# UAV-assisted Distributed Learning for Environmental Monitoring in Rural
Environments
††thanks: This work has received funding from the Horizon 2020 research and
innovation staff exchange grant agreement No 101086387, and from the Science
Fund of the Republic of Serbia, grant number 6707, REmote WAter quality
monitoRing anD IntelliGence – REWARDING

Vukan Ninkovic,12 Dejan Vukobratovic,1 Dragisa Miskovic 2  1University of Novi
Sad, Novi Sad, Serbia  2The Institute for Artificial Intelligence Research and
Development of Serbia, Novi Sad, Serbia

###### Abstract

Distributed learning and inference algorithms have become indispensable for
IoT systems, offering benefits such as workload alleviation, data privacy
preservation, and reduced latency. This paper introduces an innovative
approach that utilizes unmanned aerial vehicles (UAVs) as a coverage extension
relay for IoT environmental monitoring in rural areas. Our method integrates a
split learning (SL) strategy between edge devices, a UAV and a server to
enhance adaptability and performance of inference mechanisms. By employing
UAVs as a relay and by incorporating SL, we address connectivity and resource
constraints for applications of learning in IoT in remote settings. Our system
model accounts for diverse channel conditions to determine the most suitable
transmission strategy for optimal system behaviour. Through simulation
analysis, the proposed approach demonstrates its robustness and adaptability,
even excelling under adverse channel conditions. Integrating UAV relaying and
the SL paradigm offers significant flexibility to the server, enabling
adaptive strategies that consider various trade-offs beyond simply minimizing
overall inference quality.

###### Index Terms:

IoT, UAV, distributed learning, environmental monitoring

##  I Introduction

The pervasive issue of pollution, stemming from various sources such as
industrial activities, transportation emissions, and waste disposal, poses
significant challenges to the environment, raising concerns about its impacts
[1]. Ensuring health and hygiene is vital for both humanity’s sustainability
and a nation’s progress, that is dependent on a clean, hazard-free
environment. Therefore, monitoring these aspects is essential to promote a
healthy life for citizens, especially in rural and underdeveloped
environments. In recent years, the integration of IoT for environmental
monitoring in rural areas has emerged, utilizing interconnected devices
equipped with diverse sensors to gather real-time data on crucial
environmental parameters like air quality, soil moisture, water quality,
temperature, and humidity [2, 1]. These devices employ wireless communication
technologies such as Wi-Fi, cellular networks, LoRaWAN, or satellite
connectivity to transmit data to centralized servers or cloud platforms for
storage, analysis, and further processing [2].

Unmanned aerial vehicles (UAVs) have found widespread applications across
various industries, governmental bodies, and commercial sectors, performing
tasks ranging from telecommunications, rescue operations, to surveillance[3,
4]. Notably, they have gained significant attention for their pivotal role in
enabling end-to-end wireless communications, especially in providing
connectivity to wireless (IoT) devices in remote or rural areas where
traditional cellular coverage is scarce or absent [4]. Specifically, access
points integrated onto UAVs are being proposed as a potential solution for
anticipated data demand and congestion challenges in future wireless networks
[5]. Unlike conventional static infrastructure, UAV networks offer the
advantage of flexible deployment, enabling them to te coverage [6].

In this work, we propose a novel approach for distributed learning in IoT
environmental monitoring scenarios. Our method integrates the split learning
(SL) paradigm with UAV relaying in an IoT network, enhancing data transmission
rates and ensuring equitable distribution of computational tasks between edge
devices, UAV, and server. Furthermore, our approach enhances system
adaptability by empowering the server to determine the optimal transmission
strategy based on current channel conditions and specific performance metrics
such as latency, throughput, and energy efficiency. Numerical results
demonstrate that by utilizing proposed distributed learning approach, IoT
system shows great robustness to different channel conditions, simultaneously
achieving high performance in terms of estimation accuracy.

##  II Background

###  II-A IoT Connectivity in Rural Areas

According to [7], IoT connectivity mostly depends on the level of development
of the country. More precisely, in developed countries, rural areas are
typically accessible via transportation networks, such as railroad networks,
and power is supplied through the electricity grid. However, the challenge
lies in mobile operators obtaining a satisfactory return on investment (ROI)
for providing backhaul to these areas. Conversely, in developing countries,
particularly impoverished areas, the challenge is to bridge the digital divide
with developed nations. In rural areas, essential services like healthcare and
education depend on connectivity, but inadequate transportation infrastructure
isolates villages from major cities, while power generation often relies on
local sources. Establishing backhaul in such areas, starting from scratch and
facing limited revenue due to poverty, may require state subsidies to
emphasize the necessity for cost-effective solutions.

