[1]Nicolás Navarro-Guerrero

[1]Department of Electrical and Computer Engineering, Aarhus University,
Finlandsgade 22, 8200 Aarhus, Denmark

# AU Dataset for Visuo-Haptic Object Recognition for Robots

Lasse Emil R. Bonner  Daniel Daugaard Buhl  Kristian Kristensen
<EMAIL_ADDRESS>*

###### Abstract

Multimodal object recognition is still an emerging field. Thus, publicly
available datasets are still rare and of small size. This dataset was
developed to help fill this void and presents multimodal data for 63 objects
with some visual and haptic ambiguity. The dataset contains visual,
kinesthetic and tactile (audio/vibrations) data. To completely solve sensory
ambiguity, sensory integration/fusion would be required. This report describes
the creation and structure of the dataset. The first section explains the
underlying approach used to capture the visual and haptic properties of the
objects. The second section describes the technical aspects (experimental
setup) needed for the collection of the data. The third section introduces the
objects, while the final section describes the structure and content of the
dataset.

###### keywords:

Multimodal Object Recognition, Data Fusion, Visuo-Haptic Object Recognition,
Tactile Perception, Haptic Information, Kinesthetic Perception, Robot
Perception

Downloading and Citing this dataset: Bonner, L. E. R., Buhl, D. D.,
Kristensen, K., & Navarro-Guerrero, N. (2021). AU Dataset for Visuo-Haptic
Object Recognition for Robots. figshare.
https://doi.org/10.6084/m9.figshare.14222486

##  1 Object Exploration

In order to create the dataset, it is necessary to capture both visual and
haptic information from the selected objects. When choosing how to explore the
objects, the primary consideration is to capture relevant information from
both the visual and haptic modalities. Object explorations are based on the
exploratory procedures described by Lederman and Klatzky Lederman1987Hand ;
Lederman2009Haptic . The haptic properties of the objects can be divided into
two sub-categories: kinesthetic, which comprises size, shape and weight, and
tactile, which comprises texture and hardness. The exploration carried out for
each object can be divided into three phases:

  * •

Visual object exploration,

  * •

Kinesthetic object exploration,

  * •

Tactile object exploration.

###  1.1 Visual Exploration

In this phase, the objects are repositioned three times to expose different
faces to the camera. In addition to the three images of the object, one image
of only the background is captured, which can be used to implement background
subtraction when processing the data further. The three images are taken in
optimal lighting conditions where artificial light from multiple angles
decreases the shadows from the objects. The resolution of the images is
$4640\times 3472$. Images can later be manipulated by, for instance, scaling,
applying noise and other filters to increase the difficulty of the task as
needed. Despite the high quality of the images, visuo-haptic integration is
still necessary to reliably classify all objects as shown in the thesis of
Buhl and Bonner Buhl2021Biologically , and Kristensen Kristensen2021Better .

###  1.2 Kinesthetic exploration

For Kinesthetic Exploration, “Enclosure” and “Unsupported holding” were
selected Lederman1987Hand ; Lederman2009Haptic .

##### “Unsupported holding”

The object is lifted and held in the hand. This exploratory procedure provides
information about the weight of the object. This procedure is implemented by
mounting a human-sized robot hand (RH8D RH8D ) horizontally while placing the
object in the hand. By measuring the current needed to keep the hand still,
the weight of the objects can be inferred.

##### “Enclosure”

The object is enveloped with the hand(s) as much as possible. This exploratory
procedure provides some information about the global shape of the object. This
procedure is implemented by placing the object in the open RH8D hand, then the
hand is closed, and the final position of the fingers is recorded.

###  1.3 Tactile exploration

For Tactile Exploration, inspiration from the “Lateral motion” and “Pressure”
procedures was taken Lederman1987Hand ; Lederman2009Haptic .

##### “Lateral motion”

Sideways movements over the object help to extract information about the
object’s texture. This procedure is implemented by placing the object in the
RH8D robotic hand, ensuring that most of the object’s surface is exposed. Then
another robot – NAO NAO  – explores the object by moving one of its fingers
across the object in a side-to-side manner. This motion creates vibrations
which are recorded and later used to infer the texture of the object. This
procedure will be referred to as “feel” within the dataset.

##### “Pressure”

Two exploratory procedures inspired by the “Pressure” procedure described by
Lederman and Klatzky are implemented to capture information about the object’s
hardness. The “Pressure” procedure consists of applying a force to the object
to infer the object’s hardness. In this dataset, this procedure recorded data
for two implementations. The first implementation, called “pressure-poke”,
uses the NAO robot to poke the object while the object is being held by the
RH8D hand. The second implementation called “pressure-squeeze”, is similar to
the implementation of “Enclosure”. The object is placed in the RH8D hand, and
the hand is closed around the object. Then the fingers apply additional force
in small increments. The force and number of increments are the same for all
objects.

##  2 Experimental Setup

The experimental setup used for the data collection consists of an NAO robot,
a human-sized robotic hand RH8D, a camera, an oscilloscope, contact
microphones and an array of everyday objects that vary in colour, shape, size,
material and weight. Clip-on contact microphones are placed in different
locations on the NAO robot and the RH8D hand to measure the vibrations
produced when the objects are explored. The main parts of the experimental
setup are shown in Figure 1.

Figure 1: Experimental setup with NAO robot, RH8D Seed Robotics hand and
attached microphones.

###  2.1 Camera

The camera used is an Olympus OM-D E-M10 Mark III. The camera was mounted on a
tripod and at a fixed distance to the objects. The camera was set to auto, and
images were taken once the object was in focus. The camera remained fixed, and
only the objects were repositioned to expose different faces.

