Electron-Ion Collider in China
Daniele P. Anderle, Valerio Bertone, Xu Cao, Lei Chang, Ningbo Chang, Gu Chen, Xurong Chen, Zhuojun Chen, Zhufang Cui, Lingyun Dai, Weitian Deng, Minghui Ding, Xu Feng, Chang Gong, Longcheng Gui, Feng-Kun Guo, Chengdong Han, Jun He, Tie-Jiun Hou, Hongxia Huang, Yin Huang, Krešimir Kumeri?ki, L. P. Kaptari, Demin Li, Hengne Li, Minxiang Li, Xueqian Li, Yutie Liang, Zuotang Liang, Chen Liu, Chuan Liu, Guoming Liu, Jie Liu, Liuming Liu, Xiang Liu, Tianbo Liu, Xiaofeng Luo, Zhun Lyu, Boqiang Ma, Fu Ma, Jianping Ma, Yugang Ma, Lijun Mao, Cédric Mezrag, Hervé Moutarde, Jialun Ping, Sixue Qin, Hang Ren, Craig D. Roberts, Juan Rojo, Guodong Shen, Chao Shi, Qintao Song, Hao Sun, Pawe? Sznajder, Enke Wang, Fan Wang, Qian Wang, Rong Wang, Ruiru Wang, Taofeng Wang, Wei Wang, Xiaoyu Wang, Xiaoyun Wang, Jiajun Wu, Xinggang Wu, Lei Xia, Bowen Xiao, Guoqing Xiao, Ju-Jun Xie, Yaping Xie, Hongxi Xing, Hushan Xu, Nu Xu, Shusheng Xu, Mengshi Yan, Wenbiao Yan, Wencheng Yan, Xinhu Yan, Jiancheng Yang, Yi-Bo Yang, Zhi Yang, Deliang Yao, Peilin Yin, C.-P. Yuan, Wenlong Zhan, Jianhui Zhang, Jinlong Zhang, Pengming Zhang, Chao-Hsi Chang, Zhenyu Zhang, Hongwei Zhao, Kuang-Ta Chao, Qiang Zhao, Yuxiang Zhao, Zhengguo Zhao, Liang Zheng, Jian Zhou, Xiang Zhou, Xiaorong Zhou, et al. (2 additional authors not shown)
EElectron-Ion Collider in China
February 19, 2021 a r X i v : . [ nu c l - e x ] F e b Daniele P. ANDERLE , Valerio BERTONE , Xu CAO , Lei CHANG , Ningbo CHANG ,Gu CHEN , Xurong CHEN , Zhuojun CHEN , Zhufang CUI , Lingyun DAI , WeitianDENG , Minghui DING , Xu FENG , Chang GONG , Longcheng GUI , Feng-KunGUO , Chengdong HAN , Jun HE , Tie-Jiun HOU , Hongxia HUANG , YinHUANG , Krešimir KUMERIČKI , L. P. KAPTARI , Demin LI , Hengne LI , MinxiangLI , Xueqian LI , Yutie LIANG , Zuotang LIANG , Chen LIU , Chuan LIU , GuomingLIU , Jie LIU , Liuming LIU , Xiang LIU , Tianbo LIU , Xiaofeng LUO , Zhun LYU ,Boqiang MA , Fu MA , Jianping MA , Yugang MA , Lijun MAO , CédricMEZRAG , Hervé MOUTARDE , Jialun PING , Sixue QIN , Hang REN , Craig D.ROBERTS , Juan ROJO , Guodong SHEN , Chao SHI , Qintao SONG , Hao SUN ,Paweł SZNAJDER , Enke WANG , Fan WANG , Qian WANG , Rong WANG , RuiruWANG , Taofeng WANG , Wei WANG , Xiaoyu WANG , Xiaoyun WANG , JiajunWU , Xinggang WU , Lei XIA , Bowen XIAO , Guoqing XIAO , Ju-Jun XIE ,Yaping XIE , Hongxi XING , Hushan XU , Nu XU , Shusheng XU , Mengshi YAN ,Wenbiao YAN , Wencheng YAN , Xinhu YAN , Jiancheng YANG , Yi-Bo YANG , ZhiYANG , Deliang YAO , Peilin YIN , C.-P. YUAN , Wenlong ZHAN , Jianhui ZHANG ,Jinlong ZHANG , Pengming ZHANG , Chao-Hsi CHANG , Zhenyu ZHANG , HongweiZHAO , Kuang-Ta CHAO , Qiang ZHAO , Yuxiang ZHAO , Zhengguo ZHAO , LiangZHENG , Jian ZHOU , Xiang ZHOU , Xiaorong ZHOU , Bingsong ZOU ,LipingZOU Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, SouthChina Normal University, Guangzhou 510006, China IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China University of Chinese Academy of Sciences, Beijing 100049, China Nankai University, Tianjin 300071, China Xinyang Normal University, Xinyang 464000, China School of Physics and Materials Science, Guangzhou University, Guangzhou 510006, China Hunan University, Changsha 410082, China Nanjing University, Nanjing 210093, China Huazhong University of Science and Technology, Wuhan 430074, China European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*) andFondazione Bruno Kessler, Villa Tambosi, Strada delle Tabarelle 286, I-38123 Villazzano(TN), Italy School of Physics, Peking University, Beijing 100871, China Hunan Normal University, Changsha 410081, China Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China Nanjing normal university, Nanjing 210023, China Department of Physics, College of Sciences, Northeastern University, Shenyang 110819,
China Southwest Jiaotong University, Chengdu 610000, China Department of Physics, Faculty of Science, University of Zagreb, Bijenička c. 32, 10000Zagreb, Croatia Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna141980, Russia School of Physics and Microelectronics, Zhengzhou University, Zhengzhou 450001, China Lanzhou university, Lanzhou 730000, China Key laboratory of particle physics and particle irradiation (MOE), Shandong University,Qingdao 266237, China Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, CentralChina Normal University, Wuhan 430079, China School of Physics, Southeast University, Nanjing 211189, China Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Institute of ModernPhysics, Fudan University, Shanghai 200433, China Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800,China Department of Physics, Chongqing University, Chongqing 401331, China Department of Physics and Astronomy, Vrije Universiteit Amsterdam, De Boelelaan 10811081HV Amsterdam, The Netherlands Nikhef Theory Group Science Park 105, 1098 XG Amsterdam, The Netherlands Department of nuclear science and technology, Nanjing University of Aeronautics andAstronautics, Nanjing 211106, China Dalian University of Technology, Dalian 116024, China National Centre for Nuclear Research (NCBJ), Pasteura 7, 02-093 Warsaw, Poland School of Physics, Beihang University, Beijing 100191, China Shanghai Jiao Tong University, Shanghai 200240, China Lanzhou University of Technology, Lanzhou 730050, China University of Science and Technology of China, Hefei 100190, China School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen518172, China School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023,China Huangshan University, Huangshan 245021, China School of Physics, University of Electronic Science and Technology of China, Chengdu610054, China Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824,USA Center of Advanced Quantum Studies, Department of Physics,Beijing Normal University,
Beijing 100875, China School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, China School of Physics and Technology, Wuhan University, Wuhan 430072, China Institute of High Energy Physics and Theoretical Physics Center for Science Facilities,Chinese Academy of Sciences, Beijing 100049, China School of Mathematics and Physics, China University of Geosciences (Wuhan), Wuhan430074, China
Abstract
Lepton scattering is an established ideal tool for studying inner structure of small par-ticles 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 basedon an upgraded heavy-ion accelerator, High Intensity heavy-ion Accelerator Facility(HIAF) which is currently under construction, together with a new electron ring. Theproposed collider will provide highly polarized electrons (with a polarization of ∼ ∼ × cm − s − . Polarized deuterons andHelium-3, as well as unpolarized ion beams from Carbon to Uranium, will be alsoavailable at the EicC.The main foci of the EicC will be precision measurements of the structure of thenucleon in the sea quark region, including 3D tomography of nucleon; the partonic struc-ture 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 un-derstanding the origin of mass could be addressed by measurements of heavy quarkonianear-threshold production at the EicC. In order to achieve the above-mentioned physicsgoals, a hermetical detector system will be constructed with cutting-edge technologies.This document is the result of collective contributions and valuable inputs fromexperts across the globe. The EicC physics program complements the ongoing scientificprograms 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 wellas accelerator and detector technology in China. ontents ONTENTS –3/140– hapter 1 Executive summary
The study on the inner structure of matter and fundamental laws of interactions hasalways been one of the research forefronts of natural science. It not only allows mankindto understand the underlying laws of nature, but also promotes various advances intechnologies. 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 visiblematerial. Little is known about the first two: science can currently say almost nothingabout 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 describedwithin the Standard Model.
Figure 1.1:
The mass-energy budget of the Universe determined by Wilkinson MicrowaveAnisotropy Probe (WMAP) [1].
One of the greatest achievements of physics in the 20th century is the invention of theStandard 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 andleptons in nature. The forces in the Standard Model are carried by the so-called forcemediating gauge bosons, which are 𝛾 , 𝑊 ± and 𝑍 for electro-weak interaction, andgluons 𝑔 for the strong interaction. The Higgs boson H was introduced in the famousHiggs mechanism [8, 9] to explain the mass origin of the 𝑊 ± and 𝑍 bosons, and it alsogenerates the masses of quarks and leptons. Yet, amongst the visible matter, less-than0.1% is tied directly to the Higgs boson; hence, even concerning visible matter, too muchremains unknown. .1 Physics highlights –5/140– 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 visiblematter. First, about 99% of the visible mass is contained within nuclei [10]. WithinStandard Model, the protons and neutrons in nuclei are composite particles, built fromnearly massless quarks ( ∼
1% of the nucleon mass) and massless gluons. An immediatequestion then arises: How does 99% of the nucleon mass emerge? Besides the massissue, despite of many years of theoretical and experimental efforts, the quantitativedecomposition of nucleon spin in terms of quark and gluon degrees of freedom is notyet fully understood. To address these fundamental issues, we have to understand thenature of the subatomic force between quarks and gluons, and the internal landscape ofnucleons.The underlying theory, which describes the strong interactions between quarks andgluons, is known as Quantum Chromodynamics (QCD) [11]. As a non-Abelian gaugetheory, 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 isweak in hard scatterings with large momentum transfers. On the other hand, it has to beincredibly strong to bind quarks together within the tiny space of a nucleon. Confinementis crucial because it ensures stability of the proton. Without confinement, protons inisolation could decay; the hydrogen atom would be unstable; nucleosynthesis would beaccidental, with no lasting consequences; and without nuclei, there would be no livingUniverse. 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 ofquark and gluon degrees of freedom. Specifically, it is believed that the nucleon masscan be almost entirely derived from the kinetic energy of quarks and gluons, interactionsbetween them, as well as other novel dynamical effects of QCD. Similarly, despite beingcomposite particles, nucleons have a constant spin of 1 / .1 Physics highlights –6/140– In the following, a few highlighted physics topics, highly relevant to above mentionedessential QCD physics, that EicC can significantly contribute to will be discussed briefly.For the detailed discussions regarding physics, accelerators, and detectors for the EicCproject, please refer to the following chapters of this document . Figure 1.2:
The Standard Model of elementary particles.
In the naiive constituent quark model [14, 15], nucleons are considered as the boundstates 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 quantumproperty of QCD, quarks can radiate gluons, and these gluons, in turn, can fluctuate intoquark-antiquark pairs. Therefore, a nucleon is a composite object containing quarks,antiquarks, and gluons. Besides valence quarks (and possible intrinsic quarks), there arealso sea quarks coming out of quantum fluctuations. Especially, when the probing scalebecomes smaller as the energy scale goes higher, one sees more sea quarks comparingto valence quarks, as illustrated in Fig. 1.3. Moreover, compared to the simple picture By default, the natural unit system is used in all the physics discussions and plots. .1 Physics highlights –7/140– of the constituent quark model, the underlying dynamics among quarks/gluons is a lotmore interesting and intricate, and offers much more important information regardingthe 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 quarksand gluons, which are collectively referred to as partons. The probability distributionsof partons within the proton are called the parton distribution functions (PDFs). Ingeneral, PDFs give the probabilities of finding partons (quarks and gluons) in a hadronas a function of the momentum fraction 𝑥 w.r.t. the parent hadron carried by thepartons. Due to the QCD evolution, quarks and gluons can mix with each other, andtheir PDFs depend on the resolution scale. When the resolution scale increases, thenumbers of partons and their momentum distributions will change according to theevolution equations. These evolution equations can be derived from the perturbationQCD, although PDFs themselves are essentially non-perturbative objects. Thanks toQCD factorization theorems, PDFs can be extracted from measurments of cross-sectionsand 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 andthey do not participate in the strong interaction, they are the perfect probe for studying theinternal structure of hadrons in high energy scatterings. Therefore, the DIS experimentis also known as the “Modern Rutherford Scattering Experiment”, which opens up anew window to probe the subatomic world. In 1969, the pioneer DIS experiments atSLAC discovered the so-called Bjorken scaling [16], which showed that the proton iscomposed of point-like partons with spin 1 / .1 Physics highlights –8/140– the violation of Bjorken scaling [17], which indicates the existence of gluon and QCDevolution mentioned above. All these results across a wide range of energy scales haveverified that QCD is the correct theory for the strong interaction between quarks andgluons within hadrons. In addition, within the current experimental accuracy, leptonand quark are still point-like particles at the scale of 10 − fm, which is one-thousandthof the size of the proton.With better experimental precisions, our understanding of nucleon structure contin-ues to improve even in unpolarized PDFs. Furthermore, many interesting phenomena,such as the isospin asymmetry of ¯ 𝑢 and ¯ 𝑑 quark distributions and the asymmetry be-tween strange and anti-strange quark distributions in the proton, were discovered. Thesephenomena 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 thenucleon spin structure became possible by exploring the helicity distributions of quarksand gluons, also defined as the longitudinally polarized PDFs analog to their unpolarizedcounterparts discussed above, from high-energy scattering processes involving polarizedleptons and/or polarized nucleons. A lot more interesting phenomena have been unrav-eled 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 onlya small fraction of the total spin of a proton. It triggered a series of experimental andtheoretical 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 momentaof quarks and gluons. Currently, except the quark spin contribution, other decomposedcontributions in the spin sum rule, especially the ones from orbital angular momenta, arelargely unexplored. Through semi-inclusive DIS and other interesting processes, recentexperimental and theoretical developments have enabled us to extend our research onnucleon structure from one-dimensional PDFs to three-dimensional imaging. Thesehave been providing us new insights into the proton spin puzzle.Currently, there are two immediate and important issues in the research frontier ofnucleon structure: 1) The precision measurement of the one-dimensional spin structureof the polarized nucleon; 2) The study on the three-dimensional imaging of the partonicstructure of the nucleon.An interesting question when studying the one-dimensional spin structure of thenucleons is how to clearly decompose the individual contributions from different quarkflavors. Despite the large uncertainty, the recent measurement at Relativistic Heavy IonCollider (RHIC) implies that the sea quark helicity distributions also have flavor asym-metries. Furthermore, the polarized quark distribution of different flavors, especially forsea quarks, still have large uncertainties. This directly imposes a challenge to our efforts .1 Physics highlights –9/140– to understand the proton spin structure. Therefore, the precise determination of variousquark 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 lotof attention as well. By additionally measuring the transverse momentum and angulardistribution of the final hadron in DIS, one can extract important information about initialtransverse momentum distributions of partons in the incoming nucleon, thus explore theinternal three-dimensional structure of the nucleon in the momentum space. Meanwhile,through some exclusive processes, in which all the particles are measured, one canaccess the three-dimensional spatial distributions of partons. In general, the internalthree-dimensional structure of the nucleon in the momentum and coordinate space canbe 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 muchmore abundant information about the internal structure of the nucleon. For example, theycan allow us to access the orbital angular momenta of partons and the quantum effectof multi-parton correlations. Future experimental efforts, especially the high precisionmeasurements, can certainly have a profound impact on the theoretical development ofTMD and GPD physics.EicC, together with existing experiments at Jefferson Lab, CERN COMPASS, BNLRHIC, Fermi-Lab, and the proposed EIC in the US, can offer significant insights intothe 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 interestingproperties of proton emerge from the quark and gluon degrees of freedom. One of the biggest challenges in nuclear physics is how to study the nuclear structurein the partonic level using the QCD theory that has successfully described the partonicstructure of a free nucleon. While the focus of studying partonic structure in freenucleons has been extended from the precisely known one-dimensional PDFs to thethree-dimensional distributions such as TMD and GPD, the knowledge of the partonicstructure in nuclei, however, remain largely unknown.The most outstanding reason for this gap is that the nucleons with their sizes muchsmaller 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 thenuclear structure in the nucleonic degree of freedom without introducing the partonic .1 Physics highlights –10/140– pictures. On the other hand, the partonic structure of a bounded nucleon in a heavynucleus had been naively treated as the same as one in a free nucleon, until the discoveryof the EMC effect. In the 1980s, the European Muon Collaboration (EMC) at CERN usedheavy nuclei as a high-density target to measure the PDFs. They discovered the measuredcross-sections differed from ones using free nucleons, and meanwhile, observed thesedifferences strongly depend on the nuclear numbers [18]. This lately-called EMC effecthas been further studied at SLAC, HERMES, Fermi-Lab and lately JLab [19, 20, 21, 22]in the valance quark region (0 . < 𝑥 < .
7) and the correlation with nuclear numberswere obtained. These experimental results also reveal much richer details at lower 𝑥 where anti-shadowing and shadowing effects are present. However, the physics originof how the nuclear PDFs (nPDF) are modified in nuclei is still puzzling us and no singletheoretical interpretation is satisfactory. A full understanding of the physics behind theEMC, anti-shadowing, and shadowing effects will open a door to describe the nuclearstructure in QCD. An encouraging development in the last few years was the suggestionof possible connection between the EMC effect and the short-range correlations (SRC)which describe a case when nucleons are largely overlapping and strongly interactingwith each other[23, 24, 25]. This new finding sheds a light to cover the gap betweenstudying nuclear structure in the nucleonic level and the partonic level.The EMC effect implies that the distributions of valence quarks in the nucleus aremodified. However, no existing experimental evidence suggests that the distributions ofsea 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 globaldescription of nPDFs of different quark and gluon flavors in the entire 𝑥 region for awide range of nuclei, and finally unveil the physics origin of the EMC, anti-shadowingand shading effects. A power tool in the last many decades is to utilize the high-energyelectrons 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 detectthe additional outgoing hadrons which contain the information of the initial quark orgluon, and study their semi-inclusive DIS (SIDIS) cross-sections or other observable todecouple 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-energyparticle, it will continuously interact with its surroundings via strong interaction, generateadditional quarks and gluons, and eventually "fragment" into color-neutral hadrons orjets inside the nucleus or in the vacuum. This process is called hadronization. Studyingthe hadronization process has important implications for the formation of matter and .1 Physics highlights –11/140– even the evolution of the Universe. One can perform a detailed study of the hadronizationphysics by measuring the SIDIS processes in eA collision. With a wide variety of nucleithat serve as QCD laboratories, one can control the sizes of different nuclei so that thehadronization happens at varying depth inside the nuclei or the vacuum. 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 wasable to provide an excellent description of the mass spectrum of hadrons up to a fewexceptions (see, e.g., Refs. [26, 27]). In the traditional quark model, a meson is formedby a quark and an antiquark, and a baryon is formed by three quarks. Most of thehadrons discovered in the last century can be classified into flavor multiplets in the quarkmodel. But quarks and gluons can constitute other types of hadronic objects: the so-called compact tetraquark and pentaquark states contain more than three (anti-)quarksas a single colorless cluster; hadronic molecules are bound states of hadrons formedby the mediation of the strong force, just like that the deuteron is a proton-neutronbound 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 areshown in Fig. 1.4. Such hadrons beyond the traditional quark model are collectivelycalled exotic hadron states. Although such a classification is a quark model notation, thehadron spectrum as observed presents a grand challenge to understand from QCD, andthe experimental search of exotic hadrons is one of the most important handles towardsunderstanding how the massive hadrons emerge from the underlying nonperturbativestrong interactions among quarks and gluons.Since the beginning of the 21st century, experimental study on hadron states hasmade significant progresses. Experiments such as BESIII (Beijing Spectrometer III) atBeijing Electron-Positron Collider (BEPC) in China, Belle at KEK in Japan, B A B AR atthe SLAC National Accelerator Laboratory in US, LHCb at the Large Hadron Collider(LHC) in Europe and many others have reported fascinating discoveries of candidatesof exotic hadron states. These discoveries have opened up a new exciting window inthe 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 experimentaldiscoveries, and the internal structure of these states is still a mystery to be resolved.EicC can contribute significantly in studying exotic hadron states, especially thecharmonium-like states and hidden-charm pentaquarks, which can be produced abun- .2 Polarized electron ion collider in China (EicC) –12/140– 𝑞 𝑞𝑞𝑞 𝑞 baryonmeson 𝑞𝑞 𝑞 pentaquark 𝑞 hybrid 𝑞 𝑞 𝑞 hadronic molecule glueball 𝑞𝑞 𝑞𝑞 Conventional hadrons Exotic hadrons 𝑞𝑞 𝑞𝑞 tetraquark
Figure 1.4:
Illustration of conventional and exotic hadrons. dantly. EicC has a unique place for studying their photoproduction, beyond the JLab 12GeV programme. In particular, given the existing measurements, the interpretation ofsome of the prominent candidates of hidden-charm tetraquarks and pentaquarks (eithercompact or of hadronic molecular type) is not unambiguous due to the the so-called trian-gle singularity contribution. Such singularities are due to the simultaneous on-shellnessand collinearality of all intermediate particles in a triangle diagram and are able toproduce resonance-like signals when the special kinematics required by the Coleman-Norton theorem [28] is fulfilled [29]. However, for the photoproduction processes atEicC, the production mechanism is free of such kinematics singularities. Therefore, onecan investigate the properties of pentaquark states and other hidden-charm hadrons in amore clear way. The energy coverage of EicC also allows for the seek of hidden-bottomexotic hadrons. A clearer picture of the hadron spectrum is foreseen with the inputs fromEicC.
The polarized electron ion collider in China (EicC) aims at achieving the highlightedphysics 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 nuclearphysics, atomic physics, heavy ion applications and interdisciplinary researches in China.It is designed to provide intense beams of primary and radioactive ions for a widerange of research fields. HIAF will be a scientific user facility open to researchersfrom all over the world that enables scientists with concerted effort to explore thehitherto 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 .2 Polarized electron ion collider in China (EicC) –13/140– and heavy-ion applications beneficial to the society. HIAF is located in Huizhou City ofGuangdong Province in south China. It is funded jointly by the National Developmentand Reform Commission of China, Guangdong Province, and Huizhou City. The totalinvestment is about 2.5 billion in Chinese Yuan, including about 1.5 billion Yuan fromthe central government for facility construction and 1.0 billion Yuan from the localgovernments for infrastructure. The construction is scheduled for seven years, and thebeam commissioning is planned for 2025. HIAF is a completely new facility that aseries of upgrades for EicC in the future have been taken into consideration during thedesign 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 shapedion collider ring (pRing), an electron injector as well as a racetrack electron colliderring (eRing), as shown in Fig.1.5. The center of mass energy of the EicC will rangefrom 15 GeV to 20 GeV, with the luminosity higher than 2 . × cm − s − , and theaverage proton polarization about 70%, the average electron polarization about 80% inthe collisions of electrons with protons. The integrated luminosity is higher than 50 fb − when the operating time accounts for 80% of the entire year. All these parameters cansatisfy the physics goals required. Available particles, including heavy ions, and theircorresponding energy, polarization, luminosity, and integrated luminosity are listed inTab.1.1. Polarized Ion SourceElectron Injector iLinacBRingeRing pRingIRPolarized Electron Source IP2IP1
Figure 1.5:
Accelerators in the EicC accelerator facility.
In general, the ion accelerator complex of the EicC accelerator facility mainly consistsof a polarized ion source, iLinac, BRing, and pRing, while the electron acceleratorcomplex is composed of an electron injector and eRing. Two interaction regions will beavailable. Several key accelerator designs are listed below.
Generate low emittance ion beams . Reducing the beam emittance to the one .2 Polarized electron ion collider in China (EicC) –14/140–
Table 1.1:
Available particles and their corresponding energy, polarization, luminosity andintegrated luminosity.
Particle Momentum(GeV/c/u) CM energy(GeV/u) Average Po-larization Luminosity atthe nucleon level(cm − s − ) Integratedluminosity(fb − )e 3.5 80%p 20 16.76 70% 2 . × . × He ++ . × Li + . × C + . × Ca + . × Au + . × Pb + . × U + . × required by the design specifications is of crucial importance for achieving thetargeted luminosity in the EicC accelerator facility. To this end, the scheme ofstaged electron cooling will be adopted. In the first stage, the cooling of theproton beams with low energy will be performed by a DC electron cooler in theBRing. In the second stage, the proton beam with the energy will be cooled bythe high energy bunched beam electron cooler based on an energy recovery linac(ERL). This scheme ensures optimum efficiency for the cooling system in the ionaccelerator complex of the EicC accelerator facility. Maintain and control beam polarization . The physics goals of the EicC projectput high requirements on the average polarization and the polarization direction ofthe beams. Relevant beam polarization control schemes should be made for boththe ion accelerator complex and the electron accelerator complex. Specifically,the Siberian snake, which is a control system of spin tune, will be installed to keephigh polarization in the acceleration process in the BRing, where depolarizationresonances exist. For the acceleration in the pRing, only weak solenoid magneticfields 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 beset up along the beamlines and at both sides of the interaction regions. Such adesign makes it possible to perform the rotation of beam polarization directionsarbitrarily, as well as control the polarization directions of two beams accordingly.
Optimize interaction regions (IR) . A full-acceptance detector will be built todetect and identify almost 100% of reaction products at one of two IPs while thesecond IP will be reserved for upgrading. The specifications of the detector putforwards 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 .3 Complementarity of EicC and EIC-US –15/140– between electron beams and ion beams. Such a design will not only reduce thebackground of the detector but also ensure the features of the full acceptance ofthe detector. Furthermore, the beamlines related to the forward reaction productswill 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, includingthe polarized ion source, the photocathode polarized electron gun, the high energybunched beam electron cooler based on the energy recovery linac (ERL), the Siberiansnake, the spin rotator as well as the preservation of the polarization in the figure-8shaped synchrotron. All of them will certainly provide the technical underpinnings forthe construction of the EicC accelerator facility in the future.
Both electron-ion colliders aim at the precision exploration of the partonic structureof nucleon/nucleus, but focus on different kinematics and perspectives. The designparameters and the luminosity versus center-of-mass energy of two colliders are shownin Table 1.2 and Figure 1.6, respectively. As shown in Figure 1.7, the 𝑥 - 𝑄 coverageputs 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 controlledphysics 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 majorgoals of the EIC-US focuses on the gluon helicity contribution at small- 𝑥 . EicC isoptimized to systematically explore the nucleon spin including sea quark helicitycontribution and orbital angular momentum contributions from quarks and gluonsin the moderate 𝑥 regime. The unique 𝑄 range will position EicC at a crucialplace between JLab and EIC-US to unambiguously interpret and determine theorbital angular momentum contributions, hence providing a comprehensive 3-Dimaging for the sea quarks inside a nucleon . Proton Mass Decomposition . Electroproduction and photoproduction of heavyquarkonia near threshold have been proposed to study the proton mass decomposi-tion. EicC can contribute these important physics uniquely, through systematicallyinvestigating the Υ production with high luminosity near its threshold, where theoptimal energy range of EicC is. Because of the 3 times larger mass of Υ , thephysics behind the measurement becomes much cleaner as compared to that of 𝐽 / 𝜓 production at JLab 12GeV. Because of different kinematic coverage, EicC and .3 Complementarity of EicC and EIC-US –16/140– EIC-US will be complementary to each other for Υ near-threshold production. Exotic Hadron States . Both EicC and EIC-US can contribute to understandingthe challenge posed by the unexpected
𝑋𝑌 𝑍 structures in the heavy-quarkoniummass region. The hidden-charm pentaquarks observed at LHCb need independentconfirmation, and their hidden-bottom analogues are hard to be found at LHCbut can be sought at EicC and EIC-US. The events of these states at EIC-USare expected to be more than those at EicC due to the larger energy and higherluminosity. For exclusive productions of exotic hadrons, the final state particles atEicC are within the middle rapidity range, facilitating the detection with relativelylow background.