In the context of providing connectivity in rural areas, especially in
developing countries, unmanned aerial vehicles (UAVs) equipped with
communication equipment can play a significant role [8]. These drones can
serve as flying base stations, establishing temporary or permanent
connectivity in areas where traditional infrastructure deployment is
impractical or cost-prohibitive. By flying over remote regions, drones can
establish wireless links between users and the broader network infrastructure,
effectively extending backhaul links to underserved communities [9]. In
regions with underdeveloped or non-existent transportation infrastructure,
such as in impoverished areas of developing countries, drones offer a
versatile and efficient means of providing backhaul links [7]. They can be
swiftly deployed and are adaptable to changing conditions, making them
valuable in emergency situations or areas with limited access to resources
[10].

###  II-B Split Learning

Split learning (SL) [11, 12] is a new distributed learning paradigm, which
divides a neural network $F$ (consisting of $L$ layers) into sequential layers
across multiple participants, like an edge device and a server. In SL, the
edge device shares its training dataset securely with the server, which
oversees the training process and handling most computational tasks. This
distributed approach accelerates convergence and reduces bandwidth constraints
[12].

SL separates model training and inference processes. During training, data
remains within individual edge devices to prevent raw information transmission
across the network. The neural network can be represented as
$F=(f_{\text{E}},f_{\text{S}})$, where
$f_{\text{E}}:\mathbb{R}^{N}\rightarrow\mathbb{R}^{M}$ and
$f_{\text{S}}:\mathbb{R}^{M}\rightarrow\mathbb{R}^{1}$, ($N$ and $M$ are
dimensions of raw data and intermediate representation, respectively, with
$M<N$). During activation, the edge device sub–network produces an
intermediate representation of raw data $\boldsymbol{x}$ as
$\boldsymbol{z}=f_{\text{E}}(\boldsymbol{x})$, sent to the server for
prediction $\hat{y}=f_{\text{S}}(\boldsymbol{z})$ ($f_{\text{S}}$ is
sub–network deployed at the server side). This training enables collaborative
learning without compromising data privacy, achieved by iteratively exchanging
model updates during backward passes between the server and edge device [12].
In the realm of split inference, split learning optimizes efficiency by
employing pre–trained models distributed across multiple devices. Initial data
processing occurs locally on edge devices, generating intermediate
representations $\boldsymbol{z}$, which are then transmitted to a centralized
server for aggregation and final inference [12].

In the context of rural IoT network which, except edge device and server,
consist of relaying drone (UAV) that provides a backhaul link, neural network
$F$ is divided into three main parts, i.e.,
$F=(f_{\text{E}},f_{\text{D}},f_{\text{S}})$, where
$f_{\text{D}}:\mathbb{R}^{M}\rightarrow\mathbb{R}^{M}$ represents drone
sub–network.

###  II-C Recurrent Neural Networks

RNNs, as sequence-based models, have the capability to discern temporal
relationships between preceding and current states. Consequently, they
represent an ideal solution for processing time series data [13]. Fig. 1
presents a simple depiction of a single-layer RNN. In this illustration, the
output from the previous time step, denoted as $t-1$, is incorporated into the
input of the current time step, denoted as $t$, thus enabling the retention of
past information. The computation outcome of a single RNN cell can be
described by the following function:

$\boldsymbol{h}_{\text{t}}=\tanh(\boldsymbol{W}_{\text{ih}}\boldsymbol{x}_{\text{t}}+\boldsymbol{b}_{\text{ih}}+\boldsymbol{W}_{\text{hh}}\boldsymbol{h}_{\text{t-1}}+\boldsymbol{b}_{\text{hh}}),$
(1)

where $\tanh$ denotes the hyperbolic tangent function, $\boldsymbol{h}_{t}$
and $\boldsymbol{h}_{t-1}$ represent the hidden states at time steps $t$ and
$t-1$, respectively, while $\boldsymbol{W}_{ih}$, $\boldsymbol{W}_{hh}$,
$\boldsymbol{b}_{ih}$, and $\boldsymbol{b}_{hh}$ are the weights and biases
requiring learning, with $\boldsymbol{x}_{t}$ denoting the input at time $t$.

