# Electron-Ion Collider in China

Daniele P. ANDERLE  Guangdong Provincial Key Laboratory of Nuclear Science,
Institute of Quantum Matter, South China Normal University, Guangzhou 510006,
China  Valerio BERTONE  IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-
Yvette, France  Xu CAO  Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  University of Chinese Academy of Sciences,
Beijing 100049, China  Lei CHANG  Nankai University, Tianjin 300071, China
Ningbo CHANG  Xinyang Normal University, Xinyang 464000, China  Gu CHEN
School of Physics and Materials Science, Guangzhou University, Guangzhou
510006, China  Xurong CHEN  Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  University of Chinese Academy of Sciences,
Beijing 100049, China  Zhuojun CHEN  Hunan University, Changsha 410082, China
Zhufang CUI  Nanjing University, Nanjing 210093, China  Lingyun DAI  Hunan
University, Changsha 410082, China  Weitian DENG  Huazhong University of
Science and Technology, Wuhan 430074, China  Minghui DING  European Centre for
Theoretical Studies in Nuclear Physics and Related Areas (ECT*) and Fondazione
Bruno Kessler, Villa Tambosi, Strada delle Tabarelle 286, I-38123 Villazzano
(TN), Italy  Xu FENG  School of Physics, Peking University, Beijing 100871,
China  Chang GONG  School of Physics, Peking University, Beijing 100871, China
Longcheng GUI  Hunan Normal University, Changsha 410081, China  Feng-Kun GUO
University of Chinese Academy of Sciences, Beijing 100049, China  Institute of
Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
Chengdong HAN  Institute of Modern Physics, Chinese Academy of Sciences,
Lanzhou 730000, China  University of Chinese Academy of Sciences, Beijing
100049, China  Jun HE  Nanjing normal university, Nanjing 210023, China  Tie-
Jiun HOU  Department of Physics, College of Sciences, Northeastern University,
Shenyang 110819, China  Hongxia HUANG  Nanjing normal university, Nanjing
210023, China  Yin HUANG  Southwest Jiaotong University, Chengdu 610000, China
Krešimir KUMERIČKI  Department of Physics, Faculty of Science, University of
Zagreb, Bijenička c. 32, 10000 Zagreb, Croatia  L. P. KAPTARI  Institute of
Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China  Bogoliubov
Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna
141980, Russia  Demin LI  School of Physics and Microelectronics, Zhengzhou
University, Zhengzhou 450001, China  Hengne LI  Guangdong Provincial Key
Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal
University, Guangzhou 510006, China  Minxiang LI  Institute of Modern Physics,
Chinese Academy of Sciences, Lanzhou 730000, China  Lanzhou university,
Lanzhou 730000, China  Xueqian LI  Nankai University, Tianjin 300071, China
Yutie LIANG  Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou
730000, China  University of Chinese Academy of Sciences, Beijing 100049,
China  Zuotang LIANG  Key laboratory of particle physics and particle
irradiation (MOE), Shandong University, Qingdao 266237, China  Chen LIU  Key
laboratory of particle physics and particle irradiation (MOE), Shandong
University, Qingdao 266237, China  Chuan LIU  School of Physics, Peking
University, Beijing 100871, China  Guoming LIU  Guangdong Provincial Key
Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal
University, Guangzhou 510006, China  Jie LIU  Institute of Modern Physics,
Chinese Academy of Sciences, Lanzhou 730000, China  University of Chinese
Academy of Sciences, Beijing 100049, China  Liuming LIU  Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  University of
Chinese Academy of Sciences, Beijing 100049, China  Xiang LIU  Lanzhou
university, Lanzhou 730000, China  Tianbo LIU  Key laboratory of particle
physics and particle irradiation (MOE), Shandong University, Qingdao 266237,
China  Xiaofeng LUO  Key Laboratory of Quark and Lepton Physics (MOE) and
Institute of Particle Physics, Central China Normal University, Wuhan 430079,
China  Zhun LYU  School of Physics, Southeast University, Nanjing 211189,
China  Boqiang MA  School of Physics, Peking University, Beijing 100871, China
Fu MA  Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou
730000, China  University of Chinese Academy of Sciences, Beijing 100049,
China  Jianping MA  University of Chinese Academy of Sciences, Beijing 100049,
China  Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing
100190, China  Yugang MA  University of Chinese Academy of Sciences, Beijing
100049, China  Key Laboratory of Nuclear Physics and Ion-beam Application
(MOE), Institute of Modern Physics, Fudan University, Shanghai 200433, China
Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai
201800, China  Lijun MAO  Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  University of Chinese Academy of Sciences,
Beijing 100049, China  Cédric MEZRAG  IRFU, CEA, Université Paris-Saclay,
F-91191 Gif-sur-Yvette, France  Hervé MOUTARDE  IRFU, CEA, Université Paris-
Saclay, F-91191 Gif-sur-Yvette, France  Jialun PING  Nanjing normal
university, Nanjing 210023, China  Sixue QIN  Department of Physics, Chongqing
University, Chongqing 401331, China  Hang REN  Institute of Modern Physics,
Chinese Academy of Sciences, Lanzhou 730000, China  University of Chinese
Academy of Sciences, Beijing 100049, China  Craig D. ROBERTS  Nanjing
University, Nanjing 210093, China  Juan ROJO  Department of Physics and
Astronomy, Vrije Universiteit Amsterdam, De Boelelaan 1081 1081HV Amsterdam,
The Netherlands  Nikhef Theory Group Science Park 105, 1098 XG Amsterdam, The
Netherlands  Guodong SHEN  Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  University of Chinese Academy of Sciences,
Beijing 100049, China  Chao SHI  Department of nuclear science and technology,
Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
Qintao SONG  School of Physics and Microelectronics, Zhengzhou University,
Zhengzhou 450001, China  Hao SUN  Dalian University of Technology, Dalian
116024, China  Paweł SZNAJDER  National Centre for Nuclear Research (NCBJ),
Pasteura 7, 02-093 Warsaw, Poland  Enke WANG  Guangdong Provincial Key
Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal
University, Guangzhou 510006, China  Fan WANG  Nanjing University, Nanjing
210093, China  Qian WANG  Guangdong Provincial Key Laboratory of Nuclear
Science, Institute of Quantum Matter, South China Normal University, Guangzhou
510006, China  Rong WANG  Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  University of Chinese Academy of Sciences,
Beijing 100049, China  Ruiru WANG  Institute of Modern Physics, Chinese
Academy of Sciences, Lanzhou 730000, China  University of Chinese Academy of
Sciences, Beijing 100049, China  Taofeng WANG  School of Physics, Beihang
University, Beijing 100191, China  Wei WANG  Shanghai Jiao Tong University,
Shanghai 200240, China  Xiaoyu WANG  School of Physics and Microelectronics,
Zhengzhou University, Zhengzhou 450001, China  Xiaoyun WANG  Lanzhou
University of Technology, Lanzhou 730050, China  Jiajun WU  University of
Chinese Academy of Sciences, Beijing 100049, China  Xinggang WU  Department of
Physics, Chongqing University, Chongqing 401331, China  Lei XIA  University of
Science and Technology of China, Hefei 100190, China  Bowen XIAO  Key
Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle
Physics, Central China Normal University, Wuhan 430079, China  School of
Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172,
China  Guoqing XIAO  Institute of Modern Physics, Chinese Academy of Sciences,
Lanzhou 730000, China  University of Chinese Academy of Sciences, Beijing
100049, China  Ju-Jun XIE  Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  University of Chinese Academy of Sciences,
Beijing 100049, China  Yaping XIE  Institute of Modern Physics, Chinese
Academy of Sciences, Lanzhou 730000, China  University of Chinese Academy of
Sciences, Beijing 100049, China  Hongxi XING  Guangdong Provincial Key
Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal
University, Guangzhou 510006, China  Hushan XU  Institute of Modern Physics,
Chinese Academy of Sciences, Lanzhou 730000, China  University of Chinese
Academy of Sciences, Beijing 100049, China  Nu XU  Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  University of
Chinese Academy of Sciences, Beijing 100049, China  Key Laboratory of Quark
and Lepton Physics (MOE) and Institute of Particle Physics, Central China
Normal University, Wuhan 430079, China  Shusheng XU  School of Science,
Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Mengshi YAN  School of Physics, Peking University, Beijing 100871, China
Wenbiao YAN  University of Science and Technology of China, Hefei 100190,
China  Wencheng YAN  School of Physics and Microelectronics, Zhengzhou
University, Zhengzhou 450001, China  Xinhu YAN  Huangshan University,
Huangshan 245021, China  Jiancheng YANG  Institute of Modern Physics, Chinese
Academy of Sciences, Lanzhou 730000, China  University of Chinese Academy of
Sciences, Beijing 100049, China  Yi-Bo YANG  University of Chinese Academy of
Sciences, Beijing 100049, China  Institute of Theoretical Physics, Chinese
Academy of Sciences, Beijing 100190, China  Zhi YANG  School of Physics,
University of Electronic Science and Technology of China, Chengdu 610054,
China  Deliang YAO  Hunan University, Changsha 410082, China  Peilin YIN
School of Science, Nanjing University of Posts and Telecommunications, Nanjing
210023, China  C.-P. YUAN  Department of Physics and Astronomy, Michigan State
University, East Lansing, MI 48824, USA  Wenlong ZHAN  Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  University of
Chinese Academy of Sciences, Beijing 100049, China  Jianhui ZHANG  Center of
Advanced Quantum Studies, Department of Physics,Beijing Normal University,
Beijing 100875, China  Jinlong ZHANG  Key laboratory of particle physics and
particle irradiation (MOE), Shandong University, Qingdao 266237, China
Pengming ZHANG  School of Physics and Astronomy, Sun Yat-sen University,
Zhuhai 519082, China  Chao-Hsi CHANG  University of Chinese Academy of
Sciences, Beijing 100049, China  Institute of Theoretical Physics, Chinese
Academy of Sciences, Beijing 100190, China  Zhenyu ZHANG  School of Physics
and Technology, Wuhan University, Wuhan 430072, China  Hongwei ZHAO  Institute
of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
University of Chinese Academy of Sciences, Beijing 100049, China  Kuang-Ta
CHAO  School of Physics, Peking University, Beijing 100871, China  Qiang ZHAO
University of Chinese Academy of Sciences, Beijing 100049, China  Institute of
High Energy Physics and Theoretical Physics Center for Science Facilities,
Chinese Academy of Sciences, Beijing 100049, China  Yuxiang ZHAO  Institute of
Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China  University
of Chinese Academy of Sciences, Beijing 100049, China  Zhengguo ZHAO
University of Science and Technology of China, Hefei 100190, China  Liang
ZHENG  School of Mathematics and Physics, China University of Geosciences
(Wuhan), Wuhan 430074, China  Jian ZHOU  Key laboratory of particle physics
and particle irradiation (MOE), Shandong University, Qingdao 266237, China
Xiang ZHOU  School of Physics and Technology, Wuhan University, Wuhan 430072,
China  Xiaorong ZHOU  University of Science and Technology of China, Hefei
100190, China  Bingsong ZOU  University of Chinese Academy of Sciences,
Beijing 100049, China  Institute of Theoretical Physics, Chinese Academy of
Sciences, Beijing 100190, China  Liping ZOU  Institute of Modern Physics,
Chinese Academy of Sciences, Lanzhou 730000, China  University of Chinese
Academy of Sciences, Beijing 100049, China

Abstract

Lepton scattering is an established ideal tool for studying inner structure of
small particles such as nucleons as well as nuclei. As a future high energy
nuclear physics project, an Electron-ion collider in China (EicC) has been
proposed. It will be constructed based on an upgraded heavy-ion accelerator,
High Intensity heavy-ion Accelerator Facility (HIAF) which is currently under
construction, together with a new electron ring. The proposed collider will
provide highly polarized electrons (with a polarization of $\sim$80%) and
protons (with a polarization of $\sim$70%) with variable center of mass
energies from 15 to 20 GeV and the luminosity of (2-3) $\times$ 1033 cm-2 s-1.
Polarized deuterons and Helium-3, as well as unpolarized ion beams from Carbon
to Uranium, will be also available at the EicC.

The main foci of the EicC will be precision measurements of the structure of
the nucleon in the sea quark region, including 3D tomography of nucleon; the
partonic structure of nuclei and the parton interaction with the nuclear
environment; the exotic states, especially those with heavy flavor quark
contents. In addition, issues fundamental to understanding the origin of mass
could be addressed by measurements of heavy quarkonia near-threshold
production at the EicC. In order to achieve the above-mentioned physics goals,
a hermetical detector system will be constructed with cutting-edge
technologies.

This document is the result of collective contributions and valuable inputs
from experts across the globe. The EicC physics program complements the
ongoing scientific programs at the Jefferson Laboratory and the future EIC
project in the United States. The success of this project will also advance
both nuclear and particle physics as well as accelerator and detector
technology in China.

###### Contents

  1. 1 Executive summary
    1. 1.1 Physics highlights
      1. 1.1.1 Partonic structure and three-dimensional landscape of nucleon
      2. 1.1.2 Partonic structure of nuclei
      3. 1.1.3 Exotic hadronic states
    2. 1.2 Polarized electron ion collider in China (EicC)
    3. 1.3 Complementarity of EicC and EIC-US
  2. 2 EicC physics highlights
    1. 2.1 One-dimensional spin structure of nucleons
    2. 2.2 Three-dimensional tomography of nucleons
      1. 2.2.1 Transverse momentum dependent parton distributions
      2. 2.2.2 Generalized parton distributions
    3. 2.3 Partonic structure of nucleus
      1. 2.3.1 The nuclear quark and gluon distributions
      2. 2.3.2 Hadronization and parton energy loss in nuclear medium
    4. 2.4 Exotic hadronic states
      1. 2.4.1 Status of hidden-charm and hidden-bottom hadron spectrum
      2. 2.4.2 Exotic hadrons at EicC
      3. 2.4.3 Cross section estimates and simulations
    5. 2.5 Other important exploratory studies
      1. 2.5.1 Proton mass
      2. 2.5.2 Structure of light pseudoscalar mesons
      3. 2.5.3 Intrinsic charm
    6. 2.6 QCD theory and phenomenology
      1. 2.6.1 Synergies
      2. 2.6.2 Lattice QCD
      3. 2.6.3 Continuum theory and phenomenology
  3. 3 Accelerator conceptual design
    1. 3.1 Overall design and key parameters
    2. 3.2 Accelerator facilities
      1. 3.2.1 Ion accelerator complex
      2. 3.2.2 Electron accelerator complex
    3. 3.3 Beam cooling
    4. 3.4 Beam polarization
      1. 3.4.1 Ion polarization
      2. 3.4.2 Electron polarization
    5. 3.5 Design of the interaction regions (IR)
    6. 3.6 Pre-research on key technologies
  4. 4 Detector conceptual design
    1. 4.1 Detector performance requirements
      1. 4.1.1 Distributions of the final state particles
      2. 4.1.2 Luminosity and polarization measurements
    2. 4.2 Detector conceptual design

##  Chapter 1 Executive summary

###  1.1 Physics highlights

The study on the inner structure of matter and fundamental laws of
interactions has always been one of the research forefronts of natural
science. It not only allows mankind to understand the underlying laws of
nature, but also promotes various advances in technologies. Considering the
mass-energy budget of the Universe, illustrated in Fig. 1.1: dark energy
constitutes 71%; dark matter is another 24%; and the remaining 5% is visible
material. Little is known about the first two: science can currently say
almost nothing about 95% of the mass-energy in the Universe. On the other
hand, the remaining 5% has forever been the source of everything tangible,
which can be beautifully described within the Standard Model.

