et al._ (MicroBooNE Collaboration), Convolutional neural network for multiple particle identification in the microboone liquid argon time projection chamber, Phys. Rev. D 103, 092003 (2021) (2021).
  * Aurisano  _et al._ [2016] A. Aurisano, A. Radovic, D. Rocco, A. Himmel, M. D. Messier, E. Niner, G. Pawloski, F. Psihas, A. Sousa, and P. Vahle, A convolutional neural network neutrino event classifier, JINST 11 (09), P09001 (2016).
  * Abi  _et al._ [2020] B. Abi _et al._ (DUNE Collaboration), Neutrino interaction classification with a convolutional neural network in the dune far detector, Phys. Rev. D 102, 092003 (2020).
  * Akerib  _et al._ [2022] D. S. Akerib _et al._ (LUX Collaboration), Fast and flexible analysis of direct dark matter search data with machine learning, Phys. Rev. D 106, 072009 (2022).
  * Peters  _et al._ [2022] C. Peters, A. Higuera, S. Liang, V. Roy, W. U. Bajwa, H. Shatkay, and C. D. Tunnell, A method for quantifying position reconstruction uncertainty in astroparticle physics using bayesian networks, (2022), arXiv:2205.10305 .
  * Agnes  _et al._ [2023] P. Agnes _et al._ (DarkSide-50 Collaboration), Search for low mass dark matter in DarkSide-50: the bayesian network approach, (2023), arXiv:2302.01830 .
  * Aprile  _et al._ [2017a] E. Aprile _et al._ (XENON Collaboration), The XENON1T dark matter experiment, Eur. Phys. J. C 77, 881 (2017a).
  * Aprile  _et al._ [2017b] E. Aprile _et al._ (XENON Collaboration), Removing krypton from xenon by cryogenic distillation to the ppq level, Eur. Phys. J. C 77, 275 (2017b).
  * Aprile  _et al._ [2014] E. Aprile _et al._ (XENON Collaboration), Conceptual design and simulation of a water cherenkov muon veto for the XENON1T experiment, JINST 9 (11), P11006 (2014).
  * Aprile  _et al._ [2022b] E. Aprile _et al._ (XENON Collaboration), Material radiopurity control in the XENONnT experiment, Eur. Phys. J. C 82, 599 (2022b).
  * 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, 1104 (2022).
  * Antochi  _et al._ [2021] V. C. Antochi _et al._ , Improved quality tests of R11410-21 photomultiplier tubes for the XENONnT experiment, JINST 16 (08), P08033 (2021).
  * Aprile  _et al._ [2019] E. Aprile _et al._ (XENON Collaboration), XENON1T dark matter data analysis: Signal reconstruction, calibration and event selection, Phys. Rev. D 100, 052014 (2019).
  * Akerib  _et al._ [2018] D. S. Akerib _et al._ (LUX Collaboration), Calibration, event reconstruction, data analysis, and limit calculation for the LUX dark matter experiment, Phys. Rev. D 97, 102008 (2018).
  * Meng  _et al._ [2021] Y. Meng _et al._ (PandaX-4T Collaboration), Dark matter search results from the PandaX-4T commissioning run, Phys. Rev. Lett. 127, 261802 (2021).
  * Aalbers  _et al._ [2022] J. Aalbers _et al._ (LZ Collaboration), First dark matter search results from the LUX-ZEPLIN (LZ) experiment, (2022), arXiv:2207.03764 .
  * Aprile  _et al._ [2022c] E. Aprile _et al._ (XENON Collaboration), The XENON waveform simulator, [v1.0.1] 10.5281/zenodo.6783261 (2022c).
  * Aprile  _et al._ [2022d] E. Aprile _et al._ (XENON Collaboration), The straxen data processor, [v1.7.1] 10.5281/zenodo.6553131 (2022d).
  * Szydagis  _et al._ [2021] M. Szydagis _et al._ , Noble element simulation technique, [v2.2.1] 10.5281/zenodo.4569211 (2021).
  * Farrell  _et al._ [2021] S. Farrell, C. D. Tunnell, G. Rischbieter, and N. Carrara, Nestpy, [v1.4.9] 10.5281/zenodo.4897887 (2021).
  * Aprile  _et al._ [2022e] E. Aprile _et al._ (XENON Collaboration), The triggerless data acquisition system of the XENONnT experiment, (2022e), arXiv:2212.11032 .
  * Verma and Pearl [1988] T. Verma and J. Pearl, Causal networks: Semantics and expressiveness, in proceedings, in  _4th Workshop on Uncertainty in Artificial Intelligence_ (1988) p. 352.
  * Pearl [1988] J. Pearl,  _Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference_ (Morgan-Kaufmann, 1988).
  * Koller and Friedman [2009] D. Koller and N. Friedman,  _Probabilistic Graphical Models: Principles and Techniques_ (MIT Press, 2009).
  * Scargle  _et al._ [2013] J. D. Scargle, J. P. Norris, B. Jackson, and J. Chiang, Studies in astronomical time series analysis. vi. bayesian block representations, APJ 764, 167 (2013).
  * Domingos and Pazzani [1997] P. Domingos and M. Pazzani, On the optimality of the simple bayesian classifier under zero-oneloss, Machine Learning - ML 29, 103 (1997).
  * [37] P. S. Foundation, Python language reference, version 3.8.18.
  * Harris  _et al._ [2020] C. R. Harris _et al._ , Array programming with NumPy, [v1.18.5], Nature 585, 357 (2020).
  * Virtanen  _et al._ [2020] P. Virtanen _et al._ (SciPy 1.0 Contributors), Scipy 1.0: Fundamental algorithms for scientific computing in python, [v1.5.2], Nature Methods 17, 261 (2020).
  * Ruby  _et al._ [1971] S. L. Ruby, R. G. Clark, and L. E. Glendenin, Internal-conversion coefficients in the decay of 83Krm, Phys. Let. A 36, 321 (1971).
  * Aprile  _et al._ [2017c] E. Aprile _et al._ (XENON Collaboration), Results from a calibration of XENON100 using a source of dissolved radon-220, Phys. Rev. D 95, 072008 (2017c).
  * Boulton  _et al._ [2017] E. M. Boulton _et al._ , Calibration of a two-phase xenon time projection chamber with a 37Ar source, JINST 12 (08), P08004 (2017).
  * Amaral  _et al._ [2023] D. W. P. Amaral, D. Cerdeno, A. Cheek, and P. Foldenauer, A direct detection view of the neutrino nsi landscape, (2023), arXiv:2302.12846 .
  * Dean and Kanazawa [1989] T. Dean and K. Kanazawa, A model for reasoning about persistence and causation, Computational intelligence 5, 142 (1989).