# Identifying Risk Patterns in Brazilian Police Reports Preceding Femicides: A
Long Short Term Memory (LSTM) Based Analysis

Vinicius Lima  Polytechnic Institute
Purdue University
West Lafayette, USA
<EMAIL_ADDRESS>Jacque Almeida de Oliveira  Criminalistics Institute
Civil Police of the Federal District
Brasilia, Brazil
<EMAIL_ADDRESS>
###### Abstract

Femicide refers to the killing of a female victim, often perpetrated by an
intimate partner or family member, and is also associated with gender-based
violence. Studies have shown that there is a pattern of escalating violence
leading up to these killings, highlighting the potential for prevention if the
level of danger to the victim can be assessed. Machine learning offers a
promising approach to address this challenge by predicting risk levels based
on textual descriptions of the violence. In this study, we employed the Long
Short Term Memory (LSTM) technique to identify patterns of behavior in
Brazilian police reports preceding femicides. Our first objective was to
classify the content of these reports as indicating either a lower or higher
risk of the victim being murdered, achieving an accuracy of 66%. In the second
approach, we developed a model to predict the next action a victim might
experience within a sequence of patterned events. Both approaches contribute
to the understanding and assessment of the risks associated with domestic
violence, providing authorities with valuable insights to protect women and
prevent situations from escalating.

###### Index Terms:

Natural Language Processing, Long Short Term Memory, Violence Against Women,
Domestic Violence, Femicide, Feminicide, Gender Violence, Mach‘ine Learning.

##  I Introduction

Femicide or Feminicide is a hate crime that is broadly defined as the
”intentional killing of women or girls because they are female”, however,
definitions of the term may vary depending on the cultural context [1, 2]. In
this paper, femicide will be considered a crime related to domestic violence
against female individuals according to the Brazilian law definition [3]. The
term gained notoriety after researchers and activists studied murder cases
separated by gender, finding that murders of female victims have a high
frequency of cases related to domestic violence, where the murderer is usually
a family member or partner of the victim. In contrast, no specific motivations
behind killings were found among the male population [4]. A 2017 study
conducted by the United Nations (UN) demonstrated that when looking at the 20%
of female murders that occur around the world, 82% were killed by an ex-
partner [5].

In Brazil, the situation is no different. In a recent study, Brazilian
researchers demonstrated an increase of 4.8% in femicide cases from 2004 to
2015 [6]. Since March 2015, the country has had specific punishment for
femicide cases. While “regular” homicide authors can go to prison for 6 to 20
years, in femicide cases, the law regulates a minimum of 12 years and the
maximum time in prison in Brazil, which is 30 years [7]. Although having a
strict policy, the law did not stop the rise in cases over the past few years,
and Brazil is still considered one of the top countries where women are killed
in domestic violence [8]. The scenario is worse when considering specifically
the black population [6]. According to the World Health Organization (WHO),
the country registered one rape every ten minutes, in 2021 [6]. Furthermore,
according to data from the Brazilian Public Security Forum, in 2021 there were
a total of 1,319 femicides in the country, that is, on average, a woman was
killed every seven hours [9].

Sociologists and Criminologists have demonstrated that before a man kills his
female partner (or family member) previous violence had already been
committed, and there is an increase in abuse and violence along the toxic
relationship [10]. It is not uncommon to see police incident reports of other
physical and psychological violence cases before the final murder act. This
highlights that some female murders could be avoided or, at the very least,
safe resources could be provided to the victims beforehand. Therefore, the
development of a risk assessment tool for domestic violence against women
becomes imperative in order to prevent situations from deteriorating further.

The National Polytechnic Institute (Instituto Politécnico Nacional – IPN)
associated with the Mexican Government has created a tool to help women
understand the level of risk they may face in a relationship [11]. The tool,
known as the ”Violentómetro” or ”Violent-o-meter”, is a scale from 0 to 30,
where zero represents a non-violent situation, and 30 represents the ultimate
murder or femicide. In between, there is a progression of violent actions
observed in the aggressor. This measuring scale has been adapted to other
languages and is commonly used by activists to present the potential harm that
domestic violence victims may face. See Fig. 1.

Figure 1: Violent-o-meter scale created by IPN [11].

We aim to leverage machine learning, specifically the Long Short Term Memory
(LSTM) technique [12], to analyze police reports on domestic violence. Our
objective is to assess the risk levels associated with escalating violence and
potential femicide incidents. This analysis will provide valuable insights for
law enforcement and social work authorities, enabling them to comprehend the
circumstances surrounding female victims in reported cases. By understanding
these risk levels, appropriate safety resources can be provided to prevent
further violence and mitigate the potential for harm [13]. Our developed model
will be evaluated using textual data extracted from police reports in the
Federal District of Brazil, specifically focusing on instances leading up to
femicide cases.

We acknowledge that our proposed technique is not intended to replace existing
methods for assessing the risk of domestic violence. Instead, we view it as a
supplementary tool to aid police officers in evaluating victims’ situations,
particularly when they face challenges that hinder their ability to do so
effectively. These challenges may include insufficient training in dealing
with gender-based crimes [14], limited access to historical case records [15],
and inadequate inter-agency coordination, such as when victims register
complaints across different police stations. Furthermore, our approach offers
the advantage of minimizing the potential for human bias to underestimate the
severity of domestic violence [16].

##  II Related Work

Numerous studies have explored various approaches to risk assessment for
femicide and violence against women [17, 18, 19]. While much of the research
in this area falls under the purview of Sociology and related fields, some
researchers in Computer Science have also sought to address this issue. In
particular, we are interested in works that leverage machine learning to
predict outcomes of domestic violence or provide risk assessment. Since we
ought to adopt an interdisciplinary perspective in our research, we will
provide a brief overview of previous works that are relevant to our theme.

Smith, J. conducted a study of 372 intimate partner femicides, with the aim of
identifying patterns of behavior and sequential markers that could help in
risk assessment [10]. The study revealed that certain markers, such as abuse,
stalking, possessiveness, control, monitoring, violence, sexual violence,
isolation, threats to kill, threats to commit suicide, stalking, separation,
and escalating control or violence, were present in most of the cases studied.
By identifying eight sequential stages leading up to the killing, the author
demonstrated that understanding the phase the victim is in can be a critical
factor in protecting these women.

A significant contribution to the field was made by Campbell et al., who
conducted a seminal study that involved updating the Danger Assessment tool
[20], originally developed by the first author, to assess the potential for
lethality or near lethality in cases of intimate partner violence [21]. The
revised version of the assessment incorporated modifications to the report
sheet, providing guidance for authorities when interviewing victims of abuse.
Notably, the study conducted in 11 cities demonstrated an impressive 90%
accuracy rate when testing the revised version [22].

Risk assessment is a challenging and subjective task, as evidenced by Skeem,
J.’s research, which demonstrated that mental health professionals face
difficulties making accurate risk diagnoses in cases of domestic violence [16,
22]. Interestingly, this challenge affects both male and female professionals,
and it is explained by the previously mentioned statistics that suggest women
are subjected to lower rates of violence, leading to an underestimation of
their situations. Additionally, crimes against women often occur in private
and domestic settings, making them less visible and less likely to be reported
by third-party individuals who may be hesitant to interfere or report.

Other studies used machine learning techniques to support risk assessment in
domestic violence and gender-related crimes. González-Prieto et al. utilized
the Nearest Centroid (NC) algorithm to classify police questionnaires
completed by female victims in cases of domestic violence, with the aim of
predicting the likelihood of recidivism in three categories: zero, low, and
high [23]. The dataset used in this study was obtained from the Spanish
Police’s VioGen system, and the victims were asked a series of questions about
the abuse they had experienced, with responses provided on a Likert scale. The
system then generates a risk level of recidivism based on the answers
provided. The authors compared the performance of the NC algorithm to that of
the traditional VioGen system and found that NC achieved an f1 score of 14%
for the high-risk classification, compared to 10% for the traditional method.
They also proposed a hybrid solution that combines the algorithm with the
police’s traditional system.

Sharifirad and Matwin developed a study in which they applied NLP techniques
to classify Twitter messages containing potential sexist content [24]. They
utilized LSTM to predict tweets in five categories: Indirect Harassment,
Information Threat, Sexual Harassment, Physical Harassment, and non-sexist
content. LSTM performed better than previous algorithms, achieving an accuracy
rate of around 91%.

Similarly, Subramani et al. employed Deep Learning techniques to detect
victims of domestic violence through analysis of Facebook posts [25]. They
explored various models and found that the combination of Gated Recurrent
Network (GRU) [26] and Glove embeddings [27] outperformed other approaches,
accurately classifying the data. Such assessments play a crucial role in
providing real-time support to victims, allowing for timely intervention and
assistance.

