# Probable Object Location (POLo) Score Estimation for
Efficient Object Goal Navigation

Jiaming Wang1 and Harold Soh1,2 1Jiaming Wang and Harold Soh are with Smart
Systems Institute, National University of Singapore<EMAIL_ADDRESS>of Computer Science, National University of Singapore<EMAIL_ADDRESS>
###### Abstract

To advance the field of autonomous robotics, particularly in object search
tasks within unexplored environments, we introduce a novel framework centered
around the Probable Object Location (POLo) score. Utilizing a 3D object
probability map, the POLo score allows the agent to make data-driven decisions
for efficient object search. We further enhance the framework’s practicality
by introducing POLoNet, a neural network trained to approximate the
computationally intensive POLo score. Our approach addresses critical
limitations of both end-to-end reinforcement learning methods, which suffer
from memory decay over long-horizon tasks, and traditional map-based methods
that neglect visibility constraints. Our experiments, involving the first
phase of the OVMM 2023 challenge, demonstrate that an agent equipped with
POLoNet significantly outperforms a range of baseline methods, including end-
to-end RL techniques and prior map-based strategies. To provide a
comprehensive evaluation, we introduce new performance metrics that offer
insights into the efficiency and effectiveness of various agents in object
goal navigation.

##  I INTRODUCTION

Efficiently searching for objects in unexplored environments is a crucial
skill for intelligent agents in real-world scenarios. Humans excel at solving
this partially observable task by employing two key strategies: 1) leveraging
common object associations, such as finding a coffee mug near a coffee machine
[1, 2]; 2) employing efficient search behaviors like glancing into unexplored
rooms while passing by and thoroughly examining promising areas where the
target object is likely situated. This study concentrates on the latter
aspect: devising a method to equip autonomous robots with efficient search
behaviors.

Current state-of-the-art methods for this task can be broadly classified into
two categories: map-based methods and non-map-based methods. Non-map-based
methods [3, 4, 5] often rely on end-to-end learning paradigms, leveraging
implicit memory structures like RNNs or LSTM networks to handle the partial
observability of the environments. While effective in simple scenarios where
the target objects are conspicuous and the environment is limited in size,
these methods encounter difficulties in complex environments. It has been
shown that information stored in the memory cell in baseline LSTMs decays
exponentially [6, 7], potentially leading to a decline in spatial awareness
for the agent. This results in agents re-exploring areas they have already
traversed, ultimately causing a failure to locate the target object within the
allocated time constraints.

Conversely, map-based methods tackle the challenge by concurrently
constructing a spatial representation of the environment as the robot
explores. This constructed map serves as an explicit memory for the agent,
providing the advantage of enhanced generality and interpretability. However,
it also necessitates the development of efficient search strategies. Existing
search methodologies in this area often adopt a two-stage heuristic: initial
map exploration followed by object-specific search. However, these methods
typically overlook critical considerations such as what is visible from a
specific map position [8, 9] and prioritized exploration of promising areas
[10, 11, 12, 13], which in turn leads to suboptimal search trajectories.

In this paper, we introduce a map-based framework to address the above
limitations (Fig. 1). Central to our framework is the introduction of a new
metric called the _Probable Object Location_ (POLo) score. The POLo score
serves to: (i) quantify the likelihood of an object being located within a 3D
environment, thus guiding the agent to focus on high-probability areas while
still taking into account visibility constraints; (ii) promote the exploration
of as-yet-unmapped regions. Despite its utility, computing the POLo score can
be computationally expensive as it requires consideration of visible areas
(akin to rendering).

Figure 1: Overview of our POLo Robot Agent for Object Goal Navigation. Here,
the robot is tasked to find a tennis racquet on a table. The robot has a depth
camera and uses an object detector (DETIC [14] in our case). It maintains an
occupancy map and an object probability map, which are used to compute a
Probable Object Location (POLo) score for each robot configuration — this
score reflects the agent’s belief of an object being located within the
viewable areas from a certain configuration. Since computing the POLo score is
expensive (it requires computing which voxels are visible), we approximate it
using POLoNet, a prediction network that takes as input a tensor with
dimensions $15\times 192\times 192$, where the height dimension (15) serves as
the channel dimension for 2D convolution. This tensor is created through
cropping and down-sampling of the current global occupancy map
$\mathcal{M}^{o}$ and the probabilistic map $\mathcal{M}^{p}$. POLoNet
produces an output tensor of size $2\times 192\times 192$, representing a
dense POLo score map. The robot selects the configuration with the highest
POLo score as the next target location and navigates to the area.

To address this computational bottleneck, we introduce an approximation
technique using a trained neural network that we term POLoNet. This neural
network is engineered to estimate the POLo score efficiently, without
significantly compromising accuracy. The integration of POLoNet within our
framework enables a robot to make real-time decisions in complex environments,
thereby mitigating the computational cost associated with such comprehensive
scores.

We validate our framework using the first phase of the OVMM 2023 challenge,
and our empirical results are promising. An agent equipped with the POLoNet
framework significantly outperforms various baseline approaches; it achieves
better performance comapred to an end-to-end Reinforcement Learning (RL)
method and previously proposed map-based strategies. Specifically, our agent
demonstrates enhanced performance in terms of success rate and efficiency
metrics like Success weighted by Path Length (SPL). This evidence
substantiates the robustness and effectiveness of our approach, the POLo score
and POLoNet. In brief, our main contributions are as follows:

  * •

We propose a map-based framework for efficiently searching for objects in an
unknown environment. To the best of our knowledge, this is the first work to
incorporate a “next-best-view”-like strategy for object goal navigation tasks.
Experiments show that our POLoNet framework significantly outperforms other
baseline methods.

  * •

We conduct a comprehensive set of experiments and analyses on the proposed
method and multiple baseline methods. We introduce new metrics for evaluating
object navigation tasks, providing insights into the behavior of alternative
methods for object goal navigation.

##  II Task Definition

In the Object Goal Navigation [9, 15] task, the agent’s objective is to locate
an object specified by its object class name. At each step, the agent receives
egocentric RGB and depth images, in addition to localization (GPS) and compass
readings. The action space consists of four discrete actions: MOVE FORWARD,
TURN LEFT, TURN RIGHT, and STOP. An episode is deemed successful when the
agent confirms object discovery by executing the STOP action within a certain
threshold distance $d_{s}$ from the target object. The episode terminates
after a fixed number of timesteps.

To evaluate and compare different methods, we adopt the object goal navigation
sub-task from the 2023 Habitat Open Vocabulary Mobile Manipulation (OVMM)
challenge [16]. The challenge defines goals using natural language, e.g., “
_move an apple from the table to the counter_ ”. The OVMM challenge comprises
four distinct sub-tasks, where the agent is tasked not only with locating
objects as described in text but also with executing subsequent object
manipulation tasks, including pick and place actions directed towards
specified receptacles.

For our study, we focus on the object goal navigation phase, representing the
initial stage within the OVMM challenge. This phase is difficult; unlike the
original Habitat object navigation task, the OVMM environment more closely
simulates real-world conditions. The OVMM objects are from an open set and are
comparatively smaller, such as cups and cellphones, as opposed to the beds and
couches. The scenes in the OVMM environment are also larger, compelling the
agent to explore its surroundings more efficiently.

##  III Related Works

Object Goal Search With Implicit Memories. There is a growing body of research
dedicated to object goal navigation tasks. One research avenue focuses on
training agents directly using end-to-end reinforcement learning or imitation
learning [17, 18]. Typically, RNNs or LSTMs serve as implicit memory
mechanisms to encode the environment. To enhance agent performance and
generalization, Maksymets et al. [3] proposed the use of data augmentation by
generating additional training episodes with common household objects, while
Ye et al. [19] employed auxiliary tasks to facilitate learning. In contrast,
Ramrakhya et al. [4] collected a substantial human demonstration dataset and
demonstrated that agents trained using behavior cloning on this dataset can
acquire efficient searching behaviors. However, end-to-end methods, in
general, suffer from low sampling efficiency [20] and limited generalizability
when applied to real-world scenarios [21]. Our experiments reveal that a RL
agent tended to revisit already searched areas, potentially due to memory
decay issues in its RNN.

Object Goal Search with Explicit Maps. Our work utilizes an explicit map to
represent the environment, which enables sample efficiency and potentially
better generalization via a modular paradigm [8, 9, 22, 23]. Prior map-based
methods methods use explicit representations as proxies for robot observations
and employ either learned or heuristic policies to select high-level goals
based on the constructed map. In contrast, our approach incorporates a 3D
probabilistic map and a probable object location score, allowing the agent to
select object locations in a manner that balances exploration and
exploitation.

Exploration with Next Best View. A task that is related to object goal search
is autonomous exploration. An effective strategy for this task involves
employing a “next-best-view” selection strategy aimed at maximizing the
coverage of unexplored areas efficiently. This approach optimizes “information
gain” along the exploration trajectory, as demonstrated in [10, 11, 12, 13].
In these studies, information gain, $\textbf{Gain}(\zeta)$, is defined as

$\textbf{Gain}(\zeta)=\textbf{Visible}(\mathcal{M},\zeta)e^{-\lambda
d_{\zeta}},$ (1)

where $\textbf{Visible}(\mathcal{M},\zeta)$ represents the set of visible and
unmapped voxels from the configuration $\zeta$ within the global occupancy map
$\mathcal{M}$. $d$ is the path cost from the current configuration to $\zeta$,
and tuning factor $\lambda$ penalizes high path costs. This approach
facilitates exploration and coverage of the environment, but is not directly
applicable to object goal navigation since it does not explicitly inspect
promising regions where the target object is likely to be situated.