Partonic Structure in Nuclear Environment . Nuclear modification of the struc-ture functions and hadron production in deep inelastic scattering 𝑒 𝐴 collisionsare major focuses at both EIC-US and EicC. The kinematics at EicC provide aunique perspective to investigate the details of fast parton/hadron interactions withcold nuclear matter and shed light on energy loss and hadronization mechanisms.New information on the parton distribution in nuclei can be achieved at EicC atmoderate 𝑥 , whereas EIC-US concentrates in the small- 𝑥 region. doubly polarized beams unpolarized beams
10 1000100 HERMES C O MPASS LHeCH1/ZEUS
EicC EIC ) =2GeV x (Q -3 x10 -4 -6 ) - s - Lu m i no s i t y ( c m (GeV)sCenter of Mass Energy 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 collisionswith energy 3.5 GeV (electron) +
16 GeV (proton), 3.5 GeV +
20 GeV, 5 GeV +
26 GeV,respectively. .3 Complementarity of EicC and EIC-US –17/140–
Fraction of Momentum x - - - -
10 1 ) ( G e V M o m en t u m T r an s f e r Q
100 GeV · EIC 10
20 GeV · EicC 3.5 JLab 12 GeV . < y < . G e V · E I C . < y < . G e V · E i c C . J Lab G e V Figure 1.7:
Kinematic coverage of deep inelastic scattering process for different beam energyconfigurations at two proposed electron ion colliders as well as JLab. Note that there are otherenergy 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 inChina and in the US[30].
Facility CoM energy lum./10 cm − s − Ions PolarizationEicC 15 - 20 2 - 3 𝑝 → U 𝑒 − , 𝑝 , and light nucleiEIC-US 30 - 140 2 - 15 𝑝 → U 𝑒 − , 𝑝 , He, Li hapter 2 EicC physics highlights
EicC will enable us to study the one-dimensional structure of the nucleons in variousaspects, and to a great extent help search answers to many fundamental questions con-cerning the structure of nucleons with unprecedented precision. In particular, through alarge amount of data, EicC can provide us the direct and precise information regardingthe distributions of valence quarks, sea quarks, and gluons inside nucleons in the mod-erate and large 𝑥 regime. Furthermore, it can reveal the internal landscape of nucleonsand deepen our understanding of their structure, and give us excellent opportunities forimportant discoveries in high energy nuclear physics. In addition to the physics signifi-cance by themselves, accurate parton distribution functions are extremely important forthe precision study of particle physics and the exploration of new physics at the LargeHadron Collider.How to understand the spin of protons in terms of the quark and gluon degrees offreedom has been an important cutting-edge research problem in high energy nuclearphysics. In the 1980s, the EMC collaboration[35] used a muon beam as a probe, andfound that the sum of the spin contributions of all quarks inside the proton is very smallcomparing to the spin of the proton: ΔΣ = Δ 𝑢 + Δ 𝑑 + Δ 𝑠 = ± ( 𝑠𝑡𝑎𝑡 ) ± ( 𝑠𝑦𝑠𝑡 ) %.This measurement has then precipitated the so-called “proton spin crisis" in nuclearphysics research. The current understanding of the structure of the proton spin is that thespin of proton consists of the spin contributions from quarks and gluons, and the orbitalangular 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 measurementof the sea quark spin distribution is not particularly accurate. Through the doublepolarized collision processes, the spin distribution of different flavors of sea quarkscan be precisely measured at the EicC, and elaborate experimental analysis on the spindistribution of sea quarks can be carried out, which will help to further study the spinstructure of nucleons and enrich our understanding of non-perturbative properties ofquantum chromodynamics.With its designed high luminosity, EicC can generate an enormous amount of exper-imental data, which helps to clarify some intriguing problems and phenomena observedin experiments in the past few years. The first phenomenon is the asymmetry in the distri-bution of light sea quarks. In high-precision unpolarized scattering experiments, we have .1 One-dimensional spin structure of nucleons –19/140– observed that the unpolarized ¯ 𝑢 and ¯ 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 forpolarized light sea quarks [41, 42, 43]. Moreover, the measurement of the longitudinalspin asymmetries for weak boson production in proton–proton collisions at RHIC [44]suggests a difference between the Δ ¯ 𝑢 and Δ ¯ 𝑑 helicity distributions as well. Anotherinteresting issue is the polarized distribution of the strange ( 𝑠 ) quark and its contributionto the proton spin. Assuming the 𝑆𝑈 ( ) flavor symmetry, one finds that the analysisof DIS data [45, 46] indicates that the strange quark contribution to the proton spin isroughly − .
1. It is well-known that the strange quark contribution can be directly probedby semi-inclusive DIS (SIDIS). However, in SIDIS experiments, it is difficult to distin-guish the current fragmentation process from the target fragmentation process. Also, thefragmentation function which describes the strange quark to a hadron transition processis not sufficiently precise. Due to the above-mentioned difficulties, it is still challengingto 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 itssign 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 (cid:48) , the four-momentum of a nucleonis 𝑝 , the relevant kinematic variables can be defined as: the squared e+p collision center-of-massenergy 𝑠 = ( 𝑝 + 𝑘 ) , the squared momentum transfer of the electron 𝑄 = − 𝑞 = −( 𝑘 − 𝑘 (cid:48) ) ,the Bjorken variable 𝑥 = 𝑄 𝑝 · 𝑞 , the inelasticity 𝑦 = 𝑞 · 𝑝𝑘 · 𝑝 . In addition to these Lorentz invariants,there are two other important kinematic variables: the invariant mass of the produced hadronicsystem 𝑊 = √︁ ( 𝑞 + 𝑝 ) , the energy lost by the electron in the nucleon rest frame 𝜈 = 𝑞 · 𝑝𝑀 whereM is the nucleon mass. In the inclusive double polarized DIS process (Fig. 2.1), where only the final state .1 One-dimensional spin structure of nucleons –20/140– electrons are measured, the spin-dependent 𝑔 structure function can be extracted fromthe double spin asymmetry measurements. In the parton model, the 𝑔 structure functioncan be expressed as the sum of the contributions of various flavor of quarks 𝑔 ( 𝑥, 𝑄 ) = ∑︁ 𝑞 = ( 𝑢,𝑑,𝑠 ) 𝑒 𝑞 (cid:2) Δ 𝑞 ( 𝑥, 𝑄 ) + Δ 𝑞 ( 𝑥, 𝑄 ) (cid:3) , (2.1)where the contribution from the light favor quarks is summed over. Fig. 2.2 showsthe kinematical coverage of the 𝑔 structure function at the EicC, as compared to thecurrently available experimental data. Generally speaking, 𝑔 is often measured throughthe inclusive DIS experiment, and it allows us to extract the polarized distributionfunctions of quarks of various flavors based on the assumption of the 𝑆𝑈 ( ) flavorsymmetry. However, this method has a strong model dependence, and it mixes thecontributions from quarks of different flavors.Another method [50] is to use SIDIS processes to extract more quark and hadronflavor information from experimental data, where a leading hadron among the final statehadrons in Fig. 2.1 is detected in coincidence with the scattered electron. When aquark inside a proton absorbs a virtual photon emitted by an electron, the quark getsstruck out of the proton and becomes a final state jet, which consists of many hadronsclustered inside a narrow cone. This final state hadronization process can be describedby fragmentation functions. The final-state hadron contents in the jet carry the flavorinformation of the initial state quark, therefore this process offers a way to tag the flavorof the produced quark. If one measures a pion or a kaon in the SIDIS process in additionto the recoiled electron, one can separate spin contributions from quarks of differentflavors. In this case, the polarized structure function in the parton model can be writtenas 𝑔 ( 𝑥, 𝑄 , 𝑧 ) = ∑︁ 𝑞 𝑒 𝑞 (cid:2) Δ 𝑞 ( 𝑥, 𝑄 ) 𝐷 𝑞 → ℎ ( 𝑄 , 𝑧 ) + Δ 𝑞 ( 𝑥, 𝑄 ) 𝐷 𝑞 → ℎ ( 𝑄 , 𝑧 ) (cid:3) , (2.2)where 𝐷 𝑞 → ℎ ( 𝑄 , 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 themomentum of the produced quark, experimentally, it is defined as 𝑧 = 𝑃 ℎ𝑎𝑑𝑟𝑜𝑛 · 𝑝𝑞 · 𝑝 .Through measurements in 𝑒 + 𝑒 − and 𝑒 − 𝑝 scatterings, we have been studying andextracting various hadron fragmentation functions. Using these hadron fragmentationfunctions as inputs, we can further separate and extract the polarized quark distributionsof certain flavor accurately from polarized SIDIS data measured at EicC. Figs. 2.3 showthe EicC projection of the polarized sea quark and gluon distributions, respectively, forvarious flavors of quarks obtain from longitudinally polarized double spin asymmetry .1 One-dimensional spin structure of nucleons –21/140– ) (GeV Q i ) + c ( x , Q p 1 g x=0.0036 (i = 0) x=0.0045x=0.0055x=0.007x=0.009x=0.012x=0.017x=0.024x=0.035x=0.049x=0.077 (i = 10) x=0.12x=0.17x=0.22x=0.29x=0.41x=0.57x=0.74 i (cid:215) = 12.1 - 0.7 i c EMCSMCE143E155HERMESCOMPASS 07 (160 GeV)CLAS W>2.5 GeVCOMPASS 11 (200 GeV)COMPASS NLO fit EicC 3.5 x 20 GeV
Figure 2.2:
Global data of the polarized proton structure function 𝑔 from inclusive DISmeasurements compared with the projected EicC data based on the integrated luminosity of50 𝑓 𝑏 − (about one year of running at the EicC). .1 One-dimensional spin structure of nucleons –22/140– measurements via DIS and SIDIS processes. In these figures, the light blue bandrepresents 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] byadding DSSV14 fit with EicC DIS (SIDIS) pseudodata with integrated luminosity of 50fb − for both electron-proton (3.5 GeV + 20 GeV) and electron- He collisions (3.5 GeV+ 40 GeV). One can tell that the SIDIS data, taking advantage of 𝜋 ± and 𝐾 ± final statesfrom both proton and effective neutron targets, is more powerful comparing to DIS datain the flavor separations. The plots clearly show that EicC can significantly improve theprecision of helicity distributions of sea quarks and gluons in the 𝑥 > .
005 region. Thiscan have an impact on the understanding of the proton spin puzzle, since the currentsea quark contribution to the proton spin ∫ Δ 𝑞 ( 𝑥 ) 𝑑𝑥 ( 𝑞 = ¯ 𝑢, ¯ 𝑑, 𝑠 ) has an uncertainty of100 − x* ∆ – u ( x , Q ) x ∆ – u(x,Q) at Q =10.0 GeV -1 DISDSSV14+EicC50fb -1 SIDIS-0.020.000.020.04 10 -4 -3 -2 -1 x* ∆ – d ( x , Q ) x ∆ – d(x,Q) at Q =10.0 GeV -1 DISDSSV14+EicC50fb -1 SIDIS-0.04-0.020.000.02 10 -4 -3 -2 -1 x* ∆ s ( x , Q ) x ∆ s(x,Q) at Q =10.0 GeV -1 DISDSSV14+EicC50fb -1 SIDIS-0.010.000.010.02 10 -4 -3 -2 -1 x* ∆ g ( x , Q ) x ∆ g(x,Q) at Q =10.0 GeV -1 DISDSSV14+EicC50fb -1 SIDIS-0.3-0.2-0.10.00.10.20.30.4 10 -4 -3 -2 -1 Figure 2.3:
Results on the uncertainty band of polarized sea quark and gluon distributionsafter a next-to-leading order fit by including EicC pseudodata. The light blue band representsthe original DSSV14 global fit. The red (green) band shows the results by adding DSSV14 fitwith EicC DIS (SIDIS) pseudodata with integrated luminosity of 50 fb − (10 months of runningat 2 × /cm /s instantaneous luminosity) for both electron-proton (3.5 GeV + 20 GeV) andelectron- He collisions (3.5 GeV + 40 GeV). During the pseudodata analysis, the following cutswere applied: 𝑄 > 𝐺𝑒𝑉 , 𝑊 > 𝐺𝑒𝑉 , 0 . < 𝑦 < .
8, 0 . < 𝑧 < . 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 𝜋 cover- .2 Three-dimensional tomography of nucleons –23/140– age layout of the detector, SIDIS at EicC allows us to measure the polarized sea quarkand gluon distributions with remarkable precision. Moreover, using various polarizedhadron beams (protons and helium-3) together with the detector with the capability ofparticle identification, EicC can help to significantly improve the flavor separation andthus extract polarized quark distributions of different flavor reliably.After one year of running at the EicC, about 50 𝑓 𝑏 − integrated luminosity will beobtained, as one can see from the above statistical analysis that the measurement can besignificantly improved comparing to the existing world data. Therefore, it is critical tocontrol the systematic uncertainty. According to the study in the ongoing experiments,the major sources of systematic uncertainty are from the precision of measurements onthe beam polarization, luminosity fluctuation of beam bunches in different spin states,contamination of photon-induced electrons in the scattered electron detection, and soon. These sources are also applied to the following physics topics and will be furtherinvestigated quantitatively while the detector design is refined in the following years. The conventional parton distribution functions (PDFs) first introduced by Feynman [54]and formalized by Bjorken and Paschos [55] only contain the information on the lon-gitudinal motion of partons inside a nucleon. To gain more comprehensive knowledgeabout partonic structures of the nucleon, one may introduce multi-dimensional distribu-tions, including transverse momentum dependent parton distributions (TMDs) [56, 57]and generalized parton distributions (GPDs) [58, 59, 60, 61]. For a given longitudinalmomentum fraction 𝑥 carried by a parton, TMDs represent the transverse momentumdistribution of the partons and GPDs encode the transverse spatial distribution of thepartons. Both TMDs and GPDs provide three-dimensional images of the nucleon, al-lowing us to access much richer partonic structures, especially when the spin degrees offreedom are taken into account. Therefore, the measurement of TMDs and GPDs willlead us to a more profound understanding of strong interaction.Experimental studies of TMDs and GPDs have been carried out in the existingfacilities during the last two decades. Although valuable data have been collected fora first exploration, TMDs and GPDs are still far from well constrained, especially forsea 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 highcenter-of-mass energy region, which makes the quantitative exploration of sea quarkTMDs and gluon TMDs possible for the first time. On the other hand, EicC as a facilityat the intensity frontier with relatively high center-of-mass energy, and versatile beam .2 Three-dimensional tomography of nucleons –24/140– species, will be an ideal machine for exploring the internal landscape of the nucleon inthe 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. The extraction of partonic structures of the nucleon from high energy scattering processesrelies on the QCD factorization, which provides the link between the observed hadronsand the partons that participate in the hard scattering. In inclusive DIS, where onlythe scattered lepton is identified, the large momentum scale 𝑄 mediated by the virtualgauge boson, i.e. photon or 𝑊 ± / 𝑍 , serves as a short-distance probe, allowing us to“see” the quarks and gluons indirectly. The cross section can be factorized into thelepton-parton scattering at short-distance convoluted with the PDFs in which the activeparton’s transverse momentum 𝑘 𝑇 is integrated. Overall corrections are suppressed byinverse powers of 𝑄 . This is known as the collinear factorization. y zx had r on p l an e l e p t on p l an e l (cid:0) l S (cid:2) P h P h (cid:2) φ h φ S Figure 2.4:
The Trento convention of SIDIS kinematic variables [62]. The 𝑧 -direction isdefined by the virtual photon (or 𝑊 ± / 𝑍 ), momentum, also referred to as the photon-target frame.The incoming and outgoing leptons define the lepton plane, and the detected final-state hadrontogether with the virtual photon defines the hadron plane. The azimuthal angle 𝜙 ℎ is definedfrom the lepton plane to the hadron plane. For a transversely polarized nucleon beam/target, theazimuthal angle of the transverse spin 𝑆 ⊥ is define from the lepton plane to the transverse spindirection. Apart from the scattered lepton, one final-state hadron with momentum 𝑃 ℎ is identi-fied in SIDIS (Fig. 2.4), which not only allows us to detect quark and gluon distributionsin the nucleon as in the inclusive DIS, but also provides the opportunity to explore the .2 Three-dimensional tomography of nucleons –25/140– hadronization process, the emergence of color neutral hadrons from colored quarks andgluons. 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 givenby the transverse momentum of the observed hadron in the final state. In the Breitframe, where the virtual gauge boson and the nucleon are headed on, the SIDIS processis naturally dominated by the small transverse momentum region, 𝑃 ℎ ⊥ (cid:28) 𝑄 . In thisregime, the hard momentum scale 𝑄 localizes the probe to see the particle feature ofquarks and gluons in the nucleon and the soft scale 𝑃 ℎ ⊥ is sensitive to the confinedmotion of partons perpendicular to the colliding direction. The SIDIS cross section canbe factorized into the lepton-parton short-distance scattering convoluted with transversemomentum dependent parton distribution functions and fragmentation functions. Thisis known as the TMD factorization. Overall corrections are suppressed by powers of 𝑃 ℎ ⊥ / 𝑄 . For events with large transverse momentum comparable to 𝑄 , the SIDIS processis effectively characterized by a single large momentum scale, no longer sensitive to thetransverse motion of partons. The cross section is described by the collinear factorizationas in the previous section, where double polarized SIDIS events are utilized to extracthelicity distributions.Here we focus on the small transverse momentum regime where one can apply theTMD factorization [63, 64]. By introducing the spin degrees of freedom, one candefine 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 inparticular can shed light on our understanding of parton orbital motions and spin-orbitcorrelations. When integrating out the transverse momentum 𝑘 𝑇 of the parton, threeout of the eight leading-twist TMDs, the unpolarized distribution 𝑓 ( 𝑥, 𝑘 𝑇 ) , the helicitydistribution 𝑔 𝐿 ( 𝑥, 𝑘 𝑇 ) and the transversity distribution ℎ ( 𝑥, 𝑘 𝑇 ) reduce to their collinearcounterparts, while the other five that describe the correlations between parton transversemomentum and the parton/nucleon’s spin vanish.Under the single-photon exchange approximation, the SIDIS cross section can beexpressed in terms of 18 structure functions, corresponding to different polarizationconfigurations and final-state azimuthal modulations. The spin-dependent TMDs areusually extracted by measuring particular azimuthal asymmetries, while the unpolarizedTMDs can be obtained by analyzing unpolarized SIDIS cross section or multiplicity.Among the leading-twist spin-dependent TMDs, the Sivers function 𝑓 ⊥ 𝑇 ( 𝑥, 𝑘 𝑇 ) [66],as well as related phenomenologies, stimulates tremendous theoretical progress andexperimental investigations in recent years. It describes the correlation between quarktransverse momentum and the transverse spin of the nucleon. To put it simply, the Sivers .2 Three-dimensional tomography of nucleons –26/140– TMDs
Quark Polarization
Unpolarized (U)
Longitudinally polarized (L)
Transversely polarized (T)
Nucleon Polarization U f unpolarized h Boer-Mulders L g helicity h longi-transversity T f Sivers g trans-helicity h transversity h pretzelosity TTT
Nucleon spin Quark spin T Figure 2.5:
The leading-twist quark TMD distributions. function reflects the left-right asymmetry of quark transverse momentum distributionin a transversely polarized nucleon. One of the most distinguished features of theSivers function is its unique universality property exhibited in different processes. Iffinal/initial-state interactions, which are formally summarized into the gauge link, wereabsent between the active quark and the remnants of the nucleon, the time reversalinvariance requires the Sivers function to be zero [67], and thus it is commonly referredto 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 andfrom the initial-state interaction in the Drell-Yan process. As the staple like Wilson lineflips the direction between the final-state and initial-state interactions, the quark Siversfunctions are predicted to have an exact sign change between SIDIS and Drell-Yanprocesses, 𝑓 ⊥ 𝑇 ( 𝑥, 𝑘 𝑇 ) | SIDIS = − 𝑓 ⊥ 𝑇 ( 𝑥, 𝑘 𝑇 ) | DY [68, 69]. Although recent 𝑊 productiondata from STAR [70] and the 𝜋𝑁 Drell-Yan data from COMPASS [71] support thisprediction, the current uncertainties are too large to confirm the sign change. Futureprecise measurements of the Sivers function in different processes are of great importanceto test this prediction associated with the QCD factorization. Moreover, theoreticalstudies have suggested that the Sivers function is closely related to parton orbital angularmomentum [72]. Therefore, the experimental studies of the Sivers function are not onlycrucial for unveiling the spin structure of the nucleon, but also important for deepeningour understanding of the strong interaction and/or QCD.In SIDIS, one can access the Sivers function by measuring a transverse single-spin asymmetry, known as the Sivers asymmetry. Within the TMD factorization, thecorresponding structure function can be expressed as the convolution of the Siversfunction and the unpolarized fragmentation function. During the past two decades, greatefforts have been made to extract the Sivers function as well as other TMDs via the .2 Three-dimensional tomography of nucleons –27/140–
Table 2.1:
The existing measurements of the Sivers asymmetry in SIDIS.collaboration √ 𝑠 GeV target final state hadron literatureCOMPASS (CERN) 18 Deuterium ℎ ± , 𝜋 ± , 𝐾 ± , 𝐾 [73, 74]proton ℎ ± [75]proton 𝜋 ± , 𝐾 ± [76]HallA (JLab) 3.5 neutron 𝜋 ± , 𝐾 ± [77]HERMES (DESY) 7.4 proton 𝜋 ± [78]proton 𝜋 ± , ( 𝜋 + − 𝜋 − ) , 𝜋 , 𝐾 ± [79] 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 JLabexperiments were carried out at relatively low energies, where high-twist effects andtarget mass corrections are expected to be sizable. HERMES data were mostly collectedin the so-called valence quark region, where the contribution to the cross section isdominated by valence quarks, and hence the data are not quite sensitive to sea quarkdistributions. The ongoing and upcoming SIDIS experiments at the 12-GeV upgradedJLab aim at unprecedented precise measurements of valence quark TMDs. Recentlyapproved EIC-US at BNL is designed with a high center-of-mass energy and will havequantitative measurements of gluon and sea quark TMDs for the first time. EicC giventhe center-of-mass energy in between has unique advantages to study sea quark TMDsand fills the energy gap from JLab to EIC-US. In addition, the separation of currentfragmentation and target fragmentation remains as a challenging task at the existingfixed target facilities. The large experimental acceptance at EicC will provide a widekinematic coverage, which is crucial to make the clean selection of events in the currentfragmentation 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 tostrange quark distributions. Currently available 𝐾 meson production data from polarizedSIDIS are rather limited. EicC SIDIS experiments will have high statistics measurementsof both charged pion and charged kaon productions. Together with the combination ofthe proton beam and the He beam, EicC will allow a full separation of all light quarkflavors, 𝑢 , 𝑑 , 𝑠 , ¯ 𝑢 , ¯ 𝑑 , and ¯ 𝑠 .In Fig. 2.6, we show the 𝑥 − 𝑄 distribution of EicC SIDIS events. Instead ofpresenting all cases, we only select two examples, the 𝜋 + production from the protonbeam and the 𝐾 + production from the He beam, to cover both 𝑒 𝑝 and 𝑒 He collisions andboth pion and kaon productions. Kinematic cuts, including 𝑄 > , 𝑊 > 𝑊 (cid:48) > . < 𝑧 < .
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 Three-dimensional tomography of nucleons –28/140– coverage in the typical sea quark region ( 𝑥 ∼ .
05) ensures a reliable extraction of seaquark TMDs. Moreover, compared to the fixed-target experiments, the collider mode ofEicC allows a wide kinematic coverage, which provides the opportunity to quantitativelyestimate power suppressed corrections. x - -
10 1 ) ( G e V Q x - -
10 1 ) ( G e V Q Figure 2.6: 𝑥 − 𝑄 coverage of EicC SIDIS events from simulation. Left: 𝜋 + production fromthe proton beam. Right: 𝐾 + production from the He beam. Kinematic cuts are described in thetext.
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 iseven not yet determined without ambiguity [81]. Here we take the Sivers function as anexample to demonstrate the impact of EicC SIDIS experiments. Quark transverse momentum k T (GeV) U p qu a r k S i v er s f un c t i o n -f T ( x , k T ) ⊥ x=0.02x=0.04x=0.08x=0.16 u quark Quark transverse momentum k T (GeV) D o w n qu a r k S i v er s f un c t i o n f T ( x , k T ) ⊥ x=0.02x=0.04x=0.08x=0.16 d quark Figure 2.7:
The precision of extractions of up and down quark Sivers functions. The light greenbands represent the accuracy from the currently available SIDIS data, the red bands represent theaccuracy by including the projected EicC data with statistical uncertainty only, and the blue bandsrepresent the accuracy by including the projected EicC data with part of systematic uncertaintiesas described in the text. Integrated luminosities of 50 fb − for 𝑒 𝑝 and 50 fb − for 𝑒 He areadopted in this projection.
We simulate SIDIS events according to EicC kinematics: 3 . He beam .2 Three-dimensional tomography of nucleons –29/140–
Quark transverse momentum k T (GeV) x=0.02x=0.04x=0.08x=0.16 S t r a n g e qu a r k S i v er s f un c t i o n f T ( x , k T ) ⊥ s quark Figure 2.8:
The precision of the extraction of strange quark Sivers function. The red bandsrepresent the accuracy by including the projected EicC data with statistical uncertainty only, andthe blue bands represent the accuracy by including the projected EicC data with part of systematicuncertainties as described in the text. Integrated luminosities of 50 fb − for 𝑒 𝑝 and 50 fb − for 𝑒 He are adopted in this projection. serving as effective polarized neutron beam since the spin of He is mainly given bythe neutron spin. Integrated luminosities are chosen as 50 fb − for 𝑒 𝑝 and 50 fb − for 𝑒 He collisions. A 4 𝜋 angle coverage is assumed for the acceptance. For theprojection of EicC results, we select simulated SIDIS events with 𝑄 > , 𝑊 > 𝑊 (cid:48) > . < 𝑧 < .
7, and the current fragmentation cut [80]. Wealso require the scattered electron momentum 𝑃 𝑒 > .