###  2.2 NAO robot

The NAO robot used is version 5 with NAOqi version 2.1.14.3. The robot is used
to capture the tactile properties (texture and hardness) of the objects by
touching and tapping the objects as described in Section 1. The NAO robot does
not have any built-in sensors that are capable of registering tactile
feedback. Thus, five contact microphones are mounted in different locations on
both the NAO robot and the RH8D hand. This approach is inspired by the work of
Toprak et al. Toprak2018Evaluating , who showed that tactile sensing is
possible using contact microphones in a very similar setup.

The microphones are used to record the vibrations produced when the robot
explores the objects. The robot’s fingers are coated with rubber. Thus, the
vibrations produced when exploring the surface of the objects are attenuated
before reaching the microphones. For this reason, we created a 3D-printed
thimble covered with symmetric protuberances, emulating fingerprints, placed
on the robot’s finger. The 3D model of the thimble can be seen in Figure 2 and
can be downloaded as part of this dataset.

Figure 2: The 3D model used to print the thimble.

The thimble is printed in polylactide (PLA) and has a wall thickness of 2mm.
The protuberances are 2mm high and distributed around the finger and on the
tip with a distance of 0.3mm. The resolution of the thimble is not as fine as
a human fingerprint due to the resolution limitations of the 3D printer used,
which can print down to a precision of 0.1mm Ender3 . A test was conducted on
a few objects from the object suite to ensure that the thimble creates more
vibrations than the NAO finger itself. These experiments showed that, at a
minimum, using the thimble increased the measured signal by 166%. On the most
significant microphone – placed right under the object – the signal strength
increased by 470% using the thimble. Despite the excellent results obtained
with this thimble’s design, the thimble’s design was not systematically
optimized. Hence a thorough study of thimbles design and materials is
recommended.

Although the NAO robot could also be used to record other haptic data, such as
the kinesthetic properties: shape and weight, as it was done by Toprak et al.
Toprak2018Evaluating , the physical size of the robot poses too many
constraints on the type of objects that can be used. Additionally, the NAO’s
hand can only be controlled with a binary signal and does not allow the
implementation of the “pressure-squeeze” procedure. Thus, the RH8D hand was
used for all the kinesthetic exploration procedures and the pressure-squeeze
procedure instead.

###  2.3 RH8D Seed Robotics hand

The RH8D hand enabled us to use objects of a broader range of sizes and weight
than those possible with the NAO robot. Additionally, the affordability and
accessibility of the RH8D hand made it a good option to facilitate
reproducibility and potentially expand the dataset. The hand is human-sized,
has eight motors, and provides 19 degrees of freedom and 4096 different
position readings of each motor RH8D . From each actuator, real-time current
readings are available and can be used to determine the weight of the objects.
All these characteristics make the RH8D Seed Robotics hand a good choice to
haptically explore objects.

###  2.4 Microphones

The microphones used are Harley Benton CM-1000 clip-on contact microphones. A
PicoScope 4824 with eight channels was used to record the data from the
microphones with a sampling rate of 400kHz. A consideration when choosing the
sample rate is that the data should be suited for sound source localization as
well as object recognition.

To perform localization, it is necessary to distinguish the time of arrival of
the vibrations to each of the microphones. The speed of sound in plastic is
about 2750 m/s at 20°C Carlson2003Frequency . Because the microphones are
separated by at least 2cm, it is necessary to sample with at least 275kHz to
capture the time difference between them. Moreover, the NAO robot and the RH8D
hand are made from different types of plastic and other materials, therefore a
sample rate of 400kHz is chosen.

####  2.4.1 Finding the optimal microphone placement

The tactile features, texture and hardness, are reliant on well-placed
microphones to capture as many vibrations created when the NAO robot interacts
with the object as possible. Multiple configurations were tested to ensure
optimal placement of the microphones, which was determined with a three-step
procedure. The primary consideration was to increase the difference of the
measurements for the different objects – e.g., a soft rubber ball and a hard
wooden block.

Firstly, live measurements were carried out to test promising placements both
based on the proximity to the point of contact as well as a decent contact
between the microphone and the robot. The best placement candidates are listed
in Table 1.

Table 1: Name and placement of microphones (channel) on the NAO and RH8D. The five best placements are shown in Figure 6. Channel | Placement
---|---
NP | NAO palm
NF | NAO finger
NW | NAO wrist
R8RU | RH8D hand, right side, under
R8LU | RH8D hand, left side, under
R8RO | RH8D hand, right side, over
R8LO | RH8D hand, left side, over

Secondly, all the exploratory procedures were performed on a subset of
objects.

Finally, the best placements were determined based on the signal strength. The
placements leading to low signal strength were removed from the final setup.
From the subset of objects, we focused on a soft rubber ball and a hard wooden
box as these objects lead to very different signal patterns. Figure 3 and 4
show the measurements for the lateral motion procedure on a soft rubber ball
and a hard wooden box, respectively.

Figure 3: Measurements from all seven microphones when exploring a soft rubber
ball. Red is used for Microphones placed on the NAO, and blue is used for
microphones placed on the RH8D. Figure 4: Measurements from all seven
microphones when exploring a hard wooden box. Red is used for Microphones
placed on the NAO, and blue is used for microphones placed on the RH8D.

To quantify the difference between the channels, the absolute average
difference of a channel is compared across measurements on the two different
objects. The differences between the channels are shown in Figure 5. The
smallest difference is detected in channels NW and R8LU. Thus, these channels
are not used in the final setup. The channels NP and R8RO show the most
significant difference and are therefore expected to provide a more
significant amount of information about the haptic properties of the objects.

Figure 5: Absolute average difference of the different channels while
exploring a wooden box and a rubber ball. Red is used for Microphones placed
on the NAO, and blue is used for microphones placed on the RH8D.