##  IV Probable Object Location (POLo) for
Object Goal Navigation

When searching an object in an unknown environment, humans handle uncertainty
by considering potential object locations. For instance, when encountering an
unexplored room, we briefly investigate it. If we notice anything indicative
of the object’s presence, we examine further. Otherwise, we move on to explore
other areas. This behavior suggests a representation of the environment that
captures _probable object locations_ based on previous observations, and a
strategy that considers both exploration and exploitation.

With this in mind, we developed an agent equipped with a 3D representation to
track probable locations of the object, supplementing the conventional
occupancy map used in prior work (Fig. 1). To optimize the search using this
map, we introduce a measure known as the Probable Object Location (POLo)
score. This score quantifies the likelihood of an object’s presence within
visible voxels, thereby enabling the agent to explore areas of high
probability without neglecting visibility constraints. However, calculating
the POLo score is computationally expensive. To mitigate this issue, we
propose an approximation technique using a trained neural network, termed
POLoNet. Subsequent sections elaborate on each of these components, beginning
with the probabilistic map, followed by discussions on the POLo score and
POLoNet.

###  IV-A 3D Target Object Probability Map

As stated above, the robot maintains both a 3D object probability map,
represented as $\mathcal{M}^{p}$, and an occupancy map, denoted as
$\mathcal{M}^{o}$. This is in contrast to relying solely on a 2D/3D binary
occupancy map as in prior object navigation [8, 9, 24], and map coverage tasks
[10, 11, 12, 13]. This 3D probabilistic map represents regions that are likely
to contain the target object. It is represented as a tensor with dimensions
$\mathcal{M}^{p}\in\mathcal{R}^{L\times L\times H}$, where $L$ represents the
size of the 3D map, and $H$ denotes the height. Each voxel corresponds to a
5cm3 physical space in the environment.

The map is updated at each time-step; we generate an ego-centric local map
$\mathcal{M}_{L}\in\mathcal{R}^{N\times N\times H}$ using the current depth
image and detection results obtained from an open vocabulary detector [14].
Each entry in the local map corresponds to a detection likelihood
$p_{L}(v_{i}|o^{T})=g(s_{\text{goal}},s_{\text{recp}})$, where
$s_{\text{goal}}$ and $s_{\text{recp}}$ are the detection scores for the goal
object and its receptacle, respectively (as specified by the language
instructions). In our work, $g$ is a distance-based weighted combination of
the detection scores, but alternative functions can be used. Subsequently, we
perform a spatial transformation to convert this local map into the global
frame and update the global map using Bayes rule:

$\displaystyle p(v_{i}|o^{T},o^{1:T-1})$
$\displaystyle=\frac{p(v_{i}|o^{1:T-1})}{1-p(v_{i}|o^{1:T-1})}\times\frac{p(v_{i}|o^{T})}{1-p(v_{i}|o^{T})}$
(2)
$\displaystyle\times\frac{1-p(v_{i})}{p(v_{i})}\times(1-p(v_{i}|o^{T},o^{1:T-1}))$

where $p(v_{i}|o^{T})$ represents the likelihood of an object of interest in
voxel $v_{i}$ given the observation $o$ at timestep $T$, and $p(v_{i})$
denotes the prior probability. Note that our map assumes that the probability
of the an object in a specific voxel is independent of other voxels (once
conditioned upon the observation). Although this may not be true, this
independence assumption allows us to efficiently maintain this probabilistic
map, as each voxel can be updated independently.

In preliminary experiments, we attempted to directly use this 3D map directly
by selecting the voxel with the highest probability as the target goal
location. However, this purely exploitation-oriented approach yielded
suboptimal results. The limitations appear to stem from two primary factors:
(i) noisy detections affecting the accuracy of the probabilistic map, and (ii)
an insufficient exploration strategy that failed to investigate other
potentially viable areas. To rectify these shortcomings, we adopted a more
balanced methodology, which involves calculating the POLo score, described in
the next subsection.

###  IV-B Probable Object Location Score (POLo)

Using the global 3D object probability map, we calculate the Probable Object
Location Score (POLo). Conceptually, the POLo score gauges the “utility” of an
_area_ surrounding a given robot pose within the map. The score comprises two
key elements: (i) an exploration component, which encourages investigation of
unexplored regions rich in visible voxels, and (ii) an exploitation component,
which favors areas comprising voxels with a high probability of containing the
target object. Formally, POLo is defined as,

$\displaystyle\text{POLo}(\zeta)=\Big{(}\sum_{v_{i}\in\mathcal{V}^{\zeta}_{<\delta}}f(p(v_{i}),\zeta)+\beta\sum_{v_{i}\in\mathcal{V}^{\zeta}_{\geq\delta}}f(p(v_{i}),\zeta)\Big{)}e^{-\lambda
d_{\zeta}}$ (3)

where
$\mathcal{V}^{\zeta}_{<\delta}=\\{v\in\textbf{Visible}(\mathcal{M}^{o},\zeta)|p(v_{i})<\delta\\}$
and
$\mathcal{V}^{\zeta}_{\geq\delta}=\\{v\in\textbf{Visible}(\mathcal{M}^{o},\zeta)|p(v_{i})\geq\delta\\}$
and $\textbf{Visible}(\mathcal{M}^{o},\zeta)$ represents the set of visible
and unmapped voxels from the configuration $\zeta$ within the global occupancy
map $\mathcal{M}^{o}$. The function $f(\cdot,\zeta)$ is used to adjust
probabilities based on the voxel’s location relative to the agent’s
configuration. Considering that accuracy in object detection decreases with
distance [25], we apply a distance-based decay
$f(p(v_{i}),\zeta)=p(v_{i})/d(v_{i},\zeta)$, where $d(v_{i},\zeta)$ represents
the distance between voxel $v_{i}$ and the configuration $\zeta$.

The POLo score incorporates two summands: the first corresponds to the
exploration component, while the second represents the exploitation component.
The last exponent multiplier in the equation serves to penalize configurations
based on their distance, akin to the Gain measure. Two parameters, $\beta$ and
$\delta$, modulate the score’s behavior. Specifically, $\beta$ dictates the
degree to which high-probability voxels are prioritized during the search.
Conversely, $\delta$ represents our confidence level in the voxel-based object
probabilities. A higher $\delta$ value fosters a more conservative strategy,
as fewer voxels will contribute to the exploitation component in the score
calculation.

In our implementation, the agent’s next target location was determined by the
configuration $\zeta\in\mathcal{R}^{2}\in[0,L]\times[0,L]$—representing its
position on the map—that yielded the highest POLo score. Although the view
angle $\theta$ could potentially be incorporated into the agent’s
configuration $\zeta$, our preliminary experiments showed that omitting
$\theta$ simplifies computation without negatively impacting performance.
Therefore, $\textbf{Visible}(\mathcal{M}^{o},\zeta)$ includes all voxels
visible from $\zeta$, under the assumption that the agent has a panoramic
(360°) field of view.

###  IV-C POLoNet

Computing the POLo score is similar to 3D voxel rendering, with probabilities
associated with each voxel as features. For these calculations, we utilized
the PyTorch3D library [26]. However, calculating POLo scores for all
conceivable configurations within the map proved to be excessively time-
consuming.

To circumvent this bottleneck, we trained a neural network, termed POLoNet, to
predict POLo scores (Fig. 1). The network takes as input a cropped global
voxel map, denoted as $\mathcal{M}^{crop}\in\mathcal{R}^{N^{\prime}\times
N^{\prime}\times H}$, derived from the global occupancy map $\mathcal{M}^{o}$
and the probabilistic map $\mathcal{M}^{p}$. In this tensor, each voxel has
value -1 if unobserved or $p(\mathbf{V}_{i})$ otherwise.

Our network architecture design is based on achieving a large receptive field
covering the agent’s maximum depth range of 10m. This enables POLo score
prediction by considering the surrounding 3D structures. We employ a U-Net-
like network structure with skip connections, which enables the incorporation
of both coarse and fine-grained features. Instead of employing expensive 3D
convolution, we use 2D convolutions by treating the height dimension as a
channel dimension. The network outputs a dense POLo map
$\mathcal{M}^{\text{POLo}}\in\mathcal{R}^{2\times N^{\prime}\times
N^{\prime}}$, with the two layers in the output tensor corresponding to the
two terms in (3).

As a preliminary evaluation, we trained POLoNet on ground truth labels
calculated using Eqn. (3). Overall, we generated 19,726 data pairs
$((\mathcal{M}^{o},\mathcal{M}^{p}),\mathcal{M}^{POLo})$, with each label
$\mathcal{M}^{POLo}$ containing POLo scores sparsely rendered at 150 randomly
chosen locations due to computational budget limitations. To optimize learning
from this constrained dataset, we applied data augmentation techniques such as
random translation and rotation during training.

POLoNet was tested with 1,464 novel data pairs. We compared POLoNet against
two variants: (i) one without skip connections (w/o SC), and (ii) one without
data augmentation (w/o DA). Results in Table I reveal that POLoNet achieves a
low test Mean Absolute Error (MAE). Both skip connections and data
augmentation contributed to error reduction. Remarkably, the average
computation time for POLoNet stood at only 0.26 $\pm$ 0.06 seconds—a 76-fold
speedup compared to the conventional POLo score computation, which required 20
$\pm$ 3.23 seconds111Computed for a uniform sample of 150 locations within
navigable, mapped areas.