35 GeV and the identified final-state hadron momentum 𝑃 ℎ > . He nuclear effect.Other systematic uncertainties, e.g. detector resolution, particle identification, randomcoincidence, radiative corrections, are not expected to be dominant based on existingexperience, although more detailed studies will be carried out with the final detectordesign. We utilize the parametrization form of the Sivers function in [81] as the inputmodel. In Fig. 2.7, we show the results of the extraction of up and down quark Siversfunctions. In Fig. 2.8, we show the results of the extraction of the strange quark Siversfunction. The outer light green bands represent the present accuracy from world existingSIDIS data, the inner red bands represent the accuracy including projected EicC datawith statistical uncertainty only, and the blue bands represent the accuracy includingprojected EicC data with part of the systematic uncertainties mentioned above. As the .2 Three-dimensional tomography of nucleons –30/140– world existing 𝐾 meson production data from polarized SIDIS are very limited, thecurrent uncertainty of the strange quark Sivers function is huge, and even the sign is notyet determined. Hence the present accuracy bands are not shown in Fig. 2.8. Recenttheoretical study suggested an opposite sign between the strange quark and anti-strangequark Sivers functions [82] apart from the sign-flip prediction of the Sivers functionsprobed in SIDIS and Drell-Yan processes. The experimental test of this predictionat EicC will enrich our knowledge about the proton spin structure, particularly in therelatively small 𝑥 region. We should also note that due to the large uncertainty of thelimited available polarized SIDIS data one cannot apply a very flexible functional formin the global analysis. Once more precise data are available from EicC and other futureexperiments, we will be able to have less biased extractions of the Sivers function aswell as other TMDs by using much more flexible parametrizations and more realisticestimations of the uncertainties. Results in Figs. 2.7 and 2.8 can be understood as theimpact of EicC SIDIS experiments from statistics point of view since the same analysismethod is applied to world data and projected data.The EicC design enables us to precisely measure all 18 structure functions by combin-ing different beam polarization configurations and the separation of different azimuthalmodulation terms. Other TMDs also receive great interest. For instance, the transver-sity TMD, which survives after 𝑘 𝑇 integration, measures the net density of transverselypolarized quarks in a transversely polarized nucleon. The first moment of the integratedtransversity distribution is the tensor charge, which is a fundamental QCD quantitydefined by the matrix element of the tensor current operator. It is recognized as a bench-mark of the lattice QCD study of hadron structures. Therefore, a precise determinationof the tensor charge including the flavor separation can serve as an experimental testof lattice QCD. Due to its chiral-odd property, the transversity TMD contribution toinclusive DIS cross section is highly suppressed by the power of 𝑚 𝑞 / 𝑄 . In contrast, itcan be extracted from a leading power single spin asymmetry in SIDIS process, knownas the Collins asymmetry, which arises from the coupling of the transversity TMD andthe Collins fragmentation function. Alternatively, the transversity distribution can alsobe accessed by analyzing the di-hadron SIDIS events at EicC. In the present globalanalysis, the sea quark transversity distribution is commonly assumed to be zero. EicCas an ideal facility for the study of sea quark distributions will provide the opportunityto test this assumption.In conclusion, EicC with wide kinematic coverage and high luminosity has thecapability to deliver the high precision experimental data. The SIDIS measurements atEicC combined with those at 12-GeV upgraded JLab focusing on the study of valencequark distributions and the recently approved high-energy EIC at BNL will provide .2 Three-dimensional tomography of nucleons –31/140– 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 thatbridges the energy gap between JLab-12GeV and the future EIC at BNL is a perfectmachine to study TMD evolution effects, in particular, to constrain the non-perturbativepart of the evolution kernel [83]. Generalized parton distributions (GPDs) encode information on the three dimensionalstructure of nucleon in the joint transverse position-longitudinal momentum phasespace [58, 59, 60, 61, 84]. They were initially introduced to describe the exclusiveprocesses where an active parton participating in the hard scattering is re-absorbedinto nucleon that remains intact after collisions. GPDs depend on two longitudinalmomentum fractions 𝑥 and 𝜉 and on the squared momentum transfer 𝑡 to the proton.GPDs are widely connected to other physics quantities. In the different kinematicallimits, GPDs are reduced to the normal parton PDFs and electromagnetic form factorsof the nucleon. In particular, setting 𝜉 = 𝑡 , one obtains an impact parameter distribution,which describes the joint distribution of partons in their longitudinal momentum andtheir transverse position 𝑏 ⊥ inside the proton [85, 86].One of the most important physics motivations of GPD studies is to understandnucleon spin structure. The GPDs’ connection with partons angular momentum isquantified through the Ji’s sum rule [60], 𝐽 𝑞,𝑔 = ∫ − 𝑑𝑥𝑥 [ 𝐻 𝑞,𝑔 ( 𝑥, 𝜉, ) + 𝐸 𝑞,𝑔 ( 𝑥, 𝜉, )] . (2.3)Where 𝐽 𝑞,𝑔 represents the total angular momentum for quark and gluon, which can befurther decomposed as, 12 = 𝐽 𝑞 + 𝐽 𝑔 = ΔΣ + 𝐿 𝑞 + 𝐽 𝑔 , (2.4)with ΔΣ , 𝐿 𝑞 and 𝐽 𝑔 being the quark spin angular momentum, quark orbital angularmomentum and gluon total angular momentum respectively. The quark orbital angularmomentum can be extracted through the measurements of GPDs 𝐻 and 𝐸 in exclusiveprocesses by subtracting the quark helicity contribution. It is also worth to mentionthat GPDs encode the rich information on the mechanical properties of nucleon internalstructure [87, 88, 89, 90] through the gravitational form factors(GFFs), which is relatedto the second moment of the unpolarized GPD. These mechanical properties, such asthe pressure and shear force distributions, the mechanical radius, and the mechanical .2 Three-dimensional tomography of nucleons –32/140– stability of a particle, contain the crucial information on how the strong force insidenucleon balance to form a bound state. However, the precise extraction of GFFs atthe 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 manyaspects, the experimental studies of GPDs have been and are a cutting-edge field of highenergy nuclear physics during the last two decades. x − ξ x + ξ γ ∗ ( Q ) tp p (cid:3) e e (cid:3) GPD γ ( a ) ( c ) x − ξ x + ξ γ ∗ ( Q ) tp p (cid:3) e e (cid:3) GPD meson x − ξ x + ξ γ tp p (cid:3) e e (cid:3) GPD ( b ) e + e − γ ∗ 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 mesonproduction.
The main exclusive processes which allow to access to the GPDs in 𝑒 𝑝 collisions aredeeply virtual Compton scattering (DVCS) 𝑒 𝑝 −→ 𝑒 𝑝𝛾 (Fig. 2.9(a)), time-like Comptonscattering 𝑒 𝑝 −→ 𝑒 𝑝𝑙 + 𝑙 − (Fig. 2.9(b)) and deeply virtual meson production(DVMP) 𝑒 𝑝 −→ 𝑒 𝑝 𝑀 (Fig. 2.9 (c)) [59, 60]. At the leading order, DVCS process is described bythe partonic channel 𝑞𝛾 ∗ −→ 𝑞𝛾 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], H ( 𝑥 𝐵 , 𝑡, Q ) = ∫ − 𝑑𝑥 (cid:20) 𝜉 − 𝑥 − 𝑖𝜖 − 𝜉 + 𝑥 − 𝑖𝜖 (cid:21) ∑︁ 𝑞 = 𝑢,𝑑,𝑠, ··· 𝑒 𝑞 𝐻 𝑞 ( 𝑥, 𝜉, 𝑡, Q ) , (2.5)where 𝜉 ≈ 𝑥 𝐵 /( − 𝑥 𝐵 ) with 𝑥 𝐵 being the Bjorken’s variable. The similar relationholds for other GPDs. The precise measurements of the various angular modulationsand polarization dependence of DVCS cross section at different kinematic points in( 𝑄 , 𝑥 𝐵 , 𝑡 ) would allow us to extract different CFFs, as each of them has unique angularand polarization dependencies (see the reference [84] and therein). The correspondingGPDs can be subsequently constrained by the extracted CFFs.Let us highlight some specific features of different production channels. The mainlimitation of DVCS process is that it is sensitive only to the sum of quark and anti-quarkdistributions in a particular flavor combination. In contrast, exclusive meson productionoffers substantial help in the separation of different quark and antiquark flavors and ofgluons. For example, the valence quark and sea quark GPDs can be probed via pseudoscalar mesons ( 𝜋, 𝐾, 𝜂, ... ) production processes, whereas the vector mesons ( 𝜌, 𝜙, 𝜔 ) .2 Three-dimensional tomography of nucleons –33/140– production is more sensitive to sea quark and gluon GPDs. However, extracting GPDsfrom exclusive meson production requires the knowledge of additional non-perturbativematrix element, the meson distribution amplitude.The precise extraction of GPDs from the measurements of exclusive processes putsthe highest demands on experiments for various reasons, including the smallness of crosssections 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 reasonableconstraints for only one GPD, 𝐻 . The complete and precise extraction of all GPDsrequires high luminosity, detectors with full hemisphere coverage, beams with variouspolarization choices, and wide kinematic reach. Until now, there have been no facilitiesbeing able to meet all these demands. For example, the luminosity at HERA and COM-PASS is low, meanwhile COMPASS has its complication while flipping the muon beamhelicity, which makes the extractions of some polarization dependent GPDs extremelydifficult. On the other hand, though the luminosity at JLab-12GeV is very high, the mostDVCS events lie well below 𝑄 <
10 GeV [102, 103, 104, 105], where the various hightwist 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 uncertaintiescan be well controlled if going to higher 𝑄 region [107]. - - -
10 1 x Q ( G e V ) - - - - - y = 0.01y = 0.95
20 GeV · g ep->ep
20 GeV · g ep->ep ‡ , W ‡ p' q < 99% of beam, p' P
20 GeV · g ep->ep Figure 2.10:
The distributions of DVCS(left panel) and 𝜋 DVMP(right panel) events in the 𝑥 and 𝑄 for 3.5GeV electron beams colliding with 20GeV proton beams energy at EicC. Theevent 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 areincluded, and the used kinematic cuts and binning scheme are also shown. The programs of the experimental GPDs studies will be dramatically extended byEicC, predominantly in the sea quark kinematical region. The precise measurements ofboth DVCS and DVMP can be carried out at EicC with versatile beam species/polariza-tions. The typical 𝑄 range accessible with EicC is 1 GeV < 𝑄 <
30 GeV (see theleft panel of Fig. 2.10 adapted from MILOU package [110]). Meanwhile, the Bjorken .2 Three-dimensional tomography of nucleons –34/140– variable 𝑥 can reach down to 𝑥 ≈ .
05 when restricting 𝑄 to the perturbative region 𝑄 >
10 GeV . This kinematic coverage with the current design will make EicC aunique 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 atEicC as compared to that at JLab-12GeV due to relatively higher 𝑄 . Moreover, EicC isalso complementary to the US EIC in studying the DVCS process. This is because theinterference contribution between the Compton and the Bethe-Heitler processes is moreprominent at a lower energy machine, whereas the Compton process may dominate atEIC for given 𝑥 and 𝑄 values.As mentioned, parton orbital angular momentum can be determined by extractingGPD E and H from exclusive processes according to the Ji’s sum rule. However, inpractice, it is extremely challenging to achieve this because it requires measuring thevalues of H and E for all 𝑥 at fixed 𝜉 . Nevertheless, EicC has great potential to advanceour knowledge of GPD E and also H with a transverse polarized proton beam. Fig. 2.11displays the simulation results for the Compton scattering off a polarized proton. TheEicC measurements of the DVCS transverse polarization asymmetry 𝐴 𝑈𝑇 with a singleazimuthal modulation sin ( 𝜙 − 𝜙 𝑠 ) cos 𝜙 have a rather small statistical uncertainties for awide kinematic region with | 𝑡 | > .
01 GeV . Here the DVCS events are selected in thekinematic region 0.01 < 𝑦 < 𝛾 𝑝 center of mass energy W > E and H is displayed in Fig 2.12. The approach of global analysis utilizing theartificial neural network [94, 111, 112] is employed in order to reduce model dependencyand propagate the uncertainties properly. The poorly constrained real part of (cid:101) E and (cid:101) H simply are assumed to be vanishing [92, 111, 113] in the simulation. The light greenbands, manily driven by statistical uncertainties, represent the accuracy of the existingJLab 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 theextraction of the CFF E is reduced in the sea quark region once the EicC measurementsare included. In most of the kinematic space systematic uncertainty is at the similarlevel or even smaller than the statistical one. So we would still retain power of extractionof CFFs similar to what is shown on Fig 2.12, after including such level of systematicuncertainty. 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 configurationsand the different azimuthal modulations at EicC as well. A combined analysis with allthese measured modulations would further reduce significantly the error bands shownin Fig 2.12. So under the high luminosity design of EicC, the statistical uncertaintieswill not play essential role in the future GPD extraction and the systematic uncertainties, .2 Three-dimensional tomography of nucleons –35/140– whose main sources are discussed in previous sections, are anticipated to be dominant,which will be under good control by facility design. x - - f ) c o s S f - f s i n ( U T A -1 EicC 3-fold PROJECTION with integral Lumi =50 fb
HERMES2005, DESY-THESIS-2008-006 ~3GeV Q =1.0~1.6 GeV Q =1.6~2.6 GeV Q =2.6~4.3 GeV Q =4.3~7.0 GeV Q =7.0~18.5 GeV Q =18.5~30.0 GeV Q -3 -2 Figure 2.11:
The projected accuracy for 𝐴 sin ( 𝜙 − 𝜙 𝑠 ) cos 𝜙𝑈𝑇 asymmetry in the process of DVCS offa transversely polarized proton target at EicC in the region 1 GeV < 𝑄 <
30 GeV . Onlystatistics uncertainty is included. The size of 𝐴 𝑈𝑇 is estimated with the Goloskokov-Krollmodel [114, 115, 116]. The black star is the HERMES data of 𝐴 sin ( 𝜙 − 𝜙 𝑠 ) cos 𝜙𝑈𝑇 ,𝐼 asymmetry [117].The values of | 𝑡 | bins under the same 𝑄 are not shown here for simplicity. As discussed, EicC can deliver high precision data for the DVMP process in the large 𝑄 >
10 GeV region, where the non-perturbative effects and higher-twist contributionsare suppressed, so that GPDs can be extracted reliably. Fig. 2.10 (right panel) displaysthe expected distribution of DVMP events at EicC in bins of 𝑄 and 𝑥 . Note that DVMPcross sections rapidly decrease with increasing 𝑄 . One sees that there are substantialevent numbers in the moderate 𝑄 region where perturbative treatment is justified. Thiswill facilitate clearly separating different quark flavor contributions by combining withDVCS data. For instance, one can separate up quark and down quark contributions bycarrying out the measurements of 𝐴 cos 𝜙𝐿𝐿 which arises from the coupling of the chiral-odd GPDs and the twist-3 distribution ampliutde of pion [114, 115, 118, 119]. Thisobservable could provide valuable information on transversity PDF that is hard to accessin inclusive process. Despite the higher twist nature of this observable, we found thatthe asymmetry is significant for the DVMP channel of 𝜋 production. With the EicCDVMP pseudo-data displayed in Fig. 2.10, it is shown in Fig.2.13 that at large 𝑄 thestatistical uncertainty of the 𝐴 cos 𝜙𝐿𝐿 in 𝜋 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 greatlyadvance our knowledge about the internal structure of nucleons. The combined kinematiccoverage of the EicC, JLab and of EIC-US is essential for ultimately yielding the complete3D images of proton from the large 𝑥 down to the saturation regime, and for much more .3 Partonic structure of nucleus –36/140– Figure 2.12:
An exploratory extraction of the real ( R 𝑒 ) and the imaginary ( I 𝑚 ) part of CFF E and H at 𝑡 = − . from the pseudodata generated for kinematical points shown in Fig. 2.11using the neural network method [92, 111, 113]. The systematic uncertainty is not included yet. profound understanding of the proton spin puzzle as well. -t (GeV00.20.40.60.8 F r a c t i on o f m o m en t u m x ) f c o s LL ( A s -1 EicC, 50 fb > 10 GeV Q (a) -t (GeV00.20.40.60.8 F r a c t i on o f m o m en t u m x CLAS > = 2.83 GeV The statistics error of the projected 𝐴 cos 𝜙𝐿𝐿 asymmetry for 𝜋 production in DVMPprocess at EicC. The CLAS data is taken from Ref. [119]. The electron-ion collision has been recognized as an ideal process to explore the distri-butions of quarks and gluons inside the nucleus, as well as to study the QCD dynamicsof multiple parton interactions in the nuclear medium. In this process, the electron scat-tering part, which can be well controlled both experimentally and theoretically, provides .3 Partonic structure of nucleus –37/140– a high precision probe to reveal the detailed partonic structure of the nucleus which isimpossible to be calculated theoretically. Besides, the nucleus can also serve as a QCDlaboratory at the fermi scale to investigate the strong interactions between the energeticparton and the nuclear medium by carefully studying the so-called hadronization pro-cess which largely depends on the type of the nucleus. The detailed analysis of thesenontrivial nuclear medium effects can help us to probe the fundamental differences ofpartonic properties in free nucleons and the nuclear medium, as well as to understand themystery of hadronization mechanisms and the QCD confinement of quarks and gluons. A full understanding of the difference between the properties of quarks and gluonsinside a free nucleon and that inside a nucleon bounded within the nucleus will help usunderstand how the nucleus is formed at the partonic level. The longitudinal momentumdistributions of quarks and gluons in a free nucleon are characterized by the usualleading twist parton distribution functions (PDFs) which have been precisely measuredin the high-energy electron-proton collisions. A natural question is: how these PDFsare modified by the nuclear medium when the nucleon is bounded? To answer sucha fundamental question remains one of the biggest challenges in the nuclear physicscommunity. 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-quarksand gluons is suffering from even much larger uncertainties. It is strongly desired toperform more high-precision measurements of conventional experimental observablesas 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 measuredin free nucleons and bounded nucleons are significantly different. Shown in Fig.2.14reveals the cross-section ratios for inclusive DIS between eA and eD collisions in termsof Bjorken x distributions. The solid circles, the open squares, and stars correspond tothe data from SLAC E139 [20], BCDMS [19], and EMC [127], respectively. Despitetheir different reactions and kinematic ranges, these data exhibit a very similar nuclearmedium effect. There are four distinguishable regions [21]: 1. Fermi motion in 𝑥 > . . < 𝑥 < . 7; 3. Anti-shadowing around 𝑥 ∼ . 1; 4.Shadowing in 𝑥 < . .3 Partonic structure of nucleus –38/140– x σ A / σ D BCDMS (Fe)SLAC E139 (Fe)EMC (Cu) Figure 2.14: The cross section ratio between electron-ion and electron-deuteron deep inelasticscattering [128]. 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 wayto study the nuclear structure in the partonic level [129]. Enormous new experimentalprograms 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 existsin sea-quarks and gluons. Furthermore, the physics origins of the anti-shadowing andshadowing at small 𝑥 remain unknown due to a lack of experimental measurements andtheoretical interpolations.In the most recent nPDF determination, nNNPDF2.0, a robust quark flavor separationand a good handle of the gluon are performed [120]. However, compared to those forfree nucleons large uncertainties of nPDFs remain due to the very limited existingmeasurements. This is also true in other global fittings such as EPPS16 [121]. Thefuture EicC will place its kinematics in the sweet spot where the nuclear medium effectsof valance-quarks and sea-quarks can be extensively studied by measuring their intrinsicPDFs 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 NLOcalculation of DIS cross-section using the nNNPDF2.0 nuclear PDFs, the impact offuture EicC measurements on nuclear PDFs utilizing Bayesian reweighting is shownin Figs. 2.15 and 2.16. In Fig. 2.15, the sea quark distribution in Pb at 𝑄 = .3 Partonic structure of nucleus –39/140– GeV for both the original and reweighted nNNPDF2.0 fits are shown with uncertaintybands correspond to 90% confidence level. In particular, the reduction of reweighted ¯ 𝑢 uncertainty in the kinematic region covered by EicC, i.e. 𝑥 > . 01, strongly indicatesEicC 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 indicatesthe constraining power of EicC measurements on gluon nuclear modification. Noticethat the analysis shown in Figs. 2.15 and 2.16 are based on the integrated luminosity L = . 01 fb − , which corresponds to only a few hours of running . Therefore, the realmeasurements with high precision and large coverage will provide a stringent constrainton nPDFs from the shadowing to the anti-shadowing region. x u ( x , Q ) nPDF nNNPDF2.0nNNPDF2.0 reweightedno pseudo-data Q =10.0GeV relative uncertainty x d ( x , Q ) nNNPDF2.0nNNPDF2.0 reweightedno pseudo-data x B x s ( x , Q ) nNNPDF2.0nNNPDF2.0 reweightedno pseudo-data x B Pb lumi 0.01fb-1 x B x B Figure 2.15: Left: the ¯ 𝑢 distribution in Pb at 𝑄 = 10 GeV , the gray band comes from theoriginal nNNPDF2.0 set, the blue band corresponds to the set reweighted with the EicC pseudodata based on the integrated luminosity L = . 01 fb − . Right: the relative uncertainty for twosets of nPDFs. 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 contributionsfrom different quark flavors. The high precision data with large kinematic coverage willgreatly 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 undiscoveredmedium modification effect of sea-quarks as well as unveil the puzzle of anti-shadowingwhich remains largely unknown. Studies using EicC pseudo data with an integrated luminosity equivalent to one week or moreof running have also been performed. However, the impact on the nNNPDF2.0 PDFs estimated byreweighting is so significant that the number of effective replicas with non-zero weight “surviving” theanalysis reduces from an initial set of 1000 to a few dozen or less. This reflects the fact that the leapin precision between the data already included in the nNNPDF2.0 analysis and the future EicC data istoo 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 polarizedPDFs at the future US EIC using electron-helium SIDIS pseudo data [130]. .3 Partonic structure of nucleus –40/140– x ( x , Q ) nPDF nNNPDF2.0nNNPDF2.0 reweightedno pseudo-data Q =10.0GeV relative uncertainty x g ( x , Q ) nPDF nNNPDF2.0nNNPDF2.0 reweightedno pseudo-data relative uncertainty Pb lumi 0.01fb-1 x B x B Figure 2.16: Same as Fig. 2.15, but for gluon. On the other hand, various species of beam nuclei at EicC will also provide uniqueopportunities 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 eAcollision, the spectator-tagging DIS process serves as a powerful tool to exam the QCDorigin of nucleon-nucleon interactions, such as the link between the SRC to EMC effectsat 𝑥 > . 𝑥 that lead to theanti-shadowing and shadowing effects [131, 132]. Precise measurements and phenomenological investigations on the SIDIS process withdifferent nuclei in electron-ion collisions are the fundamental tools to analyze twowidely discussed nuclear effects, i.e., the parton energy loss effect and hadronizationin the medium [133, 134, 135, 136, 137]. In a nuclear medium, the highly energeticparton generated in the hard scattering process will continuously encounter the multiplescatterings with the surrounding nucleons before it completely escapes from the nucleusor is converted inside the nucleus into charge-neutral particles, a complicated process alsoknown as the hadronization. The collective consequence eventually leads to nontrivialphenomena of nuclear modifications, including the attenuation and broadening of thehadron spectrum in eA collisions comparing to ep collisions. These phenomena, whichare very sensitive to the nuclear parton densities and QCD dynamics of multiple partoninteractions in the nuclear environment, have been observed in semi-inclusive deepinelastic scatterings in HERMES [138] and Drell-Yan dilepton production in proton-nucleus collisions in FNAL-866 [139]. The available data are used to extract thetransport properties of cold nuclear matter and study the parton energy loss mechanism .3 Partonic structure of nucleus –41/140– in the nucleus [140, 141, 142, 143]. However, large uncertainties still exist, mainlyoriginated from two aspects: 1. limited kinematic coverage of experimental data; 2.the assumption in energy loss calculation that the partons fragments outside the nuclearmedium. To obtain more precise information about the hadronization process and themechanism of parton energy loss in medium, we need EicC to fill in the open windowthat has not been covered by existing experimental measurements.Hadronization, as encoded in fragmentation functions, describes the process ofquarks and gluons fragment into final state hadrons. In the presence of a large sizenuclear medium, the hadronization dynamics will be affected and eventually leads todifferent hadron spectrum comparing to that in a vacuum [144, 145]. As we know, partonenergy loss effects also lead to the suppression of the hadron spectrum as functions ofbeam energy 𝜈 and fragmentation fraction 𝑧 ℎ in eA collisions comparing to that inep collisions [138, 141]. Therefore, we can not disentangle these effects from theavailable experimental data, as they lead to the same phenomena but with very differentmechanisms. This requires us to perform the measurement more differentially andconsider as many as possible the final state identified hadrons. The high collision energyand the high luminosity, as well as the capability of identifying various hadrons in futureEicC, will play a key role to differentiate the parton energy loss effect and mediumhadronization effect.Shown in Fig. 2.17 is the comparison between predictions from parton energyloss model (solid curves) and hadron transport model (dashed curves) for the nuclearmodification factors, where only events with 0 . < 𝑦 < . , 𝑊 > , Q > are selected in the process when 3.5 GeV electron collides with 20 GeV (pernucleon charge) Pb beam, and various hadrons represented by different shaped pointsare considered in the simulations. By looking at the dependence of 𝑅 ℎ𝑀 as a functionof the virtual photon energy 𝜈 , the capability of particle identification as well as thekinematic coverage in EicC will allow us to disentangle the hadronization mechanismfrom the parton energy loss effect as indicated by the difference between solid anddashed curves. Though the two models give very similar nuclear modification effect for 𝜋 + production, enormous differences for 𝑝 and 𝐾 + are predicted. These differences canbe identified in EicC considering its high luminosity 50 𝑓 𝑏 − , which leads to invisiblestatistical uncertainty as shown in Fig. 2.17.The transverse momentum broadening effect is very sensitive to the QCD dynamicsof multiple parton interactions in the nuclear environment and the nuclear mediumtransport property. It has been extensively studied in heavy-ion collisions, see forexample [134, 146, 147]. Similarly, we can also use this observable to probe thefundamental properties of the nuclear medium in eA collisions. Comparing to pA .4 Exotic hadronic states –42/140– collisions, eA collisions is much cleaner due to the absence of the strong interactionbetween the beam electron and the target nucleus. Based on the assumption that thepartons hadronize outside the nuclear medium, we show in Fig. 2.17 the transversemomentum broadening for light hadron (red curve) and 𝐽 / 𝜓 (blue curve), which canbe 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 verylimited, and EicC can make a significant contribution to this subject. ν ( GeV ) ( P b / D ) M h R EicC proj + π + K + p, 0.1 SIDIS - π (× ) DIS - J / ψ x B Δ p T Figure 2.17: Left plot: the cross section ratios for 𝜋 + , 𝐾 + and 𝑝 between election-ion andelectron-proton collisions at EicC energy region, i.e., 3.5 GeV electron beam and 20 GeV percharge for heavy ion beam, as a function of virtual photon energy 𝜈 . Right plot: the transversemomentum broadening for 𝜋 and 𝐽 / 𝜓 at future EicC. Hadron spectroscopy started a new era in 2003 when the 𝐷 ∗ 𝑠 ( ) , 𝐷 𝑠 ( ) and 𝑋 ( ) were discovered at the 𝐵 factories. Since then many new hadron resonancesor resonant structures were discovered at various experiments all over the world. Inparticular, most of them contain at least one heavy (charm or bottom) quark, and haveproperties at odd with expectations from quark model. The meson states discovered inthe heavy-quarkonium mass region are called 𝑋𝑌 𝑍 states, see Table 2.2 for a list. Notableexamples include the 𝑋 ( ) , 𝑍 𝑐 ( ) , 𝑍 𝑐 ( ) and others. In 2015 and 2019, theLHCb Collaboration discovered pentaquark candidates with hidden charm, 𝑃 𝑐 ( ) , 𝑃 𝑐 ( ) and 𝑃 𝑐 ( ) . The charged heavy-quarkonium like 𝑍 𝑐 and 𝑍 𝑏 states as well asthese 𝑃 𝑐 states are clearly beyond the scope of the conventional quark model for mesonsand baryons, and thus excellent candidates of exotic multiquark states. Understandingthe nature of these structures has been the main concern for hadron spectroscopy, and isa challenge that needs to be solved toward revealing the mystery of how massive hadronsemerge from the interaction between quarks and gluons. It is denoted as 𝜒 𝑐 ( ) according to its quantum numbers in the latest version of Review of ParticlePhysics (RPP) by the Particle Data Group [148]. .4 Exotic hadronic states –43/140– Various models were proposed to explain (some of) these observations, includingmultiquark states, hadronic molecules, hybrid states, mixing of different componentsand non-resonant effects such as kinematical singularities and interference. Theseinvestigations were witnessed by a large number of review articles in the past few years,see Refs. [29, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162,163, 164, 165, 166, 167, 168, 169] emphasizing on various aspects of these new resonantstructures. 