This leads to the final setup shown in Figure 6, consisting of five
microphones from which two are on the NAO and three on the R8HD.

Figure 6: Final microphone setup. Left: the R8HD robotic hand shows channels
R8LO, R8RU and R8RO. Right: the hand of the NAO showing channel NF and NP.

##  3 Object Set

In this section, the considerations used for object selection are presented.
Additionally, pictures and properties for each of the objects are listed.

###  3.1 Choosing the objects

The objects are chosen based on their suitability for multimodal (visuo-
haptic) object recognition. We used the following criteria for the dataset:

  * •

The dataset should contain visually ambiguous objects

  * •

The dataset should contain haptically ambiguous objects

  * •

The dataset should contain objects of a variety of materials and colours

  * •

The number of objects in the dataset should exceed 50 (most visuo-haptic
datasets include less than 50 objects).

  * •

The objects should be small enough to fit in the RH8D hand but large enough to
facilitate the automated exploration procedures.

Figure 7 shows an overview of the objects included in the dataset. These
images are not part of the dataset but are merely used to identify the
objects. The objects chosen are a combination of toys and household objects.
Especially toys were found to be well suited because they come in different
shapes and colours. Objects of similar shape and colour are included to create
visual ambiguity. An example of this is the yellow ball and yellow lemon. Some
objects are filled with different content, making them only separable by their
haptic features. Examples of this are the ice cube container, which is
presented as empty and filled with Play-Doh, and the velvet bag filled with
65g salt, coffee beans, and Play-Doh, respectively. Both the ice cube
container and velvet bag are presented at the bottom right of Figure 7. The
haptic ambiguity is included by choosing objects of similar material and shape
but in a different colour. Examples of this are the balls and cubes. For
further specifications of the selected objects, please see the object list
uploaded with the dataset.

Figure 7: All objects used in the dataset. Some objects are presented several
times because they are filled with different substances, which can change the
weight and, in some cases, texture and hardness of the object.

##  4 Dataset

The final dataset consists of the previously mentioned visual and haptic data.
Each object is measured three times and repositioned each time. This data is
collected from three sources:

  * •

images of the objects,

  * •

kinesthetic data from the RH8D hand,

  * •

vibration data from the contact microphones.

The visual information consists of four images, a background image for each
object and three images of different faces of the object. The distance and
heading of the camera remain unchanged for all four images and across objects.

The kinesthetic data collected with the RH8D hand consists of current readings
from the wrist and the positions of each of the hand’s five fingers. The
current from the wrist flexion joint is measured in milliamperes (mA), and the
baseline reading (without objects) is 30mA. The fingers’ positions are
represented by a value in degrees ranging from -180 degrees (stretched) to 180
degrees (closed). All the information is stored in CSV files. There are
individual files for each exploratory procedure (“unsupported holding”,
“enclosure”, and “pressure-squeeze”) and channels for three different object
repositionings. Additionally, readings from the IR proximity sensor (located
at the centre of the palm) are provided. All in all, resulting in 60 files for
kinesthetic data. The current data is stored in the unsupported_holding_n.csv
files, and the IR proximity sensor reading is stored in the extra_n.csv files.
The fingers’ position data is stored in the enclosure_n.csv files. After the
enclosure procedure is sampled, the object is squeezed with four different
forces (400, 500, 600 and 700 units of the actuators max force in a 12bit
resolution scale, i.e., from 0 to 4095) to investigate the hardness of the
objects as described in Section 1.3. The corresponding fingers’ position
readings from each force level and the proximity from the IR sensor are stored
in the pressure-squeeze_n.csv files.

The vibration data is recorded in mV with a sampling rate of 400kHz.
Immediately after every object’s exploratory procedure, the background noise
is recorded and stored under the folder called “background”. The background
sample is recorded while the NAO robot is performing exploratory procedures,
and the RH8D is in the same position as if it were to hold an object. This is
done to compensate in case the noise characteristic from the robots’
actuators, cooling fans, and other moving parts changes during data
collection. The vibration data was collected using the five
channels/microphones in the positions described in Section 2.4.1 and stored in
CSV files. There are individual files for each exploratory procedure (“feel”
and “pressure-poke”) and channels for three different object repositionings
resulting in 30 files for vibration data.

The folder structure of the dataset is as follows:

    Data
    ---|object
    ------|background
    ------|observation
    ---------|haptic_feel_noise
    ------------|Tactile_feel_n_ch_m.csv
    ---------|haptic_feel_clean
    ------------|Tactile_feel_n_ch_m.csv
    ---------|haptic_pressure-poke_noise
    ------------|Tactile_pressure-poke_n_ch_m.csv
    ---------|haptic_pressure-poke_clean
    ------------|Tactile_pressure-poke_n_ch_m.csv
    ---------|kinesthetics
    ------------|enclosure_n.csv
    ------------|pressure-squeeze_n.csv
    ------------|unsupported_holding_n.csv
    ------------|extra_n.csv
    ------|visual
    --------|position-n.jpg