Figure 1.1:  The mass-energy budget of the Universe determined by Wilkinson
Microwave Anisotropy Probe (WMAP) [1].

One of the greatest achievements of physics in the 20th century is the
invention of the Standard Model [2, 3, 4, 5, 6, 7]. It is the theory
describing the strong, electromagnetic, and weak interactions among elementary
particles that make up the visible Universe. As shown in Fig. 1.2, now we know
that there are three generations of quarks and leptons in nature. The forces
in the Standard Model are carried by the so-called force mediating gauge
bosons, which are $\gamma$, $W^{\pm}$ and $Z^{0}$ for electro-weak
interaction, and gluons $g$ for the strong interaction. The Higgs boson H was
introduced in the famous Higgs mechanism [8, 9] to explain the mass origin of
the $W^{\pm}$ and $Z^{0}$ bosons, and it also generates the masses of quarks
and leptons. Yet, amongst the visible matter, less-than 0.1% is tied directly
to the Higgs boson; hence, even concerning visible matter, too much remains
unknown.

In particular, it is still challenging to quantitatively explain the origins
of nucleon _mass and spin_ , which are two fundamental properties of building
blocks of the visible matter. First, about 99% of the visible mass is
contained within nuclei [10]. Within Standard Model, the protons and neutrons
in nuclei are composite particles, built from nearly massless quarks ($\sim
1\%$ of the nucleon mass) and massless gluons. An immediate question then
arises: How does $99$% of the nucleon mass emerge? Besides the mass issue,
despite of many years of theoretical and experimental efforts, the
quantitative decomposition of nucleon spin in terms of quark and gluon degrees
of freedom is not yet fully understood. To address these fundamental issues,
we have to understand the nature of the subatomic force between quarks and
gluons, and the internal landscape of nucleons.

The underlying theory, which describes the strong interactions between quarks
and gluons, is known as Quantum Chromodynamics (QCD) [11]. As a non-Abelian
gauge theory, QCD has the extraordinary properties of asymptotic freedom at
short distance [12, 13] and color confinement at long distance. The strong
force mediated by gluons is weak in hard scatterings with large momentum
transfers. On the other hand, it has to be incredibly strong to bind quarks
together within the tiny space of a nucleon. Confinement is crucial because it
ensures stability of the proton. Without confinement, protons in isolation
could decay; the hydrogen atom would be unstable; nucleosynthesis would be
accidental, with no lasting consequences; and without nuclei, there would be
no living Universe. All in all, the existence of our visible Universe depends
on confinement.

In QCD, the proton mass is usually decomposed into several elements in terms
of quark and gluon degrees of freedom. Specifically, it is believed that the
nucleon mass can be almost entirely derived from the kinetic energy of quarks
and gluons, interactions between them, as well as other novel dynamical
effects of QCD. Similarly, despite being composite particles, nucleons have a
constant spin of $1/2$ which is an intrinsic property like electric charge. It
is extremely fascinating to note that proton spin can manifest itself from the
many-body system of quarks and gluons. In addition to the spin contributions
of quark and gluon, which has been measured in certain kinematic regions, the
orbital angular momentum contributions due the orbital motions of quark and
gluon have been shown to be indispensable for the proton spin.

Hence, QCD should be the physical mechanism responsible for the majority of
visible matter in the Universe. To gain a more comprehensive understanding of
the internal partonic structure of a nucleon, explore the nature of color
confinement and ultimately explain the emergence of the nucleon mass and spin,
we certainly need to expand the scope of our current experiments and enrich
our knowledge on the dynamics of the strong interaction, especially the non-
perturbative aspects of QCD.

In the following, a few highlighted physics topics, highly relevant to above
mentioned essential QCD physics, that EicC can significantly contribute to
will be discussed briefly. For the detailed discussions regarding physics,
accelerators, and detectors for the EicC project, please refer to the
following chapters of this document 111By default, the natural unit system is
used in all the physics discussions and plots..

Figure 1.2: The Standard Model of elementary particles.

####  1.1.1 Partonic structure and three-dimensional landscape of nucleon

In the naiive constituent quark model [14, 15], nucleons are considered as the
bound states of $u$\- and $d$\- quarks. The proton (neutron) corresponds to a
$uud$-state ($udd$ state). These quarks are known as valence quarks. However,
due to the quantum property of QCD, quarks can radiate gluons, and these
gluons, in turn, can fluctuate into quark-antiquark pairs. Therefore, a
nucleon is a composite object containing quarks, antiquarks, and gluons.
Besides valence quarks (and possible intrinsic quarks), there are also sea
quarks coming out of quantum fluctuations. Especially, when the probing scale
becomes smaller as the energy scale goes higher, one sees more sea quarks
comparing to valence quarks, as illustrated in Fig. 1.3. Moreover, compared to
the simple picture of the constituent quark model, the underlying dynamics
among quarks/gluons is a lot more interesting and intricate, and offers much
more important information regarding the internal structure of nucleons as a
composite many-body system.

In high-energy scatterings, the proton can be viewed as a cluster of high
energy quarks and gluons, which are collectively referred to as partons. The
probability distributions of partons within the proton are called the parton
distribution functions (PDFs). In general, PDFs give the probabilities of
finding partons (quarks and gluons) in a hadron as a function of the momentum
fraction $x$ w.r.t. the parent hadron carried by the partons. Due to the QCD
evolution, quarks and gluons can mix with each other, and their PDFs depend on
the resolution scale. When the resolution scale increases, the numbers of
partons and their momentum distributions will change according to the
evolution equations. These evolution equations can be derived from the
perturbation QCD, although PDFs themselves are essentially non-perturbative
objects. Thanks to QCD factorization theorems, PDFs can be extracted from
measurments of cross-sections and spin-dependent asymmetries.

Figure 1.3: Illustration of the quark and the partonic structure of the
proton.

The partonic structure of the nucleon was firstly studied in experiments of
electron-nucleon Deeply Inelastic Scattering(DIS). Since electrons are point-
like particles and they do not participate in the strong interaction, they are
the perfect probe for studying the internal structure of hadrons in high
energy scatterings. Therefore, the DIS experiment is also known as the “Modern
Rutherford Scattering Experiment”, which opens up a new window to probe the
subatomic world. In 1969, the pioneer DIS experiments at SLAC discovered the
so-called Bjorken scaling [16], which showed that the proton is composed of
point-like partons with spin $1/2$ (which are known as quarks afterward).
Starting from DIS with unpolarized fixed targets, DIS experiments are later
extended to unpolarized collider experiments and fixed-target experiments with
polarized beam and targets. These DIS experiments have revolutionized our
understanding of the subatomic structure of nucleons and nuclei. Later on,
high energy DIS experiments observed the violation of Bjorken scaling [17],
which indicates the existence of gluon and QCD evolution mentioned above. All
these results across a wide range of energy scales have verified that QCD is
the correct theory for the strong interaction between quarks and gluons within
hadrons. In addition, within the current experimental accuracy, lepton and
quark are still point-like particles at the scale of $10^{-3}$ fm, which is
one-thousandth of the size of the proton.

With better experimental precisions, our understanding of nucleon structure
continues to improve even in unpolarized PDFs. Furthermore, many interesting
phenomena, such as the isospin asymmetry of $\bar{u}$ and $\bar{d}$ quark
distributions and the asymmetry between strange and anti-strange quark
distributions in the proton, were discovered. These phenomena are still
compelling issues in medium and high energy physics research.

In the wake of the development of polarized source in the 1970s, the study of
the nucleon spin structure became possible by exploring the helicity
distributions of quarks and gluons, also defined as the longitudinally
polarized PDFs analog to their unpolarized counterparts discussed above, from
high-energy scattering processes involving polarized leptons and/or polarized
nucleons. A lot more interesting phenomena have been unraveled by polarized
DIS experiments. One of them is the so-called “proton spin crisis”.
Experimental data showed that the sum of the spin from quarks and anti-quarks
is only a small fraction of the total spin of a proton. It triggered a series
of experimental and theoretical investigations on the origin of the proton
spin. From the QCD perspective, we now know that the proton spin is built up
from the spin and orbital angular momenta of quarks and gluons. Currently,
except the quark spin contribution, other decomposed contributions in the spin
sum rule, especially the ones from orbital angular momenta, are largely
unexplored. Through semi-inclusive DIS and other interesting processes, recent
experimental and theoretical developments have enabled us to extend our
research on nucleon structure from one-dimensional PDFs to three-dimensional
imaging. These have been providing us new insights into the proton spin
puzzle.

Currently, there are two immediate and important issues in the research
frontier of nucleon structure: 1) The precision measurement of the one-
dimensional spin structure of the polarized nucleon; 2) The study on the
three-dimensional imaging of the partonic structure of the nucleon.

An interesting question when studying the one-dimensional spin structure of
the nucleons is how to clearly decompose the individual contributions from
different quark flavors. Despite the large uncertainty, the recent measurement
at Relativistic Heavy Ion Collider (RHIC) implies that the sea quark helicity
distributions also have flavor asymmetries. Furthermore, the polarized quark
distribution of different flavors, especially for sea quarks, still have large
uncertainties. This directly imposes a challenge to our efforts to understand
the proton spin structure. Therefore, the precise determination of various
quark helicity distributions is a fundamental issue which is needed to be
addressed.

In the meantime, three-dimensional imaging of the parton structure has
attracted a lot of attention as well. By additionally measuring the transverse
momentum and angular distribution of the final hadron in DIS, one can extract
important information about initial transverse momentum distributions of
partons in the incoming nucleon, thus explore the internal three-dimensional
structure of the nucleon in the momentum space. Meanwhile, through some
exclusive processes, in which all the particles are measured, one can access
the three-dimensional spatial distributions of partons. In general, the
internal three-dimensional structure of the nucleon in the momentum and
coordinate space can be characterized by the Transverse-Momentum-Dependent
parton distribution functions (TMDs) and Generalized Parton Distributions
(GPDs), respectively. Compared to one-dimensional PDFs, these more
sophisticated parton distribution functions encode much more abundant
information about the internal structure of the nucleon. For example, they can
allow us to access the orbital angular momenta of partons and the quantum
effect of multi-parton correlations. Future experimental efforts, especially
the high precision measurements, can certainly have a profound impact on the
theoretical development of TMD and GPD physics.

EicC, together with existing experiments at Jefferson Lab, CERN COMPASS, BNL
RHIC, Fermi-Lab, and the proposed EIC in the US, can offer significant
insights into the three-dimensional landscape of internal structure of the
proton and other hadrons, and provide us important clues on how the mass and
spin as well as other interesting properties of proton emerge from the quark
and gluon degrees of freedom.

####  1.1.2 Partonic structure of nuclei

One of the biggest challenges in nuclear physics is how to study the nuclear
structure in the partonic level using the QCD theory that has successfully
described the partonic structure of a free nucleon. While the focus of
studying partonic structure in free nucleons has been extended from the
precisely known one-dimensional PDFs to the three-dimensional distributions
such as TMD and GPD, the knowledge of the partonic structure in nuclei,
however, remain largely unknown.

The most outstanding reason for this gap is that the nucleons with their sizes
much smaller than the size of a nucleus are interacting weakly with each other
through the long-range interactions. Conventional models, such as the mean-
field theory, can describe the nuclear structure in the nucleonic degree of
freedom without introducing the partonic pictures. On the other hand, the
partonic structure of a bounded nucleon in a heavy nucleus had been naively
treated as the same as one in a free nucleon, until the discovery of the EMC
effect. In the 1980s, the European Muon Collaboration (EMC) at CERN used heavy
nuclei as a high-density target to measure the PDFs. They discovered the
measured cross-sections differed from ones using free nucleons, and meanwhile,
observed these differences strongly depend on the nuclear numbers [18]. This
lately-called EMC effect has been further studied at SLAC, HERMES, Fermi-Lab
and lately JLab [19, 20, 21, 22] in the valance quark region ($0.3<x<0.7$) and
the correlation with nuclear numbers were obtained. These experimental results
also reveal much richer details at lower $x$ where anti-shadowing and
shadowing effects are present. However, the physics origin of how the nuclear
PDFs (nPDF) are modified in nuclei is still puzzling us and no single
theoretical interpretation is satisfactory. A full understanding of the
physics behind the EMC, anti-shadowing, and shadowing effects will open a door
to describe the nuclear structure in QCD. An encouraging development in the
last few years was the suggestion of possible connection between the EMC
effect and the short-range correlations (SRC) which describe a case when
nucleons are largely overlapping and strongly interacting with each other[23,
24, 25]. This new finding sheds a light to cover the gap between studying
nuclear structure in the nucleonic level and the partonic level.

The EMC effect implies that the distributions of valence quarks in the nucleus
are modified. However, no existing experimental evidence suggests that the
distributions of sea quarks and gluons in bounded nucleons are also modified
in the nuclear medium. Joint research of theory and experiment is eagerly
needed to obtain the precise global description of nPDFs of different quark
and gluon flavors in the entire $x$ region for a wide range of nuclei, and
finally unveil the physics origin of the EMC, anti-shadowing and shading
effects. A power tool in the last many decades is to utilize the high-energy
electrons in colliding with light to heavy nuclei and measure the inclusive
DIS cross-sections by only detecting outgoing electrons. On top of that, one
can also detect the additional outgoing hadrons which contain the information
of the initial quark or gluon, and study their semi-inclusive DIS (SIDIS)
cross-sections or other observable to decouple the nPDFs of different partonic
flavors.

Another hot topic in high-energy eA physics is to understand the quark
confinement. Quarks cannot exist alone but have to be combined with other
quarks to form color-neutral hadrons such as mesons and nucleons. When a quark
is struck by a high-energy particle, it will continuously interact with its
surroundings via strong interaction, generate additional quarks and gluons,
and eventually ”fragment” into color-neutral hadrons or jets inside the
nucleus or in the vacuum. This process is called hadronization. Studying the
hadronization process has important implications for the formation of matter
and even the evolution of the Universe. One can perform a detailed study of
the hadronization physics by measuring the SIDIS processes in eA collision.
With a wide variety of nuclei that serve as QCD laboratories, one can control
the sizes of different nuclei so that the hadronization happens at varying
depth inside the nuclei or the vacuum.