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 partnerstates of the observed ones. Thus, in order to understand the pattern behind the messyspectrum of these new hadrons and to be able to classify them into a clear picture, whichcan in turn give important hints towards understanding the confinement mechanism,more experimental measurements are urgently needed. 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 variousexperiments since 2003 are also listed in Table 2.2, together with their productionprocesses and observed decay channels. The nomenclature of the latest RPP is used inthe figure and table and will be used in the following discussion.One sees that the charmonium-like structures were observed mainly in three typesof processes, and many of them were only seen in one particular production process aswell as in only one particular final state. Thus, one immediate question is whether theycan be found in other processes and, in particular, in other types of experiments suchas the electron-proton/electron-ion collisions. Let us first discuss the experiments thathave already significantly contributed to the field.Weak decays of the ground state bottom-hadrons contributed to the observation ofhidden-charm states more than other processes. The decays happen mainly via the singly-CKM suppressed 𝑏 → 𝑐 ¯ 𝑐𝑠 at the quark level. The main experiments are the 𝐵 factoriesBelle, BaBar and the LHCb experiment at LHC. There are two main processes. First, thethree-body decays of 𝐵 mesons with the final state being a kaon and a pair of charmedmesons or a charmonium and light mesons. The maximal mass of a charmonium-likestate 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 reportedso far is the 𝑋 ( ) observed by the LHCb Collaboration [174], close to this bound.Second, the three-body decays of the Λ 𝑏 , such as the Λ 𝑏 → 𝐽 / 𝜓 𝑝𝐾 − , which is theprocess where the hidden-charm pentaquark candidates 𝑃 𝑐 ( ) , 𝑃 𝑐 ( ) , 𝑃 𝑐 ( ) and 𝑃 𝑐 ( ) were discovered at LHCb [175, 176]. The hidden-charm pentaquark state .4 Exotic hadronic states –44/140– 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 statesare listed according to their quantum numbers 𝐼 𝐺 ( 𝐽 𝑃𝐶 ) . The states with quantum numbers notfully determined are listed in the column “? ?? ” with the exception of Υ ( ) which is listedin the 0 − ( −− ) bottomonium column though its 𝐼 𝐺 have not been fixed. For the experimentallyobserved states, the shaded areas indicate the central values of the widths of the observed states. .4 Exotic hadronic states –45/140– Table 2.2: Structures observed experimentally since 2003 in the charmonium mass region andtheir production and decay processes. We group the mesonic structures into three blocks: thosewith 𝑃𝐶 = −− quantum numbers are given in the second block; the isospin-1 structures are givenin the third block; the others are given in the first block. Their quantum numbers can be found inFig. 2.18. The exotic baryon candidates are listed in the fourth block. Here we use the nomenclatureof RPP [148], according to which states are named according to their quantum numbers. For moreinformation of the 𝑋𝑌 𝑍 states and their properties and the original experimental references, seeRef. [148]. 𝑋𝑌 𝑍 Production processes Decay channels 𝜒 𝑐 ( ) 𝑒 + 𝑒 − → 𝐽 / 𝜓 𝑋 , 𝛾𝛾 → 𝑋 a 𝐷 ¯ 𝐷 , 𝛾𝛾 a 𝜒 𝑐 ( ) 𝐵 → 𝐾 𝑋 / 𝐾 𝜋 𝑋, 𝑒 + 𝑒 − → 𝛾 𝑋 , 𝜋 + 𝜋 − 𝐽 / 𝜓, 𝜔𝐽 / 𝜓, 𝐷 ∗ ¯ 𝐷 , 𝐷 ¯ 𝐷 𝜋 ,𝑝 𝑝 / 𝑝 ¯ 𝑝 semi-inclusive, 𝜋 𝜒 𝑐 , 𝛾𝐽 / 𝜓, 𝛾𝜓 ( 𝑆 ) 𝛾 ∗ 𝑁 → 𝑋 𝜋 ± 𝑁 b 𝑋 ( ) 𝐵 → 𝐾 𝑋, 𝛾𝛾 → 𝑋, 𝑒 + 𝑒 − → 𝛾 𝑋 𝜔𝐽 / 𝜓, 𝛾𝛾𝜒 𝑐 ( ) 𝛾𝛾 → 𝑋 , 𝑝 𝑝 semi-inclusive 𝐷 ¯ 𝐷, 𝛾𝛾𝑋 ( ) 𝑒 + 𝑒 − → 𝐽 / 𝜓 + 𝑋 𝐷 ¯ 𝐷 ∗ 𝜒 𝑐 ( ) 𝐵 → 𝐾 𝑋 , 𝑝 ¯ 𝑝 semi-inclusive c 𝜙𝐽 / 𝜓𝑋 ( ) 𝑒 + 𝑒 − → 𝐽 / 𝜓 + 𝑋 𝐷 ∗ ¯ 𝐷 ∗ 𝜒 𝑐 ( ) 𝐵 → 𝐾 𝑋 𝜙𝐽 / 𝜓𝑋 ( ) 𝛾𝛾 → 𝑋 𝜙𝐽 / 𝜓, 𝛾𝛾𝜒 𝑐 ( ) 𝐵 → 𝐾 𝑋 𝜙𝐽 / 𝜓𝜒 𝑐 ( ) 𝐵 → 𝐾 𝑋 𝜙𝐽 / 𝜓𝜓 ( ) 𝐵 → 𝐾𝜓 , 𝑒 + 𝑒 − → 𝜋𝜋𝜓 𝛾 𝜒 𝑐 𝜓 ( ) 𝑝 𝑝 semi-inclusive 𝐷 ¯ 𝐷𝜓 ( / ) 𝑒 + 𝑒 − → 𝑌 , 𝑒 + 𝑒 − → 𝑌 𝛾 ISR 𝜋𝜋𝐽 / 𝜓, 𝜋𝜋𝜓 ( 𝑆 ) , 𝜒 𝑐 𝜔, ℎ 𝑐 𝜋𝜋,𝐷 ¯ 𝐷 ∗ 𝜋, 𝛾 𝜒 𝑐 ( ) , 𝐽 / 𝜓𝐾 ¯ 𝐾𝜓 ( ) 𝑒 + 𝑒 − → 𝑌 , 𝑒 + 𝑒 − → 𝑌 𝛾 ISR 𝜋𝜋𝜓 ( 𝑆 ) , 𝜋𝜋𝜓 ( ) d , 𝐷 ( ) ¯ 𝐷 d 𝜓 ( ) 𝑒 + 𝑒 − → 𝑌 𝜋𝜋ℎ 𝑐 , 𝜋𝜋𝜓 ( ) d 𝜓 ( ) 𝑒 + 𝑒 − → 𝑌 𝛾 ISR 𝜋𝜋𝜓 ( 𝑆 ) , Λ 𝑐 ¯ Λ 𝑐 , 𝐷 + 𝑠 𝐷 𝑠 ( ) − 𝑍 𝑐 ( ) ± 𝑒 + 𝑒 − → 𝜋𝑍 𝑐 , 𝜋𝐽 / 𝜓, 𝐷 ¯ 𝐷 ∗ 𝑏 -hadron semi-inclusive decays 𝑋 ( ) ± 𝑒 + 𝑒 − → 𝜋𝑍 𝑐 𝜋ℎ 𝑐 , 𝐷 ∗ ¯ 𝐷 ∗ 𝑋 ( ) ± 𝐵 → 𝐾 𝑍 𝑐 𝜋 ± 𝜒 𝑐 𝑋 ( ) ± 𝑒 + 𝑒 − → 𝜋 𝑋 𝜋 ± 𝜓 ( 𝑆 ) 𝑋 ( ) ± 𝐵 → 𝐾 𝑍 𝑐 𝜋 ± 𝜂 𝑐 𝑍 𝑐 ( ) ± 𝐵 → 𝐾 𝑍 𝑐 𝜋 ± 𝐽 / 𝜓𝑅 𝑐 ( ) − 𝐵 → 𝐾 𝑅 𝑐 𝜋 − 𝜓 ( 𝑆 ) 𝑋 ( ) ± 𝐵 → 𝐾 𝑍 𝑐 𝜋 ± 𝜒 𝑐 𝑍 𝑐 ( ) ± 𝐵 → 𝐾 𝑍 𝑐 𝜋 ± 𝐽 / 𝜓, 𝜋 ± 𝜓 ( 𝑆 ) 𝑃 𝑐 ( ) + Λ 𝑏 → 𝐾 − 𝑃 𝑐 e 𝑝𝐽 / 𝜓𝑃 𝑐 ( ) + Λ 𝑏 → 𝐾 − 𝑃 𝑐 𝑝𝐽 / 𝜓𝑃 𝑐 ( ) + Λ 𝑏 → 𝐾 − 𝑃 𝑐 𝑝𝐽 / 𝜓𝑃 𝑐 ( ) + Λ 𝑏 → 𝐾 − 𝑃 𝑐 𝑝𝐽 / 𝜓 a From the analysis of Ref. [171]. b It is likely a different state. It was reported by the COMPASS Collaboration in muo-production [172]; however, the 𝜋𝜋 invariant mass spectrum does not agree with thatcoming from a 𝜌 , and a negative 𝐶 -parity is preferred. c Not seen in 𝛾𝛾 → 𝐽 / 𝜓𝜙 and 𝑒 + 𝑒 − → 𝛾𝐽 / 𝜓𝜙 . d Noted as “possibly seen" in RPP. e No signal of 𝑃 𝑐 was seen in 𝛾 𝑝 → 𝐽 / 𝜓 𝑝 [173]. .4 Exotic hadronic states –46/140– that can be produced through such a process needs to have a mass lower than the massdifference between Λ 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 atleast three particles, which complicates the data analysis and may bring ambiguities dueto insufficient treatment of cross channels and three-body final state interaction.Vector charmonium(-like) states are mostly easily studied in 𝑒 + 𝑒 − collisions. Theyhave the same 𝐽 𝑃𝐶 quantum numbers as a virtual photon so that they can be directlyproduced in 𝑒 + 𝑒 − collisions; by emitting a photon to adjust the energy to the interestedregion, they can also be produced using the initial-state radiation (ISR) process, whosecross section, however, is smaller by two orders of magnitude because of the suppressionof 𝛼 . The main experiments include BESIII, CLEO-c, Belle and BaBar. Thus, morevector states have been observed than other quantum numbers, and they are normallyobserved in more channels as well due to the high luminosity of the 𝑒 + 𝑒 − machines. Thereis also one new vector state in the bottomonium mass region, the Υ ( ) , reported byBelle [177]. The structures with other quantum numbers need to be produced through thedecays of higher states or two-photon collisions, and thus have much smaller productionrates or beyond the energy reach of BESIII.Some of the structures were also produced in the prompt production processes athadron colliders, and observed semi-inclusively. The main experiments are CDF andD0 at Tevatron and CMS, ATLAS and LHCb at the LHC. Such processes have muchlarger cross sections than those via virtual photons. However, the large energy andlarge strong-interaction cross sections also imply huge backgrounds, which lowers thedetection efficiency. The types of final state particles that can be efficiently detectedare usually restricted to charged light hadrons and muons, and soft photons are hardlydetected. For the study of exotic hadrons, each of the experiments has its advantages and limita-tions. Different kinds of experiments complement to one another, and they are needed toestablish a more complete picture of the heavy-flavor hadron spectroscopy. Even in thecharm sector, the so-far collected information is not enough to build up a clear picturefor all of these new structures. Furthermore, although it is expected that there should beanalogues of resonances with open or hidden charm in the bottom sector, far fewer stateswith bottom have been observed due to the limitations of the current experiments. Letus 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 ¯ 𝑄 mass spectrum predicted in the Godfrey–Isgur .4 Exotic hadronic states –47/140– W γp (GeV)10 -1 σ γ p ( n b ) γp → c ¯ cXγp → J/ψp CIF(1979)Fermilab(1980)EMC(1982)SLAC(1986)CERN/WA58(1987) J/ψp data before 2002GlueX(2019) Figure 2.19: The dependence of the photoproduction cross sections on the 𝛾 𝑝 c.m. energy forthe exclusive 𝛾 𝑝 → 𝐽 / 𝜓 𝑝 and semi-inclusive 𝛾 𝑝 → 𝑐 ¯ 𝑐𝑋 processes. [173, 180, 181, 182, 183,184, 185, 186, 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. quark model [26, 170]. It is clear that all of the 𝑋𝑌 𝑍 structures are located above or atleast very close to the open-charm thresholds, while there are only a couple of analogousstates in the bottomonium sector. The messy situation of the charmonium(-like) statesnicely illustrates how little we understand the confinement aspect of QCD. Althoughthe importance of the open-charm coupled channels was already noticed in the seminalCornell model [178, 179], their role in forming the observed spectrum is still far frombeing understood. The highly excited states close or above the open-flavor thresholdscontain important information about the long-distance interaction between heavy quarksand about how the light degrees of freedom come into play their role. Thus, a detailedstudy of these states is highly valuable for understanding confinement.Furthermore, no matter how the hidden-charm meson spectrum emerges, one wouldexpect 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 arecrucial to form the spectrum, phenomena similar to those of the 𝑋𝑌 𝑍 states wouldrepeat in these sectors.The EicC energy region covers all these interesting physics. In the following, letus briefly discuss a few topics on heavy-flavor hadron spectroscopy that EicC cansignificantly contribute to. .4 Exotic hadronic states –48/140– Charmonium(-like) states The photoproduction cross section of the exclusive process 𝛾 𝑝 → 𝐽 / 𝜓 𝑝 is at theorder of 10 nb for the c.m. energy of the 𝛾 𝑝 within 10 to 20 GeV, which is the energyregion of EicC. The cross section of the semi-inclusive production of 𝑐 ¯ 𝑐 𝑋 is larger byalmost two orders of magnitude, see Fig. 2.19. The data shown in this figure include theexclusive 𝐽 / 𝜓 production data from Refs. [180, 181, 182, 183, 184, 185, 186] ( 𝐽 / 𝜓 𝑝 data before 2002), [173] (GlueX), and the semi-inclusive 𝑐 ¯ 𝑐 𝑋 data from Refs. [187](CIF), [188] (Fermilab), [189] (EMC), and [190] (SLAC). The data were fitted usingparametrization origined from the vector-meson dominance model of Ref. [191]. Thecross section for the electroproduction process is about two orders of magnitude smallerdue to an additional factor of electromagnetic coupling 𝛼 . Considering an integratedluminosity of 50 fb − , one may estimate that the 𝐽 / 𝜓 events produced from the exclusiveprocess is about O ( × ) . Because almost all excited charmed mesons (baryons)will decay into 𝐷 ( Λ 𝑐 ) and their antiparticles, one can expect that there must be manymore 𝐷 and Λ 𝑐 events. Therefore, in addition to the hidden-charm channels, the 𝑋𝑌 𝑍 charmonium-like states, including the highly excited ones beyond the capability ofBESIII and JLab or those that cannot be produced through the 𝐵 meson decays, canbe studied through open-channel final states. As a benchmark, the production of the 𝜒 𝑐 ( ) and 𝑍 𝑐 ( ) 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 ( ) , 𝑃 𝑐 ( ) , 𝑃 𝑐 ( ) and 𝑃 𝑐 ( ) [175, 176]. In fact, the existence ofnarrow hidden-charm baryon resonances, as hadronic molecules of a pair of charmmeson and charm baryon, have been predicted to exist in the mass region above4 GeV [193, 194, 195, 196, 197, 198, 199]. As mentioned above, similar to the existenceof many hidden-charm 𝑋𝑌 𝑍 states, there should also be lots of hidden-charm baryonicexcited states. Searching for them and verifying the LHCb observations will providevaluable inputs to understanding the spectroscopy of excited hadrons. The nonobserva-tion of the 𝑃 𝑐 states at the GlueX experiment [173] indicates that the branching fractionsof the 𝑃 𝑐 states into 𝐽 / 𝜓 𝑝 to be small (for a combined analysis of the GlueX and LHCbmeasurements, see Ref. [200]). Then the dominant decay modes of the 𝑃 𝑐 should be theopen-charm channels, including the ¯ 𝐷 (∗) Λ 𝑐 and ¯ 𝐷 (∗) Σ 𝑐 [192, 201, 202, 203]. Therefore,at EicC, the 𝑃 𝑐 need to be searched for in exclusive processes with the final states beingnot only the 𝐽 / 𝜓 𝑁 , but also the open-charm ¯ 𝐷 (∗) Λ 𝑐 and ¯ 𝐷 (∗) Σ 𝑐 channels [204, 205].Semi-inclusive processes of these processes will also be a crucial part as they have The 𝑃 𝑐 ( ) here is a broad structure introduced to improve the fitting quality in the 2015 LHCbanalysis [175], and it is not needed to fit the updated 𝐽 / 𝜓 𝑝 invariant mass distribution [176]. However,there is a hint for the existence of a narrow 𝑃 𝑐 ( ) [192] in the new LHCb data. .4 Exotic hadronic states –49/140– W γp (GeV)10 -3 -2 -1 σ γ p ( n b ) γp → b ¯ bXγp → Υ p Favart et al.: W δ Gryniuk et al.Brodsky et al.: 2-gluonMartynov et al.: Q = 0 GeV Martynov et al.: Q = 10 GeV Martynov et al.: Q = 50 GeV EMC(1981)H1(1999)ZEUS(1998) H1(2000)ZEUS(2009)CMS(2016) Figure 2.20: The dependence of the photoproduction cross sections on the 𝛾 𝑝 c.m. energy forthe exclusive 𝛾 𝑝 → Υ 𝑝 and semi-inclusive 𝛾 𝑝 → 𝑏 ¯ 𝑏 𝑋 processes. The EicC energy coverage isdenoted by the shaded area. 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 thesemi-inclusive production rates in the hadronic molecular model of the 𝑃 𝑐 states, see thenext subsection.From the above discussions, one sees that an efficient detection of the 𝐷 / ¯ 𝐷 and Λ 𝑐 particles is essential for the study of the hidden-charm mesons and baryons. FromRPP [148], one finds that the most important decay channels of the 𝐷 + are 𝐾 − 𝜋 + [ ( . ± . ) %] and 𝐾 𝑆 𝜋 + 𝜋 [ ( . ± . ) %], those for the 𝐷 are 𝐾 − 𝜋 + 𝜋 [ ( . ± . ) %] and 𝐾 − 𝜋 + [ ( . ± . ) %], and those for the Λ + 𝑐 are Λ 𝜋 + 𝜋 [ ( . ± . ) %] and 𝑝𝐾 − 𝜋 + [ ( . ± . ) %]. Thus, both the charged and neutral pions and kaons need to beefficiently detected. Once one of the open-charm final state particles is reconstructed, theevents for the other one can be selected from the missing mass spectrum in the relevantenergy region. In this way, searching for hidden-charm states in the open-charm finalstates is promising. Bottom hadrons In Fig. 2.20, we show the cross sections for the exclusive photoproduction of the Υ and for the semi-inclusive 𝑏 ¯ 𝑏 . The shaded area in corresponding to the EicC energyregion covers the hidden-bottom hadron masses. The exclusive data are taken fromRefs. [206, 207] (ZEUS), [185] (H1), and [208] (CMS); the semi-inclusive data are taken .4 Exotic hadronic states –50/140– from Refs. [209] (EMC) and [210] (H1). The models used to fit the data include theempirical 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 = 0, 10, 50 GeV ) [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 Υ 𝑝 is of O ( 10 pb ) ; thus, the correspondingelectroproduction 𝑒 − 𝑝 → 𝑒 − Υ 𝑝 cross section should be of O ( . ) . Considering anintegrated luminosity of 50 fb − , the event number of Υ that can be produced throughthe exclusive Υ 𝑝 process is of O ( ) , consistent with the simulation in Sec. 2.5.1 andthe estimate in Ref. [215]. The cross section for the semi-inclusive 𝑏 ¯ 𝑏 + anything is twoorders of magnitude higher. Thus, millions of bottom mesons 𝐵 and Λ 𝑏 can be produced.If these bottom hadrons can be efficiently detected, the EicC will be able to contributeto the study of excited bottom hadrons. Although the ground state bottom hadronsare more difficult to be detected than their charmed cousins, their life times are muchlonger, making the secondary decay vertices useful in detecting them. Hidden-bottompentaquark states that are expected to be decay into Υ 𝑁 , Λ 𝑏 𝐵 (∗) and Σ 𝑏 𝐵 (∗) final statesmay 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 spec-troscopy. Comparing with experiments utilizing electron-positron collisions and the 𝐵 / Λ 𝑏 decays, one special feature of the EicC is that it has different kinematics whichcan avoid the ambiguity of interpreting resonance signals induced by the so-called tri-angle singularity. Triangle singularity is a type of kinematical singularity, which occursbecause of the simultaneous on-shellness of three intermediate particles, and can pro-duce peaks mimicking the behavior of resonances (for a recent review, see Ref. [29]).For instance, the triangle singularity mechanism have been constructed for producingresonance-like signals for the prominent multiquark candidates 𝑃 𝑐 ( ) [216, 217], 𝑍 𝑐 ( ) ± [218, 219, 220] (see also Refs. [221, 222, 223, 224]), 𝑍 𝑐 ( , ) ± [225]and 𝑋 ( , ) ± [226]. This means that it is essential to distinguish the signals fromresonances from those from kinematical singularities. Triangle singularity is very sen-sitive to the involved kinematical variables such as masses and energies. The examplesmentioned in the above were all reported in the decays of bottom hadrons ( 𝐵 or Λ ),which have fixed masses, or 𝑒 + 𝑒 − collisions. The photoproduction or electroproductionprocesses at EicC have completely different kinematical regions from these experiments;the photon is space-like or nearly on shell, making the occurrence of triangle singular-ities in the exclusive processes impossible. Furthermore, the dependence of the signalson the energy and 𝑄 can also be measured. In addition, the double polarized beamsfacilitate the EicC to determine the quantum numbers, such as spin and parity, of hadron .4 Exotic hadronic states –51/140– e − e − l l (cid:2) p p (cid:2) γ ∗ V l + l − kq e − e − l l (cid:2) p N (cid:2) γ ∗ Z c /Xkq Figure 2.21: Left: The 𝑒 𝑝 → 𝑒 𝑝𝑉 → 𝑒 𝑝𝑙 + 𝑙 − process. Right: The 𝑒 𝑝 → 𝑒 𝜒 𝑐 ( ) 𝑝 and 𝑒 𝑝 → 𝑒𝑍 + 𝑐 ( ) 𝑛 process. resonances. In comparison with hadron colliders, the EicC has a better signal to noiseratio. Furthermore, the EicC covers all the mass regions for charmonium, bottomonium, 𝑃 𝑐 , 𝑃 𝑏 and excited heavy hadrons. As a result, the study of exotic mesons and baryonswill be one of the foci of EicC.A search for the photoproduction of 𝑍 𝑐 ( ) [227] and 𝜒 𝑐 ( ) [172] has beenperformed by COMPASS with muon beam, giving valuable input for the simulation ofEicC. Within similar range of c.m. energy, EicC can search for these and also other stateswith more than one order higher luminosity. Furthermore, with solid angle coverage,especially hadron PID in the forward angle and good vertex detector for decay topology,the acceptance and reconstruction efficiency of EicC are expected to be significantlyincreased, so the discovery potential of exotica states will be exploited. In this subsection, more quantitative estimates of the production rates for a selected list ofexotic hadron candidates and simulations of the 𝑒 𝑝 → 𝑒 𝜒 𝑐 ( ) 𝑝 , 𝑒 𝑝 → 𝑒𝑍 + 𝑐 ( ) 𝑛 , 𝑒 𝑝 → 𝑒𝑃 𝑐 → 𝑒𝐽 / 𝜓 𝑝 , and 𝑒 𝑝 → 𝑒𝑃 𝑏 → 𝑒 Υ 𝑝 processes are reported. For more modelestimates of the exclusive productions of hidden-charm and bottom exotic hadrons, werefer to Refs. [172, 204, 205, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238,239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250].Motivated by the heavy quark flavor symmetry for the potential between heavymesons and baryons, analogues of the pentaquark candidates 𝑃 𝑐 in the bottom sector,labeled as 𝑃 𝑏 here, are expected to exist [199, 237, 251, 252, 253, 254, 255, 256, 257,258]. A resonant state 𝑃 𝑏 coupling to Υ 𝑝 with a mass around 11.12 GeV and a widthranging from tens of MeV to 300 MeV is predicted by nearly all models. We simulatethe exclusive electroproduction of two 𝑃 𝑏 at EicC with a width of 30 MeV ( 𝑃 𝑏 ( narrow ) )and 300 MeV ( 𝑃 𝑏 ( wide ) ), respectively, together with the three narrow 𝑃 𝑐 states with theresonance parameters reported by LHCb.The process is depicted in the left panel of Fig. 2.21, where 𝑉 represents the 𝐽 / 𝜓 .4 Exotic hadronic states –52/140– Table 2.3: Estimated event numbers that can be collected at EicC assuming an integratedluminosity of 50 fb − . The lepton pairs 𝑙 + 𝑙 − denote both 𝜇 + 𝜇 − and 𝑒 + 𝑒 − . The event numbers areestimated using the assumed detection efficiencies listed in the third column, which are expectedto be higher in the middle rapidity than that in the forward region. Exotic states Production/decay processes Detection efficiency Expected events 𝑃 𝑐 ( ) 𝑒 𝑝 → 𝑒𝑃 𝑐 ( ) ∼ 30% 15 − 𝑃 𝑐 ( ) → 𝑝𝐽 / 𝜓𝐽 / 𝜓 → 𝑙 + 𝑙 − 𝑃 𝑐 ( ) 𝑒 𝑝 → 𝑒𝑃 𝑐 ( ) ∼ 30% 20 − 𝑃 𝑐 ( ) → 𝑝𝐽 / 𝜓𝐽 / 𝜓 → 𝑙 + 𝑙 − 𝑃 𝑐 ( ) 𝑒 𝑝 → 𝑒𝑃 𝑐 ( ) ∼ 30% 10 − 𝑃 𝑐 ( ) → 𝑝𝐽 / 𝜓𝐽 / 𝜓 → 𝑙 + 𝑙 − 𝑃 𝑏 ( narrow ) 𝑒 𝑝 → 𝑒𝑃 𝑏 ( narrow ) ∼ 30% 0 − 𝑃 𝑏 ( narrow ) → 𝑝 ΥΥ → 𝑙 + 𝑙 − 𝑃 𝑏 ( wide ) 𝑒 𝑝 → 𝑒𝑃 𝑏 ( wide ) ∼ 30% 0 − 𝑃 𝑏 ( wide ) → 𝑝 ΥΥ → 𝑙 + 𝑙 − 𝜒 𝑐 ( ) 𝑒 𝑝 → 𝑒 𝜒 𝑐 ( ) 𝑝 ∼ 50% 0 − 𝜒 𝑐 ( ) → 𝜋 + 𝜋 − 𝐽 / 𝜓𝐽 / 𝜓 → 𝑙 + 𝑙 − 𝑍 𝑐 ( ) + 𝑒 𝑝 → 𝑒𝑍 𝑐 ( ) + 𝑛 ∼ 60% 90 − 𝑍 + 𝑐 ( ) → 𝜋 + 𝐽 / 𝜓𝐽 / 𝜓 → 𝑙 + 𝑙 − ( Υ ) and the 𝑃 𝑐 ( 𝑃 𝑏 ) couples to the 𝐽 / 𝜓 𝑁 ( Υ 𝑁 ) in the 𝑠 -channel. The non-resonantbackground is modeled by Pomeron-exchange to be discussed in Sec. 2.5.1. The 𝑃 𝑐 / 𝑃 𝑏 states are produced from the interaction between the virtual photon, emitted from theelectron beam, and the proton beam in the 𝑠 -channel. The upper limit of productionrates at EicC can be determined by the upper limit of cross section of 𝛾 𝑝 → 𝑃 𝑐 → 𝐽 / 𝜓 𝑝 measured by the GlueX Collaboration [173], by properly including the photon flux and 𝑄 dependence of amplitudes. According to the analysis of the LHCb data, the lowerlimit of the branching ratio 𝑃 𝑐 → 𝐽 / 𝜓 𝑝 is around 0.5% [200], and we assume the samelower limit for the 𝑃 𝑏 → Υ 𝑝 . The lower limit of production rates at EicC is obtained bythe vector meson dominance (VMD) model, see, e.g. [245, 249].After taking into account the detection efficiency and the dilepton decay rates of the 𝐽 / 𝜓 and Υ , the expected production rates of these exotic states at EicC are shown inTable 2.3. Here the detection efficiencies in the third column are estimated from thesimulated distribution of final-state particles. The production rates on light nuclei aresupposed to be larger [241, 248], which however will have lower luminosity. The distri-butions of the invariant mass spectra, the transverse momenta, the pseudo-rapidities, and .4 Exotic hadronic states –53/140– M(GeV) E n t r i es MassMass (GeV) t p E n t r i es t p Pb narrowPb widePc4312 t p - - - - - - Rapidity E n t r i es RapidityRapidity - - - - - - h E n t r i es PseudoRapidityPseudoRapidity Figure 2.22: The distributions of invariant masses, transverse momenta, pseudo-rapidities andrapidities of the 𝑃 𝑐 and 𝑃 𝑏 states. the rapidities of the 𝑃 𝑏 / 𝑃 𝑐 states are presented in Fig. 2.22. They are obviously charac-terized by the 𝑠 -channel resonances, with small transverse momenta and narrow rangesof pseudo-rapidity and rapidity, apparently different from the non-resonant Pomeron-exchange contribution which is smoothly spanned in the full range, as demonstrated indetailed investigation [247, 249]. It is suggested to extract the pentaquark signal fromlarge non-resonant contribution with a proper kinematic cut [249].As discussed above, the cross section of the open charm channel ¯ 𝐷 (∗) Λ 𝑐 is expectedto be much bigger than the that of 𝐽 / 𝜓 𝑝 , so is the case of the open bottom channel¯ 𝐵 (∗) Λ 𝑏 in comparison with the Υ 𝑝 . In particular, the branching fractions of the 𝑃 𝑐 and 𝑃 𝑏 states into open-flavor channels are expected to be at least one-order-of-magnitudelarger than those of the 𝐽 / 𝜓 𝑝 and Υ 𝑝 . In addition, as mentioned in Section 2.4.2, theopen-charm ground state hadrons could be reconstructed at the level of 10%. Thus, it isoptimistic that the 𝑃 𝑐 states can be studied in detail through processes 𝑒 𝑝 → 𝐽 / 𝜓 𝑝 and 𝑒 ¯ 𝐷 (∗) Λ 𝑐 at EicC. If the open-bottom hadrons can also be efficiently reconstructed, thehypothesized 𝑃 𝑏 states may also be sought at EicC.In addition to the 𝑃 𝑐 and 𝑃 𝑏 states, the exclusive productions of the 𝜒 𝑐 ( ) and 𝑍 𝑐 ( ) are also simulated. The 𝜒 𝑐 ( ) is arguably the most interestingcharmonium-like state. It mass is ( . ± . ) MeV, coinciding with the 𝐷 ¯ 𝐷 ∗ .4 Exotic hadronic states –54/140– M(GeV) E n t r i es + (3900) c Mass of Z + (3900) c Mass of Z (GeV) t p E n t r i es + (3900) c of Z t p bins Q Total ) [0 - 1](GeV ) [1 - 5](GeV + (3900) c of Z t p - - - - - h E n t r i es + (3900) c PseudoRapidity of Z + (3900) c PseudoRapidity of Z - - - Rapidity E n t r i es + (3900) c Rapidity of Z + (3900) c Rapidity of Z Figure 2.23: The distributions of invariant masses, transverse momenta, pseudo-rapidities andrapidities of the 𝑍 𝑐 ( ) + in different 𝑄 ranges. threshold exactly, and width is smaller than 1.2 MeV [148]. The quantum numbersare 1 ++ [261]. It is the first discovered and most studied exotic meson candidate in thecharmonium region [262]. The mass of 𝑍 𝑐 ( ) ± is (3888.4 ± ± 𝐽 / 𝜓𝜋 ± spectrum by BESIII [263] andBelle [264] and confirmed by other experiments [265, 266]. The BESIII collaborationidentified its spin-parity as 1 + and isospin as 1 [267, 268]. As a charged state decayinginto a charmonium, the quark content of 𝑍 𝑐 ( ) contains at least 𝑢 ¯ 𝑑𝑐 ¯ 𝑐 , making it aprominent candidate of tetraquarks or molecular states.The right panel of Fig. 2.21 shows the 𝑒 𝑝 → 𝑒 𝜒 𝑐 ( ) 𝑝 and 𝑒 𝑝 → 𝑒𝑍 + 𝑐 ( ) 𝑛 processes with the yellow ellipse representing the 𝑡 -channel exchange. The 𝛾 𝑝 → 𝜒 𝑐 ( ) 𝑝 can proceed through the exchange of vector mesons (e.g. 𝜌 , 𝜔 and 𝐽 / 𝜓 ) inthe 𝑡 -channel. The 𝛾 𝑝 → 𝑍 + 𝑐 ( ) 𝑛 can proceed through charged mesons (e.g. 𝜋 + and 𝑎 + ) [228] or mesonic Regge trajectories [230] in the 𝑡 -channel. Around the averagedc.m. energy 𝑊 𝛾 𝑝 = . 𝑍 𝑐 ( ) , and the nonobservation sets an upper limitfor the cross section: B ( 𝑍 𝑐 ( ) ± → 𝐽 / 𝜓𝜋 ± ) 𝜎 ( 𝛾𝑁 → 𝑍 𝑐 ( ) ± 𝑁 ) < 52 pb at The mass quoted in RPP is from averaging previous experiments. Recently, the LHCb Collaborationreported precise determinations of the mass and width [259, 260]. In particular, a Flatté analysis, whichis more proper than the Breit-Wigner one for near-threshold states, is performed in Ref. [259]. .4 Exotic hadronic states –55/140– l l ′ γ ∗ p allXH H ′ Figure 2.24: The mechanism considered in Ref. [270] for the semi-inclusive production of exotichadrons (denoted as 𝑋 ) which couple strongly to a pair of hadrons ( 𝐻 and 𝐻 (cid:48) ) in lepton-protoncollisions. the 90% confidence level [227]. In a similar energy region, the COMPASS Collabo-ration has also obtained an upper limit for the 𝜒 𝑐 ( ) at the same confidence level: B ( 𝜒 𝑐 ( ) → 𝐽 / 𝜓𝜋𝜋 ) 𝜎 ( 𝛾𝑁 → 𝜒 𝑐 ( ) 𝑁 ) < . 