## References

  * [1] Ender-3 Pro 3D Printer.  https://www.creality.com/goods-detail/ender-3-pro-3d-printer.
  * [2] NAO the Humanoid and Programmable Robot – SoftBank Robotics.  https://www.softbankrobotics.com/emea/en/nao.
  * [3] RH8D Adult size Dexterous Robot Hand.  https://www.seedrobotics.com/rh8d-adult-robot-hand.
  * [4] Daniel Daugaard Buhl and Lasse Emil Ranulph Bonner.  Biologically Inspired Multimodal Fusion Learning for Robotic Object Recognition.  MSc, Department of Electrical and Computer Engineering, Aarhus University, Aarhus, Denmark, June 2021.
  * [5] J.E. Carlson, J. van Deventer, A. Scolan, and C. Carlander.  Frequency and Temperature Dependence of Acoustic Properties of Polymers Used in Pulse-Echo Systems.  In IEEE Symposium on Ultrasonics, volume 1, pages 885–888, Honolulu, HI, USA, October 2003. IEEE.  https://dx.doi.org/10.1109/ULTSYM.2003.1293541.
  * [6] Kristian Kristensen.  Towards Better Multimodal Object Recognition.  MSc, Department of Electrical and Computer Engineering, Aarhus University, Aarhus, Denmark, June 2021.
  * [7] Susan J. Lederman and Roberta L. Klatzky.  Hand Movements: A Window into Haptic Object Recognition.  Cognitive Psychology, 19(3):342–368, July 1987.  https://dx.doi.org/10.1016/0010-0285(87)90008-9.
  * [8] Susan J. Lederman and Roberta L. Klatzky.  Haptic Perception: A Tutorial.  Attention, Perception, & Psychophysics, 71(7):1439–1459, October 2009.  https://dx.doi.org/10.3758/APP.71.7.1439.
  * [9] Sibel Toprak, Nicolás Navarro-Guerrero, and Stefan Wermter.  Evaluating Integration Strategies for Visuo-Haptic Object Recognition.  Cognitive Computation, 10(3):408–425, June 2018.  https://dx.doi.org/10.1007/s12559-017-9536-7.