TABLE I: POLoNet Error Scores with Ablations Method | Test MAE $\downarrow$
---|---
POLoNet | 0.0117 $\pm$ 0.0468
w/o SC | 0.0258 $\pm$ 0.1270
w/o DA | 0.0190 $\pm$ 0.1257

##  V Experiments and Results

In this section, we report on experiments on object goal navigation using the
Habitat simulator [27]. Our primary goal was to validate if the POLo score and
its estimation using POLoNet led to performance gains. We evaluated POLoNet
and other baselines using 200 episodes generated from 12 novel scenes in the
test dataset. An episode was successful if the target object was found within
1250 simulation steps, and considered unsuccessful otherwise.

###  V-A Experimental Setup

Model Training. In our experimental evaluation, we trained the POLo prediction
network (POLoNet) using 38 scenes from the training dataset using the
techniques described in the previous section.

Baselines and Variants. We benchmarked the performance of POLoNet against four
baseline agents and two variants of POLoNet, each implementing distinct
navigation and search strategies:

  * •

RL: This agent, trained end-to-end with DD-PPO [20], utilizes current depth
images and segmentation masks of detected target objects to predict the next
discrete action.

  * •

FBE: Employing a frontier-based exploration strategy [28], this agent
maintains and updates a 2D semantic map at each step and advances toward the
goal object upon identification.

  * •

Max Coverage: The next high-level goal for this agent is selected based solely
on the highest Gain score, calculated from the 3D global occupancy map, in a
manner similar to prior work [11].

  * •

Max Object Probability: This agent also selects the next high-level goal based
solely on the highest probability voxel in the 3D object probability map.

and the following variants:

  * •

POLo-2D: This variant calculates the next high-level goal by considering 2D
occupancy and 2D probabilistic maps, obtained by projecting the original 3D
maps onto the XY plane.

  * •

POLo-R: This agent computes the POLo score using PyTorch3D, but restricts
computations to a uniform sample of 150 locations within mapped and navigable
areas.

For RL and FBE agents, we used the implementation and pre-trained weights from
[29]. We also experimented POLoNet agents with different $\beta$ values.

Metrics. We employed the following metrics to assess agent performance:

  * •

Success Rate: This metric represents the ratio of successful episodes to the
total number of episodes evaluated.

  * •

SPL (Success weighted by Path Length): This metric measures the efficiency of
the agent in reaching the target object, as outlined in [30].

  * •

E/D Ratio (Explored Area divided by Total Traveled Distance): This metric
evaluates the agent’s proficiency in exploration and map coverage.

  * •

CP/D Ratio (Closely Checked Promising Area divided by Total Traveled
Distance): Promising regions are defined as detected receptacles potentially
containing the goal object. This metric quantifies the agent’s efficiency in
exploitation by assessing the thoroughness in inspecting promising areas.

These latter two metrics furnish additional insights into agent performance,
complementing the standard metrics conventionally employed in object goal
navigation tasks.

TABLE II: Evaluation Metrics on the Habitat Simulator Method | Success (%) $\uparrow$ | SPL $\uparrow$ | E/D $\uparrow$ | CP/D $\uparrow$
---|---|---|---|---
RL | 12.50 | 0.060 | 1.91 | 0.014
FBE | 10.99 | 0.049 | 0.98 | 0.010
Max Coverage | 12.95 | 0.051 | 3.49 | 0.021
Max Object Prob. | 10.94 | 0.054 | 3.80 | 0.040
POLo-2D | 13.20 | 0.050 | 4.48 | 0.033
POLo-R ($\beta=5$) | 17.71 |  0.066 | 3.17 | 0.040
POLoNet ($\beta=1$) | 16.23 | 0.055 | 3.30 | 0.037
POLoNet ($\beta=3$) | 17.71 | 0.083 | 3.35 | 0.040
POLoNet ($\beta=5$) | 20.31 | 0.083 | 3.52 | 0.044
Figure 2: The exploration trajectory (top to bottom) of finding a teapot on a
couch. From left, the first image displays the third person view of the agent,
the second image is the agent’s RGB observation with overlaid object detection
results. The third image shows the constructed map, along with the agent’s
location (blue pointer) and its travelled paths (blue curves). The last image
is the predict values from the POLoNet. High values are in red. We observe
that the agent is guided by the POLo scores and checks multiple rooms by
briefly peeking into it (top). When it detects a couch, the POLo score leads
the agent to closely check the couch by predicting high values around the
couch (middle). The agent continues to explore the map, and successfully finds
the teapot (bottom).

###  V-B Results and Discussion

Comparisons against Baselines. The results from our experiment are summarized
in Table II. The proposed POLoNet with $\beta=5$ agent outperforms all the
baselines by a significant margin in terms of success rate. Moreover, it
demonstrates higher scores in terms of the SPL and CP/D ratios, indicating
more efficient navigation and exploitation of the promising regions.
Qualitatively, we observed that the POLoNet guides the agent towards check
promising areas and exploring unmapped territory. Fig. 2 visualizes an example
trajectory using POLoNet, showing RGB observations, detected objects,
projected 2D semantic maps, and predicted POLo maps at different time points
in an episode. We can observe that the agent displays efficient search
behaviors such as peeking into rooms and closely checking potential
receptacles.

The behavior of the RL agent highlights the challenges associated with long-
term planning and exploration in object goal navigation. While the RL agent
demonstrates efficient low-level control and good initial exploration, its
performance drops in longer episodes. The limitations in its implicit memory
system result in repetitive, unproductive exploration patterns. This finding
is illustrated in Fig. 3, where the exploration rate plateaus after around 800
steps. In contrast, the POLoNet agent maintains a consistent level of
efficient exploration throughout the episode, as demonstrated qualitatively in
Fig. 4. This suggests that the POLoNet provides a more effective framework for
exploration and exploitation over long time horizons.

The limitations of the Frontier-Based Exploration (FBE) strategy stem from its
lack of contextual awareness about what to observe in the environment. While
FBE excels at identifying unexplored areas by locating frontiers, it lacks the
sophistication to differentiate between areas with differing levels of
importance or information content. This often results in suboptimal behavior,
such example, choosing inefficient intermediate goals on the frontier. This
highlights the importance of using a more structured and information-rich
criterion like POLo for guiding agent behavior, as opposed to relying on more
simplistic strategies.

With regards to methods that maximize coverage or maximize object probability,
these are strategies that emphasize solely exploration or exploitation,
respectively. Neither do particularly well compared to POLoNet, which suggests
a middle-ground approach that balances the two criteria is important.

POLoNet Variants. The 2D POLo agent has relatively high E/D and CP/D ratios,
indicating the advantages of employing POLo scores even in a 2D context.
However, its lower success rate compared to the 3D POLoNet variants highlights
the limitations of 2D maps in POLo calculations; a 2D-based approach cannot
differentiate between a table and a wall. The tuning of the $\beta$ parameter
affects the CP/D ratio and success rates; a higher $\beta$ encourages the
agent to scrutinize promising areas before venturing into unexplored
territories. This is particularly beneficial in expansive environments where
transitioning between rooms incurs a higher cost.

Error Analysis. The success rates of all methods in our experiment are notably
lower compared to the success rates reported in the 2002 Habitat Object Goal
Navigation Challenge (HON) [31]. This discrepancy arises from the greater
difficulty of the OVMM environment. All the agents encounter failures stemming
from faulty perception due to small target objects. Notably, the success rate
of the POLoNet agent increases to 56.7% when employing ground truth
perception. In addition, we observed that the presence of numerous narrow
corridors and doors within the OVMM scenes frequently leads to collisions and
failures in the low-level controller employed by modular approaches. We aim to
address these issues as part of our future work.

$0$$500$$1{,}000$$0$$50$$100$$150$Number of StepsTotal Explored
AreaRLFBEPOLo$0$$500$$1{,}000$$0$$1$$2$Number of StepsTotal Checked
AreaRLFBEPOLo Figure 3: Left: Accumulated explored (mapped) area at each step,
averaged for 200 evaluated episodes. Right: Accumulated closely checked
promising area at each step, averaged for 200 evaluated episodes. Figure 4:
Exploration trajectories represented by blue curves for the RL agent (left)
and the POLoNet agent (right), for the same episode. The RL agent explores a
smaller area within an equivalent number of steps due to its tendency to
repeatedly visit the same room.

##  VI Conclusions

In this study, we introduce a framework enabling autonomous agents to
efficiently search for objects in unknown environments. Our proposed method
maintains a continuously updated 3D probabilistic map and quantifies Probable
Object Location Score (POLo) based on this map to guide the search process.
The POLo score provides the agent with a data-driven basis for decision-
making, allowing it to focus on high-probability zones without overlooking
visibility constraints. Recognizing the computational burden of calculating
the POLo score, we introduced POLoNet, a neural network designed to
approximate this score efficiently.

Our empirical evaluation, undertaken within the context of the OVMM 2023
challenge, demonstrates that an agent equipped with POLoNet outpaces a variety
of baseline methodologies. Our work also contributes to the research community
by introducing new performance metrics that allow for a more nuanced
understanding of an agent’s efficiency and effectiveness in object goal
navigation tasks. Moving forward, we are working to transfer these successes
to real-world robotic systems, accounting for sensor noise, occlusions, and
other real-world challenges.

## ACKNOWLEDGMENT

This research is supported by the National Research Foundation, Singapore
under its Medium Sized Center for Advanced Robotics Technology Innovation.