𝜒 𝑐 ( ) and 𝑍 𝑐 ( ) + are constrained by the COMPASS measurements. Thelower bounds are very roughly estimated by reducing these values by two orders ofmagnitude, as inferred from the difference between the lower and upper bounds of the 𝑃 𝑐 / 𝑃 𝑏 production rates.It is expected that a considerable amount of 𝑍 + 𝑐 ( ) could be observed while theevents of 𝜒 𝑐 ( ) are lower. The distributions of the invariant mass distribution, thetransverse momentum, the pseudo-rapidity and the rapidity for the 𝑍 + 𝑐 ( ) are shownin Fig. 2.23 for different 𝑄 regions. The red cross histogram is the contribution from0 < 𝑄 < , the blue star one is that from 1 < 𝑄 < , and the black circleone is the overall contribution. It is seen that most of the events are within the low 𝑄 range.The above simulations show that the exotic hadrons produced at EicC are close to themiddle rapidity range. This is beneficial for detection. Thus, EicC provides an excellentplatform to study the nature of known, but barely understood, charmonium-like statesand search for new states.In addition to the exclusive processes discussed so far, exotic hadrons can be searchedfor in semi-inclusive processes. In particular, for those hidden-flavor exotic hadronswhich couple strongly to a pair of heavy hadrons, such as the 𝜒 𝑐 ( ) and the 𝑍 𝑐 ( ) , one can achieve an order-of-magnitude estimate of the production crosssections following the method of Refs. [271, 272, 273, 274, 275]. The production can .4 Exotic hadronic states –56/140– k(GeV) / d k ( nb / G e V ) s d at EicC *0 D *0 D k (cid:181) fit with 0.05 0.1 0.15 0.2 0.25 0.3 0.35 k(GeV) / d k ( nb / G e V ) s d at EicC D *+c S k (cid:181) fit with Figure 2.25: Differential cross sections 𝑑𝜎 / 𝑑𝑘 (in units of nb/GeV) for the semi-inclusiveproduction of 𝐷 ∗ ¯ 𝐷 ∗ and Σ ∗+ 𝑐 ¯ 𝐷 through electron-proton scattering [270], where 𝑘 is the c.m.momentum of the open-charm hadrons. The histograms are obtained from the Pythia eventgenerator while the curves are fitted according to the momentum dependence 𝑘 . The electronand proton energies are set to 3.5 and 20 GeV, respectively. be factorized into a short-distance part and a long-distance part. At short distances thehadron pairs of interest are produced, which can be simulated using the Pythia eventgenerator [276]. The hadron pairs then merge to form the exotic hadrons which coupleto them strongly, and the long-distance piece can be computed at the hadronic level. Themechanism is shown in Fig. 2.24. This mechanism, when applied to hadron colliders,can produce cross sections for the prompt production of the 𝜒 𝑐 ( ) if the momentumintegration range for the hadron-hadron Green’s function extends up to a few hundredsof MeV [272, 274, 275].As an example, in Fig. 2.25 we show the differential cross sections generated usingPythia [276] for the semi-inclusive productions of the 𝐷 ∗ ¯ 𝐷 ∗ and Σ ∗+ 𝑐 ¯ 𝐷 pairs inelectron-proton collisions with the electron and proton beam energies set to 3.5 and20 GeV, respectively. The distribution can be well fitted by a 𝑘 dependence with 𝑘 thec.m. momentum of the open-charm hadrons. The 𝑋 𝐻𝐻 (cid:48) coupling in Fig. 2.24 can beextracted from measurements or evaluated in phenomenological models. In particular,for the hadronic molecular model, the coupling is connected to the binding energy(see [159]). The loop in Fig. 2.24 is ultraviolet divergent, and the divergence in principalneeds to be absorbed into the multiplicative renormalization of the short-distance part.For an order-of-magnitude estimate, the loop integral is evaluated using a Gaussianregulator with a cutoff Λ of 0.5 and 1 GeV. We list rough estimates for the productioncross sections of the 𝜒 𝑐 ( ) , 𝑍 𝑐 ( ) + , , 𝑋 ( ) and the 𝑃 𝑐 states observed byLHCb in Table 2.4. The estimates for four more 𝑃 𝑐 states predicted in the hadronicmolecular model using heavy quark spin symmetry [192, 197, 277] are also presentedwith masses and couplings taken from Ref. [192]. Considering an integrated luminosityof 50 fb − , this leads to O ( ) events for each of the 𝑃 𝑐 states, and O ( ) for the .5 Other important exploratory studies –57/140– Table 2.4: Rough estimates of integrated cross sections (in units of pb) at EicC for the semi-inclusive production of a few selected states in the hadronic molecular (HM) model [270], where Λ refers to the cutoff in the Gaussian regulator of the two-hadron Green’s function. The processesare 𝑒 − + 𝑝 → HM+all, where HM = 𝜒 𝑐 ( ) , 𝑍 𝑐 ( ) /+ , 𝑋 ( ) , and seven 𝑃 𝑐 states.The energy configuration considered here is 𝐸 𝑒 = . 𝐸 𝑝 = 20 GeV. The branchingfractions of further decays and the detection efficiency are not yet considered here. Channel Λ = . Λ = . 𝜒 𝑐 ( ) 𝐷 ¯ 𝐷 ∗ 21 89 𝑍 𝑐 ( ) ( 𝐷 ¯ 𝐷 ∗ ) . × . × 𝑍 𝑐 ( ) + ( 𝐷 ¯ 𝐷 ∗ ) + . × . × 𝑋 ( ) ( 𝐷 ∗ ¯ 𝐷 ∗ ) . × . × 𝑃 𝑐 ( ) Σ 𝑐 ¯ 𝐷 𝑃 𝑐 ( ) Σ 𝑐 ¯ 𝐷 ∗ 𝑃 𝑐 ( ) Σ 𝑐 ¯ 𝐷 ∗ 𝑃 𝑐 ( ) Σ ∗ 𝑐 ¯ 𝐷 𝑃 𝑐 ( ) Σ ∗ 𝑐 ¯ 𝐷 ∗ 𝑃 𝑐 ( ) Σ ∗ 𝑐 ¯ 𝐷 ∗ 𝑃 𝑐 ( ) Σ ∗ 𝑐 ¯ 𝐷 ∗ 𝜒 𝑐 ( ) and O ( ) events for 𝑍 𝑐 states. Notice that neither branching fractions offurther decays nor the detection efficiency is taken into account here. For more details,we refer to Ref. [270].To conclude this section, it is promising that EicC can contribute significantly to thestudy of heavy-flavor exotic hadrons, in particular to charmonium-like states and hidden-charm pentaquarks, and thus contribute to the understanding of how the emergent hadronspectrum is formed by the nonperturbative strong interaction. The major part of the mass of observable matter is carried by the nucleons (neutronsand protons) that constitute all the atomic nuclei in the Universe. Nucleons themselvesare constituted from the gluons and quarks of QCD. So a key piece of the puzzlesurrounding the origin of mass lies with understanding how the proton’s mass emergesfrom the QCD Lagrangian, expressed in terms of light valence-quarks, massless gluonsand the interactions between them. The current-quark masses are produced by the Higgsmechanism; but based on those masses, a straightforward application of notions fromrelativistic quantum mechanics delivers a proton mass that is two orders-of-magnitudetoo small. Plainly, the source of the proton’s mass is far more subtle. Consider, therefore, .5 Other important exploratory studies –58/140– a sum rule connected with the trace of QCD’s energy-momentum tensor (EMT) [278]: 𝑚 𝑝 = 𝐻 𝑚 + 𝐻 𝑎 , 𝐻 𝑚 = (cid:104) 𝑝 | 𝑚 ¯ 𝜓𝜓 | 𝑝 (cid:105) , 𝐻 𝑎 = (cid:104) 𝑝 | [ 𝛾 𝑚 𝑚 ¯ 𝜓𝜓 + 𝛽 ( 𝑔 ) ( 𝐸 − 𝐵 )] | 𝑝 (cid:105) , (2.6)where: (cid:104) 𝑝 | 𝑝 (cid:105) = 1; and 𝑚 represents the light-quark current masses, whose values areof the order 2-4 MeV at a renormalisation scale 𝜁 = 𝐻 𝑚 term in Eq. (2.6) is unambiguous; but there are many ways to decomposeand rearrange 𝐻 𝑎 [279, 280]. One popular approach is to focus on the energy of a protonat rest and write [281, 282, 283]: 𝑚 𝑝 = 𝐻 𝑚 + 𝐻 𝑎 = 𝐻 𝑚 + 𝐻 𝑞 + 𝐻 𝑔 + 𝐻 𝑎 , (2.7)where 𝐻 𝑞 = (cid:104) 𝑝 | 𝜓 † (− 𝑖 D · 𝛼 ) 𝜓 | 𝑝 (cid:105) , 𝐻 𝑔 = (cid:104) 𝑝 | ( 𝐸 + 𝐵 ) | 𝑝 (cid:105) (2.8)are, respectively, the quark and gluon kinetic energies. Contemporary lattice-QCD cal-culations reveal [284, 285, 286] that only about 9% of 𝑚 𝑝 is generated by the 𝑢 -, 𝑑 -, 𝑠 -quark contributions in 𝐻 𝑚 . However, even this contribution is nontrivial because itis built from products of the Higgs-generated current-quark masses and enhancementfactors that express nonperturbative QCD dynamics, viz . 𝐻 𝑚 ∼ 𝑚 Higgs × (cid:104) 𝑝 | ¯ 𝜓𝜓 | 𝑝 (cid:105) np QCD .The remaining 91% is essentially dynamical. It can be considered as the contributiongenerated by strong QCD forces through the trace anomaly; or in the second decom-position, broken into identified pieces that include those from quark and gluon kineticenergies. Nonetheless, no matter how one chooses to cut the pie, a very large fractionof the proton’s mass emerges as a dynamical consequence of strong interactions withinQCD.As noted above and described in more detail below, the appearance of a nonzerocontribution to the trace of the QCD EMT, call it Θ , is a quintessentially quantum fieldtheoretical effect. Empirically, the expectation value of Θ is large in almost every hadronstate. The exception is the chiral-limit pseudoscalar meson, for which the expectationvalue is expected to vanish. Providing a mathematically rigorous proof that theseoutcomes are truly dynamical consequences of QCD would constitute a solution to oneof the seven Millennium Prize Problems [287]. Modern progress in theory is seeminglybringing such a proof within reach; and numerical simulations of lattice-regularized .5 Other important exploratory studies –59/140– QCD are beginning to yield quantitative results for the independent terms in Eq. (2.7).Given the fundamental importance of the scale set by 𝑚 𝑝 , much attention is nowfocused on the experimental confirmation of Eq. (2.6). In this context it has been argued,using the operator product expansion and low-energy theorems [288, 289, 290], thatthe heavy-vector-meson–proton scattering amplitude near threshold is dominated by 𝐻 𝑎 and sensitive to the 𝐻 𝑚 correction. Recent theoretical study also suggests that thisprocess at large photon virtualities 𝑄 can be used to extract the gluon part of theproton gravitational form factor and sensitive to the trace anomaly effect at subleadinglevel[290]. A preliminary analysis of GlueX data on 𝐽 / 𝜓 photoproduction in Hall-D atJLab is broadly consistent with the prediction. However, a range of theoretical issuescomplicate the interpretation of such 𝐽 / 𝜓 measurements in this way and substantiallymore work is needed before firm conclusions can be drawn.On the other hand, the case for a connection between the Υ 𝑝 near-threshold scatteringamplitude and the proton mass sum rule is theoretically much cleaner. Experimentally,this system is inaccessible at JLab; and existing measurements at other facilities arerestricted to 𝑊 (cid:38) 90 GeV, as evident in Fig. 2.19, which is far above threshold. Conse-quently, the EicC can here contribute uniquely, being able to explore collision energies 𝑊 < 20 GeV. - 9 - 7 - 5 - 3 - 1 Q > 1 G e V Q < 1 G e V - 1 (cid:214) s = 1 5 . 0 G e V (cid:214) s = 1 6 . 7 5 5 G e V (cid:1)(cid:2)(cid:3)(cid:1)(cid:2) ¡ (cid:3)(cid:1)(cid:2) m + m - (cid:214) s = 1 7 . 7 5 5 G e V (cid:214) s = 2 0 . 0 G e V4 7 2 e v e n t s Counts Q ( G e V ) Counts (cid:214) s ( G e V ) E i c C 5 0 f b - 1 a l l c o u n t s c o u n t s w i t h Q < 1 G e V Figure 2.26: Distribution of 𝑒 𝑝 → 𝑒 𝑝 Υ → 𝑒 𝑝𝜇 + 𝜇 − events, assuming 50 fb − integratedluminosity. The 𝑒 𝑝 central energy √ 𝑠 = . 755 GeV in the figure corresponds to that ofEicC. Cases with central energy √ 𝑠 = . 0, 17 . 755 and 20 . √ 𝑠 = . 755 GeV is expected for a running to accumulate 50 fb − luminosity. Left panel –number of events as a function of photon virtuality, 𝑄 ; and right panel – event number as afunction of √ 𝑠 . Using the reaction 𝑒 𝑝 → 𝑒 𝑝 Υ → 𝑒 𝑝𝑙 + 𝑙 − , as pictured in Fig. 2.21 where 𝑉 = Υ andthe orange area represents a 𝑡 -channel Pomeron [214, 291], the distribution of eventsachievable with EicC is shown in Fig. 2.26. It seems that the cross section estimationwithin Pomeron exchange under a proper consideration of phase space [214] is indeedconsistent at the order-of-magnitude level with other models as shown in Fig. 2.20,in which dipole Pomeron model is used as the input of simulation. Evidently, EicC .5 Other important exploratory studies –60/140– could produce around 600 events under the proposed design, 80-85% of which lie in the 𝑄 < region, with more than 90% at 𝑄 < 10 GeV . Moreover, if the two decaychannels Υ → 𝜇 + 𝜇 − , 𝑒 + 𝑒 − are detected simultaneously, the number of reconstructedevents is even larger. Fig. 2.27 displays the anticipated reconstruction profiles of the Υ in the distributions of mass, transverse momentum, rapidity and quasi-rapidity. Thoughthe detector reconstruction efficiency would be lower than that of the resonant processin Tab. 2.3, one can confidently assume a value of 20%, given that the final states are allcharged particles. So it is feasible to investigate detailedly the 𝑡 -dependent cross sectionsat EicC. M(GeV) E n t r i es MassMass (GeV) t p E n t r i es t p t p - - - - Rapidity E n t r i es RapidityRapidity - - - - - - - - - - h E n t r i es PseudoRapidityPseudoRapidity Figure 2.27: Reconstruction profiles in the distributions of mass, transverse momentum, rapidityand quasi-rapidity, for the final state Υ in the reaction 𝑒 𝑝 → 𝑒 𝑝 Υ → 𝑒 𝑝𝜇 + 𝜇 − . This discussion demonstrates that EicC can deliver precision in the study of Υ production and potentially thereby open a window onto the origins of the proton’s mass.As a significant collateral benefit, Υ production is an important background that mustbe understood when analysing data taken in searches for the hidden-bottom five-quarkstate, 𝑃 𝑏 . Theoretical imperatives for investigating and revealing the structure of light pseudoscalarmesons are detailed in Sec. 2.6. The case has many facets because the pion is the lightest .5 Other important exploratory studies –61/140– known hadron and it has a unique and crucial position in nuclear and particle physics[292]. For example, the pion is the closest approximation to a Nambu-Goldstone (NG)boson in Nature. It is massless in the absence of Higgs-boson couplings into QCD andremains unusually light when those couplings are switched on. In addition, this lightpion is essential to the formation of nuclei, carrying the strong force over length-scaleslarge enough to enforce stability against electromagnetic repulsion between the protonswithin a nucleus. Thus, understanding pion structure is of the utmost importance. Twoclear paths are available: namely, the measurement of pion elastic form factors and ofpion structure functions.Existing empirical knowledge of pion structure is poor. Elastic form factor mea-surements do not extend beyond 𝑄 = . 45 GeV [293, 294, 295, 296, 297, 298] andexisting structure function measurements are more than thirty years old [299, 300, 301,302, 303, 304]. The kaon situation is worse; and that is unsatisfactory for many morereasons. Largest amongst them being that the standard model of particle physics hastwo sources of mass: explicit, generated by Higgs boson couplings; and emergent,arising from strong interaction dynamics, responsible for the 𝑚 𝑁 ∼ e.g . CP-violation,discovered in neutral kaon decays [305]. Thus, knowledge of kaon structure is necessarybecause it provides a window onto the interference between Higgs boson effects andemergent mass [306, 307].The impediment to experimentally mapping the structure of light pseudoscalarmesons is simply explained. These systems are unstable, they decay quickly: so, how canone build a target? One answer is to use the Drell-Yan process at high-energy accelera-tors. This is the mode exploited thirty years ago [299, 300, 301, 302, 303, 304]. Anotherapproach is to measure the leading neutron in high-energy 𝑒 𝑝 collisions [308, 309].In these processes, the range of light-front momentum fraction, 𝑥 , has been somewhatlimited and existing errors are large.At high-luminosity facilities, the Sullivan process, illustrated in Fig. 2.28, becomes avery good method for for gaining access to meson targets. The approach capitalizes on thefeature that a proton is always surrounded by a meson cloud and can sometimes be viewedas a correlated 𝜋 + 𝑛 ( 𝐾 + Λ ) system. Theory predicts [310] that such processes providereliable access to a pion target on − 𝑡 (cid:46) . ; and for the kaon, on − 𝑡 (cid:46) . .The 12 GeV-upgraded JLab facility will exploit these reactions to extend the 𝑄 reachof existing 𝜋 and 𝐾 form factor measurements [311, 312] and the 𝑥 -range of availabledata on the pion structure function [313]. Efforts will also be made to measure the .5 Other important exploratory studies –62/140– Figure 2.28: Sullivan processes: a nucleon’s pion cloud provides access to (a) pion elastic formfactor and (b) pion parton distribution functions. The intermediate pion, 𝜋 ∗ ( 𝑃 = 𝑘 − 𝑘 (cid:48) ) withthe Mandelstam variable 𝑡 = 𝑃 , is off-shell. kaon structure function [314]. Given the wider kinematic range of EicC, its capacity toachieve these goals will be far greater. At the EicC, the scattering angle and energy of thefinal state baryons can be measured precisely, to tag the Sullivan process and to measurethe invariant mass of the virtual light mesons. Technologies of the far-forward hadroncalorimeter and trackers could be learned from projects at HERA (H1 and ZEUS), andfrom similar experiments at the US-EIC. The final state neutron at the EicC has energyaround 15 GeV, a theta angle around 25 mrad, and 𝑝 𝑇 < √︁ ( 𝐸 / 𝐺𝑒𝑉 ) and the spatial resolution to be 1 cm for the far-forwardneutron detector, one can estimate the resolution for the invariant mass of the virtualmeson, 𝜎 | 𝑚 ( 𝜋 ∗) | | 𝑚 ( 𝜋 ∗ )| , to be around 27% at the EicC. (GeV Q00.20.40.6 ) ( Q / K p F Q , monopole form p F -1 , EicC 50 fb p F -1 , EicC 50 fb K F -1 , EIC-US 20 fb p FJLab 12 GeV MCJLab 6 GeV data Figure 2.29: Projected statistical errors on EicC pion form factor measurements compared withthose at the US EIC [306] and JLab 12 GeV program [315]. Also depicted: extant JLab dataobtained by the F 𝜋 -Collaboration [294, 295, 296, 297, 298]; and statistical error projections forkaon form factor measurements at EicC. Application and experience have delivered a reliable approach to obtaining the pionelastic form factor, 𝐹 𝜋 ( 𝑄 ) , from the Sullivan process [316, 317, 318, 319]. The longitu-dinal electroproduction cross-section is expressed such that 𝐹 𝜋 ( 𝑄 ) is the only unknown,which can be determined by comparison between data and the model. The 𝜋 + / 𝜋 − pro-duction ratio extracted from electron-deuteron beam collisions in the same kinematics .5 Other important exploratory studies –63/140– as charged pion data from electron-proton collisions is used to ensure that the longi-tudinal cross-section has been isolated [292]. Fig. 2.29 shows that a high-luminosity,high-energy EicC can deliver precise results on pion and kaon electromagnetic formfactors, providing detailed maps on the domain 𝑄 / GeV ∈ [ , ] , which has thehighest physics discovery potential.The estimates in Fig. 2.29 were prepared using the following cuts: | 𝑡 | < . 𝑊 / GeV ∈ ( , ) . Separating the data into ten bins on 𝑄 / GeV ∈ [ , ] ,the statistical errors on 𝐹 𝜋 ( 𝑄 ) data are competitive with all other existing proposals.Regarding the size of the estimated statistical errors, the same is true for the EicC kaonform factor measurement.Fig. 2.28(b) shows that a Sullivan process can also be used to measure 𝜋 and 𝐾 structure functions. Compared with elastic form factor measurements, the cross-sectionis much larger because the meson target is shattered. Deep inelastic 𝑒𝜋 interactions areensured by selecting events in which the transverse momentum of the tagged final-stateneutron is small and its longitudinal momentum exceeds 50% of that of the incomingproton.For kaon structure functions, the tagged outgoing system is the Λ -baryon.The projected statistical precision of an EicC pion structure function measurementis sketched in Fig. 2.30. It assumes roughly one year of running and is based on aMonte-Carlo simulation of leading-neutron tagged DIS with the pion valence-quarkdistribution function taken from Ref. [320]. Fig. 2.30 indicates that EicC can map thedomain 𝑥 𝜋 ∈ ( . , . ) with precision, yielding data that could be crucial to resolvingthe pion structure function controversy described in Sec. 2.6.3.2. Great progress has been made in the literature in understanding the fundamental structureof the nucleon in recent years. However, we still know little about the properties anddistributions of the heavy quarks in nucleon. As a potential constituent of the nucleon,information for those heavy-flavor content plays an important role in testing StandardModel (SM), and in searching for new physics beyond the SM.Heavy content in nucleon is predicted theoretically in QCD theory. In the light-coneframework, the wave function of a proton can be expanded in terms of superposition ofFock states as following, | 𝑝 (cid:105) = 𝑐 | 𝑢𝑢𝑑 (cid:105) + 𝑐 | 𝑢𝑢𝑑𝑔 (cid:105) + 𝑐 | 𝑢𝑢𝑑𝑐 ¯ 𝑐 (cid:105) + · · · . (2.9)Here, | 𝐹 (cid:105) are the Fock states, and the coefficients 𝑐 𝑗 ( 𝑗 = , , · · · ) are proportional .5 Other important exploratory studies –64/140– p x00.20.40.6 ) -t ( G e V > 0.75 L , x < 5 GeV < Q X < 0.5 GeV, M nT P -1 EicC 50 fb - - ( % ) p S t a t i s t i c a l err o r o f F Figure 2.30: Projected statistical uncertainty on pion structure function in a certain 𝑄 bin as afunction of the four-momentum-transfer − 𝑡 and the Bjorken-x of pion. The cuts for producingthe projection are also shown in the plot. In order to select the scattering between electron andvirtual pion, a cut on 𝑥 𝐿 > . 75 is made [309]. Moreover, the detection efficiency for the finalstate neutron is assumed to be 50%. The measurement at EicC could be performed on a largekinematic domain with uncertainty that is uniformly (cid:46) to the wave function amplitudes of Fock components [321, 322, 323]. It indicates thatthere are heavy charm quarks arise in the proton, even the states such as | 𝑢𝑢𝑑𝑐 ¯ 𝑐 (cid:105) areextremely rare. On the view point of QCD theory, the extra 𝑐 ¯ 𝑐 pair in the proton can begenerated in two distinct processes involving in perturbative and nonperturbative effects.One probable charm content arisen in a proton is the “extrinsic charm (EC)". Inthis case, a gluon radiates from the valence quark in the proton, and then splits to a 𝑐 ¯ 𝑐 pair associated with large transverse momentum. The gluon must be hard enoughin order to produce a heavy 𝑐 ¯ 𝑐 pair. The process is therefore governed by the QCDevolution corresponding to the short distance effects. In this scenario, the charm andanti-charm quarks have the same significant features in the proton. The EC behaveslike a sea quark and is generally softer than the gluon by a factor of ( − 𝑥 ) , where 𝑥 is the momentum fraction of EC in the proton. The parton distribution function (PDF)describes the extrinsic charm density in the proton, which is related to the momentumfraction 𝑥 and the factorization scale 𝜇 𝐹 . Using an initial form at a specific scale, suchas the charm quark mass 𝑚 𝑐 , the EC PDF can be evolved to any factorization scale 𝜇 𝐹 with the help of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolutionequations [324, 325, 326, 327]. In practice, the initial form of the EC PDF couldbe modeled, whose parameters can be fixed from a comprehensive global analysis ofhard scattering data generated from a variety of fixed-target or collision experiments.The extrinsic charm distribution is assumed to be concentrated in the small region of .5 Other important exploratory studies –65/140– momentum faction, e.g. 𝑥 ∈ [ , . ] , since it drops down quickly at 𝑥 > . 1. The ECcomponent is usually neglected in early studies on the processes with small and moderatecenter-of-mass energy (CME) in collisions, especially for the hadronic colliders wherethe small 𝑥 events are generally not recorded. With much higher CME of colliders today,the EC becomes more and more important in high energy processes.Another probable charm content arisen in a proton is the “intrinsic charm (IC)”,which is quite different from the extrinsic one and has strong hints from experimentalobservations. In year 1979, the production of charmed particles was reported by theCERN and ACCDHW Collaborations via 𝑝 𝑝 → 𝐷 + ( Λ + 𝑐 ) 𝑋 with the center-of-massenergy √ 𝑠 = 53 and 63 GeV, respectively [328, 329, 330, 331]. The cross sectionwas measured to be 0 . ∼ . ∼ 𝜇 b [332]) by about one order of magnitude. Moreover, the 𝐷 + was found to begenerated abundantly in the forward region, which is hard to be explained by simplyusing the ordinary extrinsic charm. In order to narrow the gap between experimentaldata and theoretical predictions, the idea of IC was proposed by S. J. Brodsky et al. in Ref.[333, 334, 335]. Theoretically, this fluctuation of the proton can be achievedin two ways, one is the interaction between valance quarks and multiple soft gluons,another one is vacuum polarization which is usually extremely rare and can be neglected.The intrinsic charm generated in this manner exhibits remarkable differences from theextrinsic charm, and the probability of finding IC in a proton is proportional to O ( / 𝑚 𝑐 ) .In contrast to the EC, the IC can be generated at or even below the energy scale of theheavy quark mass threshold. The intrinsic charm and anti-charm are not necessary tohave the same distributions in the proton. The IC has a “valence-like” character, whichhas small contributions in low momentum fraction 𝑥 and dominates in the relativelylarge 𝑥 region. The IC distribution is non-perturbative, and many models have beensuggested in the literature, whose inputs can be fixed by global fitting of various knownexperimental data.Some previously done measurements could indicate the existence of IC in the nu-cleon. In 1980s, the charm structure function 𝐹 𝑐 ( 𝑥, 𝜇 ) was measured by the EuropeanMuon Collaboration (EMC) [189, 336]. An enhancement at large 𝑥 beyond theoreticalexpectation was reported by EMC, and such a gap could be compensated by taking theIC into consideration [337]. The inclusive photon production with heavy-flavor 𝑄 jetsin hadronic collisions would also provide valuable information for the IC distributionsin the nucleon. The partonic process 𝑔 + 𝑄 → 𝛾 + 𝑄 + 𝑋 gives the main contributions tothe photon events, which depends strongly on the heavy contents in an incident hadron.Data from the DØ experiment at the Tevatron [338] shows disagreement between theprediction without IC and the measurement for 𝛾 + 𝑐 + 𝑋 in large transverse momentum of .5 Other important exploratory studies –66/140– the photon. By including IC contributions, the discrepancy is reduced but still prominentin the larger 𝑝 𝛾𝑇 region, in particular when 𝑝 𝛾𝑇 is larger than 80 GeV.Up to now, a definite conclusion on the existence of IC is still missing. Additional ex-periments are necessary for investigating the IC. The measurement of inclusive charmedhadron production at hadron colliders is an additional promising way to investigate theIC [339, 340]. The doubly heavy baryons (especially Ξ 𝑐𝑐 ) production associated withinitial charm quark at the parton level will be suitable to investigate the intrinsic content,since the IC impacts significantly on these production channels. The Ξ 𝑐𝑐 productionin hadronic collisions involve three typical mechanisms, i.e. the gluon-gluon fusion ( 𝑔 + 𝑔 ) , the gluon-charm collision ( 𝑔 + 𝑐 ) , and the charm-charm collision ( 𝑐 + 𝑐 ) , atthe proton-proton (or proton-antiproton) colliders. Conventionally, contributions fromthe gluon-gluon fusion are expected to be dominant in the hadronic production of Ξ 𝑐𝑐 .However, other production mechanisms may also have sizable contributions. For the ( 𝑔 + 𝑐 ) and ( 𝑐 + 𝑐 ) production mechanisms, the initial 𝑐 quark can be either extrinsicor intrinsic in the incident protons. Because the proportion of the IC components in thenucleon is small, which is only up to ∼ Ξ 𝑐𝑐 production.The hadronic production of Ξ 𝑐𝑐 baryon was investigated at the LHC, the Tevatron,and the Fixed-target Experiments at hadron collider (FixExp@HC) [341, 342, 343].Using the generator GENXICC [344, 345, 346, 347], one may simulate the hadronicproduction of Ξ 𝑐𝑐 with both extrinsic and intrinsic charm being considered. Becausethe intrinsic component at large 𝑥 will decrease at the high factorization scale, the ( 𝑔 + 𝑔 ) channel becomes dominant in the Ξ 𝑐𝑐 hadroproduction with high CME. TheIC mechanisms shall have a significant impact on the hard processes with moderatefactorization scales at those colliders with a relatively lower center-of-mass energy.Therefore, colliders with high luminosity at lower center-of-mass energy, such as thefixed-target experiment (like After@LHC [348, 349, 350, 351, 352] operating at a center-of-mass energy √ 𝑠 = 115 GeV) and future electron-ion colliders (e.g., EIC US [30] andEicC, etc.), would be ideally suited to discover or constrain the intrinsic content innucleon.The EicC will provide a brand new mode to study the production