D’Ignazio et al. employed machine learning to classify media and news articles
potentially related to femicide [28]. Their objective was to create a database
of information on the subject matter. To accomplish this, they developed an
algorithm using Naïve Bayes, which accurately predicted 81% of the texts.

Arian Yallico, T. and Fabian, J. conducted a study using data from six
sources, including news media, social media, YouTube transcripts, campaigns,
and anonymous report lines. Their objective was to train a classification
model that could detect psychological violence in five categories: ”Low Risk,”
”Emotional Blackmail,” ”Jealousy/Justification,” ”Insults/Humiliations,” and
”Threats/Possessiveness” [29]. The authors tested different algorithms and
found that the unidirectional LSTM outperformed the others, achieving an
accuracy of 93%.

##  III Objectives

Building on the reviewed literature, LSTM has emerged as a promising approach
for classifying written content concerning domestic violence. Motivated by
this, our objective is to leverage this technique to create a risk assessment
tool that analyzes police reports encompassing cases starting from domestic
violence and culminating in femicide incidents. By developing this tool, our
project aims to equip law enforcement agencies with valuable knowledge
resource that could be used to support public policies focused on safeguarding
women in perilous situations.

Our approach delves into the advantages of utilizing machine learning within
the context of natural language as a means to address classification and
prediction challenges. Recognizing that domestic violence often exhibits a
pattern of sequential behavior, which is also reflected in police reports, we
divided our work into two distinct objectives. Firstly, we focused on
accurately classifying the reports based on two levels of risk. Secondly, we
aimed to predict the subsequent behavior anticipated within a sequence of
actions. By adopting this approach, we aim to introduce an objective
perspective that complements subjective analysis, thereby enhancing our
understanding of the levels of danger depicted in pre-femicide data.

##  IV Methodology

###  IV-A Dataset

The dataset that is being used consists of police reports from the Civil
Police of the Federal District, in Brazil [30]. After a domestic violence
crime is registered, victims, suspects, and witnesses (if any) are invited to
relate their versions of what happened. Based on their testimonies, police
officers write brief descriptions in police reports. We will focus on this
small history text to build our analysis. To understand the pattern of
behavior in crimes against women, we gathered data on femicide cases, where
some previous domestic violence was also found. Data were anonymized and
provided by the Forensic Science Institution “Fundação de Peritos em
Criminalística Ilaraine Acácio Arce”, from a previous internal study conducted
by the Crime Against Life Sector in the Civil Police of the Federal District.
From 2017 to 2021, the dataset consists of 142 femicide cases, of which 39
presented previous domestic violence crimes reported, corresponding to a total
of 162 police reports. Fig. 2 presents how the cases are distributed
throughout these five years.

Figure 2: Femicide cases in the Federal District of Brazil.

Although it is not the scope of this research, there is evidence that femicide
police registration is underestimated due to several reasons [31, 15].
Moreover, as mentioned before, a significant number of victims deny reporting
their abuse [16, 22]. Previous work from a different region in Brazil
demonstrated that some femicides are neglected and some are registered as
homicides [32]. This highlights the significance of drawing attention to this
problem and serves as an additional motivation to raise awareness within the
community.

Through a word cloud visualization constructed from the 162 reports (Fig. 3),
we can see the main words presented (written in Portuguese). When translated,
we can see that among the principal words are “Victim”, “Home”, “Aggression”,
and “Protective Measures”, providing a picture of the domestic violence
scenario.

Figure 3: Word cloud (in Portuguese) resulted from the 162 reports.

###  IV-B Preprocessing and Modeling

The project encompassed two approaches aimed at exploring how NLP can extract
pattern information from domestic violence reports. The first approach
involved a straightforward classification of the reports into two categories:
low-risk and high-risk. By analyzing the dates of the murder and previous
reports, we were able to calculate the time interval between each report and
the day of the femicide. This provided us with an understanding of the level
of risk the victim faced in terms of being murdered by her partner or family
member. Some cases involved multiple reports leading up to the final killing,
while others had only one recorded incident. On average, we observed that
there were 1,336 days preceding the femicide event. For the purpose of this
study, we defined a threshold of one year (365 days) to determine the higher
risk category, considering anything beyond that threshold as a lower risk
category (though medium risk may be a more suitable term). These thresholds
can be adjusted based on the perspective of the authorities involved.
Following this approach, we identified 39 reports categorized as high risk and
79 reports classified as low risk (excluding reports specifically describing
the final murder, and focusing solely on reports preceding the femicide).

TABLE I: Reports’ labels Higher risk level | Less than one year to femicide | 39 cases
---|---|---
Lower risk level | More than one year to femicide | 79 cases

Preprocessing the data is an essential step before feeding it into the
algorithm. This involved removing symbols from the text, converting all
letters to lowercase, and eliminating Portuguese stopwords, which are non-
informative words like prepositions and pronouns. The text was then tokenized,
and the words were converted into numerical vectors in a vector space. To
ensure consistent input lengths, padding was applied to each vector. We
labeled each report into 0, for higher risk (less than one year preceding the
femicide), or 1, for lower risk (more than one year before the femicide).

Our model was trained using LSTM on 70% of the dataset and tested on the
remaining 30%. We employed 100 cells, a batch size of 64, Adam as the
optimizer, a dropout rate of 0.2, and 30 epochs for training.

The second approach involved utilizing LSTM to predict the next action on a
domestic violence scale. Similar to traditional methods used for predicting
the next word in a sentence, our objective here was to anticipate the expected
behavior if no further prevention measures were taken. To achieve this,
features or key actions and behaviors were extracted from each report and
arranged in a sequential list, which served as input to the model. The
selection of features was based on relevant literature and identified patterns
in offender-victim relationships. For example, from a specific report,
keywords such as ”yelled,” ”punch,” and ”threat” were extracted in that
specific order. The aim was to create a sequence of actions that revealed the
behavioral pattern. This approach can be considered an additional form of risk
assessment, as the results can provide authorities with insights into the
level of danger the victim faces and an understanding of what the woman may
experience next. These insights can be valuable in formulating appropriate
safety measures.

The extraction of keywords was done manually. Every report was read fully, and
special attention was given to the victim’s testimony, when present. The
supporting knowledge base to extract features was the markers provided by
Smith, J. [10] and the ”Violent-o-meter” scale [11]. In summary, the
methodology used was the following:

  1. 1.

Find and highlight keywords presented in the markers and/or the ”Violent-o-
meter”, considering the word stem in order to catch all word derivations (for
instance, verb conjugation).

  2. 2.

Read the full reports and extract implicit keywords. In some cases, a keyword
may not be explicit in the text, only its semantics. For instance, in the
sentence ”If you break up with me, I will kill you,” we observed an implicit
death threat. The co-author of this paper, who is a police officer
specializing in femicide crimes, helped in this inference process.

  3. 3.

Set the words in a sequence. For this part of the project, we only used the
cases where the murderer was also the author of previous violent crimes.
Following this analysis, we got 22 sequences of reports. Based on the date
registered, we ordered a sequence of actions from the victim’s very first
report until the final femicide report.

Table 2 shows the key action/behavior and the number of times they appeared in
the reports. It is important to mention that the content seen in the police
reports was diverse with respect to details. A few provided just simple broad
overviews of the charges and technical law descriptions, but the majority
contained detailed narratives, such as the victims’ quoted dialogues. Also,
some reports presented not only the victim’s version but also the author or
the witnesses. In these cases, we only considered the victims’ perspective to
extract the key characteristics.

TABLE II: List of features extracted for sequence analysis.  Extracted Feature | Frequency
---|---
Verbal Offense | 29
Physical Violence | 21
Death Threat | 15
Discussion | 14
Threat | 13
Jealousy | 8
Physical Fight | 7
Punches | 7
Physical Threat | 4
Object Damage | 4
Break Deny | 4
Hair Pull | 3
Kick | 3
Stalk | 3
Biting | 3
Strangling | 3
Slap | 2
Push | 2
Sexual Harassment | 2
Residence Invasion | 2
Possessive Control | 2
Relationship Persistence | 1
Rape | 1

In this second approach, we also preprocess the data to feed into the
algorithm. However, since we already have the main keywords, we did not need
to remove symbols or lowercase the words. We moved forward to tokenize each
word or term and then added zero padding to each sequence. Finally, we created
an LSTM architecture with 100 cells, Adam as the optimizer, 0.1 dropout, and
50 epochs. In both analyses, we used Python (along with Keras and TensorFlow
libraries) to build the model.