Figure 1: The structure of Recurrent Neural Network.

Basic RNN cells encounter challenges in learning long-range dependencies
primarily due to issues such as vanishing or exploding gradients. To address
this limitation, Long Short-Term Memory (LSTM) cells were introduced, as
proposed in [14]. These cells incorporate specialized units known as memory
blocks within the recurrent hidden layer, thereby augmenting their ability to
capture long-term dependencies. Each memory block constitutes a recurrently
connected sub–network comprising functional components, namely memory cells
and gates. The memory cells retain temporal states of the network, whereas the
gates regulate the flow of information from the preceding cell state.

####  II-C1 Split Learning–Based RNNs

Initially integrating the split learning/inference paradigm into LSTM neural
networks faced challenges, prompting researchers to seek alternative methods.
Some studies have advocated for using 1D-CNN instead of LSTMs to tackle these
issues effectively [15, 16, 17]. Recent research has introduced efficient
approaches to integrate split learning into LSTM networks [18, 19, 20],
embedding the split learning paradigm directly into LSTM architectures to
overcome implementation obstacles with innovative strategies.

This paper builds upon the foundational work of [19], which introduced the
LSTMSPLIT algorithm, splitting the LSTM neural network vertically, and
requiring a minimum of two LSTM layers, with the input sequence stored at the
edge device. Following the procedure outlined in Section II-B, the
intermediate representation $\boldsymbol{z}$ is transmitted from the edge
device’s LSTM layer to the server’s LSTM layer, while update gradients move in
the opposite direction (as depicted on Fig. 2). In the second approach [20],
the authors proposed a method where one LSTM layer is distributed across
multiple edge devices, partitioned into sub-networks trained individually on
each device. This enables the handling of segments within multi-segment
training sequences. Communication among edge devices and parameter sharing
facilitate inference, aligning with the federated learning paradigm.

##  III UAV–assisted Relaying in IoT

###  III-A System Model

We examine the conventional IoT system, consisting of an edge device, server,
and UAV, where the drone serves as a wireless relay, effectively functioning
as a base station with backhaul link [9] (see Fig. 2). Each of these devices
possesses unique computational capabilities, i.e,
$\mathcal{C}(f_{\text{E}})<\mathcal{C}(f_{\text{D}})<\mathcal{C}(f_{\text{S}})$
(where $\mathcal{C}(\cdot)$ is sub–network complexity). At the edge device, we
gather raw data denoted by $\boldsymbol{x}$, which may comprise sensor
measurements, and these data points are labeled with corresponding labels $y$.
Subsequently, this raw data undergoes pre–processing by the edge device
sub–network, resulting in the intermediate representation
$\boldsymbol{z}=f_{\text{E}}(\boldsymbol{x})$.

Figure 2: SL–based fronthaul/backhaul communication with different channel
conditions.

In this study, we establish assumptions concerning various levels of autonomy,
primarily concentrated on the server side, which assumes responsibility for
coordinating communication and inference processes. Specifically, taking into
account channel conditions and essential performance metrics such as error
rate, latency, and communication overhead, the server determines whether
direct communication with the edge device is warranted or if the intermediate
representation should undergo further processing by a drone sub-network.
Furthermore, we anticipate significant variations in channel conditions,
potentially differing between the edge device and drone (red arrow,
$\mathcal{W}_{\text{ED}}$ on Fig. 2) as well as between the edge device and
server ( red arrow, $\mathcal{W}_{\text{ES}}$ on Fig. 2). Notably, we expect
the channel between the drone and server (green arrow,
$\mathcal{W}_{\text{DS}}$, on Fig. 2) to maintain consistently good quality
throughout the entire network’s lifespan.

Regarding the implemented strategy, the intermediate representation
$\boldsymbol{z}$ encounters various channel conditions, resulting in its
distorted version arriving at the server side. If direct communication occurs
between the edge device and server, the intermediate representation at the
server input can be defined as
$\hat{\boldsymbol{z}}=\mathcal{W}_{\text{ES}}(\boldsymbol{z})$. Conversely, if
communication between the edge device and server traverses a drone backhaul
link, and the drone sub–network is involved in overall processing and
prediction, then
$\hat{\boldsymbol{z}}=\mathcal{W}_{\text{DS}}(f_{\text{D}}(\mathcal{W}_{\text{ED}}(\boldsymbol{z})))$.
On the server side, local decisions are made regarding desirable performance
criteria, particularly latency constraints. For example, the server determines
the optimal strategy, deciding whether the entire server sub–network will be
included in the prediction process or only its output layer. More precisely,
the estimation of $y$ can be defined as
$\hat{y}_{full}=f_{\text{S}}(\hat{\boldsymbol{z}})$ or
$\hat{y}_{FC}=\hat{f}_{\text{S}}(\hat{\boldsymbol{z}})$ if the server sub-
network comprises all layers or only its output layer, respectively.