of doubly charmedbaryon. Two important subprocesses occur in the electron-nucleus ( 𝑒 -N) collision withexchange of a virtual photon between the electron and nucleus, i.e., 𝛾 + 𝑔 → Ξ 𝑐𝑐 + ¯ 𝑐 + ¯ 𝑐 and 𝛾 + 𝑐 → Ξ 𝑐𝑐 + ¯ 𝑐 , which are classified by the virtuality 𝑄 of the photon. Numerically,we observe that the intrinsic charm enhanced the total cross sections by nearly 3 timesto that without intrinsic components with 𝐴 in = 1% in the 𝑒 -Au collision mode at the .6 QCD theory and phenomenology –67/140– EicC. Moreover, at the instantaneous luminosity of 2 . × cm − s − , the estimatednumber of Ξ 𝑐𝑐 events in one year is about 4 . × by adopting the Non-relativisticQuantum Chromodynamics [353]. It makes the precise investigation of the propertiesof the doubly charmed baryon accessible at the EicC.The observation of the doubly charmed baryon Ξ ++ 𝑐𝑐 had been reported by the LHCbcollaboration [354] in 2017. However, the Ξ + 𝑐𝑐 with a similar production rate but abit shorter lifetime than Ξ ++ 𝑐𝑐 , has not been discovered yet. The shorter lifetime meansmore loss events of Ξ + 𝑐𝑐 before tested by the detectors, which requires more efforts inexperimental measurements. Recently, the LHCb collaborations reported zero resultsof searching for Ξ + 𝑐𝑐 [355] again with higher integrated luminosity than that in 2013 byan order of magnitude. This is in contradiction with the observation of Ξ + 𝑐𝑐 baryon bythe SELEX in 2002 [356] and in 2005 [357]. This contrary may be interpreted by thedifference of kinematic cuts between those two experiments. The LHCb experiment maylose more events in the small 𝑝 𝑡 region than that in the SELEX, which are related closelyto the intrinsic content in a nucleon. Therefore, more different kinds of experiments,such as the After@LHC, the EicC, and the LHeC, etc., are needed for clarifying thepuzzle in searching for the Ξ + 𝑐𝑐 . Conversely, experimental studies on Ξ 𝑐𝑐 production atthose colliders could help to further progress in verifying the existence of IC.In conclusion, different high-energy colliders (such as the After@LHC, the EicC,etc.), are expected to increase the probability for the discovery of IC. Moreover, thosedifferent experimental platforms could provide important cross-checks to ensure thecorrectness of experimental measurements and theoretical analysis. And it shall shedlight on the intrinsic heavy mechanism and fundamental structure of the nucleon. High level theory and phenomenology are required in order to inspire, guide, andcapitalize on the wide ranging program of EicC experiments. Rigorous QCD theorymust be complemented by insightful phenomenology so that every discovery opportunitycan be seized. The lattice formulation maintains the closest connections with the QCDLagrangian. Here, steady progress continues and testable predictions are being delivered.Tight links with QCD are also provided by continuum Schwinger function methods,e.g. the Dyson-Schwinger equations (DSEs). With the added flexibility of continuummethods, DSEs provide access to a wider range of observables. Thus, with theircomplementary content, lattice QCD and DSEs have a natural synergy that can be .6 QCD theory and phenomenology –68/140– exploited for the benefit of EicC physics. Lattice QCD is a fundamental method to study strong interactions non-perturbativelyfrom first principles. It directly computes the QCD path integral in a discretized finite-volume Euclidean space-time, and then the finite lattice spacing and volume providenatural ultraviolet and infrared cut-offs. The input parameters in lattice QCD are thequark masses and the coupling constant, which is related to the lattice spacing bythe renormalization group. Today, with the help of powerful computing facilities,lattice QCD can provide important information on many aspects of EicC physics andcomparisons with experimental results. As discussed in Sec. 2.1, the proton’s spin can be decomposed into the helicity and orbitalangular momentum of quarks and gluons. The contribution from quark helicity is thesum of quark polarization along the proton spin direction, which can be obtained fromlattice QCD by computing the first Mellin moment of the polarized parton distributionfunction of quarks. There have been many lattice calculations, see Refs. [358, 359] forreviews. Recent lattice results [360, 361, 362] are mutually consistent and agree wellwith global fits; and strange flavor results are more precise than the global fits. Bothexperiment [363] and lattice calculation [364] indicate that the gluon helicity contributesconsiderably to proton spin, but improved lattice QCD calculations are needed in orderto deliver precise predictions [365].The QCD energy-momentum tensor admits several expressions for the quark andgluon orbital angular momentum contribution to the proton spin. With the Jaffe-Manohardecomposition [366], both the orbital and total angular momentum of quarks and gluonscan be defined in a gauge invariant manner with appropriate light-cone gauge links.On the other hand, gauge invariant and frame independent total angular momentum ofquarks and gluons can be defined through the symmetrized energy-momentum tensorbased on Ji’s decomposition [60], expressed in Eq. (2.3). The difference between the twois that the quark-gluon interaction term is allocated to the gluon (quark) orbital angularmomentum in the Jaffe-Manohar (Ji) decomposition. The gauge invariant total angularmomenta of quarks and gluons have been calculated in lattice QCD [360, 367, 368]: thegluon angular momentum result needs improved precision. Exploratory lattice studieshave been made for the quark orbital angular momentum and preliminary results havebeen obtained [369, 370]. .6 QCD theory and phenomenology –69/140– Lattice QCD is playing a valuable role in the study of nucleon spin structure, withimportant recent progress. Quark helicity results for different flavors have reached 10%precision, and preliminary estimates have been obtained for the gluon helicity, quarkorbital angular momentum and quark (gluon) total angular momentum. It is expectedthat lattice QCD will be able to provide more accurate and extensive information onnucleon spin structure. From the sum rule of the QCD energy-momentum tensor, Eq. (2.6), the invariant massof proton can be decomposed into quark mass term and the trace anomaly [278]. Thequark mass term is a product, involving the chiral condensate and quark current masses;hence, it is directly related to the mass generated by the Higgs mechanism and scaleinvariant. This part only contributes about 9% of the total proton mass [283] for threelight flavors; so most of the proton mass can be considered as arising from the traceanomaly [278].In the chiral limit, the pion matrix element of the trace anomaly is zero, whereas itis nonzero for the nucleon, yielding the entire nucleon mass. As yet, there is no directcalculation of the trace anomaly using lattice QCD, but the proton mass sum rule hasbeen used to predict the trace anomaly contribution to 𝑚 𝑝 [283]. A calculation of thetrace anomaly contribution to 𝑚 𝑝 is being pursued using lattice QCD; and success willenable a comparison between QCD theory and the EicC measurements described inSec. 2.5.1.Using one definition of the quark kinetic energy [281], its contribution to 𝑚 𝑝 canbe obtained from the quark light-front momentum fraction, i.e. the first moment of theunpolarized quark distribution functions; similarly, for the gluon kinetic energy contri-bution. Lattice results for the momentum fraction [283] agree with phenomenologicalanalyses [358]; but uncertainties still need to be further suppressed, especially for thesea quarks and gluons. Most lattice QCD calculations of PDF-related quantities have been limited to the firstfew PDF moments, mainly due to the fact that light-cone PDFs are not directly accessiblein Euclidean space-time. However, novel theoretical developments in recent years [371,372, 373] are enabling lattice QCD to directly calculate PDFs, including 1-D Bjorken-xdependent PDFs, generalized parton distribution functions(GPDs), and also transversemoment dependent parton distribution functions(TMDs) .6 QCD theory and phenomenology –70/140– b / fm S I S I ,MS P z = 1.05GeV, = 2.17 P z = 1.58GeV, = 3.06 P z = 2.11GeV, = 3.98 b / fm K K ( P z / P z =4/3) K ( P z / P z =4/2) HermiteBernstein Figure 2.31: Lattice results for the TMD soft function: intrinsic part (left panel) [382] andrapidity dependent part (right panel) [381, 382]. For the rapidity dependent part, the results fromRef. [382] (red/blue points) are consistent with those from Ref. [381] (green/brown points). Thelattice calculation reaches much larger transverse separation 𝑏 ⊥ than perturbative calculations. Large momentum effective theory (LaMET) is one approach [374]. It uses anequal time correlation function to reach a light cone correlation function using standardmethods of effective field theory matching and running. Namely, from the equal timecorrelations that can be computed in lattice QCD, one obtains the so-called quasi-PDFs;and when the nucleon momentum is large enough, quasi-PDFs can be matched pertur-batively to the physical PDFs, with computable large-momentum power corrections.LaMET has been employed in some lattice QCD calculations, with notable progresson the non-singlet quark PDFs ( 𝑢 ( 𝑥 ) − 𝑑 ( 𝑥 ) ), including unpolarized, polarized andtransverse distributions. The latest results agree with global fits [375, 376, 377]. Thesmall 𝑥 region is challenging for laMET because it requires simulations with high nucleonmomenta, which is difficult in lattice QCD. At present, lattice QCD can compute valence-quark PDFs on 𝑥 (cid:38) . 𝑥 for the sea quarks via PDFmoments [378]. LaMET can also be used to compute GPDs, e.g. the pion’s unpolarizedquark GPD has been explored [379] and this may be extended to the nucleon case.TMD calculations using lattice QCD are more complicated than those of PDFs andGPDs. An additional soft function is required to factorize processes involving smalltransverse momentum, like Drell-Yan production and semi-inclusive DIS. This functioninvolves two light-like gauge links along reversed light-cone directions; hence, cannot besimulated directly in Euclidean space. Recently, it was argued that this difficulty can beovercome [380]; and as shown in Fig. 2.31, several lattice QCD attempts at compuationof the soft function have been carried out [381, 382]. This opens a path to prediction ofTMD-related quantities using lattice QCD. Nucleons within the nucleus appear to interact weakly with each other via long-rangeforces and the binding energy per nucleon is small in comparison with the nucleon .6 QCD theory and phenomenology –71/140– mass; yet, as illustrated in Fig. 2.14, various experiments have indicated that the PDFsof bound nucleons are different from those in free space [20, 127, 383]. This highlightsthe importance understanding nuclear structure from the gluon-quark level. Naturally,for quarks and gluons contained within nucleons and nuclei, the non-perturbative natureof the bound-state problem makes the theoretical study very difficult. Lattice QCDsimulations can shed light on this problem.Lattice calculation at physical kinematics are very challenging owing to the signal-to-noise problem. In a first step, Ref. [384] reported a study of the PDFs of He, extractingthe first Mellin moment of the unpolarized isovector quark PDFs at an unphysical quarkmass corresponding to 𝑚 𝜋 ∼ 800 MeV. The ratio of the quark momentum fraction in He to that in a free nucleon was found to be consistent with unity. Although no EMCeffect was observed, this study together with an earlier lattice analysis of the He bindingenergy [385] show that lattice methods are reaching a level of practicable maturity forvery light nuclei. Calculation precision can be controlled to a level of few percent byusing a relatively heavy pion mass; and even in this unphysical realm, results from theHALQCD collaboration suggest that some nuclear physics remains [386].Further reduction of both statistical and systematic uncertainties requires more effortfrom the lattice QCD community. One can anticipate that, with the continuing develop-ment of computer hardware and software, lattice calculations may come to play a uniquerole in hunting the EMC effect. The methods to study hadron spectroscopy in lattice QCD are relatively mature. Onecomputes correlation functions of operators with the desired quantum numbers and ob-tains the spectrum from their time dependence. The interpolating operators encode thehadron structure information. Usually the operators are constructed by a quark–anti-quark pair (meson) or three quarks (baryon). To explore the structure of exotic hadrons,such as those discussed in Sec. 2.4, one needs to build operators that express the exotic’slikely composition, e.g. multi-quark states, hybrids and glueballs, etc. Most hadrons areunstable resonances, which appear as poles of hadron scattering amplitudes. Again, ow-ing to the Euclidean space-time used in lattice QCD, real-time dependent matrix elementsrelated to the scattering processes cannot be computed directly. One way to circumventthis problem is to use the finite volume method developed by M. Lüscher [387], by whichthe scattering information can be extracted from the energies of analogous systems ina finite box. This approach offers a path forward for lattice QCD in calculations of thestructure and properties of exotic states.EicC is ideal for the study of heavy flavor hadrons. Many charmed exotic hadrons have .6 QCD theory and phenomenology –72/140– been observed in experiments, e.g. the 𝑋𝑌 𝑍 particles and the pentaquark candidates 𝑃 𝑐 s,but the structure of these states are not known yet. Some studies on 𝑋𝑌 𝑍 particles havebeen performed in Lattice QCD [388, 389, 390, 391]. However, the results are generallycontaminated by systematic uncertainties, which come from finite lattice spacing, finitevolume, unphysical light quark mass, ignoring coupled channel effects, and so on. At thesame time, it is expected that the bottom counterpart of the charm exotic states shouldalso exist; yet the number of observed exotic bottom hadrons is fewer than in the charmsector. With continuing steady improvement, lattice QCD will be able to contribute toresolving the puzzles associated with heavy flavor hadrons. Sec. 2.5.1 highlights that the masses of the neutron and proton, the kernels of all visiblematter, are roughly 100-times larger than the Higgs-generated masses of the light 𝑢 -and 𝑑 -quarks. In contrast, Nature’s composite Nambu-Goldstone bosons are (nearly)massless. In these states, the strong interaction’s 𝑚 𝑁 ≈ 𝜋 and 𝐾 mesons are exactly massless and perturbationtheory suggests that strong interactions cannot distinguish between quarks with negativeor positive helicity. Such a chiral symmetry would have many consequences, but none ofthem is realised in Nature. Instead, the symmetry is broken by interactions. Dynamicalchiral symmetry breaking (DCSB) entails that the massless quarks in QCD’s Lagrangianacquire a large effective mass [392, 393, 394] and ensures that the interaction energybetween those quarks cancels their masses exactly so that the chiral-limit pion is massless[395, 396, 397].DCSB underpins the notion of constituent-quark masses and, hence, sets the charac-terising mass-scale for the spectrum of mesons and baryons constituted from 𝑢 , 𝑑 quarksand/or antiquarks. Moreover, restoring the Higgs mechanism, then DCSB is responsiblefor, inter alia : the measured pion mass ( 𝑚 𝜋 ≈ . 𝑚 𝑁 ); and the large mass-splitting be-tween the pion and its valence-quark spin-flip partner, the 𝜌 -meson ( 𝑚 𝜌 > 𝑚 𝜋 ). Thereare many other corollaries, extending also to the physics of hadrons with strangeness,wherein the competition between dynamical and Higgs-driven mass-generation has nu-merous observable consequences. The competition extends to the charm and bottomquark sectors; and much can be learnt by tracing its evolution.Such phenomena, their origins and corollaries, entail that the question of how didthe Universe evolve is inseparable from the questions of how does the 𝑚 𝑁 ≈ .6 QCD theory and phenomenology –73/140– mass-scale that characterizes atomic nuclei appear; why does it have the observed value;and, enigmatically, why does the dynamical generation of 𝑚 𝑁 have no apparent effecton the composite Nambu-Goldstone bosons in QCD, i.e . whence the near-absence of thepion mass? A decisive challenge is to determine whether the answers to these questionsare contained in QCD, or whether, even here, the Standard Model is incomplete.These questions are being addressed using DSEs, which provide a symmetry-preserving approach to solving the continuum hadron bound-state problem [292, 398,399, 400, 401]. In connection with the emergence of hadronic mass, the frameworkhas delivered a significant advance with the prediction of a process-independent QCDeffective charge [402]. Depicted in Fig. 2.32, ˆ 𝛼 ( 𝑘 ) saturates at infrared momenta,ˆ 𝛼 ( )/ 𝜋 = . ( ) , owing to the emergence of a gluon mass-scale: 𝑚 / GeV = . ( ) .These and other features of ˆ 𝛼 ( 𝑘 ) suggest that QCD is rigorously defined; if so, then itis unique amongst known four-dimensional quantum field theories. Numerous conse-quences can be tested with EicC experiments, a few of which are subsequently described. ���� � / �������� ���� ( ���� ) ���� ���� ( ���� ) ���� ���������� ����������� ������� �������� ���� / �������� ���� / �������� ����������� � ���� ��� ������������������� � [ ��� ] α ( � ) / π Figure 2.32: QCD’s process-independent running-coupling, ˆ 𝛼 ( 𝑘 )/ 𝜋 , obtained by combiningthe best available results from continuum and lattice analyses [402]. World data on the process-dependent charge, 𝛼 𝑔 , defined via the Bjorken sum rule, are also depicted. (Sources are detailedelsewhere [402]. Image courtesy of D. Binosi.) Meson Form Factors .The best known and most rigorous QCD predictions are those made for the electromag-netic form factors of pseudoscalar mesons, e.g . the pion and kaon. These hadrons areabnormally light; yet, their properties provide the cleanest window onto the emergenceof mass within the Standard Model [403]. This connection is expressed most forcefully,in the behaviour of meson form factors at large momentum transfers. On this domain, .6 QCD theory and phenomenology –74/140– QCD relates measurements simultaneously to low- and high-energy features of QCD, viz . to subtle features of meson wave functions and to the character of quark-quark scat-tering at high-energy [321, 322, 404]. These relationships are expressed concretely inadvanced DSE analyses, with predictions that expose the crucial role of emergent mass[405].Throughout the modern history of nuclear and particle physics, much attention hasfocused on finding evidence for power-law scaling in experimental data. This is animportant step; but it should be remembered that QCD is not found in scaling laws.Instead, since quantum field theory requires deviations from strict scaling, then QCDis to be found in the existence and character of scaling violations. Considering mesonelastic electromagnetic form factors, theory predicts that ( i ) scaling violations willbecome apparent at momentum transfers 𝑄 (cid:38) 10 GeV [405] and ( ii ) the magnitude ofany given form factor on a sizeable domain above 𝑄 = 10 GeV is determined by thephysics of emergent mass. Hence, experiments focused in this area are of the greatestimportance; and as discussed in connection with Fig. 2.29, EicC can here make crucialcontributions. Meson Structure Functions .At a similar level of rigor is the QCD prediction for the behavior of meson structurefunctions. The momentum distributions of light valence quarks within the pion have thefollowing behaviour at large- 𝑥 [406, 407, 408]: u 𝜋 ( 𝑥 ; 𝜁 ≈ 𝑚 ) ∼ ( − 𝑥 ) . The mostrecent measurements of u 𝜋 ( 𝑥 ; 𝜁 ) are thirty years old [299, 300, 301, 302, 303, 304];and conclusions drawn from those experiments have proved controversial [409]. Forexample, using a leading-order (LO) perturbative-QCD analysis, the E615 experiment[304] reported: u 𝜋 E615 ( 𝑥 ; 𝜁 = . ) ∼ ( − 𝑥 ) , in striking conflict with the expectedbehavior. Subsequent calculations [410] confirmed the QCD prediction and eventuallyprompted reconsideration of the E615 analysis, demonstrating that E615 data may beviewed as consistent with QCD [411, 412]. However, uncertainty over u 𝜋 ( 𝑥 ) remainsbecause more recent analyses of available data have failed to consistently treat higher-order effects and, crucially, modern data are lacking.Pressure is also being applied by modern advances in theory. Lattice QCD is begin-ning to yield results for the pointwise behaviour of the pion’s valence-quark distribution[416, 417, 418, 419]. Furthermore, continuum analyses [413, 414] have yielded the firstparameter-free predictions for the valence, glue and sea distributions within the pion; andrevealed that, like the pion’s leading-twist parton distribution amplitude (PDA) [420],the valence-quark distribution function is hardened as a direct consequence of emergentmass.The valence, glue and sea distributions from Refs. [413, 414] are drawn in Fig. 2.33. .6 QCD theory and phenomenology –75/140– Figure 2.33: Left panel . Blue solid curve – theory prediction for u 𝜋 ( 𝑥 ; 𝜁 = ) [413,414]; and cyan short-dashed curve – phenomenological result from Ref. [415]. Right panel .Theory predictions for the pion’s glue and sea-quark distributions [413, 414]: green solidcurve – g 𝜋 ( 𝑥 ; 𝜁 ) ; and red dot-dashed, S 𝜋 ( 𝑥 ; 𝜁 ) . The associated momentum fractions are: (cid:104) 𝑥 q 𝜋 ( 𝑥 ; 𝜁 )(cid:105) = . ( ) , (cid:104) 𝑥 g 𝜋 ( 𝑥 ; 𝜁 )(cid:105) = . ( ) , (cid:104) 𝑥 S 𝜋 ( 𝑥 ; 𝜁 )(cid:105) = . ( ) . For comparison,phenomenological results from Ref. [415]: 𝑝 = glue – dark-green long-dashed; and 𝑝 = sea –brown dashed. (The bands around the theory curves express the impact of the uncertainty inˆ 𝛼 ( 𝑘 = ) , Fig. 2.32. Normalisation: (cid:104) 𝑥 [ u 𝜋 ( 𝑥 ) + 𝑔 𝜋 ( 𝑥 ) + 𝑆 𝜋 ( 𝑥 ](cid:105) = Also shown are the phenomenological extractions from Ref. [415]. Even though thevalence distribution fitted in Ref. [415] yields a momentum fraction compatible with thetheory prediction, its 𝑥 -profile is very different. (Ref. [415] did not include the higher-order corrections discussed in Ref. [412].) It is significant, therefore, that the continuumresult for u 𝜋 ( 𝑥 ; 𝜁 ) matches that obtained using lattice QCD [419]. Consequently, theStandard Model prediction: u 𝜋 ( 𝑥 ; 𝜁 = 𝑚 ) ∼ ( − 𝑥 ) , is stronger than ever before; andas demonstrated by Fig. 2.30, EicC design specifications would enable it to deliver clearexperimental validation.If the pion’s valence-quark distributions are controversial, then its glue and seadistributions can be described as uncertain or worse. Fig. 2.33 – right panel compares thepredictions from Refs. [413, 414] with fits from a combined analysis of 𝜋 -nucleon Drell-Yan and HERA leading-neutron electroproduction data [415]. The gluon distributionpredicted in Refs. [413, 414] and that fitted in Ref. [415] are markedly different on 𝑥 (cid:46) . 05; and both glue DFs in Fig. 2.33 disagree with those inferred previously [320, 421].These remarks highlight that the pion’s gluon content is empirically uncertain. Thus,new measurements which are directly sensitive to the pion’s gluon content are necessary.Prompt photon and 𝐽 / 𝜓 production could address this need [422, 423]. The sea DFs inFig. 2.33 have different profiles on the entire 𝑥 -domain. Hence, it is fair to describe thesea-quark distribution as empirically unknown. This problem could be addressed withDY data obtained from 𝜋 ± beams on isoscalar targets [422, 424]. Equivalent taggedDIS measurements at the EicC could also provide this information. Evidently, precisionmeasurements that are sensitive to meson glue and sea-quark distributions are highlydesirable. Here, too, EicC can have a significant impact. .6 QCD theory and phenomenology –76/140–Balancing Emergent Mass and the Higgs Mechanism .The ability of form factor and structure function measurements to expose emergenthadronic mass is enhanced if one includes similar kaon data because theory has revealedthat 𝑠 -quark physics lies at the boundary between dominance of strong (emergent) massgeneration and weak (Higgs-connected) mass [403], as highlighted in Fig. 2.34-left panel.Hence, comparisons between distributions within systems constituted solely from lightvalence quarks and those associated with systems containing 𝑠 -quarks are ideally suitedto exposing measurable signals of emergent mass in counterpoint to Higgs-driven effects. Q ( GeV ) Figure 2.34: Left panel – Twist-two parton distribution amplitudes at 𝜁 = = : 𝜁 . A solid(green) curve – pion ⇐ emergent mass generation is dominant; B dot-dashed (blue) curve – 𝜂 𝑐 meson ⇐ Higgs mechanism is the primary source of mass generation; C solid (thin, purple)curve – asymptotic profile, 𝜑 as ( 𝑥 ) ; and D dashed (black) curve – “heavy-pion”, i.e . a pion-likepseudo-scalar meson in which the valence-quark current masses take values corresponding to astrange quark ⇐ the boundary, where emergent and Higgs-driven mass generation are equallyimportant. Right Panel – Solid curve: ratio of strange-to-normal matter in the 𝐾 + ; green dashedcurve and band: results obtained using the QCD hard-scattering formula [321, 322, 404]. One example can be found in the contrast between the parton distribution functionsof the pion and kaon, first theory predictions for which are now available [425, 426].Another is illustrated in Fig. 2.34 – right panel, which displays a flavor-separation ofthe charged-kaon, 𝐾 + , elastic electromagnetic form factor: 𝑠 𝐾 : = 𝐹 ¯ 𝑠𝐾 is the 𝑠 -quarkcontribution to the form factor and 𝑢 𝐾 : = 𝐹 𝑢𝐾 is the analogous 𝑢 -quark term. The rateof growth from 𝑄 = 0, the peak height and location, and the logarithmic decay awayfrom the peak are all expressions of emergent mass and its modulation by Higgs-bosoneffects [427].Analogous predictions exist or are being completed for nucleon form factors, fol-lowing the approach in Ref. [428], and parton distribution functions [429]. Simulationsindicate that the planned EicC could be used to validate the connection between emergentmass and these observables; and also many others that are members of the same class. .6 QCD theory and phenomenology –77/140– Along with the promised rewards described in Sec. 2.2, many new challenges are facedin extracting 3-D images from new-generation experiments. Phenomenological modelsof a wide variety of parton distribution functions will be crucial. They can provideguidance on the size of the cross-sections to be measured and the best means by whichto analyse them [112]. On the other hand, as experiences with meson structure functionshave shown, in order to profit fully from such experiments, one must use computa-tional frameworks that can reliably connect measurements with qualities of QCD. Here,continuum calculations can provide valuable insights [430, 431, 432, 433, 434].Regarding TMDs, there is an additional complication. Namely, every cross-sectionthat can yield a given hadronic TMD involves a related parton fragmentation function(PFF) [435], the structure of which must be known in detail. Therefore, the future ofmomentum imaging depends critically on making significant progress with the measure-ment and calculation of PFFs. Notwithstanding these demands, there are currently norealistic computations of PFFs. Even a formulation of the problem remains uncertain.Here are both a challenge and an opportunity for EicC.If EicC can provide precise data on quark fragmentation into a pion or kaon, it willdeliver results that directly test those aspects of QCD calculations which incorporate andexpress emergent phenomena, e.g . confinement, DCSB, and bound-state formation. Thefact that only bound-states emerge from such processes is one of the cleanest availablemanifestations of confinement. As a collider, EicC measurements will potentially haveenormous advantages over earlier and existing fixed-target experiments. By capitalisingon energy range, versatility, and detection capabilities in the collider environment, EicCshould be able to first cleanly single out the pion or