####  1.1.3 Exotic hadronic states

Quark model was invented before QCD to classify various hadrons composed of
light (up, down and strange) quarks [14, 15]. After incorporating the QCD
dynamics, it was able to provide an excellent description of the mass spectrum
of hadrons up to a few exceptions (see, e.g., Refs. [26, 27]). In the
traditional quark model, a meson is formed by a quark and an antiquark, and a
baryon is formed by three quarks. Most of the hadrons discovered in the last
century can be classified into flavor multiplets in the quark model. But
quarks and gluons can constitute other types of hadronic objects: the so-
called compact tetraquark and pentaquark states contain more than three
(anti-)quarks as a single colorless cluster; hadronic molecules are bound
states of hadrons formed by the mediation of the strong force, just like that
the deuteron is a proton-neutron bound state; there can be colorless states
with both quark and gluonic excitations, i.e., the hybrid states; glueballs
composed of gluons. These different types of hadrons are shown in Fig. 1.4.
Such hadrons beyond the traditional quark model are collectively called exotic
hadron states. Although such a classification is a quark model notation, the
hadron spectrum as observed presents a grand challenge to understand from QCD,
and the experimental search of exotic hadrons is one of the most important
handles towards understanding how the massive hadrons emerge from the
underlying nonperturbative strong interactions among quarks and gluons.

Figure 1.4: Illustration of conventional and exotic hadrons.

Since the beginning of the 21st century, experimental study on hadron states
has made significant progresses. Experiments such as BESIII (Beijing
Spectrometer III) at Beijing Electron-Positron Collider (BEPC) in China, Belle
at KEK in Japan, BABAR at the SLAC National Accelerator Laboratory in US, LHCb
at the Large Hadron Collider (LHC) in Europe and many others have reported
fascinating discoveries of candidates of exotic hadron states. These
discoveries have opened up a new exciting window in the nonperturbative regime
of QCD at the low-energy frontier of the Standard Model. However, until now
there is no unified picture for understanding the new experimental
discoveries, and the internal structure of these states is still a mystery to
be resolved.

EicC can contribute significantly in studying exotic hadron states, especially
the charmonium-like states and hidden-charm pentaquarks, which can be produced
abundantly. EicC has a unique place for studying their photoproduction, beyond
the JLab 12 GeV programme. In particular, given the existing measurements, the
interpretation of some of the prominent candidates of hidden-charm tetraquarks
and pentaquarks (either compact or of hadronic molecular type) is not
unambiguous due to the the so-called triangle singularity contribution. Such
singularities are due to the simultaneous on-shellness and collinearality of
all intermediate particles in a triangle diagram and are able to produce
resonance-like signals when the special kinematics required by the Coleman-
Norton theorem [28] is fulfilled [29]. However, for the photoproduction
processes at EicC, the production mechanism is free of such kinematics
singularities. Therefore, one can investigate the properties of pentaquark
states and other hidden-charm hadrons in a more clear way. The energy coverage
of EicC also allows for the seek of hidden-bottom exotic hadrons. A clearer
picture of the hadron spectrum is foreseen with the inputs from EicC.

###  1.2 Polarized electron ion collider in China (EicC)

The polarized electron ion collider in China (EicC) aims at achieving the
highlighted physics goals presented above. It will be based on the existing
High Intensity heavy-ion Accelerator Facility (HIAF). HIAF is the major
national facility focusing on nuclear physics, atomic physics, heavy ion
applications and interdisciplinary researches in China. It is designed to
provide intense beams of primary and radioactive ions for a wide range of
research fields. HIAF will be a scientific user facility open to researchers
from all over the world that enables scientists with concerted effort to
explore the hitherto unknown territories in the nuclear chart, to approach the
experimental limits, to open new domains of physics researches in experiments,
and to develop new ideas and heavy-ion applications beneficial to the society.
HIAF is located in Huizhou City of Guangdong Province in south China. It is
funded jointly by the National Development and Reform Commission of China,
Guangdong Province, and Huizhou City. The total investment is about 2.5
billion in Chinese Yuan, including about 1.5 billion Yuan from the central
government for facility construction and 1.0 billion Yuan from the local
governments for infrastructure. The construction is scheduled for seven years,
and the beam commissioning is planned for 2025. HIAF is a completely new
facility that a series of upgrades for EicC in the future have been taken into
consideration during the design stage, and its capability to run with EicC
concurrently is also reserved.

EicC will adopt the scheme of circular colliders which includes a figure-8
shaped ion collider ring (pRing), an electron injector as well as a racetrack
electron collider ring (eRing), as shown in Fig.1.5. The center of mass energy
of the EicC will range from 15 GeV to 20 GeV, with the luminosity higher than
$2.0\times 10^{33}$ $\mathrm{cm^{-2}s^{-1}}$, and the average proton
polarization about $70\%$, the average electron polarization about $80\%$ in
the collisions of electrons with protons. The integrated luminosity is higher
than $50$ $\mathrm{{fb}^{-1}}$ when the operating time accounts for $80\%$ of
the entire year. All these parameters can satisfy the physics goals required.
Available particles, including heavy ions, and their corresponding energy,
polarization, luminosity, and integrated luminosity are listed in Tab.1.1.

Figure 1.5: Accelerators in the EicC accelerator facility. Table 1.1:
Available particles and their corresponding energy, polarization, luminosity
and integrated luminosity.

Particle |  Momentum (GeV/c/u) |  CM energy (GeV/u) |  Average Polarization |  Luminosity at the nucleon level ($\rm{cm^{-2}s^{-1}}$) |  Integrated luminosity ($\mathrm{{fb}^{-1}}$)
---|---|---|---|---|---
$\rm{e}$ |  3.5 |  |  80% |  |
$\rm{p}$ |  20 |  16.76 |  70% |  $\rm{2.00\times 10^{33}}$ |  50.5
$\rm{d}$ |  12.90 |  13.48 |  Yes |  $\rm{8.48\times 10^{32}}$ |  21.4
$\rm{{}^{3}He^{++}}$ |  17.21 |  15.55 |  Yes |  $\rm{6.29\times 10^{32}}$ |  15.9
$\rm{{}^{7}Li^{3+}}$ |  11.05 |  12.48 |  No |  $\rm{9.75\times 10^{32}}$ |  24.6
$\rm{{}^{12}C^{6+}}$ |  12.90 |  13.48 |  No |  $\rm{8.35\times 10^{32}}$ |  21.1
$\rm{{}^{40}Ca^{20+}}$ |  12.90 |  13.48 |  No |  $\rm{8.35\times 10^{32}}$ |  21.1
$\rm{{}^{197}Au^{79+}}$ |  10.35 |  12.09 |  No |  $\rm{9.37\times 10^{32}}$ |  23.6
$\rm{{}^{208}Pb^{82+}}$ |  10.17 |  11.98 |  No |  $\rm{9.22\times 10^{32}}$ |  23.3
$\rm{{}^{238}U^{92+}}$ |  9.98 |  11.87 |  No |  $\rm{8.92\times 10^{32}}$ |  22.5

In general, the ion accelerator complex of the EicC accelerator facility
mainly consists of a polarized ion source, iLinac, BRing, and pRing, while the
electron accelerator complex is composed of an electron injector and eRing.
Two interaction regions will be available. Several key accelerator designs are
listed below.

  * •

Generate low emittance ion beams. Reducing the beam emittance to the one
required by the design specifications is of crucial importance for achieving
the targeted luminosity in the EicC accelerator facility. To this end, the
scheme of staged electron cooling will be adopted. In the first stage, the
cooling of the proton beams with low energy will be performed by a DC electron
cooler in the BRing. In the second stage, the proton beam with the energy will
be cooled by the high energy bunched beam electron cooler based on an energy
recovery linac (ERL). This scheme ensures optimum efficiency for the cooling
system in the ion accelerator complex of the EicC accelerator facility.

  * •

Maintain and control beam polarization. The physics goals of the EicC project
put high requirements on the average polarization and the polarization
direction of the beams. Relevant beam polarization control schemes should be
made for both the ion accelerator complex and the electron accelerator
complex. Specifically, the Siberian snake, which is a control system of spin
tune, will be installed to keep high polarization in the acceleration process
in the BRing, where depolarization resonances exist. For the acceleration in
the pRing, only weak solenoid magnetic fields are required to keep high
polarization of the ion beams, thanks to the figure-8 shaped design of the
pRing. The polarization direction control system will be set up along the
beamlines and at both sides of the interaction regions. Such a design makes it
possible to perform the rotation of beam polarization directions arbitrarily,
as well as control the polarization directions of two beams accordingly.

  * •

Optimize interaction regions (IR). A full-acceptance detector will be built to
detect and identify almost $100\%$ of reaction products at one of two IPs
while the second IP will be reserved for upgrading. The specifications of the
detector put forwards many constraints on the design and optimization of the
interaction region (IR) . The IR will be designed to be asymmetrical since
there are lots of differences between electron beams and ion beams. Such a
design will not only reduce the background of the detector but also ensure the
features of the full acceptance of the detector. Furthermore, the beamlines
related to the forward reaction products will be placed downstream of the
interaction point (IP) in the pRing and eRing.

For the design specifications listed above, a pre-research will be carried
out, including the polarized ion source, the photocathode polarized electron
gun, the high energy bunched beam electron cooler based on the energy recovery
linac (ERL), the Siberian snake, the spin rotator as well as the preservation
of the polarization in the figure-8 shaped synchrotron. All of them will
certainly provide the technical underpinnings for the construction of the EicC
accelerator facility in the future.

###  1.3 Complementarity of EicC and EIC-US

Both electron-ion colliders aim at the precision exploration of the partonic
structure of nucleon/nucleus, but focus on different kinematics and
perspectives. The design parameters and the luminosity versus center-of-mass
energy of two colliders are shown in Table 1.2 and Figure 1.6, respectively.
As shown in Figure 1.7, the $x$-$Q^{2}$ coverage puts EicC at a sweet spot to
systematically study the behavior of sea quarks. EIC-US [30] is a higher
energy machine with an emphasis on low and moderate-$x$ region. Combining the
measurements at both colliders will provide systematically controlled physics
interpretation. Here are some examples.

  * •

Nucleon Spin. With wide kinematic coverage and hermetic detector designs, EICs
will provide a final answer to this decades-old question. One of the major
goals of the EIC-US focuses on the gluon helicity contribution at small-$x$.
EicC is optimized to systematically explore the nucleon spin including sea
quark helicity contribution and orbital angular momentum contributions from
quarks and gluons in the moderate $x$ regime. The unique $Q^{2}$ range will
position EicC at a crucial place between JLab and EIC-US to unambiguously
interpret and determine the orbital angular momentum contributions, hence
providing a comprehensive 3-D imaging for the sea quarks inside a nucleon .

  * •

Proton Mass Decomposition. Electroproduction and photoproduction of heavy
quarkonia near threshold have been proposed to study the proton mass
decomposition. EicC can contribute these important physics uniquely, through
systematically investigating the $\Upsilon$ production with high luminosity
near its threshold, where the optimal energy range of EicC is. Because of the
3 times larger mass of $\Upsilon$, the physics behind the measurement becomes
much cleaner as compared to that of $J/\psi$ production at JLab 12GeV. Because
of different kinematic coverage, EicC and EIC-US will be complementary to each
other for $\Upsilon$ near-threshold production.

  * •

Exotic Hadron States. Both EicC and EIC-US can contribute to understanding the
challenge posed by the unexpected $XYZ$ structures in the heavy-quarkonium
mass region. The hidden-charm pentaquarks observed at LHCb need independent
confirmation, and their hidden-bottom analogues are hard to be found at LHC
but can be sought at EicC and EIC-US. The events of these states at EIC-US are
expected to be more than those at EicC due to the larger energy and higher
luminosity. For exclusive productions of exotic hadrons, the final state
particles at EicC are within the middle rapidity range, facilitating the
detection with relatively low background.

  * •

Partonic Structure in Nuclear Environment. Nuclear modification of the
structure functions and hadron production in deep inelastic scattering $eA$
collisions are major focuses at both EIC-US and EicC. The kinematics at EicC
provide a unique perspective to investigate the details of fast parton/hadron
interactions with cold nuclear matter and shed light on energy loss and
hadronization mechanisms. New information on the parton distribution in nuclei
can be achieved at EicC at moderate $x$, whereas EIC-US concentrates in the
small-$x$ region.

Figure 1.6:  Luminosity and center-of-mass energy of the proposed electron ion colliders[30, 31, 32, 33, 34]. For the EicC, the three data points are corresponding to electron-proton collisions with energy 3.5 GeV (electron) $+$ 16 GeV (proton), 3.5 GeV $+$ 20 GeV, 5 GeV $+$ 26 GeV, respectively.  Figure 1.7:  Kinematic coverage of deep inelastic scattering process for different beam energy configurations at two proposed electron ion colliders as well as JLab. Note that there are other energy configurations for both electron ion colliders, as shown in Fig.1.6.  Table 1.2: The comparison between the parameters of the electron-ion colliders proposed in China and in the US[30]. Facility | CoM energy |  lum./1033cm-2s-1 | Ions | Polarization
---|---|---|---|---
EicC | 15 - 20 | 2 - 3 |  $p\rightarrow$U |  $e^{-}$, $p$, and light nuclei
EIC-US | 30 - 140 | 2 - 15 |  $p\rightarrow$U |  $e^{-}$, $p$, 3He, Li

##  Chapter 2 EicC physics highlights

###  2.1 One-dimensional spin structure of nucleons

EicC will enable us to study the one-dimensional structure of the nucleons in
various aspects, and to a great extent help search answers to many fundamental
questions concerning the structure of nucleons with unprecedented precision.
In particular, through a large amount of data, EicC can provide us the direct
and precise information regarding the distributions of valence quarks, sea
quarks, and gluons inside nucleons in the moderate and large $x$ regime.
Furthermore, it can reveal the internal landscape of nucleons and deepen our
understanding of their structure, and give us excellent opportunities for
important discoveries in high energy nuclear physics. In addition to the
physics significance by themselves, accurate parton distribution functions are
extremely important for the precision study of particle physics and the
exploration of new physics at the Large Hadron Collider.

How to understand the spin of protons in terms of the quark and gluon degrees
of freedom has been an important cutting-edge research problem in high energy
nuclear physics. In the 1980s, the EMC collaboration[35] used a muon beam as a
probe, and found that the sum of the spin contributions of all quarks inside
the proton is very small comparing to the spin of the proton:
$\Delta\Sigma=\Delta u+\Delta d+\Delta s=12\pm 9(stat)\pm 14(syst)\%$. This
measurement has then precipitated the so-called “proton spin crisis” in
nuclear physics research. The current understanding of the structure of the
proton spin is that the spin of proton consists of the spin contributions from
quarks and gluons, and the orbital angular momenta of quarks and gluons. In
addition to the spins of the valence quarks, many experimental results show
that the sea quarks inside the proton also have non-zero spin contributions.
Nowadays, the pressing issue is that the current measurement of the sea quark
spin distribution is not particularly accurate. Through the double polarized
collision processes, the spin distribution of different flavors of sea quarks
can be precisely measured at the EicC, and elaborate experimental analysis on
the spin distribution of sea quarks can be carried out, which will help to
further study the spin structure of nucleons and enrich our understanding of
non-perturbative properties of quantum chromodynamics.