According to obtained estimation, appropriate loss function, which consists of
two different parameters is calculated at server side as:

$\displaystyle\mathcal{L}(y,\hat{y}_{\text{full}},\hat{y}_{\text{FC}})=MSE(y,\hat{y}_{\text{full}})+MSE(y,\hat{y}_{\text{FC}}),$
(2)

where
$MSE(y,\hat{y})=1/|\mathcal{D}_{\text{tr}}|\sum_{\mathcal{D}_{\text{tr}}}(y-\hat{y})^{2}$
is mean–squared error (MSE), $\mathcal{D}$ is training dataset and $|\cdot|$
is its cardinality.

In the backward propagation phase, gradients are determined with respect to
the loss function and then conveyed from the server, passing through a drone,
and finally directed towards the edge device, essentially reversing the neural
network’s direction (as illustrated by the blue arrows in Fig. 2). In such a
case, all three sub–networks ($f_{\text{E}}$, $f_{\text{D}}$, $f_{\text{S}}$)
are jointly optimized. The collaborative optimization typically involves fine-
tuning the parameters of all three sub–networks using optimization algorithms
like stochastic gradient descent (SGD) or its adaptations, such as Adam [21].

Under the above–mentioned setup, the main goal here is to define the most
suitable transmission strategy, regarding the channel conditions and desirable
latency, for minimization overall system error, defined as MSE error from Eq.
(2), between $y$ and $\hat{y}$ across all test examples.

###  III-B Channel Model

We consider relatively simple wireless communication link between edge device
and server ($\mathcal{W}_{\text{ES}}$), edge device and drone
($\mathcal{W}_{\text{ED}}$) and drone and server ($\mathcal{W}_{\text{DS}}$).
These links are modeled as conventional erasure channels, with an erasure
probability denoted by $p$. This channel can be represented as a binary vector
$\boldsymbol{q}\in\\{0,1\\}^{M}$, where $M$ is the length of the intermediate
representation $\boldsymbol{z}$ (as discussed in Section II-B). Individual
symbols from $\boldsymbol{z}$ are either erased or they arrive unchanged at
the server side. Consequently,
$\hat{\boldsymbol{z}}=\boldsymbol{z}\odot\boldsymbol{q}$, where $\odot$
represents element–wise multiplication [22].

##  IV Performance Evaluation

###  IV-A Training Setup

To evaluate the proposed approach and assess the influence of different
channel conditions on overall system performance, as well as the significance
of the backhaul, we utilized a dataset perfectly suited to the environmental
problem of interest. Specifically, we focus on monitoring pollution in the
Danube river near Novi Sad. Our dataset comprises 3,264 instances, with 70%
utilized for training and the remaining 30% used for testing purposes. Each
instance represents a daily measurement from November 2013 to October 2022,
encompassing eight different water quality parameters: temperature, pH value,
electrical conductivity, dissolved oxygen, oxygen saturation, ammonium, and
nitrite.

Based on the correlation matrix between all measured features, we have decided
to predict dissolved oxygen using its last 20 measurements (over the previous
20 days) along with measurements of the other 7 parameters for the current
day. More precisely, following data preprocessing and conversion to time
series, each instance in the dataset comprises 27 features (including 20
previous dissolved oxygen measurements and 7 other parameters) and one label
(representing dissolved oxygen for the current day). Additionally, considering
that different parameters are measured on varied scales, we normalize the data
to fall within the range of -1 to 1.