kaon target and subsequently thefragmentation process tag, thereby delivering an array of information that will best testtheory aimed at the calculation and interpretation of PFFs. hapter 3 Accelerator conceptual design To achieve the proposed scientific goals in chapter 2, the EicC project will constructa high performance polarized electron-proton collider which can reach the luminosityof 2 . × cm − s − at the center-of-mass energy of 16.76 GeV while ensuring anaverage polarization for electrons and protons of about 80% and 70%, respectively.For convenience, unless stated, the following polarization all represents the averagepolarization. Moreover, the center-of-mass energy of the EicC has a flexible range from15 GeV to 20 GeV in order to serve different experimental purposes. To keep a balancebetween the physics goals and the overall cost, we will take full advantage of the existingHIAF accelerator complex and its ancillary facilities. Therefore, only a new figure-8ion collider ring, a polarized electron injector, and a racetrack electron collider ringwill be constructed. This chapter is organized as follows: In Section 3.1, we presenta comprehensive overview of the EicC accelerator facility, including its design goals,main layout, key accelerator parameters, and potential technical challenges. Section 3.2will mainly discuss the basic operation modes of the ion accelerator complex and theelectron accelerator complex of the EicC. The following section 3.3 to section 3.5 willprovide a detailed description of three key conceptual design ingredients for the EicCaccelerator facility, i.e. beam cooling, beam polarization, and interaction regions (IRs).Last but not the least, several topics of the technical pre-research in the accelerators willbe presented in Section 3.6. The various scientific goals pose the various requirements that must be met in the EicCaccelerator facility. Taking the proton beam as the reference beam (also for the followingsections), these requirements are explained as follows:1. The center-of-mass energy should range from 15 GeV to 20 GeV, which corre-sponds to the energy of 2.8 GeV to 5.0 GeV for electron beams in the electroncollider ring and the energy of 19.08 GeV for proton beams in the ion colliderring. The center-of-mass energy of other ion beams can be obtained according tothe maximum momentum rigidity which is 86 T · m.2. The luminosity should reach up to 2 . × cm − s − and should be optimizedmainly at the center-of-mass energy of 16.76 GeV.3. At the interaction point (IP), the electron beams should be polarized longitudinallywith the polarization of 80%, while the proton beams should be polarized both .1 Overall design and key parameters –79/140– longitudinally and transversely with the polarization of 70%. Besides the polarizedproton beams, the ion accelerator complex should also provide polarized deuterium( D + ) beams, polarized Helium-3 ( He + ) beams as well as unpolarized heavy ionbeams.4. The design of the IRs should fully accommodate the design of the EicC detectorsof which a large number of components, such as the polarimetry, luminositymonitors, forward detectors, and so on, will be integrated into the beamlines.As shown in the Fig.3.1, the EicC was carefully designed to meet all requirementslisted above. The ion accelerator complex will fully utilize the existing HIAF complexwhich helps us to largely reduce the construction cost. On top of that, a new ion colliderring (pRing) will be constructed. The high-intensity heavy-ion booster ring (BRing) inthe HIAF can produce proton beams of energy up to 9.3 GeV, which covers the injectionenergy of 2 GeV in the pRing. Furthermore, in the BRing, there will be sufficient freespace reserved for the installation of a DC electron cooler for beam cooling and theSiberian snake for spin preservation. Therefore, the BRing in the HIAF is planned tobe upgraded and fully employed as the booster in the EicC ion accelerator complex.To avoid the depolarization resonances during the acceleration process, a figure-8 ringwill be adopted for the pRing. This design ensures the spin tune of the pRing is alwayszero and makes it possible to achieve the high polarization of proton beams during theacceleration process with a large energy range. Meanwhile, it also allows us to controlthe polarization direction of proton beams more efficiently. The figure-8 ring designis one of the essential technical solutions to achieve the high polarization in the EicCion accelerator complex. Besides the polarization design, it is also important to achievehigh luminosity in the EicC. To this end, a multistage beam cooling scheme is proposed.Firstly, the pre-cooling of proton beams will be performed in the BRing. Secondly, ahigh energy bunched beam electron cooler based on an energy recovery linac (ERL)will be installed in the pRing and employed to cool the proton beams after they areaccelerated to the energy of 19.08 GeV. The beam cooling will be employed to suppressthe intra-beam scattering effect over the whole collision process, which is the key toachieve the required luminosity.The EicC electron accelerator complex mainly consists of an electron injector and anelectron collider ring (eRing). The electron injector is a superconducting radio frequency(SRF) linac which is considered to be the best choice to deliver the electron beams withthe energy range from 2.8 GeV to 5.0 GeV. Since the eRing adopts the full energyinjection scheme which means there is no acceleration process, and the electron beamswill experience the self-polarization process, the eRing is designed as a racetrack ringwhich is widely used in the electron facilities. Meanwhile, the polarization direction of .1 Overall design and key parameters –80/140– E l ec t r on I n j ec t o r . G e V ~ . G e V I P E R L C i r c u l a t o r . M e V p R i ng19 . G e V ( p ) . m P o l a r i ze d p , D , H e - U n po l a r i z e d H ea vy I on s I P e R i ng2 . G e V ~ . G e V . m P o l a r i ze d E l ec t r on BR i ng48 M e V ~ G e V ( p ) P o l a r i ze d p , D , H e - U n po l a r i z e d H ea vy I on s H F R SS R i ng i L i n ac P o l a r i ze d I on S ou r ce F i g u re . : T h e l a you t o f E i c C acce l e r a t o rf ac ilit y . .1 Overall design and key parameters –81/140– the electron beams produced by the electron injector should be matched with the eRing.Based on the layout of the EicC accelerator facility, two IRs are available at twointersections of the long straight sections of the pRing and the eRing, as shown in theFig. 3.1. These two identical IRs will allow us to install two independent detectorsystems for different scientific goals simultaneously or the same physics goal but withdifferent experimental techniques for cross-validation. However, the current design onlyconsiders one detector to be installed in one of these IRs, with the other one reserved forthe future upgradeThe luminosity is one of the most important characteristics of a collider. Differentfrom other EIC designs in the world which commonly choose high collision frequencyand low bunch intensity, the EicC accelerator facility will adopt the unique schemeof low collision frequency and high bunch intensity to achieve a fourfold increase ofluminosity to reach the required luminosity of 2 × cm − s − , satisfying the physicsgoals of the EicC project. This is an essential part of the luminosity design of the EicC.For the collision between a proton with constant current 𝐼 𝑝 and an electron beam withconstant current 𝐼 𝑒 , the luminosity can be expressed as 𝑁 𝑝 𝑓 𝑐 ∝ 𝐼 𝑝 ≡ const , (3.1) 𝑁 𝑒 𝑓 𝑐 ∝ 𝐼 𝑒 ≡ const , (3.2) 𝐿 = 𝑁 𝑝 𝑁 𝑒 𝑓 𝑐 𝜋𝜎 𝑥 𝜎 𝑦 𝐻 ∝ 𝐼 𝑝 𝐼 𝑒 𝜎 𝑥 𝜎 𝑦 𝑓 𝑐 . (3.3)Here 𝑁 𝑝 and 𝑁 𝑒 are the numbers of particles in one proton bunch and electron bunch,respectively. 𝑓 𝑐 is the collision frequency. 𝜎 𝑥 and 𝜎 𝑦 are the transverse beam size inhorizontal and vertical directions, respectively. 𝐻 is the hourglass factor, which remainsconstant when the ratio of the 𝛽 function to the bunch length is fixed. Although thereis a positive correlation between 𝜎 𝑥 or 𝜎 𝑦 and the number of particles in the bunch, itcan be proven that the influence of 𝜎 𝑥 and 𝜎 𝑦 on the luminosity is less than that of 𝑓 𝑐 .Therefore, a decrease of 𝑓 𝑐 can increase the luminosity. In fact, constant average beamcurrent and constant intra-beam scattering in the bunch is a major factor of collisionlifetime, i.e. 1 𝜏 ∝ 𝑁 𝑝 𝜀 𝑥 𝜀 𝑦 𝜎 𝛿 𝜎 𝑠 , (3.4)from which it can be derived that if the bunch intensity is increased by 𝑚 times, theincrease of the horizontal emittance 𝜀 𝑥 , the vertical emittance 𝜀 𝑦 , the longitudinal bunch .2 Accelerator facilities –82/140– length 𝜎 𝛿 and the momentum spread 𝜎 𝑠 reads 𝜀 𝑥 ∝ 𝑚 , 𝜀 𝑦 ∝ 𝑚 , 𝜎 𝛿 ∝ 𝑚 , 𝜎 𝑠 ∝ 𝛽 ∗ 𝑥,𝑦 ∝ 𝑚 . (3.5)Substituting the Eq.3.5 to the Eq.3.3, the relationship between the luminosity and thebeam intensity is 𝐿 ∝ √ 𝑚, (3.6)indicating that the luminosity increases by √ 𝑚 times while the bunch intensity increasesby 𝑚 times.Based on the optimized luminosity scheme introduced above, the main parameters ofthe EicC accelerator facility are generated, as listed in the Tab.3.1 in which proton beamsare used as the reference beam and the optimization is performed at the center-of-massenergy of 16.76 GeV. Furthermore, several technical limitations are considered in theTab.3.1, as is shown below.1. The power density of the synchrotron radiation in the eRing should be less than20 kW / m.2. The beam-beam interaction parameter of proton beams is less than 0.03.3. The beam-beam interaction parameter of electron beams is less than 0.1.To meet the scientific goals, the parameters of collisions between electron beamsand several heavy ion beams are also shown in the Tab.3.2. In the following sections ofthis chapter, the design and the implementation of each parameter in the Tab.3.1 will bediscussed in detail. The EicC mainly consists of an ion accelerator complex and an electron acceleratorcomplex, as shown in the Fig.3.1. The Fig.3.2 illustrates the operation mode of the twoaccelerator complexes. There are a lot of differences between the ion accelerator complexand the electron accelerator complex, not only on the complicated beam manipulationsbut also on the key design and technical challenges, all of which will be described in detailin the following subsections. In Section 3.2.1, the ion accelerator complex of the EicCwill be described, mainly including the acceleration scheme of the pRing, the collectiveeffects, and so on. The details of the electron accelerator complex, including somekey designs and beam manipulations of the eRing, will be presented in Section 3.2.2.The topic of beam cooling and beam polarization will be discussed in Section 3.3 andSection 3.4, respectively. The design of the IRs, which is one of the most importantaccelerator designs in the EicC accelerator facility, will be presented in Section 3.5. .2 Accelerator facilities –83/140– Table 3.1: Main parameters for the EicC. Particle e pCircumference(m) 809.44 1341.58Kinetic energy(GeV) 3.5 19.08Momentum(GeV/c) 3.5 20Total energy(GeV) 3.5 20.02CM energy(GeV) 16.76f collision ( MHz ) 𝜌 ( T · m ) (× ) 170 125 𝜀 x , 𝜀 y ( nm · rad , rms ) 𝛽 ∗ x / 𝛽 ∗ y ( m ) 𝜉 y − s − ) 2 . × IP 2IP 1 iLinac Polarized IonSourceElectron Injector SRF Linac-ring2.8GeV ~ 5.0 GeV pRing 500 MHz RF448 Bunches5.6 10 ppp2 GeV → BRing → ppp 48 MeV → eRing 500 MHz RF270 Bunches4.59 10 ppp2.8 GeV ~ 5.0 GeV Figure 3.2: The beam path of the EicC accelerator facility. .2 Accelerator facilities –84/140– T a b l e . : M a i np a r a m e t e r s f o r t h e E i c C . P a r ti c l ee d H e ++ L i + C + C a + A u + P b + U + K i n e ti ce n e r gy ( G e V / u ) . . . . . . . . . M o m e n t u m ( G e V / c / u ) . . . . . . . . . T o t a l e n e r gy ( G e V / u ) . . . . . . . . . C M e n e r gy ( G e V / u )- . . . . . . . . f c o lli s i on ( M H z ) - . . . . . . . . P o l a r i za ti on80 % Y e s Y e s N o N o N o N o N o N o B 𝜌 ( T · m ) . . . . . . . . . P a r ti c l e s p e r bun c h ( × ) . . . . . . . . 𝜀 x , 𝜀 y ( n m · r a d , r m s ) / / / / / / / / 𝛽 ∗ x / 𝛽 ∗ y ( m ) . / . . / . . / . . / . . / . . / . . / . . / . . / . B un c h l e ng t h ( m , r m s ) . . . . . . . . . B ea m - B ea m P a r a m e t e r 𝜉 y . . . . . . . . . L a s l e ttt un e s h i f t - . . . . . . . . C u rr e n t ( A ) . . . . . . . . . C r o ss i ng a ng l e ( m r a d ) H ou r g l a ss - . . . . . . . . L u m i no s it y a t nu c l e on l e v e l ( c m − s − )- . × . × . × . × . × . × . × . × .2 Accelerator facilities –85/140– In the proposed ion accelerator complex of the EicC accelerator facility, the existingIon Linac (iLinac) and the BRing of the HIAF will be employed respectively as the ioninjector and the booster to provide injection beams for the pRing. The iLinac will beoperated in pulsed mode, in which the polarized proton beams can be accelerated tothe energy of 48 MeV, and then injected into the BRing with a matched polarizationdirection. In the BRing, a two-plane painting injection scheme will be adopted for thebeam accumulation with coasting beams to increase the beam intensity. In this scheme, atilted electrostatic septum will be employed for painting simultaneously in the horizontaland vertical directions during the injection. As a result, the beam intensity will beincreased by 100 times and as high as 4 × ppp. The proton beams of the energy of48 MeV in the BRing will be captured into two bunches and accelerated to the energyof 2 GeV. During the acceleration, the Siberian snakes will be used to maintain thepolarization of the proton beams[436], since the beams will cross several depolarizationresonances.The proton beams of the energy of 2 GeV which reach the extraction energy of theBRing in the ion accelerator complex will experience the first stage of beam coolingprovided by a DC electron cooler. There are several advantages of performing beamcooling at the energy of 2 GeV. Firstly, the beam cooling effect is still strong around suchenergy while the space charge effect is relatively weak. Secondly, as a well-developedtechnology widely used for the beam cooling, the DC electron cooler can effectivelyreduce the technical difficulties and the construction costs. At this stage, to obtain amore efficient beam cooling, a longitudinal bunch rotation at the energy of 2 GeV will beperformed before the beam cooling to minimize the bunch momentum spread as muchas possible. After the bunch rotation, the bunched proton beams will be debunched intocoasting beams to improve the beam cooling efficiency. After the beam cooling, thecoasting proton beams in the BRing will be bunched once again into one bunch andcompressed to match the injection settings of the pRing. The polarization direction ofthe proton beams extracted will get matched to the polarization direction of the pRingby using a spin rotator.The pRing will accelerate the injected proton beams of the energy of 2 GeV to reachthe energy of 19.08 GeV. For such a wide energy range, the Siberian snakes are unableto keep the polarization of the proton beams. Therefore, the pRing will be designed asa figure-8 shape, in which the spin tune purely contributed by the pRing itself remainszero. The figure-8 design, along with a solenoid in the long straight sections, ensuresthat the proton beams will not cross any depolarization resonances during acceleration. .2 Accelerator facilities –86/140– Moreover, such a design will facilitate the control of the beam polarization direction.The bucket-to-bucket injection scheme will be adopted for the injection of 14 bunchesfrom the booster BRing to the pRing. The beam intensity will increase to 5 . × ppp, equivalent to an average beam current of 2 A. After the injection, the beams will besplit into 448 bunches step by step and finally accelerated to the energy of 19.08 GeV.The collision frequency introduced by these 448 bunches is 100 MHz, which meets therequirements of the luminosity design.To increase the luminosity, the pRing will install a 500 MHz RF system to shortenthe bunch length. After the proton bunches are accelerated to the energy of 19.08 GeV,a bunch rotation will be performed. And during the bunch rotation, the bunch lengthwill be sharply shortened while the momentum spread will be increased, which is quitedifferent from the bunch rotation in the BRing. Along with the bunch rotation, the500 MHz RF system will be turned on to make the bunch length as short as possiblewhile keeping particle numbers in the bunch unchanged, so that the requirements of theluminosity design will be satisfied.The longitudinal manipulation of the proton beams is followed by the second stage ofbeam cooling which is supported by high energy bunched beam electron cooler based onan energy-recovery linac (ERL). The intra-beam scattering effect will be also suppressedduring the whole collision process by this cooler to improve the luminosity life.The luminosity optimization scheme of low collision frequency, high beam intensitycould bring strong single-bunch collective effects. Therefore, besides the thresholdvalues of the average current, and beam-beam parameters, the impedance limitationsintroduced by the single-bunch collective effects are also significant in the collider ringssince it determines the feasibility of luminosity optimization scheme in the pRing. Inprinciple, the longitudinal microwave instability, which is caused by the longitudinalbroadband impedance, is one of the most concerned longitudinal collective effects.When the particle numbers in the bunch exceed the corresponding limits, the longitudinalmicrowave instability will lead to an increase in the momentum spread, which can furtherinduce bunch lengthening and weaken the luminosity. The typical growth time of theinstability is shorter than one synchrotron period. In the pRing, it has been calculatedthat the longitudinal broadband impedance ( 𝑍 (cid:107) / 𝑛 ) should be lower than 87.4 Ω , which isachievable in practice. In the transverse planes, the transverse mode coupling instabilitycaused by the transverse broadband impedance is the most likely to occur among thesingle-bunch collective effects. When the bunch intensity exceeds the threshold, particlesin the bunch will be lost quickly. Calculation results have shown that the transversebroadband impedance threshold in the pRing is 30.3 M Ω / m, which is also achievablein practice. From the view of the pRing, the luminosity optimization scheme with low .2 Accelerator facilities –87/140– collision frequency, the high beam intensity is feasible for the EicC accelerator facility.One of the biggest challenges in the optical design of colliders is the correction of thelarge chromaticity introduced by the very small 𝛽 function at the IPs, with the requirementof large dynamic aperture. As shown in the Fig.3.1, there are four arc sections in thepRing. These arc sections are connected via two short straight sections and two longstraight sections. The long straight sections are employed for the IPs, the beam coolingsections, the spin rotators as well as the RF devices. Accelerator control devices, such asthe chromaticity correction sextupole magnets and so on, are placed on the short straightsections and the arc sections. The chromaticity correction scheme based on sextupolemagnets on the arc sections and the straight sections with dispersion will be employedin the pRing. Each arc section consists of eight FODO cells with 90 ◦ -phase advance perFODO cell, where 12 sextupole magnets will be installed. Dispersion exist in the shortstraight sections, and the optical parameters are designed symmetrically to the center ofthe short straight section. By doing this, the larger 𝛽 𝑦 -value appears at the position ± 𝜋 / 𝜎 . This scheme satisfies the requirement of the EicC accelerator facility. A recirculating superconducting radio frequency (SRF) linear accelerator will be em-ployed as the injector of the electron accelerator complex of the EicC accelerator facility.The recirculating SRF linac is considered to be the best choice for the electron injectorsince it has the advantages not only of linear accelerators, i.e. high accelerating gradient,greater compactness but also of circular accelerators, i.e. high efficiency and low cost.The polarized electron beams generated from the polarized photocathode electron gunwill get matched to the electron injector, and then accelerated to the extraction energyrange from 2.8 GeV to 5.0 GeV via passing through the RF cavities several turns toprovide electron beams for the full energy injection scheme in the eRing. In this process,the polarized electron beams will be bunched into micro bunches with the bunch lengthof picoseconds. Taking into account the limitations of beam power and beam dump, therecirculating SRF linac can provide the electron beams of micro-Ampere beam intensity.Furthermore, the polarization direction of the electron beams extracted from the electroninjector should get matched to the eRing, which can be achieved via a spin rotator.Because of the full energy injection scheme and the self-polarization effect in theelectron beams, the eRing is designed to be racetrack-shaped as many other electron .3 Beam cooling –88/140– colliders. The RF system of the eRing will adopt the frequency of 500 MHz to generate1350 stable buckets. The polarized electron beams will be injected into 270 stable buck-ets, forming into 270 equally spaced electron bunches, to meet the collision frequency of100 MHz in the luminosity design. Moreover, as the transverse and longitudinal beamsizes will decrease rapidly because of the damping effects introduced by the synchrotronradiation, the full energy injection scheme will be adopted to reach the bunch intensity of1 . × ppb required by the luminosity design. After beam accumulation is finished,the electron bunches in the eRing will be reinforced or replaced by the recirculating SRFlinac on line to maintain the luminosity.In addition to the limitations of average beam current, synchrotron radiation powerdensity, and beam-beam interaction parameters as listed in the Tab.3.1, the luminosityoptimization scheme with low collision frequency, high beam intensity could also bringlongitudinal microwave instability and transverse mode coupling instability. This issimilar to the case in the pRing. It can be calculated theoretically that the thresholds ofthe longitudinal and the transverse broadband impedance ( 𝑍 (cid:107) / 𝑛 and 𝑍 ⊥ ) in the eRing are0 . Ω and 0 . 259 M Ω / m, respectively. The thresholds are considered to be reachable,if we take into account the case in the KEKB electron-positron collider in Japan withthe corresponding thresholds of 0 . Ω and 0 . 235 M Ω / m. Therefore, the luminosityoptimization scheme of low collision frequency, the high beam intensity is feasible inthe eRing.Since the eRing is designed to be racetrack-shaped, the chromaticity correctionscheme base on the sextupole magnets on the arc sections will be adopted. Specifically,there are two arc sections in the eRing, as shown in the Fig.3.1. Each of them consists of20 FODO cells with 120 ◦ phase advance. Two pairs of FODO cells at both ends of onearc section are used for optical matching, while the other 16 FODO cells are employedfor chromaticity correction. Each three of the 16 FODO cells form a super periodicalstructure to cancel out the non-linear effects caused by the sextupole magnets within thearc sections. By using such a chromaticity correction scheme, the chromaticity can becorrected to zero while keeping the dynamic aperture larger than 20 𝜎 , which satisfiesthe accelerator design requirements. High luminosity, which is the primary goal of an electron-ion collider, is thus the mostessential parameter for the design of the EicC accelerator facility. It can be proven fromthe luminosity formula that an efficient way to increase the luminosity is to decreasethe six-dimensional emittance of ion beams. Since there is no synchrotron radiation .3 Beam cooling –89/140– Ion sources SRF linac DC e-cooling Bunched beam cooling (ERL) BRing pRing Energy Time48 MeV 2 GeV 19.08 GeV DC e-cooling Figure 3.3: The layout of the staged electron cooling scheme for the EicC accelerator facility. damping effect in the heavy ion synchrotrons, an external cooling mechanism is requiredto reduce the ion beam emittance. For decades, now electron cooling has become oneof the most effective and well-developed methods to reduce the ion beam emittance.Since electron cooling has a greater effect on the ion beams of low energy and lowemittance, the EicC accelerator facility will adopt the staged electron cooling scheme toshorten the cooling time and improve the cooling efficiency. In the first cooling stage,an electron cooler[437], based on conventional electrostatic high voltage acceleration,will be installed in the BRing to reduce the transverse emittance and the momentumspread of the medium-energy ion beams to reach the design value. In the second coolingstage, a high energy bunched beam electron cooler, based on an energy recovery linac(ERL), will be installed in the pRing to further reduce the transverse emittance and themomentum spread of the high-energy ion beams. The intra-beam scattering effect inthe collision will be suppressed by this cooler to keep the emittance and the momentumspread to be the design value, which can ensure high luminosity and long luminosity liferequired by the scientific goals. Due to a reduced emittance after the low-energy coolingin the first stage, the cooling time for the high-energy beam can also be largely reduced,leading to a shortened total cooling time and enhanced cooling efficiency. The stagedelectron cooling scheme for the ion beams of the EicC accelerator facility is shown inthe Fig.3.3.The Tab.3.3 lists the details of the staged beam cooling scheme in the EicC acceler-ator facility. Taking the polarized proton beam as an example, it will be first acceleratedto the energy of 48 MeV by the iLinac, then injected into the BRing for further accu-mulation, and accelerated rapidly to 2 GeV via the RF cavities. The proton beam will .3 Beam cooling –90/140– Table 3.3: The staged electron cooling scheme of the EicC accelerator facility. Position Function Proton en-ergy(GeV) Electronen-ergy(MeV) CoolerPhase 1 BRing Reduction of beam emit-tance 2 1.09 DCPhase 2 pRing Beam emittance reductionand intra-beam scatteringsuppression 19.08 10.4 Bunchedbeam(ERL) Electrostatic high voltage E-gunAccelerating tubeDecelerating tubeCollector Ion beamCooling section Figure 3.4: Layout of the low energy DC electron cooler. be debunched into a coasting beam after the momentum spread is reduced by a bunchrotation manipulation. The coasting beam will be cooled via DC electron beams ofthe energy of 1.09 MeV which are produced from a conventional electrostatic electroncooler. The cooling process can reduce the emittance and the momentum spread of theproton beam to the design value. After that, the high intensity polarized proton beamin the BRing will be injected to the pRing for further accumulation and acceleration.When the proton beam is accelerated to reach the energy of 19.08 GeV, the secondcooling stage, which is based on high energy, high-intensity and high-quality electronbunches produced by an energy recovery linac (ERL), will be performed to cool thebeam again and suppress the emittance growth and the bunch lengthening caused byintra-beam scattering effects over the whole collision process. For other ion beams withlower energy and higher cooling efficiency, the staged electron cooling process requiresa shorter cooling time compared to proton beams.The DC electron cooler in the BRing consists of an electron gun, an acceleratingsection, a cooling section, a decelerating section, a collector, several solenoids, andseveral correctors, as shown in the Fig.3.4. The electron beams emitted from the cathodeof the electron gun can be extracted to the accelerating section via a potential differenceintroduced at the anode. After acceleration via electrostatic high voltage to obtain thesame average speed as the ion beams, the electron beams will be transported to the cooling .3 Beam cooling –91/140– section, in which they will interact with the ion beams and absorb part of the heat fromthe ion beams