Participating as a member of ]TEXONO Collaboration

Participating as a member of ]TEXONO Collaboration

Participating as a member of ]TEXONO Collaboration

Participating as a member of ]TEXONO Collaboration

Participating as a member of ]TEXONO Collaboration

Participating as a member of ]TEXONO Collaboration

CDEX Collaboration

# Exotic Dark Matter Search with CDEX-10 Experiment at China Jinping
Underground Laboratory

W. H. Dai  L. P. Jia  H. Ma<EMAIL_ADDRESS>Q. Yue
<EMAIL_ADDRESS>K. J. Kang  Y. J. Li  Key Laboratory of Particle and
Radiation Imaging (Ministry of Education) and Department of Engineering
Physics, Tsinghua University, Beijing 100084  H. P. An  Department of Physics,
Tsinghua University, Beijing 100084  Greeshma C  [  Institute of Physics,
Academia Sinica, Taipei 11529  J. P. Chang  NUCTECH Company, Beijing 100084
Y. H. Chen  YaLong River Hydropower Development Company, Chengdu 610051  J. P.
Cheng  Key Laboratory of Particle and Radiation Imaging (Ministry of
Education) and Department of Engineering Physics, Tsinghua University, Beijing
100084  College of Nuclear Science and Technology, Beijing Normal University,
Beijing 100875  Z. Deng  Key Laboratory of Particle and Radiation Imaging
(Ministry of Education) and Department of Engineering Physics, Tsinghua
University, Beijing 100084  C. H. Fang  College of Physics, Sichuan
University, Chengdu 610065  X. P. Geng  Key Laboratory of Particle and
Radiation Imaging (Ministry of Education) and Department of Engineering
Physics, Tsinghua University, Beijing 100084  H. Gong  Key Laboratory of
Particle and Radiation Imaging (Ministry of Education) and Department of
Engineering Physics, Tsinghua University, Beijing 100084  Q. J. Guo  School of
Physics, Peking University, Beijing 100871  X. Y. Guo  YaLong River Hydropower
Development Company, Chengdu 610051  L. He  NUCTECH Company, Beijing 100084
S. M. He  YaLong River Hydropower Development Company, Chengdu 610051  J. W.
Hu  Key Laboratory of Particle and Radiation Imaging (Ministry of Education)
and Department of Engineering Physics, Tsinghua University, Beijing 100084  H.
X. Huang  Department of Nuclear Physics, China Institute of Atomic Energy,
Beijing 102413  T. C. Huang  Sino-French Institute of Nuclear and Technology,
Sun Yat-sen University, Zhuhai 519082  H. T. Jia  X. Jiang  College of
Physics, Sichuan University, Chengdu 610065  S. Karmakar  [  Institute of
Physics, Academia Sinica, Taipei 11529  H. B. Li  [  Institute of Physics,
Academia Sinica, Taipei 11529  J. M. Li  J. Li  Key Laboratory of Particle and
Radiation Imaging (Ministry of Education) and Department of Engineering
Physics, Tsinghua University, Beijing 100084  Q. Y. Li  R. M. J. Li  College
of Physics, Sichuan University, Chengdu 610065  X. Q. Li  School of Physics,
Nankai University, Tianjin 300071  Y. L. Li  Key Laboratory of Particle and
Radiation Imaging (Ministry of Education) and Department of Engineering
Physics, Tsinghua University, Beijing 100084  Y. F. Liang  Key Laboratory of
Particle and Radiation Imaging (Ministry of Education) and Department of
Engineering Physics, Tsinghua University, Beijing 100084  B. Liao  College of
Nuclear Science and Technology, Beijing Normal University, Beijing 100875  F.
K. Lin  [  Institute of Physics, Academia Sinica, Taipei 11529  S. T. Lin  S.
K. Liu  College of Physics, Sichuan University, Chengdu 610065  Y. D. Liu
College of Nuclear Science and Technology, Beijing Normal University, Beijing
100875  Y. Liu  College of Physics, Sichuan University, Chengdu 610065  Y. Y.
Liu  College of Nuclear Science and Technology, Beijing Normal University,
Beijing 100875  Z. Z. Liu  Key Laboratory of Particle and Radiation Imaging
(Ministry of Education) and Department of Engineering Physics, Tsinghua
University, Beijing 100084  Y. C. Mao  School of Physics, Peking University,
Beijing 100871  Q. Y. Nie  Key Laboratory of Particle and Radiation Imaging
(Ministry of Education) and Department of Engineering Physics, Tsinghua
University, Beijing 100084  J. H. Ning  YaLong River Hydropower Development
Company, Chengdu 610051  H. Pan  NUCTECH Company, Beijing 100084  N. C. Qi
YaLong River Hydropower Development Company, Chengdu 610051  J. Ren  X. C.
Ruan  Department of Nuclear Physics, China Institute of Atomic Energy, Beijing
102413  Z. She  Key Laboratory of Particle and Radiation Imaging (Ministry of
Education) and Department of Engineering Physics, Tsinghua University, Beijing
100084  M. K. Singh  [  Institute of Physics, Academia Sinica, Taipei 11529
Department of Physics, Banaras Hindu University, Varanasi 221005  T. X. Sun
College of Nuclear Science and Technology, Beijing Normal University, Beijing
100875  C. J. Tang  College of Physics, Sichuan University, Chengdu 610065  W.
Y. Tang  Y. Tian  Key Laboratory of Particle and Radiation Imaging (Ministry
of Education) and Department of Engineering Physics, Tsinghua University,
Beijing 100084  G. F. Wang  College of Nuclear Science and Technology, Beijing
Normal University, Beijing 100875  L. Wang  Department of Physics, Beijing
Normal University, Beijing 100875  Q. Wang  Y. Wang  Key Laboratory of
Particle and Radiation Imaging (Ministry of Education) and Department of
Engineering Physics, Tsinghua University, Beijing 100084  Department of
Physics, Tsinghua University, Beijing 100084  Y. X. Wang  School of Physics,
Peking University, Beijing 100871  H. T. Wong  [  Institute of Physics,
Academia Sinica, Taipei 11529  S. Y. Wu  YaLong River Hydropower Development
Company, Chengdu 610051  Y. C. Wu  Key Laboratory of Particle and Radiation
Imaging (Ministry of Education) and Department of Engineering Physics,
Tsinghua University, Beijing 100084  H. Y. Xing  College of Physics, Sichuan
University, Chengdu 610065  R. Xu  Key Laboratory of Particle and Radiation
Imaging (Ministry of Education) and Department of Engineering Physics,
Tsinghua University, Beijing 100084  Y. Xu  School of Physics, Nankai
University, Tianjin 300071  T. Xue  Key Laboratory of Particle and Radiation
Imaging (Ministry of Education) and Department of Engineering Physics,
Tsinghua University, Beijing 100084  Y. L. Yan  College of Physics, Sichuan
University, Chengdu 610065  L. T. Yang  Key Laboratory of Particle and
Radiation Imaging (Ministry of Education) and Department of Engineering
Physics, Tsinghua University, Beijing 100084  N. Yi  Key Laboratory of
Particle and Radiation Imaging (Ministry of Education) and Department of
Engineering Physics, Tsinghua University, Beijing 100084  C. X. Yu  School of
Physics, Nankai University, Tianjin 300071  H. J. Yu  NUCTECH Company, Beijing
100084  J. F. Yue  YaLong River Hydropower Development Company, Chengdu 610051
M. Zeng  Z. Zeng  B. T. Zhang  Key Laboratory of Particle and Radiation
Imaging (Ministry of Education) and Department of Engineering Physics,
Tsinghua University, Beijing 100084  F. S. Zhang  College of Nuclear Science
and Technology, Beijing Normal University, Beijing 100875  L. Zhang  College
of Physics, Sichuan University, Chengdu 610065  Z. H. Zhang  Z. Y. Zhang  Key
Laboratory of Particle and Radiation Imaging (Ministry of Education) and
Department of Engineering Physics, Tsinghua University, Beijing 100084  K. K.
Zhao  College of Physics, Sichuan University, Chengdu 610065  M. G. Zhao
School of Physics, Nankai University, Tianjin 300071  J. F. Zhou  YaLong River
Hydropower Development Company, Chengdu 610051  Z. Y. Zhou  Department of
Nuclear Physics, China Institute of Atomic Energy, Beijing 102413  J. J. Zhu
College of Physics, Sichuan University, Chengdu 610065

###### Abstract

A search for exotic dark matter (DM) in the sub-GeV mass range has been
conducted using 205 kg$\cdot$day data taken from a p-type point contact
germanium detector of CDEX-10 experiment at China Jinping underground
laboratory. New low-mass dark matter searching channels, neutral current
fermionic DM absorption ($\chi+A\rightarrow\nu+A$) and DM-nucleus
3$\rightarrow$2 scattering ($\chi+\chi+A\rightarrow\phi+A$), have been
analyzed with an energy threshold of 160 eVee. No significant signal was
found, thus new limits on the DM-nucleon interaction cross section are set for
both models at sub-GeV DM mass region. A cross section limit for the fermionic
DM absorption is set to be $\rm 2.5\times 10^{-46}cm^{2}$(90% C.L.) at DM mass
of 10 MeV/c2. For the DM-nucleus 3$\rightarrow$2 scattering scenario, limits
are extended to DM mass of 5 MeV/c2 and 14 MeV/c2 for the massless dark photon
and bound DM final state, respectively.

Key words

sub-GeV dark matter, fermionic dark matter absorption, DM-nucleus
3$\rightarrow$2 scattering, CJPL.

††preprint: APS/123-QED

Introduction- Various evidence from cosmological and astronomical observations
strongly supports the existence of dark matter (DM) in our Universe [1]. The
weakly interacting massive particle (WIMP) DM candidate has been searched for
several decades [2-4], and the limit on the WIMP-nucleus cross section has
been pushed near the neutrino floor for DM masses around the GeV scale in
direct detection experiments [5-12].