With its designed high luminosity, EicC can generate an enormous amount of
experimental data, which helps to clarify some intriguing problems and
phenomena observed in experiments in the past few years. The first phenomenon
is the asymmetry in the distribution of light sea quarks. In high-precision
unpolarized scattering experiments, we have observed that the unpolarized
$\bar{u}$ and $\bar{d}$ are asymmetrically distributed inside the proton, and
the measured asymmetry is larger than what people have expected [36, 37, 38,
39, 40]. The theories and models which explain this asymmetry also predict the
asymmetry for polarized light sea quarks [41, 42, 43]. Moreover, the
measurement of the longitudinal spin asymmetries for weak boson production in
proton–proton collisions at RHIC [44] suggests a difference between the
$\Delta\bar{u}$ and $\Delta\bar{d}$ helicity distributions as well. Another
interesting issue is the polarized distribution of the strange ($s$) quark and
its contribution to the proton spin. Assuming the $SU(3)$ flavor symmetry, one
finds that the analysis of DIS data [45, 46] indicates that the strange quark
contribution to the proton spin is roughly $-0.1$. It is well-known that the
strange quark contribution can be directly probed by semi-inclusive DIS
(SIDIS). However, in SIDIS experiments, it is difficult to distinguish the
current fragmentation process from the target fragmentation process. Also, the
fragmentation function which describes the strange quark to a hadron
transition process is not sufficiently precise. Due to the above-mentioned
difficulties, it is still challenging to draw any firm conclusions on the
polarization of strange quarks[47, 48]. In addition, whether the distribution
function of the polarized $s$ quark as a function of $x$ changes its sign or
not is also an interesting research question[49].

Figure 2.1:  Diagram of the Deep Inelastic Scattering (DIS) process. In this
process, if the four-momentum of the incoming and outgoing electron are $k$
and $k^{\prime}$, the four-momentum of a nucleon is $p$, the relevant
kinematic variables can be defined as: the squared e+p collision center-of-
mass energy $s=(p+k)^{2}$, the squared momentum transfer of the electron
$Q^{2}=-q^{2}=-(k-k^{\prime})^{2}$, the Bjorken variable
$x=\frac{Q^{2}}{2p\cdot q}$, the inelasticity $y=\frac{q\cdot p}{k\cdot p}$.
In addition to these Lorentz invariants, there are two other important
kinematic variables: the invariant mass of the produced hadronic system
$W=\sqrt{(q+p)^{2}}$, the energy lost by the electron in the nucleon rest
frame $\nu=\frac{q\cdot p}{M}$ where M is the nucleon mass.

In the inclusive double polarized DIS process (Fig. 2.1), where only the final
state electrons are measured, the spin-dependent $g_{1}$ structure function
can be extracted from the double spin asymmetry measurements. In the parton
model, the $g_{1}$ structure function can be expressed as the sum of the
contributions of various flavor of quarks

$g_{1}(x,Q^{2})=\frac{1}{2}\sum_{q=(u,d,s)}e_{q}^{2}\big{[}\Delta
q(x,Q^{2})+\Delta\overline{q}(x,Q^{2})\big{]},$ (2.1)

where the contribution from the light favor quarks is summed over. Fig. 2.2
shows the kinematical coverage of the $g_{1}$ structure function at the EicC,
as compared to the currently available experimental data. Generally speaking,
$g_{1}$ is often measured through the inclusive DIS experiment, and it allows
us to extract the polarized distribution functions of quarks of various
flavors based on the assumption of the $SU(3)$ flavor symmetry. However, this
method has a strong model dependence, and it mixes the contributions from
quarks of different flavors.

Another method [50] is to use SIDIS processes to extract more quark and hadron
flavor information from experimental data, where a leading hadron among the
final state hadrons in Fig. 2.1 is detected in coincidence with the scattered
electron. When a quark inside a proton absorbs a virtual photon emitted by an
electron, the quark gets struck out of the proton and becomes a final state
jet, which consists of many hadrons clustered inside a narrow cone. This final
state hadronization process can be described by fragmentation functions. The
final-state hadron contents in the jet carry the flavor information of the
initial state quark, therefore this process offers a way to tag the flavor of
the produced quark. If one measures a pion or a kaon in the SIDIS process in
addition to the recoiled electron, one can separate spin contributions from
quarks of different flavors. In this case, the polarized structure function in
the parton model can be written as

$g_{1}(x,Q^{2},z)=\frac{1}{2}\sum_{q}e_{q}^{2}\big{[}\Delta
q(x,Q^{2})D^{q\rightarrow
h}(Q^{2},z)+\Delta\overline{q}(x,Q^{2})D^{\overline{q}\rightarrow
h}(Q^{2},z)\big{]},$ (2.2)

where $D^{q\rightarrow h}(Q^{2},z)$ describes the fragmentation process from a
quark $q$ to a hadron $h$. $z$ represents the momentum fraction of the final
state hadron with respect to the momentum of the produced quark,
experimentally, it is defined as $z=\frac{P_{hadron}\cdot p}{q\cdot p}$.

Figure 2.2:  Global data of the polarized proton structure function $g_{1}$
from inclusive DIS measurements compared with the projected EicC data based on
the integrated luminosity of 50$fb^{-1}$ (about one year of running at the
EicC).

Through measurements in $e^{+}e^{-}$ and $e-p$ scatterings, we have been
studying and extracting various hadron fragmentation functions. Using these
hadron fragmentation functions as inputs, we can further separate and extract
the polarized quark distributions of certain flavor accurately from polarized
SIDIS data measured at EicC. Figs. 2.3 show the EicC projection of the
polarized sea quark and gluon distributions, respectively, for various flavors
of quarks obtain from longitudinally polarized double spin asymmetry
measurements via DIS and SIDIS processes. In these figures, the light blue
band represents the original uncertainty of the DSSV14 global data fit [51].
The red (green) dashed band is the uncertainty from a next-to-leading order
fit using ePump [52, 53] by adding DSSV14 fit with EicC DIS (SIDIS) pseudodata
with integrated luminosity of 50 fb-1 for both electron-proton (3.5 GeV + 20
GeV) and electron-3He collisions (3.5 GeV + 40 GeV). One can tell that the
SIDIS data, taking advantage of $\pi^{\pm}$ and $K^{\pm}$ final states from
both proton and effective neutron targets, is more powerful comparing to DIS
data in the flavor separations. The plots clearly show that EicC can
significantly improve the precision of helicity distributions of sea quarks
and gluons in the $x>0.005$ region. This can have an impact on the
understanding of the proton spin puzzle, since the current sea quark
contribution to the proton spin $\int\Delta q(x)dx$ ($q=\bar{u},\bar{d},s$)
has an uncertainty of $100-200\%$. The measurement at EicC can help to improve
precision by more than a factor of five.

Figure 2.3:  Results on the uncertainty band of polarized sea quark and gluon
distributions after a next-to-leading order fit by including EicC pseudodata.
The light blue band represents the original DSSV14 global fit. The red (green)
band shows the results by adding DSSV14 fit with EicC DIS (SIDIS) pseudodata
with integrated luminosity of 50 fb-1 (10 months of running at
2$\times$1033/cm2/s instantaneous luminosity) for both electron-proton (3.5
GeV + 20 GeV) and electron-3He collisions (3.5 GeV + 40 GeV). During the
pseudodata analysis, the following cuts were applied: $Q^{2}>2GeV^{2}$,
$W^{2}>12GeV^{2}$, $0.05<y<0.8$, $0.05<z<0.8$.

As a short summary, thanks to the particular energy range of EicC, the high-
luminosity and versatile capability of the accelerator machine design, and the
$4\pi$ coverage layout of the detector, SIDIS at EicC allows us to measure the
polarized sea quark and gluon distributions with remarkable precision.
Moreover, using various polarized hadron beams (protons and helium-3) together
with the detector with the capability of particle identification, EicC can
help to significantly improve the flavor separation and thus extract polarized
quark distributions of different flavor reliably.

After one year of running at the EicC, about 50$fb^{-1}$ integrated luminosity
will be obtained, as one can see from the above statistical analysis that the
measurement can be significantly improved comparing to the existing world
data. Therefore, it is critical to control the systematic uncertainty.
According to the study in the ongoing experiments, the major sources of
systematic uncertainty are from the precision of measurements on the beam
polarization, luminosity fluctuation of beam bunches in different spin states,
contamination of photon-induced electrons in the scattered electron detection,
and so on. These sources are also applied to the following physics topics and
will be further investigated quantitatively while the detector design is
refined in the following years.

###  2.2 Three-dimensional tomography of nucleons

The conventional parton distribution functions (PDFs) first introduced by
Feynman [54] and formalized by Bjorken and Paschos [55] only contain the
information on the longitudinal motion of partons inside a nucleon. To gain
more comprehensive knowledge about partonic structures of the nucleon, one may
introduce multi-dimensional distributions, including transverse momentum
dependent parton distributions (TMDs) [56, 57] and generalized parton
distributions (GPDs) [58, 59, 60, 61]. For a given longitudinal momentum
fraction $x$ carried by a parton, TMDs represent the transverse momentum
distribution of the partons and GPDs encode the transverse spatial
distribution of the partons. Both TMDs and GPDs provide three-dimensional
images of the nucleon, allowing us to access much richer partonic structures,
especially when the spin degrees of freedom are taken into account. Therefore,
the measurement of TMDs and GPDs will lead us to a more profound understanding
of strong interaction.

Experimental studies of TMDs and GPDs have been carried out in the existing
facilities during the last two decades. Although valuable data have been
collected for a first exploration, TMDs and GPDs are still far from well
constrained, especially for sea quarks and gluons, due to the low luminosity
and the limited kinematic coverage. Recently approved electron-ion collider to
be built at BNL is designed to reach a high center-of-mass energy region,
which makes the quantitative exploration of sea quark TMDs and gluon TMDs
possible for the first time. On the other hand, EicC as a facility at the
intensity frontier with relatively high center-of-mass energy, and versatile
beam species, will be an ideal machine for exploring the internal landscape of
the nucleon in the sea quark region.

In this section, we describe the TMD and GPD programs at EicC via the semi-
inclusive deep inelastic scattering (SIDIS), deeply virtual Compton scattering
(DVCS), and deeply virtual meson production (DVMP) processes.

####  2.2.1 Transverse momentum dependent parton distributions

The extraction of partonic structures of the nucleon from high energy
scattering processes relies on the QCD factorization, which provides the link
between the observed hadrons and the partons that participate in the hard
scattering. In inclusive DIS, where only the scattered lepton is identified,
the large momentum scale $Q$ mediated by the virtual gauge boson, i.e. photon
or $W^{\pm}/Z$, serves as a short-distance probe, allowing us to “see” the
quarks and gluons indirectly. The cross section can be factorized into the
lepton-parton scattering at short-distance convoluted with the PDFs in which
the active parton’s transverse momentum $k_{T}$ is integrated. Overall
corrections are suppressed by inverse powers of $Q$. This is known as the
collinear factorization.

Figure 2.4:  The Trento convention of SIDIS kinematic variables [62]. The
$z$-direction is defined by the virtual photon (or $W^{\pm}/Z$), momentum,
also referred to as the photon-target frame. The incoming and outgoing leptons
define the lepton plane, and the detected final-state hadron together with the
virtual photon defines the hadron plane. The azimuthal angle $\phi_{h}$ is
defined from the lepton plane to the hadron plane. For a transversely
polarized nucleon beam/target, the azimuthal angle of the transverse spin
$S_{\perp}$ is define from the lepton plane to the transverse spin direction.

Apart from the scattered lepton, one final-state hadron with momentum $P_{h}$
is identified in SIDIS (Fig. 2.4), which not only allows us to detect quark
and gluon distributions in the nucleon as in the inclusive DIS, but also
provides the opportunity to explore the hadronization process, the emergence
of color neutral hadrons from colored quarks and gluons. It also allows us to
learn the flavor dependence by selecting different hadrons, e.g. pions and
kaons, in the final state, as explained in the previous section.

In addition to the large momentum scale $Q$, an adjustable momentum scale is
given by the transverse momentum of the observed hadron in the final state. In
the Breit frame, where the virtual gauge boson and the nucleon are headed on,
the SIDIS process is naturally dominated by the small transverse momentum
region, $P_{h_{\perp}}\ll Q$. In this regime, the hard momentum scale $Q$
localizes the probe to see the particle feature of quarks and gluons in the
nucleon and the soft scale $P_{h_{\perp}}$ is sensitive to the confined motion
of partons perpendicular to the colliding direction. The SIDIS cross section
can be factorized into the lepton-parton short-distance scattering convoluted
with transverse momentum dependent parton distribution functions and
fragmentation functions. This is known as the TMD factorization. Overall
corrections are suppressed by powers of $P_{h_{\perp}}/Q$. For events with
large transverse momentum comparable to $Q$, the SIDIS process is effectively
characterized by a single large momentum scale, no longer sensitive to the
transverse motion of partons. The cross section is described by the collinear
factorization as in the previous section, where double polarized SIDIS events
are utilized to extract helicity distributions.

Here we focus on the small transverse momentum regime where one can apply the
TMD factorization [63, 64]. By introducing the spin degrees of freedom, one
can define eight independent leading-twist quark/gluon TMDs [65] as shown in
Fig. 2.5. The spin-dependent TMDs encode rich information of the nucleon
structure, and in particular can shed light on our understanding of parton
orbital motions and spin-orbit correlations. When integrating out the
transverse momentum $k_{T}$ of the parton, three out of the eight leading-
twist TMDs, the unpolarized distribution $f_{1}(x,k_{T})$, the helicity
distribution $g_{1L}(x,k_{T})$ and the transversity distribution
$h_{1}(x,k_{T})$ reduce to their collinear counterparts, while the other five
that describe the correlations between parton transverse momentum and the
parton/nucleon’s spin vanish.

Figure 2.5:  The leading-twist quark TMD distributions.