##  V Results and Discussion

###  V-A LSTM for identification of higher or lower risk.

Our primary objective can be likened to performing sentiment analysis on the
text data. After conducting tests, we achieved a reasonable accuracy of 66%,
taking into account the subjective nature of the task and the strong presence
of pattern-sequential behavior.

It is worth noting that the analysis encompassed the entire content of the
report descriptions. While the majority of cases involved the same perpetrator
as previous domestic violence crimes, there were also instances where the
murderer in the femicide case was unknown or unrelated to previous reports.
Nonetheless, employing machine evaluation of risk presents an interesting
approach to supplement decision-making and allocate resources for the
protection of these women victims.

A criminal report classified as high-risk, despite a 66% accuracy, should
serve as a catalyst for authorities to take action before a more severe
outcome occurs, irrespective of the identity of the perpetrator. The aim is to
prioritize the safety of potential victims and mitigate risks associated with
domestic violence situations.

###  V-B LSTM for sequence behavior prediction.

In our second approach, we employed LSTM to perform a sort of ”next word”
analysis. The objective was to extract key features, in the form of keywords
or terms, from the police reports and establish a sequential pattern that the
algorithm could utilize to predict the subsequent action or key feature.

Once LSTM was trained with the defined sequences, we were able to observe
outputs given a sequence of words. For instance, the sequence ”Discussion,
Verbal Offense, Physical Violence” resulted in the output ”Verbal Offense,”
while the sequence ”Punches, Verbal Offense, Physical Violence, Physical
Violence, Death Threat” yielded the output ”Feminicide.” Refer to Table III
for examples of this next behavior prediction approach.

TABLE III: Examples of LSTM predicting next action abuse. Discussion →Verbal
Offense →Physical Violence →Verbal Offense
---
Punches →Physical Violence →Physical Fight →Verbal Offense →
Death Threat
Punches →Verbal Offense →Physical Violence →Physical Violence →
Death Threat →Femicide
Object Damage →Physical Violence →Verbal Offense →Rape →
Sexual Harassment →Verbal Offense →Death Threat →
Verbal Offense →Death Threat →Femicide

During the experiments, we made an important observation: some broad
definitions needed to be broken down into more specific words. For example,
the term ”Physical Aggression” (or simply ”aggression”) appeared in nearly all
the reports. When using this broad term, the algorithm consistently produced
the same output value. This also applied to the term ”Threat.” To provide the
algorithm with a greater understanding of the data nuances, we disaggregated
”Physical Aggression” into more detailed words such as ”Punches,” ”Slaps,” or
”Strangle” whenever such details were present. Similarly, ”Threat” was further
broken down into ”Physical Threat” and ”Death Threat.”

The results once again highlighted the potential usefulness of this tool in
determining the level of risk for victims of domestic violence. The analysis
can offer victims and authorities a more realistic perspective on the
potential harm that may occur if no action is taken to protect the victim. We
argue that this method can provide a more impactful response to the victim
than a simple indication of the risk of criminal recidivism. Additionally,
when examining individual reports in isolation, although some patterns may be
discernible, extracting the sequential behavior and assessing the potential
risk of future violence is not straightforward.

##  VI Conclusion

Domestic violence against women is a worrisome problem that is proven to have
a gradual effect of violence, not rarely ending in murder or femicide. Due to
the underestimation of such crimes, it is hard to evaluate the level of danger
the victims are situated. Therefore, it is important to have tools or
mechanisms to assess risk for the women involved in domestic violence, aiming
to protect them from worsening the case and prevent fatalities.

Some useful tools have been proposed to understand the level of harm a female
victim can be such as the “Violent-o-meter”, which provides a scale of gradual
violent behavior from the offender. We proposed a complementary tool, based on
a machine learning technique, able to evaluate risk in domestic violence
against female victims, thus, having not only a human assessment but also a
trained machine interpretation.

Our goal in this work was to provide risk assessment based on police report
information using artificial intelligence, or more specifically natural
language processing. femicide cases were collected from the Civil Police of
the Federal District in Brazil, from 2017 to 2021, along with previous
domestic violence preceding these murders. A total of 162 reports were
analyzed containing brief written descriptions collected from police officers.
We used LSTM due to its good performance with sequentially written data and
previous work that demonstrated the potentiality of the algorithm along with
NLP (Natural Language Processing) methods. In this work, we followed two
methodologies frequently observed with the support of LSTM.

The first approach involved using LSTM purely as a classification method.
After preprocessing the text from the 162 reports, we employed LSTM to
classify them as either Higher Risk (if the report preceded the femicide by
less than one year) or Lower Risk (if the report was filed more than one year
prior to the final murder). When tested on 30% of the data, the algorithm
achieved an accuracy of 66%.

In the second approach, we employed LSTM to predict the next action in a
sequence of behaviors observed in the reports. We manually extracted key
features from the texts, preprocessed them, and inputted them into the
algorithm. These features were identified by observing explicit and implicit
content, such as Physical Aggression, Threat, Stalking, Damaging Objects,
among others. The results demonstrated the effectiveness of this tool in
understanding the sequential behavior in domestic violence crimes and
predicting the next action in a series of events.

However, our work has some limitations that require attention. Although the
results are promising, it is premature to consider the analysis applicable to
real police work, as the data sample used is still relatively small for an
artificial intelligence application. Additionally, a deeper examination of
bias within the data should be conducted. Furthermore, the manual feature
extraction process should be evaluated by other specialists to explore the
inclusion or exclusion of additional potential parameters. In future work, we
intend to automate the feature extraction process using other Information
Retrieval techniques and test alternative algorithms, such as Attention
mechanisms [33]. The challenge lies in developing a tool capable of extracting
not only keywords but also implicit and relevant content, which may require
advanced machine-learning classification methods. It is worth noting that
another limitation is the varying level of detail in the reports. This
research also contributes to highlighting the importance of a detailed
description of the victim’s abuse to provide a confident risk assessment.

In conclusion, this work demonstrates that NLP and LSTM are potential tools
for supporting and complementing risk assessment in cases of domestic
violence. Through the two studied methods, we were able to gain a better
understanding of the level of violence endured by the victims and the
potential future consequences if no measures are taken to ensure their safety.
Although lives have already been lost to femicide, this research presents an
opportunity to leverage the data to study the nuances of such cases more
deeply and prevent domestic violence situations from worsening. Machine
learning, particularly LSTM, can supplement human evaluations and assist the
police and social workers in combating emerging cases.

## Acknowledgment

We appreciate the support of the Forensic Science non-profit organization
Ilaraine Acácio Arce, and the Civil Police of the Federal District, in
Brasilia, Brazil, for providing data and investing not only on this but many
other important research topics.

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# First application of a liquid argon time projection chamber for the search
for intranuclear neutron-antineutron transitions and annihilation in 40Ar
using the MicroBooNE detector