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# First Observation of the Direct Production of the $\chi_{c1}$ in
$e^{+}e^{-}$ Annihilation

M. Ablikim1, M. N. Achasov10,b, P. Adlarson69, S. Ahmed15, M. Albrecht4, R.
Aliberti29, A. Amoroso68A,68C, M. R. An33, Q. An65,51, X. H. Bai59, Y. Bai50,
O. Bakina30, R. Baldini Ferroli24A, I. Balossino25A, Y. Ban40,i, V.
Batozskaya1,38, D. Becker29, K. Begzsuren27, N. Berger29, M. Bertani24A, D.
Bettoni25A, F. Bianchi68A,68C, J. Bloms62, A. Bortone68A,68C, I. Boyko30, R.
A. Briere5, A. Brueggemann62, H. Cai70, X. Cai1,51, A. Calcaterra24A, G. F.
Cao1,56, N. Cao1,56, S. A. Cetin55A, J. F. Chang1,51, W. L. Chang1,56, G.
Chelkov30,a, C. Chen37, G. Chen1, H. S. Chen1,56, M. L. Chen1,51, S. J.
Chen36, T. Chen1, X. R. Chen26, X. T. Chen1, Y. B. Chen1,51, Z. J. Chen21,j,
W. S. Cheng68C, G. Cibinetto25A, F. Cossio68C, J. J. Cui43, H. L. Dai1,51, J.
P. Dai72, A. Dbeyssi15, R. E. de Boer4, D. Dedovich30, Z. Y. Deng1, A.
Denig29, I. Denysenko30, M. Destefanis68A,68C, F. De Mori68A,68C, Y. Ding34,
J. Dong1,51, L. Y. Dong1,56, M. Y. Dong1,51,56, X. Dong70, S. X. Du74, P.
Egorov30,a, Y. L. Fan70, J. Fang1,51, S. S. Fang1,56, Y. Fang1, R.
Farinelli25A, L. Fava68B,68C, F. Feldbauer4, G. Felici24A, C. Q. Feng65,51, J.
H. Feng52, M. Fritsch4, C. D. Fu1, H. Gao56,h, Y. N. Gao40,i, Yang Gao65,51,
I. Garzia25A,25B, P. T. Ge70, C. Geng52, E. M. Gersabeck60, A Gilman63, K.
Goetzen11, L. Gong34, W. X. Gong1,51, W. Gradl29, M. Greco68A,68C, M. H.
Gu1,51, Y. T. Gu13, C. Y Guan1,56, A. Q. Guo26, L. B. Guo35, R. P. Guo42, Y.
P. Guo9,g, A. Guskov30,a, T. T. Han43, W. Y. Han33, X. Q. Hao16, F. A.
Harris58, K. K. He48, K. L. He1,56, F. H. Heinsius4, C. H. Heinz29, Y. K.
Heng1,51,56, C. Herold53, M. Himmelreich11,e, T. Holtmann4, G. Y. Hou1,56, Y.
R. Hou56, Z. L. Hou1, H. M. Hu1,56, J. F. Hu49,k, T. Hu1,51,56, Y. Hu1, G. S.
Huang65,51, K. X. Huang52, L. Q. Huang66, X. T. Huang43, Y. P. Huang1, Z.
Huang40,i, T. Hussain67, N Hüsken23,29, W. Imoehl23, M. Irshad65,51, J.
Jackson23, S. Jaeger4, S. Janchiv27, Q. Ji1, Q. P. Ji16, X. B. Ji1,56, X. L.
Ji1,51, Y. Y. Ji43, H. B. Jiang43, S. S. Jiang33, X. S. Jiang1,51,56, Y.
Jiang56, J. B. Jiao43, Z. Jiao19, S. Jin36, Y. Jin59, M. Q. Jing1,56, T.
Johansson69, N. Kalantar-Nayestanaki57, X. S. Kang34, R. Kappert57, M.
Kavatsyuk57, B. C. Ke74, I. K. Keshk4, A. Khoukaz62, P. Kiese29, R. Kiuchi1,
R. Kliemt11, L. Koch31, O. B. Kolcu55A, B. Kopf4, M. Kuemmel4, M. Kuessner4,
A. Kupsc38,69, W. Kühn31, J. J. Lane60, J. S. Lange31, P. Larin15, A.
Lavania22, L. Lavezzi68A,68C, Z. H. Lei65,51, H. Leithoff29, M. Lellmann29, T.
Lenz29, C. Li37, C. Li41, C. H. Li33, Cheng Li65,51, D. M. Li74, F. Li1,51, G.
Li1, H. Li65,51, H. Li45, H. B. Li1,56, H. J. Li16, H. N. Li49,k, J. Q. Li4,
J. S. Li52, J. W. Li43, Ke Li1, L. J Li1, L. K. Li1, Lei Li3, M. H. Li37, P.
R. Li32,l,m, S. X. Li9, S. Y. Li54, T. Li43, W. D. Li1,56, W. G. Li1, X. H.
Li65,51, X. L. Li43, Xiaoyu Li1,56, Z. Y. Li52, H. Liang28, H. Liang1,56, H.
Liang65,51, Y. F. Liang47, Y. T. Liang26, G. R. Liao12, L. Z. Liao43, J.
Libby22, A. Limphirat53, C. X. Lin52, D. X. Lin26, T. Lin1, B. J. Liu1, C. X.
Liu1, D. Liu15,65, F. H. Liu46, Fang Liu1, Feng Liu6, G. M. Liu49,k, H. B.
Liu13, H. M. Liu1,56, Huanhuan Liu1, Huihui Liu17, J. B. Liu65,51, J. L.
Liu66, J. Y. Liu1,56, K. Liu1, K. Y. Liu34, Ke Liu18, L. Liu65,51, M. H.
Liu9,g, P. L. Liu1, Q. Liu56, S. B. Liu65,51, T. Liu9,g, W. K. Liu37, W. M.
Liu65,51, X. Liu32,l,m, Y. Liu32,l,m, Y. B. Liu37, Z. A. Liu1,51,56, Z. Q.
Liu43, X. C. Lou1,51,56, F. X. Lu52, H. J. Lu19, J. G. Lu1,51, X. L. Lu1, Y.
Lu1, Y. P. Lu1,51, Z. H. Lu1, C. L. Luo35, M. X. Luo73, T. Luo9,g, X. L.
Luo1,51, X. R. Lyu56, Y. F. Lyu37, F. C. Ma34, H. L. Ma1, L. L. Ma43, M. M.
Ma1,56, Q. M. Ma1, R. Q. Ma1,56, R. T. Ma56, X. Y. Ma1,51, Y. Ma40,i, F. E.
Maas15, M. Maggiora68A,68C, S. Maldaner4, S. Malde63, Q. A. Malik67, A.
Mangoni24B, Y. J. Mao40,i, Z. P. Mao1, S. Marcello68A,68C, Z. X. Meng59, J. G.
Messchendorp57,d, G. Mezzadri25A, H. Miao1, T. J. Min36, R. E. Mitchell23, X.
H. Mo1,51,56, N. Yu. Muchnoi10,b, H. Muramatsu61, S. Nakhoul11,e, Y.
Nefedov30, F. Nerling11,e, I. B. Nikolaev10,b, Z. Ning1,51, S. Nisar8,n, Y.
Niu 43, S. L. Olsen56, Q. Ouyang1,51,56, S. Pacetti24B,24C, X. Pan9,g, Y.
Pan60, A. Pathak1, A. Pathak28, P. Patteri24A, M. Pelizaeus4, H. P. Peng65,51,
K. Peters11,e, J. Pettersson69, J. L. Ping35, R. G. Ping1,56, S. Plura29, S.
Pogodin30, R. Poling61, V. Prasad65,51, H. Qi65,51, H. R. Qi54, M. Qi36, T. Y.
Qi9,g, S. Qian1,51, W. B. Qian56, Z. Qian52, C. F. Qiao56, J. J. Qin66, L. Q.
Qin12, X. P. Qin9,g, X. S. Qin43, Z. H. Qin1,51, J. F. Qiu1, S. Q. Qu54, K. H.
Rashid67, K. Ravindran22, C. F. Redmer29, K. J. Ren33, A. Rivetti68C, V.
Rodin57, M. Rolo68C, G. Rong1,56, Ch. Rosner15, M. Rump62, H. S. Sang65, A.
Sarantsev30,c, Y. Schelhaas29, C. Schnier4, K. Schoenning69, M.
Scodeggio25A,25B, K. Y. Shan9,g, W. Shan20, X. Y. Shan65,51, J. F.
Shangguan48, L. G. Shao1,56, M. Shao65,51, C. P. Shen9,g, H. F. Shen1,56, X.
Y. Shen1,56, B.-A. Shi56, H. C. Shi65,51, R. S. Shi1,56, X. Shi1,51, X. D
Shi65,51, J. J. Song16, W. M. Song28,1, Y. X. Song40,i, S. Sosio68A,68C, S.
Spataro68A,68C, F. Stieler29, K. X. Su70, P. P. Su48, Y.-J. Su56, G. X. Sun1,
H. Sun56, H. K. Sun1, J. F. Sun16, L. Sun70, S. S. Sun1,56, T. Sun1,56, W. Y.
Sun28, X Sun21,j, Y. J. Sun65,51, Y. Z. Sun1, Z. T. Sun43, Y. H. Tan70, Y. X.
Tan65,51, C. J. Tang47, G. Y. Tang1, J. Tang52, Q. T. Tao21,j, J. X.
Teng65,51, V. Thoren69, W. H. Tian45, Y. T. Tian26, I. Uman55B, B. Wang1, D.
Y. Wang40,i, H. J. Wang32,l,m, H. P. Wang1,56, K. Wang1,51, L. L. Wang1, M.
Wang43, M. Z. Wang40,i, Meng Wang1,56, S. Wang9,g, T. J. Wang37, W. Wang52, W.
H. Wang70, W. P. Wang65,51, X. Wang40,i, X. F. Wang32,l,m, X. L. Wang9,g, Y.
D. Wang39, Y. F. Wang1,51,56, Y. Q. Wang1, Y. Y. Wang32,l,m, Ying Wang52, Z.
Wang1,51, Z. Y. Wang1, Ziyi Wang56, D. H. Wei12, F. Weidner62, S. P. Wen1, D.
J. White60, U. Wiedner4, G. Wilkinson63, M. Wolke69, L. Wollenberg4, J. F.
Wu1,56, L. H. Wu1, L. J. Wu1,56, X. Wu9,g, X. H. Wu28, Y. Wu65, Z. Wu1,51, L.
Xia65,51, T. Xiang40,i, H. Xiao9,g, S. Y. Xiao1, Y. L. Xiao9,g, Z. J. Xiao35,
X. H. Xie40,i, Y. Xie43, Y. G. Xie1,51, Y. H. Xie6, Z. P. Xie65,51, T. Y.
Xing1,56, C. F. Xu1, C. J. Xu52, G. F. Xu1, Q. J. Xu14, S. Y. Xu64, X. P.
Xu48, Y. C. Xu56, F. Yan9,g, L. Yan9,g, W. B. Yan65,51, W. C. Yan74, H. J.
Yang44,f, H. X. Yang1, L. Yang45, S. L. Yang56, Y. X. Yang1,56, Yifan
Yang1,56, Zhi Yang26, M. Ye1,51, M. H. Ye7, J. H. Yin1, Z. Y. You52, B. X.
Yu1,51,56, C. X. Yu37, G. Yu1,56, J. S. Yu21,j, T. Yu66, C. Z. Yuan1,56, L.
Yuan2, S. C. Yuan1, X. Q. Yuan1, Y. Yuan1,56, Z. Y. Yuan52, C. X. Yue33, A. A.
Zafar67, F. R. Zeng43, X. Zeng6, Y. Zeng21,j, Y. H. Zhan52, A. Q. Zhang1, B.
L. Zhang1, B. X. Zhang1, G. Y. Zhang16, H. Zhang65, H. H. Zhang52, H. H.
Zhang28, H. Y. Zhang1,51, J. L. Zhang71, J. Q. Zhang35, J. W. Zhang1,51,56, J.
Y. Zhang1, J. Z. Zhang1,56, Jianyu Zhang1,56, Jiawei Zhang1,56, L. M. Zhang54,
L. Q. Zhang52, Lei Zhang36, P. Zhang1, Shulei Zhang21,j, X. D. Zhang39, X. M.
Zhang1, X. Y. Zhang48, X. Y. Zhang43, Y. Zhang63, Y. T. Zhang74, Y. H.
Zhang1,51, Yan Zhang65,51, Yao Zhang1, Z. H. Zhang1, Z. Y. Zhang70, Z. Y.
Zhang37, G. Zhao1, J. Zhao33, J. Y. Zhao1,56, J. Z. Zhao1,51, Lei Zhao65,51,
Ling Zhao1, M. G. Zhao37, Q. Zhao1, S. J. Zhao74, Y. B. Zhao1,51, Y. X.
Zhao26, Z. G. Zhao65,51, A. Zhemchugov30,a, B. Zheng66, J. P. Zheng1,51, Y. H.