Training procedure follows conventional SL, introduced in [12], with slight
adjustments to fit the scenario of interest. In more detail, after raw data
$\boldsymbol{x}$ is collected, it undergoes pre–processing on the edge device,
and an intermediate representation is then sent either directly to the server
(via $\mathcal{W}_{\text{ES}}$) or across the backhaul (using a drone, through
both $\mathcal{W}_{\text{ED}}$ and $\mathcal{W}_{\text{DS}}$). If the backhaul
is utilized, the drone introduces additional processing of the intermediate
representation, as depicted in Fig. 2. The neural network $F$ is divided into
sub-networks across the edge device (comprising one LSTM layer), the drone
(comprising two LSTM layers), and the server side (comprising 3 LSTM layers
followed by a fully connected (FC) layer) as depicted in Fig. 2. The number of
LSTM hidden units, denoted as $H$, remains fixed for all conducted
experiments, and it is set equal to the length of the intermediate
representation $M$, i.e., $H=M=10$. The additional fully connected (FC) layer
at the server side also consists of 10 neurons. Training is conducted using a
learning rate of $\alpha=0.01$, $\beta_{1}=0.9$, and $\beta_{2}=0.999$ on a
batch-by-batch basis, with a batch size of 64. We utilize stochastic gradient
descent (SGD) with the Adam optimizer, as detailed in Section III-A.

Channel conditions remain fixed during the training phase, following the
approach proposed by [23]. However, during testing, we assess the model’s
performance across a range of erasure probabilities $p$. It is important to
emphasize that we investigate the impact of different channel conditions
introduced during the training phase by varying the training erasure
probabilities, $p_{\text{tr}}$, in $\mathcal{W}_{\text{ES}}$ and
$\mathcal{W}_{\text{ED}}$, while ensuring that the backhaul between the drone
and the server $\mathcal{W}_{\text{DS}}$ always maintains good channel
conditions with a small erasure probability (Section III-A). The erasure
channel conditions are simulated by incorporating additional dropout layers
[24] during the training process. These dropout layers replace all three
wireless links in Fig. 2, akin to the approach outlined in [22], albeit on a
symbol basis. We specify a particular dropout probability to regulate the
occurrence of channel erasures within our simulations.

###  IV-B Numerical Results

To examine the behavior of the proposed system under diverse conditions, we
consistently assume that one of the channels, either $\mathcal{W}_{\text{ES}}$
or $\mathcal{W}_{\text{ED}}$, introduces significant distortions in the
intermediate representation.Additionally, during the testing phase, we set the
erasure probability for the more distorted channel to $p_{1}$, and for the
less distorted channel to $p_{2}$=$p_{1}-0.3$. Meanwhile,
$\mathcal{W}_{\text{DS}}$ remains constant, with its erasure probability set
to 0.05 during both the training and testing phases.

$0.3$$0.35$$0.4$$0.45$$0.5$$0.55$$0.6$$0.65$$0.7$$0.75$$0.8$$0.85$$0.9$$10^{-2}$$10^{-1}$$p_{1}$MSE$f_{\text{E}}+f_{\text{S}}$
\- $\mathcal{W}_{\text{ES}}=0.1$,
$\mathcal{W}_{\text{ED}}=0.5$$f_{\text{E}}+\hat{f}_{\text{S}}$ \-
$\mathcal{W}_{\text{ES}}=0.1$,
$\mathcal{W}_{\text{ED}}=0.5$$f_{\text{E}}+f_{\text{D}}+f_{\text{S}}$ \-
$\mathcal{W}_{\text{ES}}=0.1$,
$\mathcal{W}_{\text{ED}}=0.5$$f_{\text{E}}+f_{\text{D}}+\hat{f}_{\text{S}}$ \-
$\mathcal{W}_{\text{ES}}=0.1$, $\mathcal{W}_{\text{ED}}=0.5$ Figure 3: MSE
versus $p_{1}$ erasure probabilities: Improved edge-to-server channel
conditions ($p_{\text{tr}}$ for
$\mathcal{W}_{\text{ED}}>\mathcal{W}_{\text{ES}}$) with
$\mathcal{W}_{\text{DS}}=0.05$.

In Fig. 3, we compare the MSE performances of the fronthaul and backhaul
systems, where the backhaul ($\mathcal{W}_{\text{ED}}$) significantly alters
the intermediate representation due to a high erasure probability. More
precisely, training erasure probability for $\mathcal{W}_{\text{ED}}$ is set
to 0.5, while for $\mathcal{W}_{\text{ES}}$ to 0.1. Consequently, during the
testing phase, erasure probability $p_{1}$ is associated with
$\mathcal{W}_{\text{ED}}$, while the fronthaul link $\mathcal{W}_{\text{ES}}$
is tested with $p_{2}$. It becomes evident that channel conditions play a
significant role in overall system performance. For instance, the fronthaul
system, characterized by full server processing under favorable channel
conditions (indicated by the red solid line in Fig. 3), surprisingly
demonstrates superior performance despite its lower processing complexity. It
is also notable that, within the backhaul system, additional processing does
not lead to the recovery of lost symbols. This is evident from the
performances achieved by deploying the full server sub–network (solid blue
line in Fig. 3), which are similar to those obtained when only the output FC
layer is utilized (dashed blue line in Fig. 3).