P. Abratenko  O. Alterkait  D. Andrade Aldana  L. Arellano  J. Asaadi  A.
Ashkenazi  S. Balasubramanian  B. Baller  G. Barr  D. Barrow  J. Barrow  V.
Basque  O. Benevides Rodrigues  S. Berkman  A. Bhanderi  A. Bhat  M.
Bhattacharya  M. Bishai  A. Blake  B. Bogart  T. Bolton  J. Y. Book  L.
Camilleri  Y. Cao  D. Caratelli  I. Caro Terrazas  F. Cavanna  G. Cerati  Y.
Chen  J. M. Conrad  M. Convery  L. Cooper-Troendle  J. I. Crespo-Anadón  R.
Cross  M. Del Tutto  S. R. Dennis  P. Detje  A. Devitt  R. Diurba  Z. Djurcic
R. Dorrill  K. Duffy  S. Dytman  B. Eberly  P. Englezos  A. Ereditato  J. J.
Evans  R. Fine  O. G. Finnerud  B. T. Fleming  W. Foreman  N. Foppiani  D.
Franco  A. P. Furmanski  D. Garcia-Gamez  S. Gardiner  G. Ge  S. Gollapinni
O. Goodwin  E. Gramellini  P. Green  H. Greenlee  W. Gu  R. Guenette  P.
Guzowski  L. Hagaman  O. Hen  R. Hicks  C. Hilgenberg  G. A. Horton-Smith  Z.
Imani  B. Irwin  R. Itay  C. James  X. Ji  L. Jiang  J. H. Jo  R. A. Johnson
Y.-J. Jwa  D. Kalra  N. Kamp  G. Karagiorgi  W. Ketchum  M. Kirby  T.
Kobilarcik  I. Kreslo  I. Lepetic  J.-Y. Li  K. Li  Y. Li  K. Lin  B. R.
Littlejohn  H. Liu  W. C. Louis  X. Luo  C. Mariani  D. Marsden  J. Marshall
N. Martinez  D. A. Martinez Caicedo  S. Martynenko  A. Mastbaum  N. McConkey
V. Meddage  J. Micallef  K. Miller  A. Mogan  T. Mohayai  M. Mooney  A. F.
Moor  C. D. Moore  L. Mora Lepin  M. M. Moudgalya  S. Mulleriababu  D. Naples
A. Navrer-Agasson  N. Nayak  M. Nebot-Guinot  J. Nowak  N. Oza  O. Palamara
N. Pallat  V. Paolone  A. Papadopoulou  V. Papavassiliou  H. B. Parkinson  S.
F. Pate  N. Patel  Z. Pavlovic  E. Piasetzky  I. D. Ponce-Pinto  I. Pophale
X. Qian  J. L. Raaf  V. Radeka  A. Rafique  M. Reggiani-Guzzo  L. Ren  L.
Rochester  J. Rodriguez Rondon  M. Rosenberg  M. Ross-Lonergan  C. Rudolf von
Rohr  I. Safa  G. Scanavini  D. W. Schmitz  A. Schukraft  W. Seligman  M. H.
Shaevitz  R. Sharankova  J. Shi  E. L. Snider  M. Soderberg  S. Söldner-
Rembold  J. Spitz  M. Stancari  J. St. John  T. Strauss  A. M. Szelc  W. Tang
N. Taniuchi  K. Terao  C. Thorpe  D. Torbunov  D. Totani  M. Toups  Y.-T. Tsai
J. Tyler  M. A. Uchida  T. Usher  B. Viren  M. Weber  H. Wei  A. J. White  S.
Wolbers  T. Wongjirad  M. Wospakrik  K. Wresilo  N. Wright  W. Wu  E. Yandel
T. Yang  L. E. Yates  H. W. Yu  G. P. Zeller  J. Zennamo  C. Zhang

###### Abstract

We present a novel methodology to search for intranuclear neutron-antineutron
transition ($n\rightarrow\bar{n}$) followed by $\bar{n}$-nucleon annihilation
within an 40Ar nucleus, using the MicroBooNE liquid argon time projection
chamber (LArTPC) detector. A discovery of $n\rightarrow\bar{n}$ transition or
a new best limit on the lifetime of this process would either constitute
physics beyond the Standard Model or greatly constrain theories of
baryogenesis, respectively. The approach presented in this paper makes use of
deep learning methods to select $n\rightarrow\bar{n}$ events based on their
unique features and differentiate them from cosmogenic backgrounds. The
achieved signal and background efficiencies are (70.22$\pm$6.04)% and
(0.0020$\pm$0.0003)%, respectively. A demonstration of a search is performed
with a data set corresponding to an exposure of $3.32\times 10^{26}\,$neutron-
years, and where the background rate is constrained through direct
measurement, assuming the presence of a negligible signal. With this approach,
no excess of events over the background prediction is observed, setting a
demonstrative lower bound on the $n\rightarrow\bar{n}$ lifetime in 40Ar of
$\tau_{\textrm{m}}\gtrsim 1.1\times 10^{26}\,$years, and on the free
$n\rightarrow\bar{n}$ transition time of $\tau_{\textrm{$n\rightarrow\bar{n}$
}}\gtrsim 2.6\times 10^{5}\,$s, each at the $90\%$ confidence level. This
analysis represents a first-ever proof-of-principle demonstration of the
ability to search for this rare process in LArTPCs with high efficiency and
low background.

##  1 Introduction

Processes such as neutron-antineutron transition [1] can provide a unique test
of theoretical extensions to the Standard Model of particle physics that allow
for the violation of baryon number conservation [2]. The transition of a
neutron to antineutron ($n\rightarrow\bar{n}$) is a theoretically motivated
beyond-Standard Model process which violates baryon number by two units [3, 4,
5, 6, 7]. The process of intranuclear $n\rightarrow\bar{n}$ involves the
transformation of a bound neutron into an antineutron. This antineutron then
annihilates with a nearby nucleon (neutron or proton) and produces, on
average, $3$–$4$ final state pions [8, 9]. The branching ratios of $\bar{n}p$
and $\bar{n}n$ annihilation products are based on past measurements of
$\bar{p}n$ and $\bar{p}p$ interactions, respectively [8, 9, 10, 11]. In a
vacuum, the final state pions produced by a motionless and unbound
annihilating pair are expected to have zero total momentum and a total
invariant mass corresponding to the sum of the masses of the two
(anti)nucleons. Deviations from this expectation are due to nuclear
effects—specifically, intranuclear Fermi motion of the annihilating
(anti)nucleons, their nuclear binding energy, and final state interactions as
the initial state mesons traverse the nuclear medium—leading to smearing
effects of the observed final state kinematics. The annihilation has a star-
like, spherical topological signature, which can be used to differentiate it
from background interactions.

An experimental discovery or stringent lower bound, surpassing the current
best limits [8, 12], on the rate of intranuclear $n\rightarrow\bar{n}$ would
make an important contribution to our understanding of the baryon asymmetry of
the Universe. To date, limits have been placed on the mean lifetime of this
process by various experiments using either free neutrons or neutrons bound in
nuclei [13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. The free-neutron
$n\rightarrow\bar{n}$ lifetime ($\tau_{\textrm{$n\rightarrow\bar{n}$ }}$) and
bound-neutron $n\rightarrow\bar{n}$ lifetime ($\tau_{\textrm{m}}$) are related
through a factor ($R$) [23, 24, 25] as shown in eq. (1.1), which accounts for
the high suppression of the transition due to differences in the nuclear
potentials of neutrons and antineutrons within the nucleus where this process
could take place,

$\tau_{\textrm{m}}=R\tau_{\textrm{$n\rightarrow\bar{n}$ }}^{2}.$ (1.1)

For 40Ar nuclei, $R$ is expected to take on a value of $5.6\times
10^{22}\,$s-1 with an uncertainty of $20\%$ [23]. The most stringent limit on
the free neutron transition time is provided by ILL in Grenoble [12] at
$0.86\times 10^{8}\,$s at the $90\%$ confidence level (CL), while the Super-
Kamiokande experiment [19], using oxygen-bound neutrons and an associated
suppression factor of $5.17\times 10^{22}\,$s-1 [24, 25], corresponds to
$\tau_{\textrm{$n\rightarrow\bar{n}$ }}>4.7\times 10^{8}\,$s at the $90\%$ CL
[8].

The future Deep Underground Neutrino Experiment (DUNE) will be able to provide
competitive limits on the lifetime of this process because of its much larger
detector mass [26, 27, 28]. The preliminary simulation studies from DUNE [29]
show the ability of deep-learning (DL) networks when combined with high-
resolution images from liquid argon time projection chamber (LArTPC) detectors
to extend the sensitivity reach for $n\rightarrow\bar{n}$ process. However,
the DUNE simulation studies do not account for detector mismodeling, a
simplified assumption that is not the reality. Therefore, it is crucial to
develop and validate DL-based techniques to select $n\rightarrow\bar{n}$ like
signals using real LArTPC data.

This work presents a DL-based analysis of MicroBooNE data, making use of a
sparse convolutional neural network (CNN) [30, 31], to search for
$n\rightarrow\bar{n}$ like signals using primarily their topological
signature. The results reported in this paper use the MicroBooNE off-beam data
(data collected when the neutrino beam was not running) with a total exposure
of $372\,$s corresponding to $3.32\times 10^{26}\,$neutron-years. The limited
exposure is attributed to the design of the MicroBooNE detector, whose primary
requirement was the study of neutrinos from a pulsed accelerator beam, thus
restricting the data collection to short periods of time associated with beam
and other external triggers.

##  2 Experimental setup

The MicroBooNE LArTPC detector [32] employs an active volume of 85 metric
tonnes of liquid argon (LAr). The detector is a $10.4\,$m long, $2.6\,$m wide,
and $2.3\,$m high LArTPC and is located on-surface and on-axis to the Booster
Neutrino Beamline [33] at Fermilab. Due to its on-surface location, the
MicroBooNE detector is exposed to a large flux of cosmic rays, leading to a
variety of cosmogenic activity in the detector. Charged particles produced
from interactions within the LAr leave a trail of ionization electrons which
drift, under the effect of a uniform electric field, with a maximum electron
drift time (time taken by ionization electrons to drift to the anode wires) of
$2.3\,$ms towards anode wire planes. Three anode wire planes named $U$, $V$,
and $Y$, with $U$ and $V$ plane wires oriented at $\pm 60^{\circ}$ relative to
vertical, and $Y$ plane wires oriented vertically, sense and collect the
ionization charge. A light detection system composed of photomultiplier tubes
(PMT) detects scintillation light produced in the interaction which in turn
helps to determine the drift time, achieving 3D particle reconstruction. Data
was collected from 2015–2021 and includes off-beam data during periods when
there was no neutrino beam.