Zheng56, B. Zhong35, C. Zhong66, X. Zhong52, H. Zhou43, L. P. Zhou1,56, X.
Zhou70, X. K. Zhou56, X. R. Zhou65,51, X. Y. Zhou33, J. Zhu37, K. Zhu1, K. J.
Zhu1,51,56, L. X. Zhu56, S. H. Zhu64, T. J. Zhu71, W. J. Zhu9,g, W. J. Zhu37,
Y. C. Zhu65,51, Z. A. Zhu1,56, B. S. Zou1, and J. H. Zou1 (BESIII
Collaboration) 1 Institute of High Energy Physics, Beijing 100049, People’s
Republic of China
2 Beihang University, Beijing 100191, People’s Republic of China
3 Beijing Institute of Petrochemical Technology, Beijing 102617, People’s
Republic of China
4 Bochum Ruhr-University, D-44780 Bochum, Germany
5 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
6 Central China Normal University, Wuhan 430079, People’s Republic of China
7 China Center of Advanced Science and Technology, Beijing 100190, People’s
Republic of China
8 COMSATS University Islamabad, Lahore Campus, Defence Road, Off Raiwind Road,
54000 Lahore, Pakistan
9 Fudan University, Shanghai 200433, People’s Republic of China
10 G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090,
Russia
11 GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
12 Guangxi Normal University, Guilin 541004, People’s Republic of China
13 Guangxi University, Nanning 530004, People’s Republic of China
14 Hangzhou Normal University, Hangzhou 310036, People’s Republic of China
15 Helmholtz Institute Mainz, Staudinger Weg 18, D-55099 Mainz, Germany
16 Henan Normal University, Xinxiang 453007, People’s Republic of China
17 Henan University of Science and Technology, Luoyang 471003, People’s
Republic of China
18 Henan University of Technology, Zhengzhou 450001, People’s Republic of
China
19 Huangshan College, Huangshan 245000, People’s Republic of China
20 Hunan Normal University, Changsha 410081, People’s Republic of China
21 Hunan University, Changsha 410082, People’s Republic of China
22 Indian Institute of Technology Madras, Chennai 600036, India
23 Indiana University, Bloomington, Indiana 47405, USA
24 INFN Laboratori Nazionali di Frascati , (A)INFN Laboratori Nazionali di
Frascati, I-00044, Frascati, Italy; (B)INFN Sezione di Perugia, I-06100,
Perugia, Italy; (C)University of Perugia, I-06100, Perugia, Italy
25 INFN Sezione di Ferrara, (A)INFN Sezione di Ferrara, I-44122, Ferrara,
Italy; (B)University of Ferrara, I-44122, Ferrara, Italy
26 Institute of Modern Physics, Lanzhou 730000, People’s Republic of China
27 Institute of Physics and Technology, Peace Avenue 54B, Ulaanbaatar 13330,
Mongolia
28 Jilin University, Changchun 130012, People’s Republic of China
29 Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45,
D-55099 Mainz, Germany
30 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
31 Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-
Buff-Ring 16, D-35392 Giessen, Germany
32 Lanzhou University, Lanzhou 730000, People’s Republic of China
33 Liaoning Normal University, Dalian 116029, People’s Republic of China
34 Liaoning University, Shenyang 110036, People’s Republic of China
35 Nanjing Normal University, Nanjing 210023, People’s Republic of China
36 Nanjing University, Nanjing 210093, People’s Republic of China
37 Nankai University, Tianjin 300071, People’s Republic of China
38 National Centre for Nuclear Research, Warsaw 02-093, Poland
39 North China Electric Power University, Beijing 102206, People’s Republic of
China
40 Peking University, Beijing 100871, People’s Republic of China
41 Qufu Normal University, Qufu 273165, People’s Republic of China
42 Shandong Normal University, Jinan 250014, People’s Republic of China
43 Shandong University, Jinan 250100, People’s Republic of China
44 Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
45 Shanxi Normal University, Linfen 041004, People’s Republic of China
46 Shanxi University, Taiyuan 030006, People’s Republic of China
47 Sichuan University, Chengdu 610064, People’s Republic of China
48 Soochow University, Suzhou 215006, People’s Republic of China
49 South China Normal University, Guangzhou 510006, People’s Republic of China
50 Southeast University, Nanjing 211100, People’s Republic of China
51 State Key Laboratory of Particle Detection and Electronics, Beijing 100049,
Hefei 230026, People’s Republic of China
52 Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
53 Suranaree University of Technology, University Avenue 111, Nakhon
Ratchasima 30000, Thailand
54 Tsinghua University, Beijing 100084, People’s Republic of China
55 Turkish Accelerator Center Particle Factory Group, (A)Istinye University,
34010, Istanbul, Turkey; (B)Near East University, Nicosia, North Cyprus,
Mersin 10, Turkey
56 University of Chinese Academy of Sciences, Beijing 100049, People’s
Republic of China
57 University of Groningen, NL-9747 AA Groningen, Netherlands
58 University of Hawaii, Honolulu, Hawaii 96822, USA
59 University of Jinan, Jinan 250022, People’s Republic of China
60 University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
61 University of Minnesota, Minneapolis, Minnesota 55455, USA
62 University of Muenster, Wilhelm-Klemm-Straße 9, 48149 Muenster, Germany
63 University of Oxford, Keble Road, Oxford, United Kingdom OX13RH
64 University of Science and Technology Liaoning, Anshan 114051, People’s
Republic of China
65 University of Science and Technology of China, Hefei 230026, People’s
Republic of China
66 University of South China, Hengyang 421001, People’s Republic of China
67 University of the Punjab, Lahore-54590, Pakistan
68 University of Turin and INFN, (A)University of Turin, I-10125, Turin,
Italy; (B)University of Eastern Piedmont, I-15121, Alessandria, Italy;
(C)INFN, I-10125, Turin, Italy
69 Uppsala University, Box 516, SE-75120 Uppsala, Sweden
70 Wuhan University, Wuhan 430072, People’s Republic of China
71 Xinyang Normal University, Xinyang 464000, People’s Republic of China
72 Yunnan University, Kunming 650500, People’s Republic of China
73 Zhejiang University, Hangzhou 310027, People’s Republic of China
74 Zhengzhou University, Zhengzhou 450001, People’s Republic of China
a Also at the Moscow Institute of Physics and Technology, Moscow 141700,
Russia.
b Also at the Novosibirsk State University, Novosibirsk, 630090, Russia.
c Also at the NRC “Kurchatov Institute”, PNPI, 188300, Gatchina, Russia.
d Currently at Istanbul Arel University, 34295 Istanbul, Turkey.
e Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany.
f Also at Key Laboratory for Particle Physics, Astrophysics and Cosmology,
Ministry of Education; Shanghai Key Laboratory for Particle Physics and
Cosmology; Institute of Nuclear and Particle Physics, Shanghai 200240,
People’s Republic of China.
g Also at Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and
Institute of Modern Physics, Fudan University, Shanghai 200443, People’s
Republic of China.
h Also at Harvard University, Department of Physics, Cambridge, Massachusetts,
02138, USA.
i Also at State Key Laboratory of Nuclear Physics and Technology, Peking
University, Beijing 100871, People’s Republic of China.
j Also at School of Physics and Electronics, Hunan University, Changsha
410082, China.
k Also at Guangdong Provincial Key Laboratory of Nuclear Science, Institute of
Quantum Matter, South China Normal University, Guangzhou 510006, China.
l Also at Frontiers Science Center for Rare Isotopes, Lanzhou University,
Lanzhou 730000, People’s Republic of China.
m Also at Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou
730000, People’s Republic of China.
n Also at the Department of Mathematical Sciences, IBA, Karachi , Pakistan.