The null results in WIMP search have motived building of alternative dark
matter models [13-15]. Recently, two sub-GeV light DM interaction scenarios,
the neural current fermionic DM absorption and DM-nucleus 3$\rightarrow$2
scattering, have been proposed and searched for experimentally [16-20].

The fermionic DM ($\chi$) may convert to a neutrino ($\nu$) upon interaction
with a target ($A$) via a neural current absorption process
($\chi+A\rightarrow\nu+A$) [16,17]. The absorption generates a monoenergetic
signal with an energy proportional to the DM mass in direct detection
experiments. Experiments with a low energy threshold, low background, and good
energy resolution can provide strong constraints on the interaction cross
section. In direct detection experiments, only two searches have been
performed to date. The the most stringent limit at 15$\sim$125 MeV/c2 DM mass
range is given by PandaX-4T experiment and the lowest limits on the cross
section of 1.7$\times 10^{-50}$ cm2 (90%C.L.) is placed at DM mass of 35
MeV/c2 [18]. The Majorana Demonstrator set limits on the fermionic DM
absorption cross section at the DM mass of 25$\sim$190 MeV/c2 via the high
purity germanium detector technology [19].

In recent work, another direct detection channel for sub-GeV DM via a DM-
nucleus 3$\rightarrow$2 scattering process ($\chi+\chi+A\rightarrow\phi+A$) is
proposed [20]. Two DM candidates ($\chi$) may combine into a DM composite
state or dark radiation ($\phi$) upon the interaction with a target ($A$).
Similar to the fermionic DM absorption, a monoenergetic signal is generated in
the three-body scattering, and the energy passed to the nucleon is related to
the mass of the initial and final states of DM. The Majorana Demonstrator
performed searches for DM-nucleus 3$\rightarrow$2 scattering signals with 52.6
kg$\cdot$year exposure data and an analysis threshold of 1 keVee [19].

In this letter, we report the search results of the neural current fermionic
DM absorption and DM-nucleus 3$\rightarrow$2 scattering using 205 kg$\cdot$day
exposure data from the CDEX-10 experiment with an analysis threshold of 160
eVee.

CDEX-10 Experiment- The CDEX-10 experiment operates a 10-kg p-type point-
contact germanium (PPCGe) detector array to search for light DM in China
Jinping Underground Laboratory (CJPL) [11,21]. The detector array consists of
three triple-element PPCGe detector strings, C10-A, B, C, respectively. The
detector array surrounded by a 20 cm high-purity oxygen-free copper shielding
is directly immersed in a liquid nitrogen (LN) cryostat for cooling. The LN
cryostat and data acquisition (DAQ) systems are placed inside a polyethylene
room at CJPL-I [22]. The detailed configuration of the experimental setup can
be found in [11,22].

One of the C10 detectors, C10-B1, achieved the lowest analysis threshold (160
eVee) during its data taking from February 2017 to August 2018 [11,23]. The
dead layer thicknesses of C10-B1 is evaluated to be (0.88$\pm$0.12 mm)
[11,12]. The dead layer results in a fiducial mass of 939 g and, accordingly,
an exposure of 205 kg$\cdot$day.

The data processing procedures, including energy calibration, pedestal cut,
physics event selection, and bulk or surface event discrimination, were
discussed in our previous works [11,24]. The dead time of the DAQ system was
measured to be 5.7% by random trigger signals. Efficiencies of event trigger
and event selection were derived from a 137Cs source. The 0.16 eVee$\sim$4
keVee spectrum after all event selections and efficiency correction is used
for DM analysis.

Data Analysis- A minimum $\chi^{2}$ method, similar to our previous WIMP
analysis [11,23,25], is used to search for the fermionic DM absorption and DM-
nucleus 3$\rightarrow$2 scattering. The $\chi^{2}$ is constructed as

$\chi^{2}=\sum_{i}\frac{\left[n_{i}-S_{i}(m_{\chi},\sigma_{\chi})-B_{i}\right]^{2}}{\sigma_{stat,i}^{2}+\sigma_{syst,i}^{2}}$
(1)

Where $n_{i}$ is the measured event rate in $i^{th}$ energy bin,
$\sigma_{stat,i}$ and $\sigma_{syst,i}$ are the statistic and systematic
uncertainty, respectively. $S_{i}(m_{\chi},\sigma_{\sigma})$ is the expected
DM event rate in $i^{th}$ energy bin at DM mass mχ and DM-nucleus cross
section $\sigma_{\chi}$. $B_{i}$ is the background event rate in the $i^{th}$
energy bin.

The background event rate ($B$) of C10-B1 detector consists of a flat
continuum ($p_{0}$) plus L-shell and M-shell X-ray peaks from 68Ge
($E_{L}=$1.298 keV, $E_{M}=$0.16 keV), 68Ga ($E_{L}=$1.194 keV, $E_{M}=$0.14
keV), 65Zn ($E_{L}=$1.096 keV), 55Fe ($E_{L}=$0.764 keV), 54Mn ($E_{L}=$0.695
keV), and 49V ($E_{L}=$0.564 keV):

$\displaystyle B=p_{0}+\sum
I_{L}\cdot\frac{1}{\sqrt{2\pi}\sigma_{L}}\exp\left(-\frac{(E-E_{L})^{2}}{2\sigma_{L}^{2}}\right)$
(2) $\displaystyle+\sum
I_{M}\cdot\frac{1}{\sqrt{2\pi}\sigma_{M}}\exp\left(-\frac{(E-E_{M})^{2}}{2\sigma_{M}^{2}}\right)$

Where $E_{L}$ and $E_{M}$ are the energies of the L-shell and M-shell X-rays,
and $I_{L}$ and $I_{M}$ are the corresponding peak intensities. $\sigma_{L}$
and $\sigma_{M}$ are the energy resolutions at the peak energy. As shown in
Fig.1, The K-shell X-ray peaks in the 4$\sim$12 keVee spectrum are measured to
constrain the intensities of the L/M-shell peaks with known K/L and k/M ratios
[11,26].