##  3 Analysis overview

The methodology used to search for a $n\rightarrow\bar{n}$ intranuclear
transition in MicroBooNE was developed using off-beam data that were recorded
using an external, random trigger. Each trigger corresponds to an exposure of
$2.3\,$ms (an “event”), the standard readout length of MicroBooNE. The readout
window (or exposure interval) ensures that all ionization information
associated with a given interaction at trigger time occurring anywhere in the
active volume is collected by the readout. During this period, light and
unbiased (raw) ionization charge data were collected and analyzed, searching
for interaction “clusters” with a characteristic star-like topology. The
dominant source of interactions during these short beam-off exposures comes
from cosmic ray muons (straight track-like features) and other cosmogenic
activity, and/or products of their electromagnetic and hadronic showers, which
are expected to contribute as the dominant background to this
$n\rightarrow\bar{n}$ search. This source of background is a unique issue to a
search using the MicroBooNE detector, due to its on-surface location, whereas
searches with detectors located deep underground, such as DUNE, are expected
to be limited by atmospheric neutrino backgrounds [27].

###  3.1 Data-driven background

MicroBooNE does not use a dedicated Monte Carlo simulation for cosmic
backgrounds (which includes any activity produced by primary cosmic muons,
cosmic neutrons, cosmic antineutrons, and cosmic antiprotons) but instead
relies on in situ measurements to directly measure and thus constrain the rate
of these interactions as backgrounds to beam-related analyses. As such, a
data-driven approach was followed to search for $n\rightarrow\bar{n}$ under
the assumption of negligible signal being present in the data. In this
approach, the off-beam data sample was divided into four statistically
independent sub-samples, where $40\%$ was reserved for analysis development
and, in particular, to train machine learning algorithms, $50\%$ was reserved
as the test sample to determine signal selection efficiency and predict
background rates, $5\%$ was set aside for the development validation of a
blinded analysis using “fake data”, and the remaining $5\%$ corresponding to
$372\,$s of exposure was reserved as the “data” sample for the final
measurement and reported results. This analysis was performed blind, with
final data distributions and extracted $n\rightarrow\bar{n}$ limits obtained
only after the review of the analysis and its validation using fake data as
will be described in section 7. The data-driven approach used to generate the
signal and background samples automatically enables accurate “modeling” of
cosmogenic activity and noise sources, including any time dependence in the
detector response. However, this approach assumes that there are $<10^{-6}$
$n\rightarrow\bar{n}$ interaction events in the off-beam data corresponding to
$372\,$s of exposure. This is a safe assumption given the current best limits
on $n\rightarrow\bar{n}$ from the Super-Kamiokande experiment [8] and
MicroBooNE’s low exposure as explained in section 1.

###  3.2 Signal simulation

Signal $n\rightarrow\bar{n}$ interactions are simulated across the detector’s
active volume using the GENIE neutrino event generator (GENIE v.3.00.04) [34,
29]. These interactions are simulated with annihilation vertices uniformly
distributed across the active volume of the TPC and as a consequence, a
significant fraction of the signal interactions are only partially visible in
the TPC. This leads to inefficiencies which are accounted for in the reported
signal efficiencies which are shown in table 3. In the model, the
(anti)nucleon’s Fermi motion and binding energy are modeled using a local
Fermi gas model, and the empirical, data-driven hA Intranuke algorithm is used
to simulate final state interactions (FSI). The 40Ar nucleus is assumed to be
at rest during the $n\rightarrow\bar{n}$ process. The position of a neutron
(to be oscillated into an antineutron) within the nucleus is simulated using
GENIE’s density profile of nucleons (Woods-Saxon distribution [35]),

$\rho(r)=\frac{\rho_{0}}{1+e^{\frac{r-R_{0}}{a}}}~{},$ (3.1)

where $r$ is the radial position inside the nucleus,
$R_{0}=r_{0}A^{\frac{1}{3}}$ is the nuclear radius, with $r_{0}$ defined as
$1.4\,$fm in GENIE. $\rho_{0}$ is normalized in order to express nuclear
density as a probability distribution, and $a$ is a parameter describing the
surface thickness of the nucleus, set to $a=0.54$ fm.

This analysis considers the annihilation of an antineutron with either a
neutron or a proton and simulates the resulting products of annihilation
($3$–$4$ pions on an average) using the branching ratios informed by previous
measurements [8, 10, 11], reproduced in table 1, accounting for the available
kinematic phase-space on an event-by-event basis [29]. The final state
particles are subsequently propagated through the detector with Geant4 [36].
This is followed by the custom detector simulation for the MicroBooNE detector
[37, 38, 39] to take account of the detector response.

Table 1: Effective branching ratios for antineutron annihilation in 40Ar, as implemented in GENIE. The branching ratios are adapted from analysis by the Super-Kamiokande collaboration [8] and are derived from past antiproton annihilation measurements on hydrogen and deuterium, with a phase-space approximation [29]. $\bar{n}+p$ | $\bar{n}+n$
---|---
Channel | Branching ratio | Channel | Branching ratio
$\pi^{+}\pi^{0}$ | 1.2% | $\pi^{+}\pi^{-}$ | 2.0%
$\pi^{+}2\pi^{0}$ | 9.5% | $2\pi^{0}$ | 1.5%
$\pi^{+}3\pi^{0}$ | 11.9% | $\pi^{+}\pi^{-}\pi^{0}$ | 6.5%
$2\pi^{+}\pi^{-}\pi^{0}$ | 26.2% | $\pi^{+}\pi^{-}2\pi^{0}$ | 11.0%
$2\pi^{+}\pi^{-}2\pi^{0}$ | 42.8% | $\pi^{+}\pi^{-}3\pi^{0}$ | 28.0%
$2\pi^{+}\pi^{-}2\omega$ | 0.003% | $2\pi^{+}2\pi^{-}$ | 7.1%
$3\pi^{+}2\pi^{-}\pi^{0}$ | 8.4% | $2\pi^{+}2\pi^{-}\pi^{0}$ | 24.0%
|  | $\pi^{+}\pi^{-}\omega$ | 10.0%
|  | $2\pi^{+}2\pi^{-}2\pi^{0}$ | 10.0%

###  3.3 Overlay generation

Neutron-antineutron transition signal interactions are simulated within GENIE
as described in section 3.2 and are then overlaid onto the background (real
cosmic data) at waveform level to emulate the events used to estimate the
effective signal efficiency. An example of overlay generation is shown in
figure 1 where the top panel shows the background event and the bottom panel
shows the overlay scenario where the GENIE simulated signal interaction,
circled in red, is overlaid on the same background event shown in the top
panel.

Because of abundant cosmogenic activity, each $2.3\,$ms event includes
multiple reconstructed cosmic candidate interactions in the LAr volume,
referred to as “clusters”. Three-dimensional clusters are reconstructed using
the WireCell reconstruction package [40] as collections of $3$D spacepoints,
where each spacepoint carries information about its corresponding wire
position, time-tick, and charge deposition. The true $n\rightarrow\bar{n}$
interaction clusters are identified through the comparison of two events (one
with and one without a signal interaction) with the same background source, as
depicted in figure 1. The topological features of the signal clusters (“star-
like”) and the background clusters (“straight track-like”) are then used to
develop the selection as described in the next section.

Figure 1:  (top) Event display showing an event collected in MicroBooNE off-
beam data. (bottom) Event display showing the same off-beam data event with a
GENIE-simulated $n\rightarrow\bar{n}$ signal cluster (highlighted in the red
circle). The vertical and horizontal scales are the same. The $x$-axis
represents the collection plane channels and the $y$-axis represents the time-
tick space. Color represents the amount of deposited ionization charge in
units of ADC values.

##  4 Analysis techniques and selection criteria

The cluster reconstruction is followed by a series of selection criteria which
are applied in three stages as discussed in the following subsections.