$0.3$$0.35$$0.4$$0.45$$0.5$$0.55$$0.6$$0.65$$0.7$$0.75$$0.8$$0.85$$0.9$$10^{-2}$$10^{-1}$$p_{1}$MSE$f_{\text{E}}+f_{\text{S}}$
\- $\mathcal{W}_{\text{ES}}=0.5$,
$\mathcal{W}_{\text{ED}}=0.1$$f_{\text{E}}+\hat{f}_{\text{S}}$ \-
$\mathcal{W}_{\text{ES}}=0.5$,
$\mathcal{W}_{\text{ED}}=0.1$$f_{\text{E}}+f_{\text{D}}+f_{\text{S}}$ \-
$\mathcal{W}_{\text{ES}}=0.5$,
$\mathcal{W}_{\text{ED}}=0.1$$f_{\text{E}}+f_{\text{D}}+\hat{f}_{\text{S}}$ \-
$\mathcal{W}_{\text{ES}}=0.5$, $\mathcal{W}_{\text{ED}}=0.1$ Figure 4: MSE
versus $p_{1}$ erasure probabilities: Improved edge-to-drone channel
conditions ($p_{\text{tr}}$ for
$\mathcal{W}_{\text{ED}}<\mathcal{W}_{\text{ES}}$) with
$\mathcal{W}_{\text{DS}}=0.05$.

Examining Fig. 4, we observe that when subjecting our approach to testing
conditions resembling real-world scenarios—where the fronthaul link between
the edge device and server is highly corrupted, necessitating fallback
solutions like the backhaul—we find that additional processing successfully
extracts all temporal connections within the time series data. Consequently,
the system that integrates all three sub-networks demonstrates superior
performance, as indicated by the blue solid line in Fig. 4.

The results depicted in Figs. 3 and 4 provide compelling evidence that the
proposed approach, which integrates backhaul transmission and SL paradigm,
offers significant robustness to the server. This robustness enables the
server to adapt to unexpected changes in wireless links and define an optimal
transmission strategy within various operating conditions. Moreover, it also
provides a significant degree of freedom to the server. With this flexibility,
the server can incorporate various trade-offs into the implemented strategy,
beyond just considering MSE. For instance, it can now factor in parameters
such as latency or communication overhead, allowing for a more nuanced and
adaptive approach.

##  V Conclusion

In this work, we present a novel approach that offers a single, versatile
framework for the integration of distributed learning and UAV-assisted
relaying in IoT environmental monitoring systems. The proposed architecture
demonstrates significant adaptability to varying channel conditions in IoT
systems, offering different trade-offs that can be defined by the server,
primarily based on desired performance metrics. Furthermore, the introduction
of the SL paradigm optimally balances the computational load between each
component (edge device, UAV, and server). In future work, our goal is to
incorporate additional parameters into the server decision-making process,
such as latency and energy efficiency.

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# First Direct Observation of the Dead-Cone Effect

Nima Zardoshti
on behalf of the ALICE Collaboration

###### Abstract

We report the first direct measurement of the dead-cone effect at colliders,
using iterative jet declustering techniques in pp collisions at $\sqrt{s}=13$
TeV. The procedure exposes the splittings of $\rm{D^{0}}$ mesons in the jet
shower, by iteratively declustering the angular ordered C/A tree. The
splitting history of the $\rm{D^{0}}$ meson initiated jet is mapped onto the
Lund Plane, where appropriate cuts can be made to suppress hadronisation
effects. The reported variable is the splitting angle with respect to the
$\rm{D^{0}}$ meson axis, which is updated after each splitting. Track-based
jet finding, along with the low transverse momentum reach for charged tracks
of the ALICE detector, allow for an accurate reconstruction of the splitting
angle in the phase-space where the dead-cone effect is expected to be largest.
The results are compared to those of inclusive jets, where the dead-cone
effect is expected to be negligible.