###### Abstract

We study the direct production of the $J^{PC}=1^{++}$ charmonium state
$\chi_{c1}(1P)$ in electron-positron annihilation by carrying out an energy
scan around the mass of the $\chi_{c1}(1P)$. The data were collected with the
BESIII detector at the BEPCII collider. An interference pattern between the
signal process $e^{+}e^{-}\to\chi_{c1}(1P)\to\gamma
J/\psi\to\gamma\mu^{+}\mu^{-}$ and the background processes
$e^{+}e^{-}\to\gamma_{\mathrm{ISR}}J/\psi\to\gamma_{\rm{ISR}}\mu^{+}\mu^{-}$
and $e^{+}e^{-}\to\gamma_{\rm{ISR}}\mu^{+}\mu^{-}$ are observed by combining
all the data samples. The $\chi_{c1}(1P)$ signal is observed with a
significance of 5.1$\sigma$. This is the first observation of a $C$-even state
directly produced in $e^{+}e^{-}$ annihilation. The electronic width of the
$\chi_{c1}(1P)$ resonance is determined to be
$\Gamma_{ee}=(0.12^{+0.13}_{-0.08})~{}\mathrm{eV}$, which is of the same order
of magnitude as theoretical calculations.

In the process $e^{+}e^{-}\to R$, where $R$ represents a hadronic resonance,
the dominant production mechanism, when allowed, is through one virtual
photon. This results in the copious production of vector mesons with
$J^{PC}=1^{--}$, where the quantum numbers $J$, $P$, and $C$ denote the spin,
parity, and charge conjugation of $R$, respectively. In principle, $C$-even
resonances can also be produced directly in $e^{+}e^{-}$ annihilation through
processes with two timelike virtual photons or neutral currents. Notice that
the production via two real photons is forbidden due to the Landau-Yang
theorem. Such processes were discussed already 40 years ago [1] and were
revisited in Refs. [2, 3, 4, 5]. Experimental searches for $e^{+}e^{-}$
annihilation to the $\eta$, $\eta^{\prime}$, $f_{0}(980)$, $f_{0}(1300)$,
$f_{1}(1285)$, $f_{2}(1270)$, $a_{0}(980)$, $a_{2}(1320)$, and the $X(3872)$
[also known as $\chi_{c1}(3872)$] have been carried out at the VEPP-2M [6, 7,
8], VEPP-2000 [9, 10, 11], and BEPCII [12] colliders. The most significant
signal (2.5$\sigma$) was obtained for the $f_{1}(1285)$ [11]. All others
resulted in upper limits on the electronic widths ($\Gamma_{ee}$) of the
corresponding resonances. In a spacelike two-photon scattering process,
$e^{+}e^{-}\to e^{+}e^{-}X(3872)$, evidence ($3.2\sigma$) for the $X(3872)$
production has also been found [13] at Belle. As for the $\chi_{c1}(1P)$,
which we refer to as the $\chi_{c1}$, there have been no previous searches.

Following the strategy for calculating the electronic width of the $\chi_{c1}$
suggested in Ref. [1], the authors of Ref. [14] predict
$\Gamma_{ee}=0.41~{}\mathrm{eV}$. This work also considers the interference
between the signal process, $e^{+}e^{-}\to\chi_{c1}\to\gamma
J/\psi\to\gamma\mu^{+}\mu^{-}$, and the irreducible background processes
$e^{+}e^{-}\to\gamma_{\rm ISR}J/\psi\to\gamma_{\rm ISR}\mu^{+}\mu^{-}$ and
nonresonant $e^{+}e^{-}\to\gamma\mu^{+}\mu^{-}$, see blue and red curves in
Fig. 1. Here ISR stands for initial state radiation. Depending on the value of
the relative phase $\phi$ between the signal and background amplitudes, the
interference changes the total cross section line shape dramatically.

Figure 1:  The colored curves are energy-dependent cross sections of the
process $e^{+}e^{-}\to\gamma J/\psi\to\gamma\mu^{+}\mu^{-}$ including (green
and blue curves) and not including (red curve) the direct production of
$e^{+}e^{-}\to\chi_{c1}$ (see text for more details). The gray curve denotes
the signal strength in the hypothetical case of no interference. The location
of the $\chi_{c1}$ mass is indicated by the vertical line. The black dots with
error bars represent $\sigma_{\rm ISR~{}BG}^{\rm
MC}+(\sigma_{\chi_{c1}}+\sigma_{\rm int})^{\rm data}$ at the $\chi_{c1}$ scan
data samples. The numbers next to the four data points indicate the
statistical significances associated with the $\chi_{c1}$ production.

In this Letter, we report a search for the reaction $e^{+}e^{-}\to\chi_{c1}$
at the BESIII experiment at the BEPCII collider. First, the background
processes are studied and then we carry out a search for the signal process
beyond the background. The data samples are collected at four center-of-mass
(c.m.) energies (3.5080, 3.5097, 3.5104, and 3.5146 GeV) in the $\chi_{c1}$
mass region (referred to as the $\chi_{c1}$ scan sample) with the BESIII
detector [15]. The first two scan points are located below the $\chi_{c1}$
mass, where according to Ref. [14] a constructive interference effect between
the signal process and the irreducible background processes is expected. The
third scan point is very slightly below the mass position, hence a minimal
effect is predicted. The fourth point is above the $\chi_{c1}$ mass, which
should lead to a reduction of events with respect to the scenario with no
direct production of the $\chi_{c1}$. If there was no interference, the excess
at the third point would be expected to be the largest (see gray line in Fig.
1). The data samples are listed in Table 1. The c.m. energies are measured
using a beam energy measurement system (BEMS) [16] with an uncertainty of $\pm
0.05~{}\mathrm{MeV}$ and the beam-energy spread is measured to be $(736\pm
27)$ keV. The total integrated luminosity of the four data samples is
$446~{}\mathrm{pb}^{-1}$, which is measured using large angle Bhabha events.
To verify the background description, we have also analyzed four already
existing control samples, in which the signal process is absent, with a total
integrated luminosity of $6294~{}\mathrm{pb}^{-1}$, of which two samples have
a large integrated luminosity ($\sqrt{s}=3.773~{}\mathrm{GeV}$, and
$4.178~{}\mathrm{GeV}$), while the other two are comparable in size to the
scan samples ($\sqrt{s}=3.581~{}\mathrm{GeV}$ and $3.670~{}\mathrm{GeV}$), as
summarized in Table 1.

The $\chi_{c1}$ is reconstructed via its radiative decay $\chi_{c1}\to\gamma
J/\psi$, with the subsequent decay $J/\psi\to\mu^{+}\mu^{-}$. The $J/\psi\to
e^{+}e^{-}$ mode is not used due to large background from the Bhabha process
($e^{+}e^{-}\to e^{+}e^{-}$).