###  4.1 BDT-based preselection

The first, or preselection, stage makes use of a machine learning boosted
decision tree (BDT) algorithm using xgboost [41] to significantly reduce the
number of background clusters while maintaining high signal efficiency. The
BDT is trained using variables that contain information about the number of
spacepoints in each cluster, with their wire positions and times. The
distributions of these input variables are shown in figure 2, corresponding to
the “No selection” stage of table 3. We define the “extent” of a cluster as
the number of wires or time-ticks over which the cluster is contained in the
$U$, $V$, or $Y$ wire-plane or time-tick dimension (one time-tick corresponds
to $0.5$ $\mu$s), respectively. These variables enable us to distinguish
between signal and background clusters based on their topological features,
such as the more localized, spherical topology for the signal
$n\rightarrow\bar{n}$ clusters and the straight, track-like topology for the
background clusters; effective in significantly suppressing the cosmic muon
backgrounds

Figure 2: Distributions of topological variables from 2D cluster projections
for the signal (blue) and background (red) clusters. The background is shown
along with its systematic uncertainty band (see section 5 for details on
assessing systematic uncertainties). The systematic uncertainty is small and
of the order of a few percent. The data points corresponding to $372\,$s of
exposure are shown (after unblinding) in black along with statistical
uncertainty. The background clusters, generated with a test sample, are
normalized exactly to match the data exposure of $372\,$s, whereas the signal
clusters, which were simulated and overlaid onto the background clusters, are
arbitrarily normalized as they cannot be precisely scaled to match the data
exposure. The samples used to obtain background prediction and data are
assumed to have a negligible signal.

The BDT training outcome exhibits a clear separation between the signal
($n\rightarrow\bar{n}$) and background (cosmic) processes, as shown in figure
3 (the BDT score distribution corresponds to the “No selection” stage of table
3.). Therefore, a “loose” cut on the BDT score is chosen by visual inspection
to meet our primary goal of rejecting the majority of background events at
this stage. Selecting clusters with BDT score $>0.1$ (see figure 3) rejects
$91\%$ of the background clusters and maintains a high signal selection
efficiency of $86\%$.

Figure 3:  Classification performance of the BDT (left) and CNN (right) for
the signal $n\rightarrow\bar{n}$ (blue) and background (red) clusters. The
background is shown along with the systematic uncertainty band (see section 5
for details on assessing systematic uncertainties). The data points
corresponding to $372\,$s of exposure are shown (after unblinding) in black
along with statistical uncertainty. The background clusters, generated with a
test sample, are normalized exactly to match the data exposure of $372\,$s,
whereas the signal clusters, which were simulated and overlaid onto the
background clusters, are arbitrarily normalized as they cannot be precisely
scaled to match the data exposure. The samples used to obtain background
prediction and data are assumed to have a negligible signal.

###  4.2 CNN-based selection

The second stage of selection applies an image-based selection criterion,
using a sparse CNN with the VGG16 network architecture [30, 31, 42, 43].
Convolutional neural networks perform successive layers of convolutions on
full images to identify features and associate these features with labels
[44]. A sparse CNN makes use of localized inputs within an image (star-like
topology for the signal clusters and straight track-like topology for the
background clusters) that highlight features on which the network trains
rather than the full image. This selection stage makes use of 2D projections
of the preselected clusters onto three sense wire planes of the MicroBooNE
detector. These projections contain information about the wire position, time-
tick, and charge deposition associated with each cluster, and are formatted in
such a way as to retain only the pixels associated with the signal or
background clusters, thus making it highly memory efficient.

The network is trained using nearly a million events. One challenge in
training arises from having a finite dataset, leading to the possible risk of
overtraining (or overfitting). In overtraining, the network learns a
combination of features associated with a specific type of event and may
occasionally incorporate features that are not representative of the broader
event type. Therefore, it is crucial to validate the effectiveness of the
network, which in this case is achieved by monitoring training loss and
validation accuracy. The training loss represents the classification error in
the training set and a decreasing training loss typically indicates that the
model is learning to better fit the training data. The validation accuracy
measures the performance of a model on a separate dataset that the model has
not been trained on. An increasing validation accuracy indicates that the
model is generalizing well to new data, whereas a decreasing validation
accuracy may suggest overtraining. Figure 4 shows the training loss and
validation accuracy versus number of iterations which refer to the number of
updates made to the model’s parameters during the training. For CNN-based
classification, 20,000 iterations were chosen by monitoring training loss and
validation accuracy. The performance of the trained CNN on the test sample is
shown in figure 3 (the right CNN score distribution corresponds to the “Stage
1” of table 3).

Figure 4: Distributions of training loss (left) and validation accuracy
(right) versus number of iterations. The current accuracy is shown as green
solid line, whereas the best accuracy is shown as blue solid line. The best
accuracy represents the highest validation accuracy observed throughout the
training process.

The CNN score criterion is optimized with respect to the projected sensitivity
at 90% CL. As a prerequisite for the sensitivity calculation, efficiencies for
the signal and background events are calculated for various CNN score criteria
and are shown in table 2. For these particular CNN score criteria (where the
background rejection is $\sim 99\%$), individual preliminary sensitivity
values were calculated, using the TRolke statistical method in ROOT [45]
following a frequentist approach and accounting for both statistical and
systematic uncertainties on the background and signal efficiency, based on the
following assumptions:

  * •

The assumed search region statistics correspond to $372\,$s of exposure, and
are evaluated by scaling the test sample (containing $\times 10\,$ higher
statistics) by a factor of 0.1, making it equivalent in size to the MicroBooNE
“data” statistics for the analysis.

  * •

The statistical uncertainty on the background is considered within the TRolke
method, assuming Gaussian fluctuations on the data-sized test. The sensitivity
calculation within TRolke assumes zero signal and hence no statistical
uncertainty is assumed on the signal.

  * •

For the CNN score criterion optimization study, the systematic uncertainty on
the signal selection efficiency was assumed to be $15\%$. The systematic
uncertainty on the background is evaluated as the statistical uncertainty on
the background obtained using the test sample, as the background is measured
in situ.

Considering sensitivity (see table 2) as a figure of merit, the optimal CNN
criterion is found to be $0.80$.

Table 2: Preliminary sensitivity for various CNN score criteria around the optimized score of $0.80$. The signal and background efficiencies are calculated using the test sample. The background is also estimated using the test sample and then scaled by a factor of $0.1$ to make it equivalent in size to the MicroBooNE data sample which corresponds to $372\,$s of exposure. Uncertainties in the table account for finite MC statistics only.  CNN criterion |  Signal Efficiency |  Background Efficiency ($10^{-4}$) |  Normalized Background Estimate |  Sensitivity ($10^{25}$ yrs)
---|---|---|---|---
0.797 | 0.8274 $\pm$ 0.0003 | 1.53 $\pm$ 0.10 | 24.8 $\pm$ 1.6 | 2.62
0.798 | 0.8222 $\pm$ 0.0003 | 1.27 $\pm$ 0.09 | 20.5 $\pm$ 1.4 | 2.83
0.799 | 0.8012 $\pm$ 0.0003 | 1.08 $\pm$ 0.08 | 17.5 $\pm$ 1.3 | 2.98
0.800 | 0.7360 $\pm$ 0.0003 | 0.88 $\pm$ 0.07 | 14.2 $\pm$ 1.2 | 2.99
0.801 | 0.6392 $\pm$ 0.0004 | 0.66 $\pm$ 0.06 | 10.7 $\pm$ 1.0 | 2.95
0.802 | 0.5081 $\pm$ 0.0004 | 0.50 $\pm$ 0.06 | 8.1 $\pm$ 0.9 | 2.65
0.803 | 0.3490 $\pm$ 0.0004 | 0.43 $\pm$ 0.05 | 6.9 $\pm$ 0.8 | 1.95

###  4.3 Topological-based final selection

After CNN selection, approximately $2\%$ of the remaining clusters have zero
extent in time or one of the wire dimensions, as a consequence of
reconstruction inefficiencies [46]. Those clusters looked similar before the
preselection stage (as shown in figure 2), causing the BDT to be unable to
distinguish between them. Therefore, a third and final selection stage, based
on topological information, is applied to reject zero- and low-extent
clusters, which cannot represent the signal topology. The distributions of
extent variables after CNN selection (“Stage 2” of table 3) are shown in
figure 5 and the final selection criteria are chosen by visual inspection of
these variables. The final selection requires the extent of a cluster in at
least one of the three wire dimensions to be $>70$ wires, and in the time
dimension to be $>70$ time-ticks. The final selection criteria were chosen to
effectively reject the majority of background events, particularly those
peaking in the range between 0 and 70 in extent as shown in figure 5.
The number of signal and background events in the test sample before and after
each of the three selection stages is shown in table 3. The analysis yields an
overall signal selection efficiency of $70.22\%$, corresponding to the ratio
of events at Stage $3$ to events before any selection. At the same time, it
rejects $99.99\%$ of the total background resulting in background efficiency
of $0.0020\%$