###### keywords:

dead-cone effect , charm-tagged jets , Lund Planes , jet splittings ,
reclustering

††volume: 00

Nuclear Physics A nupha Nuclear Physics A

XXVIIIth International Conference on Ultrarelativistic Nucleus-Nucleus
Collisions
(Quark Matter 2019)

##  1 Introduction

The dead-cone effect is a fundamental property of all radiative theories. It
defines an angle relative to the emitter, within which emissions are
parametrically suppressed. This angle is defined as $m_{\rm{q}}/E_{\rm{q}}$,
where $m_{\rm{q}}$ and $E_{\rm{q}}$ are the rest mass and energy of the
emitter, respectively [2]. This carries consequences for all massive emitters
in a given theory. In QCD these emitters are the quarks, which have a non-zero
mass. At the lower end of the energies accessible at ALICE, the effects are
significant for charm and beauty quarks. The presence of a dead-cone region
results in a harder fragmentation of these heavy quarks in the vacuum, due to
the reduced available phase-space for emissions, and has implications for
their energy loss when they traverse the deconfined Quark-Gluon Plasma medium.

A direct observation of the dead-cone effect at colliders had not been
possible till now, due to a number of challenging experimental factors.
Primarily, the dead-cone region is susceptible to pollution by both the decay
products of the heavy quarks (and their subsequent emissions) and
hadronisation effects. Another experimental constraint was the accurate
determination of the emission axis, as this must be updated after each
subsequent emission. Previous attempts at an indirect measurement of the
effect were made at DELPHI [3], using generalised axes such as the event
thrust or the jet axis. Recently, new techniques for uncovering the dead-cone
effect using jet reclusetering algorithms have been proposed. One technique
involves the statistical separation of radiation emitted from heavy quarks in
a 4-body top quark decay [4]. Another method [5], which this analysis is based
on, allows for the measurement of the dead-cone effect for charm and beauty
quarks by taking advantage of Lund Planes [6].

##  2 Jet Splittings

The jet splitting tree can be accessed by reclustering track-based jets with a
given jet reclustering algorithm which maintains angular ordering. In such a
configuration, unwinding the reclustering process orders the splittings
chronologically. Two-dimensional maps of the splitting kinematic parameters,
known as Lund Planes, can be constructed and filled per splitting. These maps
allow for a visualisation of the splitting phase-space. The relevant splitting
kinematics for this report are $\theta$, $E_{\rm{rad}}$ and $k_{\rm{T}}$,
which denote the splitting opening angle, energy of the mother particle and
transverse scale of the subleading prong, respectively. Comparing the angular
axis of Lund Planes for heavy flavour tagged and inclusive jets, can provide
an experimental handle on the dead-cone effect. This would manifest as a
suppression of splittings at small angles for heavy-flavour tagged jets
compared to their inclusive counterparts.

##  3 Analysis

###  3.1 $\rm{D^{0}}$-tagged Jets

This analysis was performed on minimum bias pp data at $\sqrt{s}=13$ TeV, with
events comprising of charged tracks, with transverse momentum of
$p_{\rm{T}}^{\rm{ch}}\geq 0.15$ GeV/$\it{c}$, constrained within the ALICE TPC
acceptance (pseudorapidity of $|\eta|<0.9$). The $\rm{D^{0}}\rightarrow K\pi$
(and charge conj.) hadronic channel, which has a branching ratio of $3.89\%$,
was used to reconstruct the $\rm{D^{0}}$ candidates which were selected using
topological and PID cuts. These $\rm{D^{0}}$candidates have a transverse
momentum range of $2\leq p_{\rm{T,D}}<36$ GeV/$\it{c}$. Jet finding was
performed independently for each $\rm{D^{0}}$ candidate in an event, as if it
was the only one. Prior to jet finding, the $\rm{D^{0}}$ daughters were
replaced by a vector comprising of the sum of their four momenta, which is
labeled as the $\rm{D^{0}}$ candidate. This improves the measured jet energy
scale in cases where the opening angle between the daughters is larger than
the jet radius. The event was then clustered into anti-$k_{\rm{T}}$ jets [7]
with $R=0.4$ and a jet transverse momentum range of $5\leq
p_{\rm{T}}^{\rm{ch,jet}}<50$ GeV/$\it{c}$. The jet containing the fully
reconstructed $\rm{D^{0}}$ candidate was then selected.