Table 1:  The c.m. energies, integrated luminosities, and fit results for the control samples (above the horizontal line) and for the $\chi_{c1}$ scan sample (below). The number of signal events ($N_{\rm sig}$) is obtained from a two-dimensional fit without ($N_{\rm sig}$ w/o Corr.) and with ($N_{\rm sig}$ w/ Corr.) the two-dimensional correction described in the text. The first uncertainty is statistical, and the second is systematic (if applied). The first value in parentheses denotes the statistical significance. The second value in parentheses for the control samples is the significance when the size of the data set is normalized to $180~{}\mathrm{pb}^{-1}$ (thereby increasing the statistical errors); the second value for the $\chi_{c1}$ scan samples is the significance including the systematic uncertainties. The last column shows the number of signal events derived from a MC sample where the values of $\Gamma_{ee}$ and $\phi$ are fixed to the values obtained from a common fit to all $\chi_{c1}$ scan samples (the error includes systematic effect). $\sqrt{s}$ ($\mathrm{MeV}$) |  ${\cal L}$ ($\mathrm{pb}^{-1}$) |  $N_{\rm sig}$ w/o Corr. |  $N_{\rm sig}$ w/ Corr. |  $N_{\rm sig}$ w/ Corr. common fit
---|---|---|---|---
$3773.0$ | $2932.4~{}~{}~{}$ |  $1027\pm 140$ ($7.5\sigma$; $1.9\sigma_{180}$) |  $49\pm 141$ ($0.3\sigma$; $0.1\sigma_{180}$) | $\cdots$
$4178.4$ | $3192.5~{}~{}~{}$ |  $522\pm 104$ ($5.1\sigma$; $1.2\sigma_{180}$) |  $40\pm 104$ ($0.4\sigma$; $0.1\sigma_{180}$) | $\cdots$
$3581.5$ | $85.3~{}~{}~{}$ |  $31\pm 29$ ($1.1\sigma$; $1.6\sigma_{180}$) |  $-5\pm 29$ ($0.2\sigma$; $0.3\sigma_{180}$) | $\cdots$
$3670.2$ | $83.6~{}~{}~{}$ |  $38\pm 26$ ($1.5\sigma$; $2.2\sigma_{180}$) |  $4\pm 26$ ($0.2\sigma$; $0.2\sigma_{180}$) | $\cdots$
$3508.0$ | $181.8~{}~{}~{}$ |  $320\pm 51$ ($6.5\sigma$) |  $210\pm 52\pm 18$ ($4.1\sigma$; $4.0\sigma_{\rm low}$) | $191^{+60}_{-59}$
$3509.7$ | $39.3~{}~{}~{}$ |  $85\pm 24$ ($3.9\sigma$) |  $63\pm 24\pm 6$ ($2.8\sigma$; $2.7\sigma_{\rm low}$) |  $41^{+20}_{-19}$
$3510.4$ | $183.6~{}~{}~{}$ |  $100\pm 48$ ($1.7\sigma$) |  $0^{+16}_{-19}\pm 23$ ($0.0\sigma$; $0.0\sigma_{\rm low}$) |  $42^{+79}_{-77}$
$3514.6$ | $40.9~{}~{}~{}$ |  $-16^{+16}_{-21}$ ($0.7\sigma$) |  $-40\pm 22\pm 7$ ($1.8\sigma$; $1.6\sigma_{\rm low}$) | $-29^{+8}_{-10}$
Combined | $445.6~{}~{}~{}$ | $\cdots$ |  $\cdots$ ($5.3\sigma$; $5.1\sigma_{\rm low}$) |  $\cdots$ ($5.1\sigma$; $4.2\sigma_{\rm low}$)

Monte Carlo (MC) samples are used to determine the detection efficiencies and
to estimate the background contributions. Simulated samples are produced with
a geant4-based [17] MC package, which includes the geometric description of
the BESIII detector and the detector response. The phokhara [18] event
generator is used to describe the signal process
($e^{+}e^{-}\to\chi_{c1}\to\gamma J/\psi\to\gamma\mu^{+}\mu^{-}$), the
irreducible background processes ($e^{+}e^{-}\to\gamma_{\rm
ISR}J/\psi\to\gamma_{\rm ISR}\mu^{+}\mu^{-}$ and
$e^{+}e^{-}\to\gamma\mu^{+}\mu^{-}$), and the interference between them.
Angular distributions for the signal process are implemented into the phokhara
event generator using Ref. [14], while the background ISR processes are
modeled using Ref. [18]. Non-$\gamma_{(\rm ISR)}\mu^{+}\mu^{-}$ background
events are found to be negligible ($<0.2\%$) by studying control samples [19]
and inclusive MC simulations, which include the production of open-charm
mesons, the ISR production of vector charmonium(like) states, and continuum
processes.

A full reconstruction method is used to select $\gamma\mu^{+}\mu^{-}$
candidate events. The charged tracks and photons are selected with the same
method as described in Ref. [19]. Muon tracks are identified by the energy
they deposit in the electromagnetic calorimeter (EMC) and requiring $E_{\rm
EMC}<0.4~{}\mathrm{GeV}$. A four constraint (4$C$) kinematic fit is applied
with two charged tracks and one of the photons constraining the total
reconstructed four momentum to that of the initial state. The photon with
minimum $\chi^{2}_{4C}$ is chosen as the best photon candidate. As checked
within a MC simulation, the probability to select a wrong photon is
negligible. We require the polar angle of the best photon candidate to be
$|\cos\theta_{\gamma}|<0.80$ to suppress background events from ISR processes.

The verification of background description is done quantitatively by
performing a two-dimensional fit to the $\mu^{+}\mu^{-}$ invariant mass
($M_{\mu^{+}\mu^{-}}$) distribution and the $|\cos\theta_{\mu}|$ distribution
with noninterfering signal and background components, whose line shapes are
extracted from the corresponding MC simulations. The signal line shape is
taken from the $\chi_{c1}$ signal MC simulation at $\sqrt{s}=3.5080~{}$GeV,
smeared with two Gaussian functions, one to account for the resolution
difference between data and MC simulations and the other for line-shape
differences between different energy points. In the $\mu^{+}\mu^{-}$ invariant
mass distribution, we expect the irreducible background events to feature a
$J/\psi$ peak
($e^{+}e^{-}\to\gamma_{\mathrm{ISR}}J/\psi\to\gamma_{\rm{ISR}}\mu^{+}\mu^{-}$)
on top of a smooth distribution ($e^{+}e^{-}\to\gamma\mu^{+}\mu^{-}$). The
relative sizes of these background contributions are fixed using our best
estimate for the electronic width of the $J/\psi$ ($\Gamma_{ee}^{J/\psi}$).
The number of signal events ($N_{\rm sig}$) is expected to be zero in the
control samples. The statistical significance of the signal contribution is
determined by the difference of the best log-likelihood ($-\ln{L}$) value and
the log-likelihood value for a fit with null-signal hypothesis. However, as
summarized in the third column of Table 1, nonzero values for $N_{\rm sig}$
have been found, representing a discrepancy between the data and the MC
simulation of the irreducible background process. We have verified that this
discrepancy is not due to differences between data and MC simulation in the
experimental efficiencies, but rather can be explained by uncertainties in the
input $\Gamma_{ee}^{J/\psi}$ and limitations of the phokhara event generator
in simulating the ISR production of the narrow $J/\psi$ resonance for large-
angle ISR photons [20]. The statistical significance of the discrepancy
differs sizably for the four control samples. When normalizing the effect of
the discrepancy to an integrated luminosity of $180~{}\mathrm{pb}^{-1}$, which
corresponds to a typical luminosity of the $\chi_{c1}$ scan points, we observe
significances below 2.3$\sigma$.

We carry out a two-dimensional correction to the distributions of
$M_{\mu^{+}\mu^{-}}$ and $|\cos\theta_{\mu}|$ by re-weighting MC simulated
events to correct the discrepancy. The correction factors are extracted using
data and MC samples at $\sqrt{s}=3.773~{}\mathrm{GeV}$ or $4.178$ GeV and are
applied to the MC simulations at other data samples (see Supplemental Material
[21]). After applying these correction factors, $N_{\rm sig}$ is consistent
with zero within one standard deviation for all control samples.

In order to extract the number of signal events at the four $\chi_{c1}$ scan
points, the $M_{\mu^{+}\mu^{-}}$ and $|\cos\theta_{\mu}|$ distributions are
investigated using a similar method as above. The fit is performed at each
data sample individually using a two-dimensional unbinned maximum likelihood
fit method. The line shapes for the contributions from the $\chi_{c1}$
production, the irreducible background, and the interference between them are
derived from the corresponding individual MC simulations (see Supplemental
Material [21] for the angular distributions). The same two-dimensional
correction as above is applied to the shapes of the background processes, and
the square root of the same factor is used for the interference. The numbers
of $\chi_{c1}$ ($N_{\chi_{c1}}$) and irreducible background events ($N_{\rm
bg}$) are free parameters, while the interference ($N_{\rm int}$) is written
as $f\cdot\sqrt{N_{\chi_{c1}}\cdot N_{\rm bg}}$, where the factor $f$ is
determined from signal MC sample with the $\Gamma_{ee}$ and $\phi$ parameters
set to the optimal values from a common fit to all scan points, as will be
explained below.

The fit results are shown in Fig. 2 and are listed in Table 1. Significant
signal components are seen at $\sqrt{s}=3.5080~{}\mathrm{GeV}$ and
$3.5097~{}\mathrm{GeV}$ with $N_{\rm sig}=N_{\chi_{c1}}+N_{\rm int}$ (and its
statistical significance) determined to be $210\pm 52$ (4.1$\sigma$) and
$63\pm 24$ (2.8$\sigma$), respectively. The signal component is not
significant at $\sqrt{s}=3.5104~{}\mathrm{GeV}$ with $N_{\rm
sig}=0^{+16}_{-19}$ (0.0$\sigma$). A negative signal component is seen at
$\sqrt{s}=3.5146~{}\mathrm{GeV}$ with $N_{\rm sig}=-40\pm 22$ (1.8$\sigma$).
The combined statistical significance, obtained by adding the log-likelihoods
from each of the four data samples, is $5.3\sigma$. The cross section of the
signal component and its uncertainty is calculated as $\sigma_{\rm
sig}\equiv(\sigma_{\chi_{c1}}+\sigma_{\rm int})^{\rm data}=N_{\rm sig}/({\cal
L}\cdot\epsilon)$, where the efficiency $\epsilon$ is calculated from the
simulated signal MC samples. The sum of $\sigma_{\rm sig}$ and $\sigma_{\rm
ISR~{}BG}$ at each $\chi_{c1}$ scan point is shown in Fig. 1 (black dots),
which is in good agreement with the theoretical prediction [14]. Here
$\sigma_{\rm ISR~{}BG}$ is fixed using the phokhara generator. Statistical
tests are performed to the $\chi_{c1}$ scan samples individually using
likelihood ratios $t=-(\ln{L_{\rm s}}-\ln{L_{\rm ns}})$ to discriminate the
hypothesis with or without signal components (distributions to be found in
Supplemental Material [21]).