Under the single-photon exchange approximation, the SIDIS cross section can be
expressed in terms of 18 structure functions, corresponding to different
polarization configurations and final-state azimuthal modulations. The spin-
dependent TMDs are usually extracted by measuring particular azimuthal
asymmetries, while the unpolarized TMDs can be obtained by analyzing
unpolarized SIDIS cross section or multiplicity. Among the leading-twist spin-
dependent TMDs, the Sivers function $f_{1T}^{\perp}(x,k_{T})$ [66], as well as
related phenomenologies, stimulates tremendous theoretical progress and
experimental investigations in recent years. It describes the correlation
between quark transverse momentum and the transverse spin of the nucleon. To
put it simply, the Sivers function reflects the left-right asymmetry of quark
transverse momentum distribution in a transversely polarized nucleon. One of
the most distinguished features of the Sivers function is its unique
universality property exhibited in different processes. If final/initial-state
interactions, which are formally summarized into the gauge link, were absent
between the active quark and the remnants of the nucleon, the time reversal
invariance requires the Sivers function to be zero [67], and thus it is
commonly referred to as naive time-reversal odd (T-odd) distribution. Once
turning on QCD interactions, the Sivers function can arise from the final-
state interaction in the SIDIS process and from the initial-state interaction
in the Drell-Yan process. As the staple like Wilson line flips the direction
between the final-state and initial-state interactions, the quark Sivers
functions are predicted to have an exact sign change between SIDIS and Drell-
Yan processes, $f_{1T}^{\perp}(x,k_{T})|_{\rm
SIDIS}=-f_{1T}^{\perp}(x,k_{T})|_{\rm DY}$ [68, 69]. Although recent $W$
production data from STAR [70] and the $\pi N$ Drell-Yan data from COMPASS
[71] support this prediction, the current uncertainties are too large to
confirm the sign change. Future precise measurements of the Sivers function in
different processes are of great importance to test this prediction associated
with the QCD factorization. Moreover, theoretical studies have suggested that
the Sivers function is closely related to parton orbital angular momentum
[72]. Therefore, the experimental studies of the Sivers function are not only
crucial for unveiling the spin structure of the nucleon, but also important
for deepening our understanding of the strong interaction and/or QCD.

Table 2.1: The existing measurements of the Sivers asymmetry in SIDIS. collaboration |  $\sqrt{s}$ GeV | target | final state hadron | literature
---|---|---|---|---
COMPASS (CERN) | 18 | Deuterium | $h^{\pm},\pi^{\pm},K^{\pm},K^{0}$ |  [73, 74]
|  | proton | $h^{\pm}$ | [75]
|  | proton | $\pi^{\pm},K^{\pm}$ | [76]
HallA (JLab) | 3.5 | neutron | $\pi^{\pm},K^{\pm}$ | [77]
HERMES (DESY) | 7.4 | proton | $\pi^{\pm}$ | [78]
|  | proton | $\pi^{\pm},(\pi^{+}-\pi^{-}),\pi^{0},K^{\pm}$ | [79]

In SIDIS, one can access the Sivers function by measuring a transverse single-
spin asymmetry, known as the Sivers asymmetry. Within the TMD factorization,
the corresponding structure function can be expressed as the convolution of
the Sivers function and the unpolarized fragmentation function. During the
past two decades, great efforts have been made to extract the Sivers function
as well as other TMDs via the SIDIS process at many experimental facilities
around the world, including HERMES, COMPASS, and JLab, as summarized in Table
2.1. However, TMDs, especially the spin-dependent ones, are still very poorly
determined due to various difficulties. The JLab experiments were carried out
at relatively low energies, where high-twist effects and target mass
corrections are expected to be sizable. HERMES data were mostly collected in
the so-called valence quark region, where the contribution to the cross
section is dominated by valence quarks, and hence the data are not quite
sensitive to sea quark distributions. The ongoing and upcoming SIDIS
experiments at the 12-GeV upgraded JLab aim at unprecedented precise
measurements of valence quark TMDs. Recently approved EIC-US at BNL is
designed with a high center-of-mass energy and will have quantitative
measurements of gluon and sea quark TMDs for the first time. EicC given the
center-of-mass energy in between has unique advantages to study sea quark TMDs
and fills the energy gap from JLab to EIC-US. In addition, the separation of
current fragmentation and target fragmentation remains as a challenging task
at the existing fixed target facilities. The large experimental acceptance at
EicC will provide a wide kinematic coverage, which is crucial to make the
clean selection of events in the current fragmentation region, allowing us to
apply more strict kinematic cuts, especially for $K$ meson productions that
play an important role in flavor separation due to its sensitivity to strange
quark distributions. Currently available $K$ meson production data from
polarized SIDIS are rather limited. EicC SIDIS experiments will have high
statistics measurements of both charged pion and charged kaon productions.
Together with the combination of the proton beam and the 3He beam, EicC will
allow a full separation of all light quark flavors, $u$, $d$, $s$, $\bar{u}$,
$\bar{d}$, and $\bar{s}$.

In Fig. 2.6, we show the $x-Q^{2}$ distribution of EicC SIDIS events. Instead
of presenting all cases, we only select two examples, the $\pi^{+}$ production
from the proton beam and the $K^{+}$ production from the 3He beam, to cover
both $ep$ and $e^{3}{\rm He}$ collisions and both pion and kaon productions.
Kinematic cuts, including $Q^{2}>1\,\rm GeV^{2}$, $W>5\,\rm GeV$,
$W^{\prime}>2\,\rm GeV$, $0.3<z<0.7$, and the current fragmentation cut as
described in [80], have been applied. One can see that with the current EicC
design, the relatively high $Q^{2}$ coverage in the typical sea quark region
($x\sim 0.05$) ensures a reliable extraction of sea quark TMDs. Moreover,
compared to the fixed-target experiments, the collider mode of EicC allows a
wide kinematic coverage, which provides the opportunity to quantitatively
estimate power suppressed corrections.

Figure 2.6: $x-Q^{2}$ coverage of EicC SIDIS events from simulation. Left:
$\pi^{+}$ production from the proton beam. Right: $K^{+}$ production from the
3He beam. Kinematic cuts are described in the text.

Among the $k_{T}$-odd TMDs, quark Sivers function is the most extensively
studied, but it is still poorly constrained, particularly in the sea quark
region where the sign is even not yet determined without ambiguity [81]. Here
we take the Sivers function as an example to demonstrate the impact of EicC
SIDIS experiments.

Figure 2.7: The precision of extractions of up and down quark Sivers
functions. The light green bands represent the accuracy from the currently
available SIDIS data, the red bands represent the accuracy by including the
projected EicC data with statistical uncertainty only, and the blue bands
represent the accuracy by including the projected EicC data with part of
systematic uncertainties as described in the text. Integrated luminosities of
$50\,\rm fb^{-1}$ for $ep$ and $50\,\rm fb^{-1}$ for $e\,^{3}\rm He$ are
adopted in this projection. Figure 2.8: The precision of the extraction of
strange quark Sivers function. The red bands represent the accuracy by
including the projected EicC data with statistical uncertainty only, and the
blue bands represent the accuracy by including the projected EicC data with
part of systematic uncertainties as described in the text. Integrated
luminosities of $50\,\rm fb^{-1}$ for $ep$ and $50\,\rm fb^{-1}$ for
$e\,^{3}\rm He$ are adopted in this projection.

We simulate SIDIS events according to EicC kinematics: $3.5\,\rm GeV$ electron
beam, $20\,\rm GeV$ transverse polarized proton beam, and $40\,\rm GeV$
transverse polarized 3He beam serving as effective polarized neutron beam
since the spin of 3He is mainly given by the neutron spin. Integrated
luminosities are chosen as $50\,\rm fb^{-1}$ for $ep$ and $50\,\rm fb^{-1}$
for $e\,^{3}\rm He$ collisions. A $4\pi$ angle coverage is assumed for the
acceptance. For the projection of EicC results, we select simulated SIDIS
events with $Q^{2}>1\,\rm GeV^{2}$, $W>5\,\rm GeV$, $W^{\prime}>2\,\rm GeV$,
$0.3<z<0.7$, and the current fragmentation cut [80]. We also require the
scattered electron momentum $P_{e}>0.35\,\rm GeV$ and the identified final-
state hadron momentum $P_{h}>0.3\,\rm GeV$ for detection reason. Apart from
the statistical uncertainty, we consider some major systematic uncertainties,
including $3\%$ relative uncertainty for beam polarizations and $5\%$ relative
uncertainty for 3He nuclear effect. Other systematic uncertainties, e.g.
detector resolution, particle identification, random coincidence, radiative
corrections, are not expected to be dominant based on existing experience,
although more detailed studies will be carried out with the final detector
design. We utilize the parametrization form of the Sivers function in [81] as
the input model. In Fig. 2.7, we show the results of the extraction of up and
down quark Sivers functions. In Fig. 2.8, we show the results of the
extraction of the strange quark Sivers function. The outer light green bands
represent the present accuracy from world existing SIDIS data, the inner red
bands represent the accuracy including projected EicC data with statistical
uncertainty only, and the blue bands represent the accuracy including
projected EicC data with part of the systematic uncertainties mentioned above.
As the world existing $K$ meson production data from polarized SIDIS are very
limited, the current uncertainty of the strange quark Sivers function is huge,
and even the sign is not yet determined. Hence the present accuracy bands are
not shown in Fig. 2.8. Recent theoretical study suggested an opposite sign
between the strange quark and anti-strange quark Sivers functions [82] apart
from the sign-flip prediction of the Sivers functions probed in SIDIS and
Drell-Yan processes. The experimental test of this prediction at EicC will
enrich our knowledge about the proton spin structure, particularly in the
relatively small $x$ region. We should also note that due to the large
uncertainty of the limited available polarized SIDIS data one cannot apply a
very flexible functional form in the global analysis. Once more precise data
are available from EicC and other future experiments, we will be able to have
less biased extractions of the Sivers function as well as other TMDs by using
much more flexible parametrizations and more realistic estimations of the
uncertainties. Results in Figs. 2.7 and 2.8 can be understood as the impact of
EicC SIDIS experiments from statistics point of view since the same analysis
method is applied to world data and projected data.

The EicC design enables us to precisely measure all 18 structure functions by
combining different beam polarization configurations and the separation of
different azimuthal modulation terms. Other TMDs also receive great interest.
For instance, the transversity TMD, which survives after $k_{T}$ integration,
measures the net density of transversely polarized quarks in a transversely
polarized nucleon. The first moment of the integrated transversity
distribution is the tensor charge, which is a fundamental QCD quantity defined
by the matrix element of the tensor current operator. It is recognized as a
benchmark of the lattice QCD study of hadron structures. Therefore, a precise
determination of the tensor charge including the flavor separation can serve
as an experimental test of lattice QCD. Due to its chiral-odd property, the
transversity TMD contribution to inclusive DIS cross section is highly
suppressed by the power of $m_{q}/Q$. In contrast, it can be extracted from a
leading power single spin asymmetry in SIDIS process, known as the Collins
asymmetry, which arises from the coupling of the transversity TMD and the
Collins fragmentation function. Alternatively, the transversity distribution
can also be accessed by analyzing the di-hadron SIDIS events at EicC. In the
present global analysis, the sea quark transversity distribution is commonly
assumed to be zero. EicC as an ideal facility for the study of sea quark
distributions will provide the opportunity to test this assumption.

In conclusion, EicC with wide kinematic coverage and high luminosity has the
capability to deliver the high precision experimental data. The SIDIS
measurements at EicC combined with those at 12-GeV upgraded JLab focusing on
the study of valence quark distributions and the recently approved high-energy
EIC at BNL will provide complementary extractions of TMDs covering the full
$x$ range towards a complete three-dimensional imaging of the nucleon in the
momentum space. EicC as a facility that bridges the energy gap between
JLab-12GeV and the future EIC at BNL is a perfect machine to study TMD
evolution effects, in particular, to constrain the non-perturbative part of
the evolution kernel [83].

####  2.2.2 Generalized parton distributions

Generalized parton distributions (GPDs) encode information on the three
dimensional structure of nucleon in the joint transverse position-longitudinal
momentum phase space [58, 59, 60, 61, 84]. They were initially introduced to
describe the exclusive processes where an active parton participating in the
hard scattering is re-absorbed into nucleon that remains intact after
collisions. GPDs depend on two longitudinal momentum fractions $x$ and $\xi$
and on the squared momentum transfer $t$ to the proton.

GPDs are widely connected to other physics quantities. In the different
kinematical limits, GPDs are reduced to the normal parton PDFs and
electromagnetic form factors of the nucleon. In particular, setting $\xi=0$
and performing a Fourier transform with respect to the transverse component of
$t$, one obtains an impact parameter distribution, which describes the joint
distribution of partons in their longitudinal momentum and their transverse
position $b_{\perp}$ inside the proton [85, 86].

One of the most important physics motivations of GPD studies is to understand
nucleon spin structure. The GPDs’ connection with partons angular momentum is
quantified through the Ji’s sum rule [60],

$J_{q,g}=\frac{1}{2}\int_{-1}^{1}dxx[H_{q,g}(x,\xi,0)+E_{q,g}(x,\xi,0)].$
(2.3)

Where $J_{q,g}$ represents the total angular momentum for quark and gluon,
which can be further decomposed as,

$\frac{1}{2}=J_{q}+J_{g}=\frac{1}{2}\Delta\Sigma+L_{q}+J_{g},$ (2.4)

with $\frac{1}{2}\Delta\Sigma$, $L_{q}$ and $J_{g}$ being the quark spin
angular momentum, quark orbital angular momentum and gluon total angular
momentum respectively. The quark orbital angular momentum can be extracted
through the measurements of GPDs $H$ and $E$ in exclusive processes by
subtracting the quark helicity contribution. It is also worth to mention that
GPDs encode the rich information on the mechanical properties of nucleon
internal structure [87, 88, 89, 90] through the gravitational form
factors(GFFs), which is related to the second moment of the unpolarized GPD.
These mechanical properties, such as the pressure and shear force
distributions, the mechanical radius, and the mechanical stability of a
particle, contain the crucial information on how the strong force inside
nucleon balance to form a bound state. However, the precise extraction of GFFs
at the current facilities remains problematic due to poor data constraints
[91, 92, 93, 94]. As GPDs play an essential role in exploring the internal
nucleon structure from many aspects, the experimental studies of GPDs have
been and are a cutting-edge field of high energy nuclear physics during the
last two decades.

Figure 2.9: Diagrams of various processes to study Generalized Parton
Distributions (GPDs). (a) deeply virtual compton scattering, (b) time-like
compton scattering, (c) deeply virtual meson production.