The DM-nucleus cross section is probed by minimizing the $\chi^{2}$ value at a
certain DM mass, and the upper limit at the 90% confidence level (C.L.) is
computed using the Feldman-Cousins method [27]. The nuclear recoil quenching
factor of Ge is computed by the trim software package [11,28-30].

Figure 1:  Spectra fit for the intensities of the six K-shell X-ray peaks, the
1$\sigma$ uncertainty band derived from the fit uncertainty is labeled in
gray.

Fermionic DM Absorption- As proposed in [16,17], the fermionic DM may interact
with Ge via a neutral current (NC) absorption, $\chi+Ge\rightarrow\nu+Ge$,
modeled as a Yukawa-like interaction with a bosonic mediator. Considering a
non-relativistic fermionic DM, its mass dominates its energy and results in a
momentum transfer $q\simeq m_{\chi}$ and nuclear recoil energy $E_{R}\simeq
m_{\chi}^{2}/2M$, where $M$ is the mass of the target. The differential event
rate ($dR_{NC}/dE_{R}$) and total event rate ($R_{NC}$) of the neutral current
absorption signal can be expressed as [17]:

$\displaystyle\frac{dR_{NC}}{dE_{R}}=\frac{\rho_{\chi}}{m_{\chi}}\cdot\sigma_{NC}$
(3) $\displaystyle\times\frac{1}{M_{T}}\sum_{j}N_{j}M_{j}A_{j}^{2}F_{j}^{2}$
$\displaystyle(m_{\chi})\frac{\sqrt{2E_{R}M_{j}}}{2p_{\nu}m_{\chi}^{2}}\left\langle\frac{1}{v_{\chi}}\right\rangle_{v_{\chi}>v_{min}}$

$\displaystyle
R_{NC}=\frac{\rho_{\chi}}{m_{\chi}}\cdot\sigma_{NC}\cdot\frac{1}{M_{T}}\sum_{j}N_{j}M_{j}A_{j}^{2}F_{j}^{2}(m_{\chi})$
(4)

Where $\sigma_{NC}$ is the DM-nucleon interaction cross section, $m_{\chi}$ is
the DM mass. The local DM density $\rho_{\chi}$ is set to 0.3 GeV/cm3 as
recommended in Ref [31]. $M_{T}=\sum_{j}N_{j}M_{j}$ is the total target mass
with $N_{j}$ and $M_{j}$ corresponding to the number and mass of isotope $j$,
respectively. $F_{j}(m_{\chi})$ is the normalized Helm form factor for isotope
$j$ evaluated at momentum transfer $q=m_{\chi}$ [32].
$p_{\nu}=\sqrt{q(2m_{\chi}-q-2E_{R})}$ denotes the momentum of the outgoing
neutrino. $v_{min}$ is the minimum DM velocity at a given recoil energy
$E_{R}$ [17].

As shown in Eq(3), the DM signal rate is contributed by all Ge isotopes, and
their abundance in the natural Ge are adopted for the C10-B1 detector: 76Ge
(7.6%), 74Ge (36.3%), 73Ge (7.7%), 72Ge (27.5%), and 70Ge (20.9%).
Contributions from different Ge isotopes in the nuclear recoil energy spectrum
are shown in the Fig.2. Converting the nuclear recoil energy in Eq(3) into
visible energy and folding the energy resolution of the detector, the expected
spectra of the fermionic DM absorption signals are derived for several
$m_{\chi}$ and a certain $\sigma_{NC}$, as shown in Fig.3.

Figure 2:  Nuclear recoil energy spectra of the fermionic DM absorption
signals for Ge target, with a DM mass $m_{\chi}$ = 40 MeV/c2 and the DM-
nucleon cross section $\sigma_{NC}=10^{-45}$ cm2 for all Ge isotopes. Figure
3:  Expected spectra of the fermionic DM absorption signals for $m_{\chi}$ =
10, 20, 30, 40 MeV/c2 with a DM-nucleon cross section $\sigma_{NC}=10^{-45}$
cm2. The C10-B1 spectrum is shown as the black dots with a bin size of 100
eVee. The red dash line represents the analysis threshold.

We scan the DM mass in the range of 10$\sim$45 MeV/c2, and no significant
signal is observed. The best fit spectrum for $m_{\chi}\sim$40 MeV/c2 and the
corresponding 90% C.L. upper limit of the DM signal are displayed in Fig.4.
Upper limits of the DM-nucleon cross section superimposed with previous
results from direct detection experiments [18,19] and Z0 monojet searches at
the LHC [33] are illustrated in Fig.5. The most stringent limit on DM-nucleon
cross section is $\sigma_{NC}<2.4\times 10^{-47}$ cm2 at DM mass of 43.0
MeV/c2 in this work. The upper limit on cross section is set to
$\sigma_{NC}<2.5\times 10^{-46}$ cm2 at 10 MeV/c2 DM mass.

Figure 4: An example of fermionic DM absorption analysis for $m_{\chi}$=40
MeV/c2. The best-fit background model is shown in the red line, the gray lines
represent the contributions from L-shell and M-shell X-ray peaks, and the flat
background is depicted by the yellow line. The best-fit the DM signal is
labeled in blue. Figure 5: Upper limit (90% C.L.) of the fermionic DM
absorption cross section $\sigma_{NC}$. The shadow region represents the
constraints from Z0 monojet searches at the LHC (indirect detection). The
result in this work (red line) is compared with two other direct detection
experiments, the Majorana Demonstrator (MJD, blue line) and PandaX-4T (black
line). constraints on $\sigma_{NC}$ for DM mass of $\sim$10 MeV/c2 is achieved
in this work.