A side-band subtraction procedure was then performed in bins of
$p_{\rm{T,D}}$. In each $p_{\rm{T,D}}$ bin, the invariant mass of the
$\rm{D^{0}}$ candidates was fitted with a Gaussian function for the signal and
an exponential function for the background, with initial parameters taken from
a Monte-Carlo simulation. The region within $2\sigma$ of the Gaussian peak was
taken as the signal region whilst the regions at $4-9\sigma$ on either side of
the peak were taken as the side-band regions. The side-bands are far enough
away from the peak that they are considered to be fully background dominated.
Consequently, they were used to model the background underneath the peak in
the signal region.

Once the $\rm{D^{0}}$-tagged jets in the signal and side-band regions had been
identified, they were reclustered with the Cambridge-Aachen algorithm [8]. The
reclustering history was unwound, following the prong containing the fully
reconstructed $\rm{D^{0}}$ at each step, and the splittings in the jet were
accessed. For each $p_{\rm{T,D}}$ bin, signal and side-band Lund Planes with
axes of $E_{\rm{rad}}$ and $\ln(1/\theta)$ were filled. In order to remove
non-perturbative effects, only splittings passing a given minimum $k_{\rm{T}}$
cut were accepted. The side-band Lund Plane was then scaled by a quantity
reflecting the difference between the areas of the side-band regions and that
of the background under the signal peak. The scaled side-band Lund Plane was
then subtracted from the signal Lund Plane to obtain a subtracted
distribution. Before summing the subtracted Lund Plane across the
$p_{\rm{T,D}}$ bins, they were each scaled by the efficiency (PYTHIA [9]
derived) of finding $\rm{D^{0}}$ tagged jets using the given selection cuts in
that $p_{\rm{T,D}}$ bin. Finally this led to the $\rm{D^{0}}$-tagged jet Lund
Planes in data.

###  3.2 Inclusive Jets

Jet finding and reclustering of the inclusive jet sample was performed with
the same parameters as in the $\rm{D^{0}}$-tagged case. It was observed, with
percent-level accuracy, that the fully reconstructed $\rm{D^{0}}$ was always
found in the hardest prong of each splitting. Therefore when following the
splitting tree of inclusive jets, at each step the hardest daughter prong was
followed. Additionally, in order to mimic the same interaction $Q^{2}$ as was
selected by the $p_{\rm{T,D}}\geq$ 2 GeV/$\it{c}$ cut, we required a
$p_{\rm{T}}\geq$ 2.8 GeV/$\it{c}$ cut on the leading track of the hardest
prong of each splitting entering the Lund Planes. This value corresponds to
the transverse mass scale of a 2 GeV/$\it{c}$ $\rm{D^{0}}$.

##  4 Results

The final $\rm{D^{0}}$-tagged jet and inclusive jet Lund Planes are shown in
Fig. 1. For illustrative purposes the Lund Planes shown here have $\ln(k_{T})$
instead of $E_{\rm{rad}}$ on the $y$-axis. At this stage already a visual hint
of a suppression of splittings at small angles in the $\rm{D^{0}}$-tagged jets
compared to inclusive ones can been observed.

Figure 1: Lund Planes for $\rm{D^{0}}$-tagged jets (left) and Inclusive jets
(right) are shown.

In order to directly observe the dead-cone effect, projections of the angular
axis of the $\rm{D^{0}}$-tagged jet and inclusive jet Lund Planes were made in
bins of $E_{\rm{rad}}$. Ratios of these projections were then taken, as shown
in Fig. 2. It can be seen that the distribution of splittings for the
$\rm{D^{0}}$-tagged jets is suppressed at small angles compared to inclusive
jets. As expected, this dead-cone effect is more significant for low
$E_{\rm{rad}}$ splittings. Higher cuts of $k_{\rm{T}}$ remove more non-
perturbative effects which in turn provide a cleaner dead-cone signal. However
this comes at a cost to statistics.

Figure 2: Ratio of the angular distribution of splittings for
$\rm{D^{0}}$-tagged jets vs inclusive jets are shown for $5\leq
E_{\rm{rad}}<15$ GeV (left) and $15\leq E_{\rm{rad}}<35$ GeV (right).

##  5 Conclusions

We have reported the first direct measurement of the dead-cone effect by
comparing the angular distribution of jet splittings involving a fully
reconstructed $\rm{D^{0}}$ to that of inclusive jets. A strong suppression of
splittings for $\rm{D^{0}}$-tagged jets at small angles is observed. The
energy dependence of the dead-cone effect is also highlighted by comparing the
suppression of splittings in different radiator energy bins.

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