The main exclusive processes which allow to access to the GPDs in $ep$
collisions are deeply virtual Compton scattering (DVCS) $ep\longrightarrow
ep\gamma$ (Fig. 2.9(a)), time-like Compton scattering $ep\longrightarrow
epl^{+}l^{-}$ (Fig. 2.9(b)) and deeply virtual meson production(DVMP)
$ep\longrightarrow epM$ (Fig. 2.9 (c)) [59, 60]. At the leading order, DVCS
process is described by the partonic channel $q\gamma^{*}\longrightarrow
q\gamma$ where the virtual photon is provided by the electron. GPDs enter the
cross section of DVCS process through the Compton form factors(CFF) defined as
(for example, the quark GPD $H^{q}$) [95, 96, 97, 98],

${\mathcal{H}}(x_{B},t,{\cal Q}^{2})=\int_{-1}^{1}\\!dx\,\left[\frac{1}{\xi-
x-i\epsilon}-\frac{1}{\xi+x-i\epsilon}\right]\sum_{q=u,d,s,\cdots}e_{q}^{2}H^{q}(x,\xi,t,{\cal
Q}^{2})\,,$ (2.5)

where $\xi\approx x_{B}/(2-x_{B})$ with $x_{B}$ being the Bjorken’s variable.
The similar relation holds for other GPDs. The precise measurements of the
various angular modulations and polarization dependence of DVCS cross section
at different kinematic points in ($Q^{2},x_{B},t$) would allow us to extract
different CFFs, as each of them has unique angular and polarization
dependencies (see the reference [84] and therein). The corresponding GPDs can
be subsequently constrained by the extracted CFFs.

Let us highlight some specific features of different production channels. The
main limitation of DVCS process is that it is sensitive only to the sum of
quark and anti-quark distributions in a particular flavor combination. In
contrast, exclusive meson production offers substantial help in the separation
of different quark and antiquark flavors and of gluons. For example, the
valence quark and sea quark GPDs can be probed via pseudo scalar mesons
($\pi,K,\eta,...$) production processes, whereas the vector mesons
($\rho,\phi,\omega$) production is more sensitive to sea quark and gluon GPDs.
However, extracting GPDs from exclusive meson production requires the
knowledge of additional non-perturbative matrix element, the meson
distribution amplitude.

The precise extraction of GPDs from the measurements of exclusive processes
puts the highest demands on experiments for various reasons, including the
smallness of cross sections in exclusive processes, the interference with the
Bethe-Heitler (BH) process, etc. The measurements of GPD-related observables
in the region of moderate to large $x$ have been carried out at HERMES [99],
COMPASS [100], and JLab [101]. However, most of these measurements have
sizable statistical uncertainties and provide reasonable constraints for only
one GPD, $H$. The complete and precise extraction of all GPDs requires high
luminosity, detectors with full hemisphere coverage, beams with various
polarization choices, and wide kinematic reach. Until now, there have been no
facilities being able to meet all these demands. For example, the luminosity
at HERA and COMPASS is low, meanwhile COMPASS has its complication while
flipping the muon beam helicity, which makes the extractions of some
polarization dependent GPDs extremely difficult. On the other hand, though the
luminosity at JLab-12GeV is very high, the most DVCS events lie well below
$Q^{2}<10\,{\rm GeV}^{2}$ [102, 103, 104, 105], where the various high twist
effects or high order effects can play a role and complicate the extraction of
GPDs (see _e.g._ [106, 107, 108, 109]). It is usually believed that these
theoretical uncertainties can be well controlled if going to higher $Q^{2}$
region [107].

Figure 2.10: The distributions of DVCS(left panel) and $\pi^{0}$ DVMP(right
panel) events in the $x$ and $Q^{2}$ for 3.5GeV electron beams colliding with
20GeV proton beams energy at EicC. The event number with arbitrary
normalization is indicated by different colors. In the left panel, the
contributions from both the DVCS and the BH processes as well as their
interference are included, and the used kinematic cuts and binning scheme are
also shown.

The programs of the experimental GPDs studies will be dramatically extended by
EicC, predominantly in the sea quark kinematical region. The precise
measurements of both DVCS and DVMP can be carried out at EicC with versatile
beam species/polarizations. The typical $Q^{2}$ range accessible with EicC is
$1$ GeV${}^{2}<Q^{2}<30$ GeV2 (see the left panel of Fig. 2.10 adapted from
MILOU package [110]). Meanwhile, the Bjorken variable $x$ can reach down to
$x\approx 0.05$ when restricting $Q^{2}$ to the perturbative region $Q^{2}>10$
GeV2. This kinematic coverage with the current design will make EicC a unique
machine to explore parton spatial imaging of the nucleon in the sea quark
region. In the valence quark region, the theoretical uncertainties will be
substantially reduced at EicC as compared to that at JLab-12GeV due to
relatively higher $Q^{2}$. Moreover, EicC is also complementary to the US EIC
in studying the DVCS process. This is because the interference contribution
between the Compton and the Bethe-Heitler processes is more prominent at a
lower energy machine, whereas the Compton process may dominate at EIC for
given $x$ and $Q^{2}$ values.

As mentioned, parton orbital angular momentum can be determined by extracting
GPD E and H from exclusive processes according to the Ji’s sum rule. However,
in practice, it is extremely challenging to achieve this because it requires
measuring the values of H and E for all $x$ at fixed $\xi$. Nevertheless, EicC
has great potential to advance our knowledge of GPD E and also H with a
transverse polarized proton beam. Fig. 2.11 displays the simulation results
for the Compton scattering off a polarized proton. The EicC measurements of
the DVCS transverse polarization asymmetry $A_{UT}$ with a single azimuthal
modulation ${\sin(\phi-\phi_{s})\cos\phi}$ have a rather small statistical
uncertainties for a wide kinematic region with $|t|>0.01$ GeV2. Here the DVCS
events are selected in the kinematic region 0.01 $<y<$ 0.95 and $\gamma p$
center of mass energy W $>$ 2 GeV.

The impact of these pseudodata on the extraction of DVCS Compton form factors
(CFF) ${\mathcal{E}}$ and ${\mathcal{H}}$ is displayed in Fig 2.12. The
approach of global analysis utilizing the artificial neural network [111, 112,
94] is employed in order to reduce model dependency and propagate the
uncertainties properly. The poorly constrained real part of
$\widetilde{\mathcal{E}}$ and $\widetilde{\mathcal{H}}$ simply are assumed to
be vanishing [111, 92, 113] in the simulation. The light green bands, manily
driven by statistical uncertainties, represent the accuracy of the existing
JLab and HERMES data. The red bands show the accuracy after including the
projected $A_{UT}$ data of EicC with statistical uncertainty only. One can see
that the uncertainty for the extraction of the CFF ${\mathcal{E}}$ is reduced
in the sea quark region once the EicC measurements are included. In most of
the kinematic space systematic uncertainty is at the similar level or even
smaller than the statistical one. So we would still retain power of extraction
of CFFs similar to what is shown on Fig 2.12, after including such level of
systematic uncertainty. In addition to the $A_{UT}$ asymmetry, other
asymmetries, e.g. $A_{LU}$, $A_{UL}$, $A_{LL}$ and $A_{LT}$ can be precisely
measured with the different beam polarization configurations and the different
azimuthal modulations at EicC as well. A combined analysis with all these
measured modulations would further reduce significantly the error bands shown
in Fig 2.12. So under the high luminosity design of EicC, the statistical
uncertainties will not play essential role in the future GPD extraction and
the systematic uncertainties, whose main sources are discussed in previous
sections, are anticipated to be dominant, which will be under good control by
facility design.

Figure 2.11: The projected accuracy for $A_{UT}^{\sin(\phi-\phi_{s})\cos\phi}$
asymmetry in the process of DVCS off a transversely polarized proton target at
EicC in the region 1 GeV${}^{2}<Q^{2}<30$ GeV2. Only statistics uncertainty is
included. The size of $A_{UT}$ is estimated with the Goloskokov-Kroll model
[114, 115, 116]. The black star is the HERMES data of
$A_{UT,I}^{\sin(\phi-\phi_{s})\cos\phi}$ asymmetry [117]. The values of $|t|$
bins under the same $Q^{2}$ are not shown here for simplicity.  Figure 2.12:
An exploratory extraction of the real (${\mathcal{R}e}$) and the imaginary
(${\mathcal{I}m}$) part of CFF ${\mathcal{E}}$ and ${\mathcal{H}}$ at
$t=-0.2\,{\rm GeV}^{2}$ from the pseudodata generated for kinematical points
shown in Fig. 2.11 using the neural network method [111, 92, 113]. The
systematic uncertainty is not included yet.

As discussed, EicC can deliver high precision data for the DVMP process in the
large $Q^{2}>10$ GeV2 region, where the non-perturbative effects and higher-
twist contributions are suppressed, so that GPDs can be extracted reliably.
Fig. 2.10 (right panel) displays the expected distribution of DVMP events at
EicC in bins of $Q^{2}$ and $x$. Note that DVMP cross sections rapidly
decrease with increasing $Q^{2}$. One sees that there are substantial event
numbers in the moderate $Q^{2}$ region where perturbative treatment is
justified. This will facilitate clearly separating different quark flavor
contributions by combining with DVCS data. For instance, one can separate up
quark and down quark contributions by carrying out the measurements of
$A_{LL}^{\cos\phi}$ which arises from the coupling of the chiral-odd GPDs and
the twist-3 distribution ampliutde of pion [114, 115, 118, 119]. This
observable could provide valuable information on transversity PDF that is hard
to access in inclusive process. Despite the higher twist nature of this
observable, we found that the asymmetry is significant for the DVMP channel of
$\pi^{0}$ production. With the EicC DVMP pseudo-data displayed in Fig. 2.10,
it is shown in Fig.2.13 that at large $Q^{2}$ the statistical uncertainty of
the $A_{LL}^{\cos\phi}$ in $\pi^{0}$ production is significantly reduced.
Therefore, EicC presents an unique opportunity to study the chiral odd GPDs.

In summary, judging from our simulation results presented here, EicC will
greatly advance our knowledge about the internal structure of nucleons. The
combined kinematic coverage of the EicC, JLab and of EIC-US is essential for
ultimately yielding the complete 3D images of proton from the large $x$ down
to the saturation regime, and for much more profound understanding of the
proton spin puzzle as well.

Figure 2.13: The statistics error of the projected $A_{LL}^{\cos\phi}$
asymmetry for $\pi^{0}$ production in DVMP process at EicC. The CLAS data is
taken from Ref. [119].

###  2.3 Partonic structure of nucleus

The electron-ion collision has been recognized as an ideal process to explore
the distributions of quarks and gluons inside the nucleus, as well as to study
the QCD dynamics of multiple parton interactions in the nuclear medium. In
this process, the electron scattering part, which can be well controlled both
experimentally and theoretically, provides a high precision probe to reveal
the detailed partonic structure of the nucleus which is impossible to be
calculated theoretically. Besides, the nucleus can also serve as a QCD
laboratory at the fermi scale to investigate the strong interactions between
the energetic parton and the nuclear medium by carefully studying the so-
called hadronization process which largely depends on the type of the nucleus.
The detailed analysis of these nontrivial nuclear medium effects can help us
to probe the fundamental differences of partonic properties in free nucleons
and the nuclear medium, as well as to understand the mystery of hadronization
mechanisms and the QCD confinement of quarks and gluons.

####  2.3.1 The nuclear quark and gluon distributions

A full understanding of the difference between the properties of quarks and
gluons inside a free nucleon and that inside a nucleon bounded within the
nucleus will help us understand how the nucleus is formed at the partonic
level. The longitudinal momentum distributions of quarks and gluons in a free
nucleon are characterized by the usual leading twist parton distribution
functions (PDFs) which have been precisely measured in the high-energy
electron-proton collisions. A natural question is: how these PDFs are modified
by the nuclear medium when the nucleon is bounded? To answer such a
fundamental question remains one of the biggest challenges in the nuclear
physics community. Due to the lack of experimental data and the limited
kinematic coverage, the precision for nPDFs global extraction is far less than
that for PDFs in free nucleons [120, 121, 122, 123, 124, 125, 126]. In
particular, the extraction of nPDFs of sea-quarks and gluons is suffering from
even much larger uncertainties. It is strongly desired to perform more high-
precision measurements of conventional experimental observables as well as to
explore new observables that are sensitive to the sea-quark and gluons.

In the past three decades, various experiments have confirmed that the PDFs
measured in free nucleons and bounded nucleons are significantly different.
Shown in Fig.2.14 reveals the cross-section ratios for inclusive DIS between
eA and eD collisions in terms of Bjorken x distributions. The solid circles,
the open squares, and stars correspond to the data from SLAC E139 [20], BCDMS
[19], and EMC [127], respectively. Despite their different reactions and
kinematic ranges, these data exhibit a very similar nuclear medium effect.
There are four distinguishable regions [21]: 1. Fermi motion in $x>0.7$; 2.
EMC effect in the range of $0.3<x<0.7$; 3. Anti-shadowing around $x\sim 0.1$;
4. Shadowing in $x<0.01$.

Figure 2.14:  The cross section ratio between electron-ion and electron-
deuteron deep inelastic scattering [128].

Among them, the Fermi motion region can be interpolated as the result of the
momentum distributions of nucleons bounded in the nucleus which differ among
light to heavy nuclei. The so-called EMC effect, which is believed to be due
to the modification of the valance quarks in the nuclear medium, has been
exclusively studied since its discovery in 1980s but no satisfactory
explanation has yet been reached to address its root cause. The most recent
discovery of its strong correlations with the short-range corrections (SRC)
[23, 24, 25] sheds a light to fully unveil this mystery and provide a new way
to study the nuclear structure in the partonic level [129]. Enormous new
experimental programs and theoretical calculations have been planned to
continue studying this effect. On the other hand, no experimental evidence has
shown that such an effect also exists in sea-quarks and gluons. Furthermore,
the physics origins of the anti-shadowing and shadowing at small $x$ remain
unknown due to a lack of experimental measurements and theoretical
interpolations.

In the most recent nPDF determination, nNNPDF2.0, a robust quark flavor
separation and a good handle of the gluon are performed [120]. However,
compared to those for free nucleons large uncertainties of nPDFs remain due to
the very limited existing measurements. This is also true in other global
fittings such as EPPS16 [121]. The future EicC will place its kinematics in
the sweet spot where the nuclear medium effects of valance-quarks and sea-
quarks can be extensively studied by measuring their intrinsic PDFs in bound
nucleons using the eA DIS processes with a wide range of nuclei beams. Based
on the projections for the EicC pseudo-data which are generated through NLO
calculation of DIS cross-section using the nNNPDF2.0 nuclear PDFs, the impact
of future EicC measurements on nuclear PDFs utilizing Bayesian reweighting is
shown in Figs. 2.15 and 2.16. In Fig. 2.15, the sea quark distribution in Pb
at $Q^{2}=10$ GeV2 for both the original and reweighted nNNPDF2.0 fits are
shown with uncertainty bands correspond to $90\%$ confidence level. In
particular, the reduction of reweighted $\bar{u}$ uncertainty in the kinematic
region covered by EicC, i.e. $x>0.01$, strongly indicates EicC pseudo data are
adding a significant amount of new information to the global fit. A similar
analysis for gluon distribution in Pb is shown in Fig. 2.16, which indicates
the constraining power of EicC measurements on gluon nuclear modification.
Notice that the analysis shown in Figs. 2.15 and 2.16 are based on the
integrated luminosity $\mathcal{L}=0.01$ fb-1, which corresponds to only a few
hours of running 111Studies using EicC pseudo data with an integrated
luminosity equivalent to one week or more of running have also been performed.
However, the impact on the nNNPDF2.0 PDFs estimated by reweighting is so
significant that the number of effective replicas with non-zero weight
“surviving” the analysis reduces from an initial set of 1000 to a few dozen or
less. This reflects the fact that the leap in precision between the data
already included in the nNNPDF2.0 analysis and the future EicC data is too
wide for reweighting techniques to return viable results and strongly suggests
the need of a new fit. Similar conclusions on the reweighting procedure have
been found recently in impact studies for polarized PDFs at the future US EIC
using electron-helium SIDIS pseudo data [130].. Therefore, the real
measurements with high precision and large coverage will provide a stringent
constraint on nPDFs from the shadowing to the anti-shadowing region.