Figure 5:  The distributions of $U$,$V$,$Y$-plane and time-tick extents for the signal $n\rightarrow\bar{n}$ (blue) and background (red) events after the CNN score cut are shown. The data points corresponding to $372\,$s of exposure are shown (after unblinding) in black along with statistical uncertainty. The background events, generated with a test sample, are normalized to match the data exposure of $372\,$s, whereas the signal events, for which the clusters are simulated and overlaid onto the background clusters, are arbitrarily normalized as they cannot be precisely scaled to match the data exposure. The samples used to obtain background prediction and data are assumed to have a negligible signal. Table 3: The number of predicted signal and background events in the test sample before and after each of the three selection stages. Selection Stage | Signal | Background
---|---|---
No selection | 1,633,525 | 1,618,827
Stage 1 | 1,411,164 | 139,802
Stage 2 | 1,202,281 | 142
Stage 3 | 1,147,157 | 32
Signal selection efficiency | 70.22% | -
Background efficiency | - | 0.0020%

##  5 Systematic uncertainties

The systematic uncertainties on signal and background events are assessed
independently. Systematic uncertainties on the signal selection efficiency
include contributions from GENIE, Geant4, and detector model variations.

###  5.1 GENIE systematics

The default GENIE nuclear model configuration used in MicroBooNE to simulate
$n\rightarrow\bar{n}$ interactions is the hA-Local Fermi Gas (hA-LFG) [47].
The signal efficiency using simulations with other possible model variations
has been evaluated. GENIE offers various models to describe the energy and
momentum of the initial state nucleon, such as Bodek-Ritchie (BR) [48] or
Local Fermi Gas (LFG). Similarly, final state interactions (FSI) are described
in GENIE either through a full cascade model (hN) or an effective model that
parameterizes FSI as a single interaction (hA) [47]. For each variation, a new
independent signal sample is generated, and the entire selection, as described
in section 4, is applied to each of them to evaluate signal selection
efficiency, and subsequently, the associated uncertainty. Table 4 shows the
quantitative estimate of uncertainty due to various GENIE models on signal
selection efficiency. The fractional uncertainty on the signal selection
efficiency, $\eta$, is the uncertainty on the efficiency for each model
($\varepsilon$) with respect to the nominal GENIE hA-LFG model
($\varepsilon_{\mathrm{nom}}$), defined as

$\eta=\frac{\varepsilon_{\mathrm{nom}}-\varepsilon}{\varepsilon_{\mathrm{nom}}}.$
(5.1)

This equation does not consider statistical uncertainty on the efficiency
evaluated for each model, which is found to be negligible ($2\times 10^{-4}$).
The total fractional uncertainty on the signal efficiency due to GENIE
systematic uncertainties is estimated to be 4.85%.

Table 4: The fractional uncertainty in signal efficiency $\eta$ is shown for various samples with different GENIE models. The total uncertainty due to GENIE modeling, obtained by taking the squared sum of $\eta$, is estimated to be 4.85%. GENIE model |  $\eta$ (%)
---|---
hA-BR | 1.17
hN-BR | 4.56
hN-LFG | 1.14
Total | 4.85

###  5.2 Geant4 systematics

Uncertainty from Geant4 accounts for hadron-40Ar reinteraction uncertainties.
Charged hadrons can interact with external 40Ar nuclei while traveling through
the liquid argon volume. Inelastic reinteractions of charged hadrons
($\pi^{+},\pi^{-},p$) in the LAr volume are simulated by Geant4, and the cross
sections of these hadronic reinteractions are varied to account for the
corresponding systematic uncertainty. The uncertainty of these scattering
processes of protons and charged pions could be significant, especially when
there are many charged hadrons in the final state, such as in
$n\rightarrow\bar{n}$ interactions. The impact of hadron reinteraction
uncertainty on $n\rightarrow\bar{n}$ signal efficiency has been evaluated
using an event reweighting scheme [49]. The systematic uncertainty ($\sigma$)
due to charged hadron ($\pi^{+},\pi^{-},p$) reinteractions is assessed using
the following equation for each hadron,

$\sigma=\frac{1}{N_{\textrm{w}}}\sum_{i=1}^{N_{\textrm{w}}}(W_{\textrm{i}}-N)^{2},$
(5.2)

where $i$ runs over the number of re-weights ($N_{\textrm{w}}$=$1000$)
generated for each of the $\pi^{+}$, $\pi^{-}$ and $p$ reinteractions.
$W_{\textrm{i}}$ represents the weighted sample which takes weights generated
for charged hadrons into account and $N$ represents the nominal sample. Table
5 shows the fractional uncertainty on the signal efficiency due to hadron
reinteraction uncertainties with a total Geant4 uncertainty evaluated to be
$2.32\%$.

Table 5: The fractional uncertainty in signal efficiency $\sigma$ is shown for various samples with different Geant4 reinteraction weights in the last column. The total uncertainty due to Geant4 modeling, obtained by taking the squared sum of each $\sigma$, is estimated to be 2.32%. Geant4 reinteractions |  $\sigma$ (%)
---|---
$\pi^{+}$ | 0.89
$\pi^{-}$ | 1.3
proton | 1.7
Total | 2.32

###  5.3 Detector systematics

The detector modeling and response uncertainties are evaluated for the signal
sample using a novel data-driven technique [50] to account for discrepancies
between data and simulation in charge and light response. This uses in situ
measurements of distortions in the TPC wire readout signals due to various
detector effects, such as diffusion, electron drift lifetime, electric field,
and electronics response, to parametrize these effects at the TPC wire level.

For each variation, a new independent signal MC sample is generated. The final
selection is applied to each of these samples and signal efficiency is
calculated. Table 6 shows the fractional uncertainty due to various detector
variations on the signal selection efficiency. The fractional uncertainty on
signal selection efficiency (quoted in the last column) includes a statistical
uncertainty in efficiency, $\eta_{\textrm{err}}$, and uncertainty in
efficiency due to each detector variation with respect to the nominal,
$\eta_{\textrm{errnom}}$, which are defined as

$\eta_{\textrm{err}}=\sqrt{\frac{\epsilon(1-\epsilon)}{N}},\\\ $ (5.3)

where $\epsilon$ and $N$ are the signal efficiency and the number of generated
events, respectively, for any given model, and

$\eta_{\textrm{errnom}}=\frac{\epsilon_{\textrm{nom}}-\epsilon}{\epsilon_{\textrm{nom}}},$
(5.4)

where $\epsilon_{\textrm{nom}}$ represents the signal efficiency with the
nominal sample. The total fractional uncertainty due to detector modeling is
evaluated to be 6.72%.

The total fractional uncertainty on the signal selection efficiency when
treating GENIE, Geant4, and detector systematics as being uncorrelated is
$8.61\%$. The systematic uncertainty on the background is $17.68\%$, and it
corresponds to the statistical uncertainty on the number of final selected
background events in the test sample shown in Table 3.

Table 6: The percent uncertainty in signal efficiency, $\eta$, is shown for various samples with different detector systematic variations in the last column. The total uncertainty due to detector systematics, obtained by taking the squared sum of the last column, is estimated to be 6.72%. Detector variation |  $\eta_{\textrm{err}}$ % |  $\eta_{\textrm{errNom}}$ % |  $\eta$ %
---|---|---|---
Recombination | 0.13 | 0.53 | 0.54
Light yield | 0.22 | 1.15 | 1.17
Space charge effect | 0.12 | 0.13 | 0.18
TPC waveform modeling | 0.24 | 6.59 | 6.59
Total |  |  | 6.72

##  6 Sensitivity evaluation

The final event selection, as described in section 4, yields an expected
background of $3.20\pm 1.79\textrm{(stat.)}\pm 0.57\textrm{(syst.)}$ events
corresponding to $372\,$s ($3.32\times 10^{26}\,$neutron-years) of exposure,
obtained by normalizing the background events reported in table 3 by a factor
of 0.1 to predict the background from the data-sized sample. A sensitivity to
the intranuclear $n\rightarrow\bar{n}$ lifetime in 40Ar is evaluated from this
exposure using the TRolke statistical method, following a frequentist approach
and accounting for both statistical and systematic uncertainties on the
background and signal efficiency [45]. This sensitivity is evaluated assuming
the absence of any signal contribution in the sample used for data-driven
background determination, treating any observed events as indistinguishable
from the background events. The resulting $\tau_{m}$ sensitivity for 40Ar
corresponds to $6.0\times 10^{25}\,$years at $90\%\,$CL.