Figure 2: One-dimensional projections of the two-dimensional fit to the
$M_{\mu^{+}\mu^{-}}$ and $|\cos\theta_{\mu}|$ distributions from the
$\chi_{c1}$ scan samples. The black dots with error bars are from data, the
gray histograms are the irreducible background predicted by the corrected MC
simulation. The red curve is the best fit result, the red dotted (blue dashed)
curve is the signal (background) contribution. The region between
$0.8<|\cos\theta_{\mu}|<0.86$ corresponds to the gap between the barrel and
end cap modules of the EMC.

Using a common fit to the four $\chi_{c1}$ scan points, the values of
$\Gamma_{ee}$ and $\phi$ can be determined directly from data. Since it is not
easy to obtain an analytic formula for the total cross section of
$e^{+}e^{-}\to\gamma_{(\rm ISR)}\mu^{+}\mu^{-}$ as a function of $\Gamma_{ee}$
and $\phi$, the analysis is done via a scan method. At each c.m. energy of the
$\chi_{c1}$ scan sample, the MC samples of $e^{+}e^{-}\to\gamma_{(\rm
ISR)}\mu^{+}\mu^{-}$ are produced with different sets of ($\Gamma_{ee}$,
$\phi$) values, see open circles in Fig. 3. The total likelihood from the four
samples in the $\chi_{c1}$ mass region is then calculated using the same two-
dimensional distributions used previously with the number of events at each
energy point constrained to the expected number of events calculated from MC.
The best $\Gamma_{ee}$ and $\phi$ parameters are determined to be
$(0.12^{+0.08}_{-0.07})$ eV and $(205.0^{+10.0}_{-17.0})^{\circ}$,
respectively, where the uncertainty corresponding to $68.3\%$ C.L. is
statistical only. The $68.3\%$ C.L. contour region in the ($\Gamma_{ee}$,
$\phi$) plane is shown in Fig. 3, in which the red dot represents the best-
fitted value. The green curve in Fig. 1 shows the cross section line shape for
such a set of parameters. Using this best set of ($\Gamma_{ee},\phi$) values,
the number of signal events is estimated for each $\chi_{c1}$ scan sample and
is found to be 191, 41, 42, $-$29 events for the four scan samples. The
uncertainties on $N_{\rm sig}$ are estimated by varying the
($\Gamma_{ee},\phi$) values within their $68.3\%$ C.L. contour and finding the
largest variations of $N_{\rm sig}$. Combining the four samples, the
statistical significance is 5.1$\sigma$ and is found to be in very good
agreement with the previous estimate by fitting each scan sample individually,
where $\Gamma_{ee}$ and $\phi$ are not constrained to be the same.

Figure 3:  The 68.3% C.L. contour of $\Gamma_{ee}$ and $\phi$ on a
distribution of log-likelihood ($-\ln{L}$) values. The distribution of
$-\ln{L}$ in a larger parameter space region is shown in Supplemental Material
[21].

Systematic uncertainties for the extraction of $\Gamma_{ee}$ and $\phi$ mainly
come from the luminosity measurement, the detection efficiency, the line
shapes used in the fit, the fit range, the two-dimensional correction factor,
the non-$\gamma_{\rm(ISR)}\mu^{+}\mu^{-}$ background contribution, and the
c.m. energy measurement.

The systematic uncertainty on the measurement of the integrated luminosity is
$0.6\%$ for each data sample. We take 0.5% as the uncertainty for muon
reconstruction, which is assumed to be the same as for electron
reconstruction. The uncertainty in photon reconstruction is estimated to be
$0.2\%$, obtained using control samples of the
$e^{+}e^{-}\to\gamma\mu^{+}\mu^{-}$ process. The systematic uncertainties from
the integrated luminosity measurement and detection efficiency are considered
simultaneously by changing the normalization factor used in the scan fit by
$1.0\%$. The uncertainty from the requirement on $|\cos\theta_{\gamma}|$ is
studied by tightening the requirement from 0.8 to 0.79, 0.78, 0.77, and 0.76,
the largest deviation with respect to the default one is taken as the
systematic uncertainty. Systematic uncertainties from other selection criteria
are negligible.

The uncertainties from the binning strategy and the fit procedure are studied
using toy MC samples, no bias is found. The uncertainty from the beam energy
spread is considered by changing it from 736 to 1000 keV, the change is much
larger than its standard deviation measured by BEMS (27 keV). The fit range of
the $M_{\mu^{+}\mu^{-}}$ distribution is varied and the difference between the
nominal result is considered as the systematic uncertainty. The uncertainty
from the two-dimensional correction factor is estimated by replacing the
nominal one extracted from the $\sqrt{s}=3.773~{}\mathrm{GeV}$ data sample
with that from the $\sqrt{s}=4.178~{}\mathrm{GeV}$ data sample. In addition,
the square root of the correction factor is applied to the interference term
based on the assumption that the discrepancy observed at the control sample
comes entirely from the generator level. The uncertainty from this assumption
is studied by dropping the correction to the interference term. The
non-$\gamma_{\rm(ISR)}\mu^{+}\mu^{-}$ background contribution is neglected in
the nominal fit, the uncertainty from it is considered by including it.

We change the $\sqrt{s}$ in MC simulation at each energy point by $\pm
0.05~{}\mathrm{MeV}$ and take the changes as systematic uncertainty from the
c.m. energy. Assuming all the systematic uncertainties are uncorrelated and
adding them in quadrature, the largest parameter ranges of $\Gamma_{ee}$ and
$\phi$ corresponding to 68.3% C.L. are determined to be
$(0.12^{+0.13}_{-0.08})~{}\mathrm{eV}$ and $(205.0^{+15.4}_{-22.4})^{\circ}$,
respectively. The total systematic uncertainties are of a similar size as the
statistical effects. After having estimated the statistical and systematic
uncertainties associated with our fit to $\Gamma_{ee}$ and $\phi$, we study
the dependence of signal events by varying these input parameters within the
contour determined at 68.3% C.L., as listed in the last column of Table 1.

Systematic uncertainties for the individual fits are estimated using similar
methods as listed above. However, when considering the systematic
uncertainties on $N_{\rm sig}$, the one on the requirement of
$|\cos\theta_{\gamma}|$ is excluded since the signal yields change. One extra
term comes from the input $\Gamma_{ee}$ and $\phi$ values, which affect the
signal line shape and is considered by varying the values within the 68.3%
C.L. contour.

As summarized in Table 1, we list the minimum significance found both in the
case of individual fits (column “$N_{\rm sig}$ w/ Corr.”) and in the case of a
common fit (column “$N_{\rm sig}$ w/ Corr. common fit”). After including the
systematic uncertainties, the minimum significance is found to be 5.1$\sigma$
in the first and 4.2$\sigma$ in the second case. As the significance obtained
by combining individual fits is more robust to systematic effects and does not
rely on the specific model of Ref. [14], we take it as our nominal result.

In summary, using data samples taken in the $\chi_{c1}$ mass region, we
observe the direct production of the $C$-even resonance, $\chi_{c1}$, in
$e^{+}e^{-}$ annihilation for the first time with a statistical significance
larger than 5$\sigma$. We observe a typical interference pattern around the
$\chi_{c1}$ mass, which previously was predicted in Ref. [14]. The electronic
width of the $\chi_{c1}$ has been determined for the first time from a common
fit to the four scan samples to be
$\Gamma_{ee}=(0.12^{+0.13}_{-0.08})~{}\mathrm{eV}$. This observation
demonstrates that with the current generation of electron-positron colliders,
the direct production of $C$-even resonances through two virtual photons is
possible. As a next step, we intend to embark on a scan around the $\chi_{c2}$
resonance at BESIII. Using future super-tau-charm factories with increased
luminosity [22], the $\Gamma_{ee}$ and other properties such as the line
shapes of $C$-even states could be determined by performing a similar scan
method. This will shed light on the intrinsic nature of charmoniumlike
resonances.

The BESIII Collaboration thanks the staff of BEPCII and the IHEP computing
center for their strong support. We acknowledge the continuous theory support
for this analysis by Henryk Czyż and Hans Kühn. This work is supported in part
by National Key R&D Program of China under Contracts No. 2020YFA0406300, No.
2020YFA0406400; National Natural Science Foundation of China (NSFC) under
Contracts No. 11635010, No. 11735014, No. 11835012, No. 11935015, No.
11935016, No. 11935018, No. 11961141012, No. 12022510, No. 12025502, No.
12035009, No. 12035013, No. 12192260, No. 12192261, No. 12192262, No.
12192263, No. 12192264, No. 12192265; the Chinese Academy of Sciences (CAS)
Large-Scale Scientific Facility Program; Joint Large-Scale Scientific Facility
Funds of the NSFC and CAS under Contracts No. U1832207, No. U2032108; CAS Key
Research Program of Frontier Sciences under Contract No. QYZDJ-SSW-SLH040; 100
Talents Program of CAS; Shanghai Pujiang Program (20PJ1401700); INPAC and
Shanghai Key Laboratory for Particle Physics and Cosmology; ERC under Contract
No. 758462; European Union’s Horizon 2020 research and innovation programme
under Marie Sklodowska-Curie grant agreement under Contract No. 894790; German
Research Foundation DFG under Contracts Nos. 443159800, Collaborative Research
Center CRC 1044, GRK 2149; Istituto Nazionale di Fisica Nucleare, Italy;
Ministry of Development of Turkey under Contract No. DPT2006K-120470; National
Science and Technology fund; STFC (United Kingdom); The Royal Society, UK
under Contracts No. DH140054, No. DH160214; The Swedish Research Council; U.
S. Department of Energy under Contract No. DE-FG02-05ER41374.

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