Figure 2.15:  Left: the $\bar{u}$ distribution in Pb at $Q^{2}=10$ GeV2, the
gray band comes from the original nNNPDF2.0 set, the blue band corresponds to
the set reweighted with the EicC pseudo data based on the integrated
luminosity $\mathcal{L}=0.01$ fb-1. Right: the relative uncertainty for two
sets of nPDFs. Figure 2.16:  Same as Fig. 2.15, but for gluon.

In addition to the electrons, the detection of varied final-state hadrons,
such as pions, kaons and heavier mesons, serves as the flavor-tagging to
decouple the contributions from different quark flavors. The high precision
data with large kinematic coverage will greatly improve the global extraction
of quark nPDFs in the medium to low $x$ regions. Most importantly, EicC will,
for the first time, precisely measure the undiscovered medium modification
effect of sea-quarks as well as unveil the puzzle of anti-shadowing which
remains largely unknown.

On the other hand, various species of beam nuclei at EicC will also provide
unique opportunities to shedding light on studying the nuclear structure at
the partonic level. By detecting the outgoing protons and neutrons at the
forward angles during the eA collision, the spectator-tagging DIS process
serves as a powerful tool to exam the QCD origin of nucleon-nucleon
interactions, such as the link between the SRC to EMC effects at $x>0.2$
region as well as the nucleon coherence phenomena at low $x$ that lead to the
anti-shadowing and shadowing effects [131, 132].

####  2.3.2 Hadronization and parton energy loss in nuclear medium

Precise measurements and phenomenological investigations on the SIDIS process
with different nuclei in electron-ion collisions are the fundamental tools to
analyze two widely discussed nuclear effects, i.e., the parton energy loss
effect and hadronization in the medium [133, 134, 135, 136, 137]. In a nuclear
medium, the highly energetic parton generated in the hard scattering process
will continuously encounter the multiple scatterings with the surrounding
nucleons before it completely escapes from the nucleus or is converted inside
the nucleus into charge-neutral particles, a complicated process also known as
the hadronization. The collective consequence eventually leads to nontrivial
phenomena of nuclear modifications, including the attenuation and broadening
of the hadron spectrum in eA collisions comparing to ep collisions. These
phenomena, which are very sensitive to the nuclear parton densities and QCD
dynamics of multiple parton interactions in the nuclear environment, have been
observed in semi-inclusive deep inelastic scatterings in HERMES [138] and
Drell-Yan dilepton production in proton-nucleus collisions in FNAL-866 [139].
The available data are used to extract the transport properties of cold
nuclear matter and study the parton energy loss mechanism in the nucleus [140,
141, 142, 143]. However, large uncertainties still exist, mainly originated
from two aspects: 1. limited kinematic coverage of experimental data; 2. the
assumption in energy loss calculation that the partons fragments outside the
nuclear medium. To obtain more precise information about the hadronization
process and the mechanism of parton energy loss in medium, we need EicC to
fill in the open window that has not been covered by existing experimental
measurements.

Hadronization, as encoded in fragmentation functions, describes the process of
quarks and gluons fragment into final state hadrons. In the presence of a
large size nuclear medium, the hadronization dynamics will be affected and
eventually leads to different hadron spectrum comparing to that in a vacuum
[144, 145]. As we know, parton energy loss effects also lead to the
suppression of the hadron spectrum as functions of beam energy $\nu$ and
fragmentation fraction $z_{h}$ in eA collisions comparing to that in ep
collisions [138, 141]. Therefore, we can not disentangle these effects from
the available experimental data, as they lead to the same phenomena but with
very different mechanisms. This requires us to perform the measurement more
differentially and consider as many as possible the final state identified
hadrons. The high collision energy and the high luminosity, as well as the
capability of identifying various hadrons in future EicC, will play a key role
to differentiate the parton energy loss effect and medium hadronization
effect.

Shown in Fig. 2.17 is the comparison between predictions from parton energy
loss model (solid curves) and hadron transport model (dashed curves) for the
nuclear modification factors, where only events with
$0.1<y<0.85,~{}W^{2}>4\rm{GeV}^{2},~{}Q^{2}>1\rm{GeV}^{2}$ are selected in the
process when 3.5 GeV electron collides with 20 GeV (per nucleon charge) Pb
beam, and various hadrons represented by different shaped points are
considered in the simulations. By looking at the dependence of $R_{M}^{h}$ as
a function of the virtual photon energy $\nu$, the capability of particle
identification as well as the kinematic coverage in EicC will allow us to
disentangle the hadronization mechanism from the parton energy loss effect as
indicated by the difference between solid and dashed curves. Though the two
models give very similar nuclear modification effect for $\pi^{+}$ production,
enormous differences for $p$ and $K^{+}$ are predicted. These differences can
be identified in EicC considering its high luminosity $50fb^{-1}$, which leads
to invisible statistical uncertainty as shown in Fig. 2.17.

The transverse momentum broadening effect is very sensitive to the QCD
dynamics of multiple parton interactions in the nuclear environment and the
nuclear medium transport property. It has been extensively studied in heavy-
ion collisions, see for example [134, 146, 147]. Similarly, we can also use
this observable to probe the fundamental properties of the nuclear medium in
eA collisions. Comparing to pA collisions, eA collisions is much cleaner due
to the absence of the strong interaction between the beam electron and the
target nucleus. Based on the assumption that the partons hadronize outside the
nuclear medium, we show in Fig. 2.17 the transverse momentum broadening for
light hadron (red curve) and $J/\psi$ (blue curve), which can be used to probe
the jet transport parameters for quark jet and gluon jet, respectively. Notice
that the available measurements on the gluon jet transport parameter are very
limited, and EicC can make a significant contribution to this subject.

Figure 2.17:  Left plot: the cross section ratios for $\pi^{+},K^{+}$ and $p$
between election-ion and electron-proton collisions at EicC energy region,
i.e., 3.5 GeV electron beam and 20 GeV per charge for heavy ion beam, as a
function of virtual photon energy $\nu$. Right plot: the transverse momentum
broadening for $\pi$ and $J/\psi$ at future EicC.

###  2.4 Exotic hadronic states

Hadron spectroscopy started a new era in 2003 when the $D_{s0}^{*}(2317)$,
$D_{s1}(2460)$ and $X(3872)$222It is denoted as $\chi_{c1}(3872)$ according to
its quantum numbers in the latest version of Review of Particle Physics (RPP)
by the Particle Data Group [148]. were discovered at the $B$ factories. Since
then many new hadron resonances or resonant structures were discovered at
various experiments all over the world. In particular, most of them contain at
least one heavy (charm or bottom) quark, and have properties at odd with
expectations from quark model. The meson states discovered in the heavy-
quarkonium mass region are called $XYZ$ states, see Table 2.2 for a list.
Notable examples include the $X(3872)$, $Z_{c}(3900)$, $Z_{c}(4020)$ and
others. In 2015 and 2019, the LHCb Collaboration discovered pentaquark
candidates with hidden charm, $P_{c}(4312)$, $P_{c}(4440)$ and $P_{c}(4457)$.
The charged heavy-quarkonium like $Z_{c}$ and $Z_{b}$ states as well as these
$P_{c}$ states are clearly beyond the scope of the conventional quark model
for mesons and baryons, and thus excellent candidates of exotic multiquark
states. Understanding the nature of these structures has been the main concern
for hadron spectroscopy, and is a challenge that needs to be solved toward
revealing the mystery of how massive hadrons emerge from the interaction
between quarks and gluons.

Various models were proposed to explain (some of) these observations,
including multiquark states, hadronic molecules, hybrid states, mixing of
different components and non-resonant effects such as kinematical
singularities and interference. These investigations were witnessed by a large
number of review articles in the past few years, see Refs. [149, 150, 151,
152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166,
167, 168, 169, 29, 148] emphasizing on various aspects of these new resonant
structures. Many of the observed structures need to be confirmed by other
experiments, and most of the theoretical models also predicted light-flavor
and/or heavy-quark partner states of the observed ones. Thus, in order to
understand the pattern behind the messy spectrum of these new hadrons and to
be able to classify them into a clear picture, which can in turn give
important hints towards understanding the confinement mechanism, more
experimental measurements are urgently needed.

####  2.4.1 Status of hidden-charm and hidden-bottom hadron spectrum

Figure 2.18:  Comparison of the mass spectra of the observed heavy quarkonia
and quarkonium-like states [148] with those predicted by the Godfrey–Isgur
quark model [26, 170]. The states are listed according to their quantum
numbers $I^{G}(J^{PC})$. The states with quantum numbers not fully determined
are listed in the column “$?^{??}$” with the exception of $\Upsilon(10753)$
which is listed in the $0^{-}(1^{--})$ bottomonium column though its $I^{G}$
have not been fixed. For the experimentally observed states, the shaded areas
indicate the central values of the widths of the observed states. Table 2.2:
Structures observed experimentally since 2003 in the charmonium mass region
and their production and decay processes. We group the mesonic structures into
three blocks: those with $PC=--$ quantum numbers are given in the second
block; the isospin-1 structures are given in the third block; the others are
given in the first block. Their quantum numbers can be found in Fig. 2.18. The
exotic baryon candidates are listed in the fourth block. Here we use the
nomenclature of RPP [148], according to which states are named according to
their quantum numbers. For more information of the $XYZ$ states and their
properties and the original experimental references, see Ref. [148].

$XYZ$ | Production processes | Decay channels
---|---|---
$\chi_{c0}(3860)$ |  $e^{+}e^{-}\rightarrow J/\psi X$, $\gamma\gamma\rightarrow X$a |  $D\bar{D}$, $\gamma\gamma$a
$\chi_{c1}(3872)$ |  $B\rightarrow KX/K\pi X,e^{+}e^{-}\rightarrow\gamma X$, | $\pi^{+}\pi^{-}J/\psi,\omega J/\psi,D^{*0}\bar{D}^{0},D^{0}\bar{D}^{0}\pi^{0},$
|  $pp/p\bar{p}$ semi-inclusive, | $\pi^{0}\chi_{c1},\gamma J/\psi,\gamma\psi(2S)$
|  $\gamma^{*}N\rightarrow X\pi^{\pm}N$b |
$X(3915)$ | $B\rightarrow KX,\,\gamma\gamma\rightarrow X,e^{+}e^{-}\rightarrow\gamma X$ | $\omega J/\psi,\gamma\gamma$
$\chi_{c2}(3930)$ |  $\gamma\gamma\rightarrow X$, $pp$ semi-inclusive | $D\bar{D},\gamma\gamma$
$X(3940)$ | $e^{+}e^{-}\rightarrow J/\psi+X$ | $D{\bar{D}}^{*}$
$\chi_{c1}(4140)$ |  $B\rightarrow KX$, $p\bar{p}$ semi-inclusivec | $\phi J/\psi$
$X(4160)$ | $e^{+}e^{-}\rightarrow J/\psi+X$ | $D^{*}{\bar{D}}^{*}$
$\chi_{c1}(4274)$ | $B\rightarrow KX$ | $\phi J/\psi$
$X(4350)$ | $\gamma\gamma\rightarrow X$ | $\phi J/\psi,\gamma\gamma$
$\chi_{c0}(4500)$ | $B\rightarrow KX$ | $\phi J/\psi$
$\chi_{c0}(4700)$ | $B\rightarrow KX$ | $\phi J/\psi$
$\psi_{2}(3823)$ | $B\rightarrow K\psi_{2},e^{+}e^{-}\rightarrow\pi\pi\psi_{2}$ | $\gamma\chi_{c1}$
$\psi_{3}(3842)$ |  $pp$ semi-inclusive | $D\bar{D}$
$\psi(4230/4260)$ | $e^{+}e^{-}\rightarrow Y,e^{+}e^{-}\rightarrow Y\gamma_{\rm ISR}$ | $\pi\pi J/\psi,\pi\pi\psi(2S),\chi_{c0}\omega,h_{c}\pi\pi,$
|  | $D\bar{D}^{*}\pi,\gamma\chi_{c1}(3872),J/\psi K\bar{K}$
$\psi(4360)$ | $e^{+}e^{-}\rightarrow Y,e^{+}e^{-}\rightarrow Y\gamma_{\rm ISR}$ |  $\pi\pi\psi(2S)$, $\pi\pi\psi_{2}(3823)$d, $D_{1}(2420)\bar{D}$d
$\psi(4390)$ | $e^{+}e^{-}\rightarrow Y$ |  $\pi\pi h_{c},\pi\pi\psi(3770)$d
$\psi(4660)$ | $e^{+}e^{-}\rightarrow Y\gamma_{\rm ISR}$ | $\pi\pi\psi(2S),\Lambda_{c}\bar{\Lambda}_{c},D_{s}^{+}D_{s1}(2536)^{-}$
$Z_{c}(3900)^{\pm}$ | $e^{+}e^{-}\rightarrow\pi Z_{c},$ | $\pi J/\psi,D\bar{D}^{*}$
|  $b$-hadron semi-inclusive decays |
$X(4020)^{\pm}$ | $e^{+}e^{-}\rightarrow\pi Z_{c}$ | $\pi h_{c},D^{*}\bar{D}^{*}$
$X(4050)^{\pm}$ | $B\rightarrow KZ_{c}$ | $\pi^{\pm}\chi_{c1}$
$X(4055)^{\pm}$ | $e^{+}e^{-}\rightarrow\pi X$ | $\pi^{\pm}\psi(2S)$
$X(4100)^{\pm}$ | $B\rightarrow KZ_{c}$ | $\pi^{\pm}\eta_{c}$
$Z_{c}(4200)^{\pm}$ | $B\rightarrow KZ_{c}$ | $\pi^{\pm}J/\psi$
$R_{c0}(4240)^{-}$ | $B\rightarrow KR_{c0}$ | $\pi^{-}\psi(2S)$
$X(4250)^{\pm}$ | $B\rightarrow KZ_{c}$ | $\pi^{\pm}\chi_{c1}$
$Z_{c}(4430)^{\pm}$ | $B\rightarrow KZ_{c}$ | $\pi^{\pm}J/\psi,\pi^{\pm}\psi(2S)$
$P_{c}(4312)^{+}$ |  $\Lambda_{b}\rightarrow K^{-}P_{c}$e | $pJ/\psi$
$P_{c}(4380)^{+}$ | $\Lambda_{b}\rightarrow K^{-}P_{c}$ | $pJ/\psi$
$P_{c}(4440)^{+}$ | $\Lambda_{b}\rightarrow K^{-}P_{c}$ | $pJ/\psi$
$P_{c}(4457)^{+}$ | $\Lambda_{b}\rightarrow K^{-}P_{c}$ | $pJ/\psi$

  * a

From the analysis of Ref. [171]. b It is likely a different state. It was
reported by the COMPASS Collaboration in muoproduction [172]; however, the
$\pi\pi$ invariant mass spectrum does not agree with that coming from a
$\rho$, and a negative $C$-parity is preferred. c Not seen in
$\gamma\gamma\rightarrow J/\psi\phi$ and $e^{+}e^{-}\rightarrow\gamma
J/\psi\phi$. d Noted as “possibly seen” in RPP. e No signal of $P_{c}$ was
seen in $\gamma p\rightarrow J/\psi p$ [173].