The DUNE exposure ($1.3\times 10^{35}\,$neutron-years) is projected to be
$10^{9}$ orders of magnitude larger than MicroBooNE’s. If similar signal
selection efficiency can be obtained with DUNE as for MicroBooNE, while
maintaining the atmospheric neutrino background rejection reported by DUNE
[29], then DUNE’s statistical-only sensitivity would increase seven-fold.

##  7 Fake-data analysis

The analysis is developed as a blind analysis and the final selection is
tested on a dedicated fake-data sample before looking at the data sample
reserved for making the final measurement. The fake-data sample corresponds to
a data-sized sample of unbiased, off-beam data events ($372\,$s of exposure),
which is statistically independent of the data sample and is prepared with a
blinded fraction of $x$% injected $n\rightarrow\bar{n}$ signal, where $x$% is
unknown to the analyzer. As part of the fake-data test, the $x$% is estimated
from the developed analysis framework by performing a fit to the fake data.
The final selection, as described in section 4, is applied to the fake-data
sample. Out of 158,681 events, 268 events passed the selection, with an
expected background of 3.20.

Next, the compatibility of the fake-data observation with the expectation was
quantized by constructing a $\chi^{2}$ as follows:

$\chi^{2}=\frac{(O-E)^{2}}{E},$ (7.1)

where $O=268$ is the observed number of events in the fake-data sample, and
$E$ is the expected background plus $n\rightarrow\bar{n}$ signal events and is
defined as

$E=x_{\textrm{fit}}N_{\textrm{g}}\epsilon_{\textrm{s}}+(1-x_{\textrm{fit}})N_{\textrm{g}}\epsilon_{\textrm{b}},$
(7.2)

where $x_{\textrm{fit}}$ is the assumed fraction of injected
$n\rightarrow\bar{n}$ events in the fake-data sample, $N_{\textrm{g}}=158,681$
is the number of events in the fake-data sample, $\epsilon_{\textrm{s}}=0.70$
is the signal selection efficiency, and $\epsilon_{\textrm{b}}=1.97\times
10^{-5}$ is the background efficiency. $x_{\textrm{fit}}$ is varied to obtain
the minimum $\chi^{\textrm{2}}$ value, corresponding to the best-fit
$x_{\textrm{bf}}$. Figure 6 shows the expected number of events and $\chi^{2}$
distribution as a function of $x_{\textrm{fit}}$. The best-fit fraction of
$n\rightarrow\bar{n}$ signal is found to be $0.23\%$, whereas the actual
fraction revealed after this measurement was performed is 0.25%. The estimated
fraction matches the actual fraction within the $1\sigma$ uncertainty of
$0.03\%$ demonstrating the overall validity of the selection methods and
associated image-based analysis.

Figure 6: Distributions of expected events (left) and $\chi^{2}$ (right) of
fake-data observation are shown as a function of the fraction of injected
$n\rightarrow\bar{n}$ events in the fake-data sample, $x_{\textrm{fit}}$.

##  8 Results

In this section, a “demonstrative” experimental lower bound on the
intranuclear $n\rightarrow\bar{n}$ lifetime in 40Ar is evaluated at
$90\%\,$CL. Unlike the sensitivity which is evaluated in section 6, the
“demonstrative” lower bound calculation does not assume a zero-signal
hypothesis and treats the number of observed events differently from the
background events. After successfully validating the developed analysis
selection using the fake-data sample as shown in section 7, the analysis
examined the data sample reserved for reporting the final measurement. Upon
applying the analysis selection criteria, $2$ events are observed, consistent
with an expected background of $3.20\pm 1.79\textrm{(stat.)}\pm
0.57\textrm{(syst.)}$ events. The observed events are shown in figure 7. The
selected clusters in both of these events are localized to tens of wires and
therefore were mistaken as signal events by the network.

Figure 7: Event displays of the two data events (showing the selected
interaction cluster) that pass the final analysis selection. Only the selected
cluster from the final selection is shown for both events. The $x$-axis
represents the collection plane channels and the $y$-axis represents the time-
ticks. Color represents the amount of deposited charge in units of ADC values.

The absence of an excess of events above the expected background prediction
leads to a “demonstrative” lower bound on the intranuclear
$n\rightarrow\bar{n}$ lifetime in 40Ar of $\tau_{m}\gtrsim 1.1\times 10^{26}$
years at $90\%~{}$CL (evaluated using the TRolke package in ROOT [45]). Using
eq. (1.1) and $R=5.6\times 10^{22}$ s-1 for 40Ar [23], a limit on the free-
neutron equivalent $n\rightarrow\bar{n}$ lifetime is derived as
$\tau_{\textrm{n}-\bar{n}}\gtrsim 2.6\times 10^{5}\,$s at $90\%~{}$CL. Note
that such a conversion is subject to an additional uncertainty associated with
the use of $R$, which is estimated at $\sim 20\%$ [23].

##  9 Conclusions

We have developed and validated a novel approach to search for neutron-
antineutron transitions in 40Ar using the MicroBooNE detector and derived a
“demonstrative” experimental lower limit on $n\rightarrow\bar{n}$ lifetime
with 90% CL. This methodology, based on state-of-the-art reconstruction tools
and deep learning methods specifically tailored to LArTPC experiments
showcases the high sensitivity capabilities of LArTPCs for this topologically
unique search. As a proof-of-principle demonstration, we make use of the off-
beam data from the MicroBooNE detector under the assumption that this data
contains negligible signal events, consistent with Super-Kamiokande results
[8], and provide a “demonstrative” experimental lower limit on the mean
intranuclear neutron-antineutron transition time. As expected, the
“demonstrative” experimental lower limit is far lower compared to those of
previous measurements due to limited exposure and a non-competitive detector
mass. The purely topologically-based selection achieves a uniquely high signal
selection efficiency of $70.0\%$ and a background rejection efficiency of
$99.99\%$; the former of these represents a large improvement over previous
results, some of which reported $<10\%$ signal efficiency [8]. With an already
well-developed methodology, this study demonstrates the future potential of
enhanced sensitivities within forthcoming LArTPC-based detectors such as DUNE
as mentioned in section 6, in their searches for such rare signals. Further
improvements, such as delineating the actual kinematics of signals and
backgrounds, along with integration of particle identification, show still
more promise. It is important to note that the backgrounds in DUNE and
MicroBooNE are distinct. While cosmic ray muons are the dominant backgrounds
in MicroBooNE on the surface, atmospheric neutrino interactions are expected
to be the main source of backgrounds in DUNE. Nonetheless, the presented
analysis demonstrates the usefulness of machine learning techniques,
particularly when applied to simple topological extent variables. These
variables are unique to LArTPCs due to their fine spatial resolution. The
demonstration presented in this paper confirms the capabilities of larger,
well-shielded LArTPCs such as DUNE in performing future high-sensitivity
searches for baryon number violation.

## Acknowledgments

This document was prepared by the MicroBooNE collaboration using the resources
of the Fermi National Accelerator Laboratory (Fermilab), a U.S. Department of
Energy, Office of Science, HEP User Facility. Fermilab is managed by Fermi
Research Alliance, LLC (FRA), acting under Contract No. DE-AC02-07CH11359.
MicroBooNE is supported by the following: the U.S. Department of Energy,
Office of Science, Offices of High Energy Physics and Nuclear Physics; the
U.S. National Science Foundation; the Swiss National Science Foundation; the
Science and Technology Facilities Council (STFC), part of the United Kingdom
Research and Innovation; the Royal Society (United Kingdom); the UK Research
and Innovation (UKRI) Future Leaders Fellowship; and the NSF AI Institute for
Artificial Intelligence and Fundamental Interactions. Additional support for
the laser calibration system and cosmic ray tagger was provided by the Albert
Einstein Center for Fundamental Physics, Bern, Switzerland. We also
acknowledge the contributions of technical and scientific staff to the design,
construction, and operation of the MicroBooNE detector as well as the
contributions of past collaborators to the development of MicroBooNE analyses,
without whom this work would not have been possible. We gratefully acknowledge
W. J. Willis for his leadership on the MicroBooNE experiment and formative
contributions to $n\rightarrow\bar{n}$ searches with LArTPCs. For the purpose
of open access, the authors have applied a Creative Commons Attribution (CC
BY) public copyright license to any Author Accepted Manuscript version arising
from this submission.

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