DM-nucleus 3$\rightarrow$2 scattering- Recent work has proposed that the DM
may interact with the nucleus via an inelastic 3$\rightarrow$2 scattering
process, $\chi+\chi+A\rightarrow\phi+A$, where the DM final state ($\phi$) can
be either a DM composite state or any dark radiation [20]. The signature of
this process is similar to that of the fermionic DM absorption. The
monoenergetic nuclear recoil energy is:

$E_{R}\simeq\frac{(4-\xi^{2})m_{\chi}^{2}}{2(M+2m_{\chi})}$ (5)

Where M is the mass of the nucleus, $\xi$ is the mass ratio of the final and
initial dark matter states $\phi$ and $\chi$. The mass ratio $\xi$ is model-
dependent. In this study, we considered two models: a massless DM final state
($\phi$=dark photon, $\xi$=0) and a bound DM final state. For the bound DM
final state, the mass ratio $\xi=2(m_{\chi}+\epsilon)/m_{\chi}$, where the
binding energy $\epsilon$ is decided by a new gauge coupling $g_{D}$:
$\epsilon=-(g_{D}^{4}\cdot m_{\chi})/(64\pi^{2})$ [34]. We set the gauge
coupling $|g_{D}|=3$ as in [20] and obtain a mass ratio $\xi=1.9$ for the
bound DM final state.

The total event rate of the 3$\rightarrow$2 scattering is similar in form to
that of the fermionic DM absorption:

$\displaystyle R_{3\rightarrow 2}=\frac{\rho_{\chi}}{m_{\chi}}\cdot
n_{\chi}\left\langle\sigma_{3\rightarrow 2}\cdot v_{\chi}^{2}\right\rangle$
(6) $\displaystyle\times\frac{1}{M_{T}}\sum_{j}N_{j}M_{j}A_{j}^{2}F_{j}^{2}$
$\displaystyle(q_{3\rightarrow 2})$

Where the $\left\langle\sigma_{3\rightarrow 2}\cdot v_{\chi}^{2}\right\rangle$
is the average three-body inelastic cross section with a DM initial velocity
of $v_{\chi}$. $n_{\chi}=\rho_{\chi}/m_{\chi}$ is the number density. The
momentum transfer in the 3$\rightarrow$2 scattering is $q_{3\rightarrow
2}=\sqrt{4-\xi^{2}}m_{\chi}$. In the calculation of DM expected spectra, the
quenching factor, and energy resolution are the same as in fermionic DM
absorption calculation. Fig.6 shows the expected spectra of the
3$\rightarrow$2 scattering signals for the massless dark photon and bound DM
final state. The shape of the expected spectra is also similar to that of the
fermionic DM absorption.

Figure 6:  Expected spectra of the DM-nucleus 3$\rightarrow$2 scattering
signals. Black solid lines represent the spectra of the massless dark photon
final state ($\xi=0$), Black dash lines denote a bound final state
($\xi=1.9$). The DM-nucleus coupling $\left\langle\sigma_{3\rightarrow 2}\cdot
v_{\chi}^{2}\right\rangle n_{\chi}$ is set to $10^{-45}$ cm2 for both final
states. The C10-B1 spectrum is shown as the black dots with the red dash line
denoting the analysis threshold. Figure 7: Upper limit (90% C.L.) of the DM-
nucleus 3$\rightarrow$2 scattering coupling $\left\langle\sigma_{3\rightarrow
2}\cdot v_{\chi}^{2}\right\rangle n_{\chi}$. $\xi=0$ is a massless dark photon
final state, and $\xi=1.9$ is a bound state. The results of this work (red and
black line) are compared with the results from the Majorana Demonstrator (MJD,
blue and green lines). This work places limits on a lower DM mass region for
both massless and bound DM final states with a lower analysis threshold of 160
eVee.

We place limits on the $(m_{\chi},\left\langle\sigma_{3\rightarrow 2}\cdot
v_{\chi}^{2}\right\rangle n_{\chi})$ parameter as suggested in Ref [20] for
the massless dark photon and the bound DM final state. The 90% upper limit for
the coupling $\left\langle\sigma_{3\rightarrow 2}\cdot
v_{\chi}^{2}\right\rangle n_{\chi}$ is shown in Fig.7. Compared with the
results from the Majorana Demonstrator [19], this work achieved a lower
analysis threshold of 160 eVee and excluded new parameter space in lower DM
mass regions.

Conclusion- In this Letter, we report search results for the sub-GeV fermionic
DM absorption and DM-nucleus 3$\rightarrow$2 scattering using 205.4
kg$\cdot$day exposure data from the C10-B1 PPCGe detector in the CDEX-10
experiment. The expected DM signal is analyzed in the 160 eVee$\sim$4 keVee
spectrum via a minimum $\chi^{2}$ method. With an analysis threshold of 160
eVee, we set new experimental limits on the fermionic DM absorption cross
section in $10\sim 45$ MeV/c2 DM mass. For the DM-nucleus 3$\rightarrow$2
scattering, we place limit on on lower DM mass of 5 MeV/c2 for a massless dark
photon DM final state, and 14 MeV/c2 for the bound DM final state. Those
limits achieve the lowest DM mass among the searches in direct detection
experiments to date.

###### Acknowledgements.

This work was supported by the National Key Research and Development Program
of China (Grant No. 2017YFA0402200) and the National Natural Science
Foundation of China (Grants No. 12175112, No. 12005111, No. 11725522, No.
11675088, No.11475099).

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