In Fig. 2.18, we show the spectrum of the charmonium(-like) and
bottomonium(-like) states listed in RPP [148]. The hidden-charm structures
that were reported in various experiments since 2003 are also listed in Table
2.2, together with their production processes and observed decay channels. The
nomenclature of the latest RPP is used in the figure and table and will be
used in the following discussion.

One sees that the charmonium-like structures were observed mainly in three
types of processes, and many of them were only seen in one particular
production process as well as in only one particular final state. Thus, one
immediate question is whether they can be found in other processes and, in
particular, in other types of experiments such as the electron-
proton/electron-ion collisions. Let us first discuss the experiments that have
already significantly contributed to the field.

Weak decays of the ground state bottom-hadrons contributed to the observation
of hidden-charm states more than other processes. The decays happen mainly via
the singly-CKM suppressed $b\rightarrow c\bar{c}s$ at the quark level. The
main experiments are the $B$ factories Belle, BaBar and the LHCb experiment at
LHC. There are two main processes. First, the three-body decays of $B$ mesons
with the final state being a kaon and a pair of charmed mesons or a charmonium
and light mesons. The maximal mass of a charmonium-like state that can be
produced in this way is the mass difference between the $B$ and $K$ mesons,
which is about 4.8 GeV. In fact, the highest charmonium-like structure
reported so far is the $X(4700)$ observed by the LHCb Collaboration [174],
close to this bound. Second, the three-body decays of the $\Lambda_{b}$, such
as the $\Lambda_{b}^{0}\rightarrow J/\psi pK^{-}$, which is the process where
the hidden-charm pentaquark candidates $P_{c}(4312)$, $P_{c}(4380)$,
$P_{c}(4440)$ and $P_{c}(4457)$ were discovered at LHCb [175, 176]. The
hidden-charm pentaquark state that can be produced through such a process
needs to have a mass lower than the mass difference between $\Lambda_{b}$ and
$K$, which is about 5.1 GeV. For these weak decay processes, the mass of the
initial particle is fixed. Furthermore, the final states always involve at
least three particles, which complicates the data analysis and may bring
ambiguities due to insufficient treatment of cross channels and three-body
final state interaction.

Vector charmonium(-like) states are mostly easily studied in $e^{+}e^{-}$
collisions. They have the same $J^{PC}$ quantum numbers as a virtual photon so
that they can be directly produced in $e^{+}e^{-}$ collisions; by emitting a
photon to adjust the energy to the interested region, they can also be
produced using the initial-state radiation (ISR) process, whose cross section,
however, is smaller by two orders of magnitude because of the suppression of
$\alpha$. The main experiments include BESIII, CLEO-c, Belle and BaBar. Thus,
more vector states have been observed than other quantum numbers, and they are
normally observed in more channels as well due to the high luminosity of the
$e^{+}e^{-}$ machines. There is also one new vector state in the bottomonium
mass region, the $\Upsilon(10753)$, reported by Belle [177]. The structures
with other quantum numbers need to be produced through the decays of higher
states or two-photon collisions, and thus have much smaller production rates
or beyond the energy reach of BESIII.

Some of the structures were also produced in the prompt production processes
at hadron colliders, and observed semi-inclusively. The main experiments are
CDF and D0 at Tevatron and CMS, ATLAS and LHCb at the LHC. Such processes have
much larger cross sections than those via virtual photons. However, the large
energy and large strong-interaction cross sections also imply huge
backgrounds, which lowers the detection efficiency. The types of final state
particles that can be efficiently detected are usually restricted to charged
light hadrons and muons, and soft photons are hardly detected.

####  2.4.2 Exotic hadrons at EicC

For the study of exotic hadrons, each of the experiments has its advantages
and limitations. Different kinds of experiments complement to one another, and
they are needed to establish a more complete picture of the heavy-flavor
hadron spectroscopy. Even in the charm sector, the so-far collected
information is not enough to build up a clear picture for all of these new
structures. Furthermore, although it is expected that there should be
analogues of resonances with open or hidden charm in the bottom sector, far
fewer states with bottom have been observed due to the limitations of the
current experiments. Let us take heavy quarkonia as an example.

In Fig. 2.18, we present a comparison of the observed heavy quarkonia and
quarkonium-like states with the predictions of the $Q\bar{Q}$ mass spectrum
predicted in the Godfrey–Isgur quark model [26, 170]. It is clear that all of
the $XYZ$ structures are located above or at least very close to the open-
charm thresholds, while there are only a couple of analogous states in the
bottomonium sector. The messy situation of the charmonium(-like) states nicely
illustrates how little we understand the confinement aspect of QCD. Although
the importance of the open-charm coupled channels was already noticed in the
seminal Cornell model [178, 179], their role in forming the observed spectrum
is still far from being understood. The highly excited states close or above
the open-flavor thresholds contain important information about the long-
distance interaction between heavy quarks and about how the light degrees of
freedom come into play their role. Thus, a detailed study of these states is
highly valuable for understanding confinement.

Furthermore, no matter how the hidden-charm meson spectrum emerges, one would
expect to have an analogous spectrum for hidden-bottom mesons as well as in
hidden-charm and hidden-bottom baryonic sectors. Especially, if the coupled
channels are crucial to form the spectrum, phenomena similar to those of the
$XYZ$ states would repeat in these sectors.

The EicC energy region covers all these interesting physics. In the following,
let us briefly discuss a few topics on heavy-flavor hadron spectroscopy that
EicC can significantly contribute to.

Figure 2.19: The dependence of the photoproduction cross sections on the
$\gamma p$ c.m. energy for the exclusive $\gamma p\rightarrow J/\psi p$ and
semi-inclusive $\gamma p\rightarrow c\bar{c}X$ processes. [180, 181, 182, 183,
184, 185, 186, 173, 187, 188, 189, 190]. The EicC energy coverage is denoted
by the shaded area. Here, $X$ denotes the all particles that are not detected
and should not be confused with the $X$ charmonium-like states.

  * •

Charmonium(-like) states

The photoproduction cross section of the exclusive process $\gamma
p\rightarrow J/\psi p$ is at the order of 10 nb for the c.m. energy of the
$\gamma p$ within 10 to 20 GeV, which is the energy region of EicC. The cross
section of the semi-inclusive production of $c\bar{c}X$ is larger by almost
two orders of magnitude, see Fig. 2.19. The data shown in this figure include
the exclusive $J/\psi$ production data from Refs. [180, 181, 182, 183, 184,
185, 186] ($J/\psi p$ data before 2002), [173] (GlueX), and the semi-inclusive
$c\bar{c}X$ data from Refs. [187] (CIF), [188] (Fermilab), [189] (EMC), and
[190] (SLAC). The data were fitted using parametrization origined from the
vector-meson dominance model of Ref. [191]. The cross section for the
electroproduction process is about two orders of magnitude smaller due to an
additional factor of electromagnetic coupling $\alpha$. Considering an
integrated luminosity of 50 fb-1, one may estimate that the $J/\psi$ events
produced from the exclusive process is about $\mathcal{O}(5\times 10^{6})$.
Because almost all excited charmed mesons (baryons) will decay into $D$
($\Lambda_{c}$) and their antiparticles, one can expect that there must be
many more $D$ and $\Lambda_{c}$ events. Therefore, in addition to the hidden-
charm channels, the $XYZ$ charmonium-like states, including the highly excited
ones beyond the capability of BESIII and JLab or those that cannot be produced
through the $B$ meson decays, can be studied through open-channel final
states. As a benchmark, the production of the $\chi_{c1}(3872)$ and
$Z_{c}(3900)$ are simulated and will be discussed in Section 2.4.3.

  * •

Hidden-charm pentaquarks

So far, the only observations of hidden-charm pentaquarks came from LHCb:
$P_{c}(4312)$, $P_{c}(4380)$, $P_{c}(4440)$ and $P_{c}(4457)$ [175,
176].333The $P_{c}(4380)$ here is a broad structure introduced to improve the
fitting quality in the 2015 LHCb analysis [175], and it is not needed to fit
the updated $J/\psi p$ invariant mass distribution [176]. However, there is a
hint for the existence of a narrow $P_{c}(4380)$ [192] in the new LHCb data.
In fact, the existence of narrow hidden-charm baryon resonances, as hadronic
molecules of a pair of charm meson and charm baryon, have been predicted to
exist in the mass region above 4 GeV [193, 194, 195, 196, 197, 198, 199]. As
mentioned above, similar to the existence of many hidden-charm $XYZ$ states,
there should also be lots of hidden-charm baryonic excited states. Searching
for them and verifying the LHCb observations will provide valuable inputs to
understanding the spectroscopy of excited hadrons. The nonobservation of the
$P_{c}$ states at the GlueX experiment [173] indicates that the branching
fractions of the $P_{c}$ states into $J/\psi p$ to be small (for a combined
analysis of the GlueX and LHCb measurements, see Ref. [200]). Then the
dominant decay modes of the $P_{c}$ should be the open-charm channels,
including the $\bar{D}^{(*)}\Lambda_{c}$ and $\bar{D}^{(*)}\Sigma_{c}$ [201,
202, 192, 203]. Therefore, at EicC, the $P_{c}$ need to be searched for in
exclusive processes with the final states being not only the $J/\psi N$, but
also the open-charm $\bar{D}^{(*)}\Lambda_{c}$ and $\bar{D}^{(*)}\Sigma_{c}$
channels [204, 205]. Semi-inclusive processes of these processes will also be
a crucial part as they have much larger cross sections. Pentaquarks with both
hidden charm and hidden (or open) strangeness can also be searched for in
analogous processes. For an estimate of the semi-inclusive production rates in
the hadronic molecular model of the $P_{c}$ states, see the next subsection.

From the above discussions, one sees that an efficient detection of the
$D/\bar{D}$ and $\Lambda_{c}$ particles is essential for the study of the
hidden-charm mesons and baryons. From RPP [148], one finds that the most
important decay channels of the $D^{+}$ are $K^{-}2\pi^{+}$ [$(9.38\pm
0.16)\%$] and $K_{S}^{0}\pi^{+}\pi^{0}$ [$(7.36\pm 0.21)\%$], those for the
$D^{0}$ are $K^{-}\pi^{+}\pi^{0}$ [$(14.4\pm 0.5)\%$] and $K^{-}\pi^{+}$
[$(3.950\pm 0.031)\%$], and those for the $\Lambda_{c}^{+}$ are
$\Lambda\pi^{+}\pi^{0}$ [$(7.1\pm 0.4)\%$] and $pK^{-}\pi^{+}$ [$(6.28\pm
0.32)\%$]. Thus, both the charged and neutral pions and kaons need to be
efficiently detected. Once one of the open-charm final state particles is
reconstructed, the events for the other one can be selected from the missing
mass spectrum in the relevant energy region. In this way, searching for
hidden-charm states in the open-charm final states is promising.

  * •

Bottom hadrons

Figure 2.20: The dependence of the photoproduction cross sections on the
$\gamma p$ c.m. energy for the exclusive $\gamma p\rightarrow\Upsilon p$ and
semi-inclusive $\gamma p\rightarrow b\bar{b}X$ processes. The EicC energy
coverage is denoted by the shaded area.

In Fig. 2.20, we show the cross sections for the exclusive photoproduction of
the $\Upsilon$ and for the semi-inclusive $b\bar{b}$. The shaded area in
corresponding to the EicC energy region covers the hidden-bottom hadron
masses. The exclusive data are taken from Refs. [206, 207] (ZEUS), [185] (H1),
and [208] (CMS); the semi-inclusive data are taken from Refs. [209] (EMC) and
[210] (H1). The models used to fit the data include the empirical formula for
the deeply-virtual meson production (DVMP) model [211] (Favart et al.), the
2-gluon exchange model [212] (Brodsky et al.), the parametrization [191]
(Gryniuk et al.), and the dipole Pomeron model ($Q^{2}=$0, 10, 50 GeV2) [213,
214] (Martynov et al.). One sees that for the c.m. energy in the range between
15 and 20 GeV, the photoproduction cross section for $\Upsilon p$ is of
$\mathcal{O}(10~{}\text{pb})$; thus, the corresponding electroproduction
$e^{-}p\rightarrow e^{-}\Upsilon p$ cross section should be of
$\mathcal{O}(0.1~{}\text{pb})$. Considering an integrated luminosity of 50
fb-1, the event number of $\Upsilon$ that can be produced through the
exclusive $\Upsilon p$ process is of $\mathcal{O}(10^{4})$, consistent with
the simulation in Sec. 2.5.1 and the estimate in Ref. [215]. The cross section
for the semi-inclusive $b\bar{b}+\text{anything}$ is two orders of magnitude
higher. Thus, millions of bottom mesons $B$ and $\Lambda_{b}$ can be produced.
If these bottom hadrons can be efficiently detected, the EicC will be able to
contribute to the study of excited bottom hadrons. Although the ground state
bottom hadrons are more difficult to be detected than their charmed cousins,
their life times are much longer, making the secondary decay vertices useful
in detecting them. Hidden-bottom pentaquark states that are expected to be
decay into $\Upsilon N$, $\Lambda_{b}B^{(*)}$ and $\Sigma_{b}B^{(*)}$ final
states may also be searched for in processes similar to those for the
searching of the $P_{c}$ states.

Next, let us briefly discuss the advantages of EicC in the study of hadron
spectroscopy. Comparing with experiments utilizing electron-positron
collisions and the $B/\Lambda_{b}$ decays, one special feature of the EicC is
that it has different kinematics which can avoid the ambiguity of interpreting
resonance signals induced by the so-called triangle singularity. Triangle
singularity is a type of kinematical singularity, which occurs because of the
simultaneous on-shellness of three intermediate particles, and can produce
peaks mimicking the behavior of resonances (for a recent review, see Ref.
[29]). For instance, the triangle singularity mechanism have been constructed