via the Coulomb interaction. Then the electron beams will pass throughthe decelerating section and be collected in the collector. The repeated electron beamswith low temperatures can finally reduce the emittance and the momentum spread of theion beams to the design value. Nowadays the technology of the DC electron coolinghas already been well-developed and there are many DC electron coolers around theworld, with the energy ranging from a few tens of KeV to a few MeV. For instance, inthe Recycler Ring, Fermi-Lab, USA, the energy of the electron beam is as high as 4.3MeV. In the COSY electron cooler in the Jülich, Germany, the electron beam reachesthe energy of 2 MeV. And also the first RF linac-based electron cooler (bunched beamcooling) with an electron energy of 1.6 and 2.0 MeV was successfully commissioned atRHIC. For the EicC accelerator facility, the energy of the electron beam is designed tobe 1.09 MeV for the DC electron cooler, which is technically achievable.In the pRing, beam cooling requires electron beams with a maximum energy of 10.4MeV. Since the conventional DC electron cooler are unable to accelerate the electronbeams to this energy, it is necessary to employ the electron beams accelerated by RFcavities, which is high energy bunched beam electron cooling. However, the specificelectron beams cannot be used in the beam cooling for a very long time and should bealways replaced by new electron beams, because the electron cooling requires the electronbeams of very high quality (low emittance, low energy spread, high beam intensity).Moreover, the discarded electron beams should be collected to avoid radiation protectionissues, since there is almost no energy loss during beam cooling. The quality of theelectron beams in the synchrotrons hardly satisfies the requirement of the beam cooling.It is limited by the equilibrium conditions of the synchrotron radiation effects. Theelectron linear accelerator can accelerate, transport beams effectively, and keep the highbeam quality. However, the high power level of the RF cavity increases the cost ofconstruction and operation. Meanwhile, the collection of such high power electronbeams can cause severe issues of radiation protection, such as neutron activation, andenvironmental pollution. In comparison, the energy recovery linac (ERL) cannot onlyaccumulate the electron beam intensity as effectively as a synchrotron but also keephigh beam quality as the linear accelerators, which satisfies the requirement of the highenergy bunched beam cooling. The electron beams in the ERL can be sent back intothe RF cavities with a decelerating phase, where the power of the high energy electronbeams can be transferred to the power of the microwave acceleration field which canbe used to accelerate newly injected electron beams. The energy recovery from thediscarded electron beams in the ERL cannot only largely reduce the technical difficultyand the costs of the RF power, but also decrease the power deposition in the beam .3 Beam cooling –92/140– Laser e-gunPre-acceleration cavitySC cavityDumpCooling section-1 Kicker Kicker Cooling section-2Circulating ringBy-pass beam line Figure 3.5: The high energy bunched beam cooler based on the ERL. collector, solving the possible problems of the radiation protection and environmentalpollution caused by the high power electron beam. The ERL-based high energy bunchedbeam electron cooler employed in the EicC accelerator facility is shown in the Fig.3.5.It consists of a photocathode electron gun, merger line, superconducting RF cavities,arc sections, two 25-meter-long cooling sections, beam matching sections, circulatingsections, and collectors.The high intensity, high-quality electron bunches generated from the photocathodewill be firstly accelerated via the pre-accelerating cavity to 2 MeV, then transported intothe main accelerating section of the ERL through the merger line while keeping theinitial emittance and energy spread. The electron bunches are further accelerated bythe superconducting RF cavities to reach the energy of 10.4 MeV. The electron bunchesare transported through the arc sections to the cooling sections to travel along with theion beams. Then, the electron bunches interact with the ion bunches within the coolingsections in the strong solenoid magnetic field. After that, the electron bunches arestored in the circulating ring until making 53 bunches in the circulating ring, with thefrequency between the bunches being 100 MHz. Then, the first stored electron bunch iskicked out of the circulating ring by an ultra-fast kicker cavity, with its energy recoveredin the superconducting RF cavities. Finally, the residual power can be deposited in thecollectors. The newly-injected electron beams will be accelerated by the recycled energyin the RF cavities and replace the bunch which had been kicked out of the circulating ringevery 6.25 MHz. This process will be repeated until the emittance and the momentumspread of the ion beams meet the design requirements. The ERL and its circulating ringare shown in the Tab.3.4.In recent years, compared to many other types of high energy particle accelerators,the ERL has been paid more attention and experienced rapid development and wideapplication, since it has the advantages of less power consumption, high beam quality,and so on. The ERLs are being considered to replace the conventional linear or ringaccelerator for the application of the free-electron laser (FEL), the synchrotron radiationsources, the colliders, as well as the electron coolers. Up to now, there exist several .4 Beam polarization –93/140– Table 3.4: The main parameters of ERL and circulating ring. Gun type SRF RMS energy spread 5 × − PRF 6.25 MHz Cooling energy 10.4 MeVMain RF frequency 700 MHz Cooling section length 50 mCharge per bunch 4 nC Cryostat number 1Injection energy 2 MeV Cryostat length 1.5 mBeam current in ERL 25 mA Beam current in circulat-ing ring 400 mARMS bunch length in thecooling sections 150 ps Circumference of circu-lating ring 159 mTransverse RMS nor-malized emittance 2.5 𝜋 · mm · mrad Bunch frequency in cir-culating ring 100 MHzestablished ERL facilities around the world, including the Novosibirsk ERL at BINP inRussia, the CEBAF-ER and the IR ERL in the Jefferson laboratories (JLab) in the USA,the S-DALINAC ERL at Technical University Darmstadt in Germany and the ERL ofthe High Energy Accelerator Research Organization (KEK) in Japan, and so on. BNLhas also tried to build test ERL and CeC ERL for high-energy beam cooling before.With the technology development of the photocathode gun and the superconductingradio frequency (SRF), the difficulties for the construction of the high energy, high-intensity ERL has been reduced a lot. There are several ERLs under construction orproposed, including the bERLinPro of the Helmholtz-Zentrum Berlin(HZB) and theMESA at the Johannes Gutenberg-Universität Mainz in Germany, Cornell-BNL-ERL-Test-Accelerator (CBETA), the light source in the Cornell University, the US-EIC in theBNL and the LHeC in CERN. Some of them will be employed as high energy bunchedbeam electron cooler, which can lay a solid foundation for the construction of the highenergy bunched beam electron cooler based on the ERL in the EicC accelerator facilitywhile largely reducing the technical risk of the beam cooling in the project. As a dual-polarized electron-ion collider, the beam polarization is another importantpart of the design of the EicC accelerator facility, besides the luminosity and the beamcooling which are typical designs of a collider. The physics goals of the EicC projectpose the following requirements on the beam polarization design of the EicC acceleratorfacility.1. The polarized electron beams will collide with the polarized proton beams,the polarized deuterium beams, and the polarized Helium-3 beams, respectively. Therequired polarization here is about 80% for the electron beams, 70% for the protonbeams. Other ion beams are non-polarized. .4 Beam polarization –94/140– IP 2IP 1 iLinac Polarized IonSourceElectron Injector SRF Linac-ring pRing BRingeRing eRing Solenoid Spin RotatorpRing Solenoid Spin RotatorBRing solenoid SnakesElectron PolarimeterIon PolarimeterSpin Rotator for Match HIAF pRing eRing Figure 3.6: The polarization design of the EicC accelerator facility. 2. At the IPs, the polarization direction of the electron beams should be longitu-dinal, while for the proton beams, the deuterium beams, and the Helium-3 beams, thepolarization direction could be arbitrary.3. The measuring errors of the polarization for the proton beams, the deuteriumbeams, and the Helium-3 beams should be less than 5%, while for the electron beams itis less than 2%.For these requirements and goals listed above, the scheme of the beam polarizationis designed and optimized based on the layout in the Fig.3.1 and the operation modein the Fig.3.2, including polarization control and polarization measurement, which isshown in the Fig.3.6. For the ion accelerator complex, the atomic beam polarized ion source (ABPIS) canproduce both polarized and non-polarized proton beams, while other polarized ionbeams are similar to the proton beams. There are four successive processes to transformhydrogen atoms into polarized proton beams, i.e. the dissociation, the separation in asextupole magnet, the transition in a weak RF field, and ionization. Since the dissociatedhydrogen atom has an isotropic spin distribution, the hydrogen atoms of high energy leveland with an electron spin of 1 / − / / .4 Beam polarization –95/140– Furthermore, with the selection of the polarization direction of the weak RF field, thepolarization direction of the atomic beams in the transition module can be controlled tomatch the polarization directions of the following beamlines and accelerators. Protonbeams of high intensity and high polarization can thus be produced via the ionizationof such atomic beams. The ABPIS is one of the most widely-employed ion sources andcan generate the proton beams of polarization as high as 90%[438].The polarized proton beams extracted from the polarized ion source will be measuredvia a Lamb-shift polarimeter. The Lamb-shift polarimeter scans the magnetic field inthe rf spin filter to quench the different meta-stable hydrogen atoms and measures theLyman - 𝛼 photons from the quenching downstream. The meta-stable hydrogen atomsneutralized from the polarized protons will be quenched at special spin filter magneticfield values and emit Lyman - 𝛼 photons. The polarized proton beams will be acceleratedin the iLinac to reach the energy of 48 MeV needed by the injection of the BRing, andfinally injected to the BRing via a beamline for injection. During this process, thepolarization of the proton beams remains unaffected since there is no spin resonance.However, to measure the polarization direction of the beams injected into the BRing, apolarimeter will be still installed in the beamline for the polarization direction matchingto the BRing. The polarimeter mainly records the counting rate of the Coulomb elasticscattering between the polarized proton beams and the target at different angles, fromwhich the polarization at a certain angle can be calculated.High intensity polarized proton beams of the energy of 48 MeV will be acceleratedto 2 GeV in the BRing. During the acceleration, the polarization of the beam will signif-icantly decline because the spin tune will experience several depolarization resonances.To maintain high polarization, two Siberian snakes will be installed at the two ends of theelectron cooling section of the BRing to change the spin tune of the ring. The Siberiansnakes, i.e. the solenoids whose magnetic fields are synchronized with the beam energy,can keep the spin tune always to be 1 / .4 Beam polarization –96/140– Figure 3.7: The spin rotation in a spin rotator. Based on a set of magnets consisting of solenoid-horizontal bending dipole magnet-solenoid-horizontal bending dipole magnet, the polarization direction can be guidedarbitrarily. This is one of the most essential polarization control devices in the EicCaccelerator facility. The polarization direction control scheme is illustrated in the Fig.3.7,taking as the example of a vertical polarization rotating to the longitudinal polarization.In the Fig.3.7, the blue line denotes the rotation of polarization direction contributed bythe solenoids, and the purple line represents the rotation from the horizontal bendingdipole magnets. The initial and final polarization directions are shown in red. Whenpassing through a solenoid, the polarization direction of the polarized beam will rotatewith a certain angle with the beam direction as the axis. In the horizontal bendingdipole magnets, the polarization direction will rotate around the vertical direction. Withonce more such rotations in another solenoid and horizontal bending dipole magnet,the polarization direction of the beam can be transferred from the vertical direction tothe horizontal direction. Similarly, the polarization direction of the beam will rotate toan arbitrary direction by this spin rotator with carefully-chosen rotation angles in thesolenoids and the bending dipole magnets. Moreover, the polarization direction canbe well-controlled in a wide energy range while leaving the closed orbit unchanged,because the four spin angles provide sufficient polarization control variables, whichmakes it possible to provide multiple solutions for the adjustment of a certain polarizationdirection. With the help of the spin rotator, the polarization direction of the extractedhigh intensity polarized proton beams can be matched with one of the arc sections inthe pRing, thus avoiding the depolarization caused by the mismatch of the polarizationdirection. Another polarimeter will be installed near the injection section of the pRingto ensure an efficient and complete matching of the polarization direction during theinjection.After injected into the pRing, the polarized proton beams will be further accelerated .4 Beam polarization –97/140– to the energy of 19.08 GeV. During the acceleration, the proton beams will experi-ence several depolarization resonances, which means it is very difficult to maintainthe polarization of the proton beams in the conventional racetrack-shaped accelerators.Furthermore, for the large energy range in the pRing, there are quite a lot of technicalchallenges in Siberian snakes consisting of solenoids. However, the alternative Siberiansnakes consisting of dipole magnets will cause the closed orbit distortion. These makeit difficult to avoid the depolarization resonances by only using the Siberian snakes. Tosolve the issues, the pRing of the EicC accelerator facility is designed to be a novelfigure-8 structure, in which the spin precession in the arc sections of one side can bealways exactly canceled by the ones of the other side, keeping the total spin tune in thering to be zero. The spin precession angle of the proton along the reference orbit is G 𝛾 times the bending angle. The total bending angle of figure-8 ring is zero, so the spin tunewill be zero independent of the beam energy for the convenience of spin control and thespin tune is far away from all intrinsic depolarization resonances. Meanwhile, a smallsolenoid added in the long straight section to introduce additional spin precession anglecan ensure the spin tune to be far away from the imperfection depolarization resonances.It can be shown that in the optimized condition the solenoid at the IPs can also meetrequirements for adjusting the spin tune, which is a novel scheme for the ion acceleratorcomplex design in the EicC project.Due to the arbitrary polarization direction of the proton beams needed at the IPs,two spin rotators will be placed on either side of the long straight section containing theIPs and the arc sections at both ends of the long straight section. As discussed above,each spin rotator can perform polarization direction rotation to generate the arbitrarydirection needed by the experiments. Moreover, by using the spin rotator, the polarizationdirection will get matched to the direction of the arc sections before the proton beamsenter the arc sections upstream of the IPs. With this scheme, the requirements of thearbitrary polarization directions and the polarization matching can be satisfied easily.A polarimeter will also be installed in the pRing for the online measurement ofthe polarization direction and the polarization of the proton beams at the IPs, as wellas providing measuring data of the polarization for various physics experiments. Themeasuring accuracy of the polarimeter should be as high as 5%, which meets the physicsexperiment requirements. In the electron accelerator complex, the polarized electron beams can be produced via thephotocathode polarized electron gun. Since the energy band of the electron excitation inthe cathode plated by Cs and GaAs can overlap with the energy band of the vacuum, the .4 Beam polarization –98/140– electrons will become free electrons when transiting to the excitation energy band. Witha laser of a specified energy and polarization direction, the electrons of the specified spinstate will transit to the excitation energy band, forming highly-polarized electron beams.The polarization direction of the electron beams can be controlled by changing thepolarization direction of the laser. Up to now, the polarization of the beam generated fromthe polarized electron gun can be as high as 90%[439], which can meet the requirementof the EicC project. Before electron beams are injected into the electron injector, theirpolarization characteristics will be measured via a polarimeter. This polarimeter canbe also employed to adjust the parameters of the photocathode polarized electron gunaccording to the requirements of physics experiments and accelerator operations.After the polarized electron beams are injected into the electron injector, it will beaccelerated to reach the energy range from 2.8 GeV to 5.0 GeV. During the acceleration,the depolarization resonances will not occur since the electron beam travels throughdifferent arc sections in the different turns, causing a lack of resonances between theperiodic transverse and longitudinal motion, as well as the spin periodic precession[440].Therefore, it is not necessary to place any polarization preservation devices in the electroninjector.The polarized electron beam will be accelerated to its maximum energy in the electroninjector and then injected into the eRing. During this process, the polarization directionof the electron beam should get matched to one of the arc sections of the eRing. Thepolarization matching can be realized via a spin rotator in the ion accelerator complex.The polarization direction and the polarization of the beam will be measured beforethe beam is injected into the eRing. It is different from the case in the ion acceleratorcomplex or in the low energy electron accelerators, where the internal-target measuringscheme is adopted. The differential Compton cross section is a function of the initialelectron and photon polarizations[441]. The polarization direction and the polarizationof the electron beams can be obtained indirectly via detecting the backscattered photonsafter the scattering of circularly polarized photons on polarized electrons. This is anon-interception measurement scheme that will not affect the beam quality.The polarized electron beams should preserve the polarization of 80% during thewhole collision. The eRing is designed to be racetrack-shaped as other facilities accord-ing to the experiment results of the existing facilities in the world[442]. Such a designhas the advantage that the depolarization effects can be canceled by the self-polarizationeffect introduced by the synchrotron radiation of the electron beams, resulting in highequilibrium polarization at the level of 80% during the whole collision.When the beamenergy lies nearly on the depolarization resonance energy and it is not enough for theself-polarization effect to cancel the depolarization effects, the spin tune can be moved .5 Design of the interaction regions (IR) –99/140– away from the depolarization resonance via a solenoid at the IR. At the IR, the polar-ization direction of the electron beam is longitudinal, so the spin tune is moved via thesolenoid while the polarization direction remains longitudinal. When colliding withthe polarized proton beams, the polarization direction of the polarized electron beamsshould be longitudinal, but the polarization direction matching to the arc sections of theeRing is transverse. Therefore, it is necessary to place two spin rotators between thelong straight sections containing the IPs and the arc sections to satisfy the matching ofthe polarization direction and the requirement of the physics goals. The spin rotatorhere is similar to the one in the ion accelerator complex. The online measurement ofthe polarization direction and the polarization in the eRing, as well as its beamline forinjection, is also designed based on the Compton backscatter, only with an accuracy of2% required by the physics experiments. To achieve the physics goals, one full-acceptance detector will be built at one IR fordetection and identification of reaction products, such as charged particles, i.e. electrons 𝑒 , muon 𝜇 , 𝜋 -meson 𝜋 , k-meson 𝐾 , proton 𝑝 and so on, as well as neutral particles,i.e. photon 𝛾 , neutron 𝑛 , etc. Another IR will be reserved for the future upgrade. Thisdetector consists of a central detector with end caps and forward detectors. The centraldetector with end caps will be placed around a superconducting solenoid and can bedivided into two parts: the barrel part and the end cap part on both sides, which isused to detect the reaction products in a large angular range. It consists of a series ofdetectors, including vertex detectors, tracking detectors, time-of-flight (TOF) detectors,Cherenkov detectors, electromagnetic calorimeters, and hadron calorimeters. Free spacewith a length of 8 m is required for the installation of the central detector with end caps.The forward detectors will be mainly used for the detection of the final-state particlesemitted from the reaction in a small or ultra-small angle. Those detectors are far from theIP and dipole magnets are required to separate the particles. The particle detection of theelectron forward detectors is realized with the help of dipole magnets and several longdrift sections after the first quadrupole magnet. For the ion forward detectors, a dipolemagnet should be installed in front of the first quadrupole magnet to make it possibleto identify the reaction products at a small angle. Furthermore, other dipole magnetsand long drift sections will be placed behind the first quadrupole magnet to allow theidentification of the reaction products in ultra-small angles. Compared to conventionalcolliders, such specifications from the detectors raise many more requirements of theinteraction region design of the EicC accelerator facility. .5 Design of the interaction regions (IR) –100/140– Typically, a conventional collider poses the following requirements about the layoutof the interaction region and its optics design.1. The beam transverse size or the 𝛽 ∗ at the IP should be as small as possible.2. The devices in the interaction region should meet the required minimum installa-tion length of the central detector.3. The 𝛽 function in the first quadruple magnet in the interaction region should benot too large.4. The optics design in the interaction region should satisfy the chromaticity correc-tion of the collider ring.5. The cross angle at the IP should be larger than the minimum value required for thebunch separation, and smaller than the maximum acceptable value decided by thecrab cavity.6. In the optics design of the interaction region, the size of each magnet shouldnot exceed the space limit introduced by the detectors, and there should be nointerference among the magnets.Furthermore, in order to identify nearly 100% of the reaction products with higherresolution, the full-acceptance detector poses more requirements on the design of theinteraction region in the EicC accelerator facility.1. In the interaction region of the eRing, a large deflection of electron beams shouldbe avoided to reduce the impact of the synchrotron radiation background generatedby the electron beams themselves on the detectors in the interaction region.2. The interaction region of the pRing should be designed as close as possible to thearc sections to reduce the hadron background produced by the collision among theproton beams and the residual gas molecules which could affect the detectors inthe interaction region.3. In the pRing, a dipole magnet should be placed downstream of the IP to improvethe detecting resolution of the reaction products at small angles.4. In the pRing, a set of dipole magnets should be placed after the first focusingquadrupole magnet to improve the detecting resolution of the reaction products atultra-small angles.5. In the eRing, at least one set of dipole magnets should be placed after the firstfocusing quadrupole magnet to improve the detecting resolution of the reactionproducts at small angles [443].6. In the interaction region, the transverse aperture of the magnets should be largerthan the clear zone, which is at least ten times of the transverse RMS beam size,to let the debris at larger scattering angles in the small-angle reaction productspass through the vacuum pipe of the magnets and reach the forward detectors .5 Design of the interaction regions (IR) –101/140– IP Central detector installation regionCrab cavity eP e Ultra small angleforward detectorCentral detector Small angle forward detector Small angle forward detector Figure 3.8: The interaction region of the EicC accelerator facility. downstream of the IP.Taking each item listed above into consideration, the overall design of the interactionregion is shown in the Fig.3.8. Since there are significant differences between electronbeams and proton beams, the detectors in the different collider rings have differentdemands on the layout of the interaction region. So, the interaction region of theEicC accelerator facility is designed to be asymmetric. In the pRing, the interactionregion is close to the upstream arc sections to reduce the hadron background causedby the interaction between the residual gas molecules and the proton beams, improvingthe resolution of the detectors. In the eRing, a long straight section will be placedupstream of the interaction region, keeping the interaction region away from the arcsections. Meanwhile, synchrotron radiation absorbers will be installed. These schemescan reduce the synchrotron radiation background, further improving the resolution ofthe detectors.The interaction region mainly consists of two parts, i.e. the straight section withfew devices close to the IP for the installation of the central detector with end caps,and the beamline that is relatively distant from the IP and contains dipole magnets anddrift lines for the installation of the forward detectors. The installation of the centraldetector with end caps requires an 8-meter free space. To follow the magnetic fieldlimits of the magnets and make full use of the installation space in the interaction region,all of the magnets are designed to be superconductive for increasing the length of thefree space and save the installation space so that all the final state particles except thereaction products at the small and very small angles can be detected. Based on thesuperconducting magnets, the crossing angle at the IP is chosen to be 50 mrad, whichcan achieve a fast separation between the electron beams and the ion beams and suppressthe long-range beam-beam interactions, so as to reduce the limit of the length of thestraight section at the IP. And this design can optimize the minimum 𝛽 function at the .5 Design of the interaction regions (IR) –102/140– IP, the maximum 𝛽 function at the first focusing quadrupole magnet, and the dipolemagnetic field required by the forward detectors for small-angle reaction products.The 𝛽 function values at the IP in the pRing are 0.04 m in the horizontal directionand 0.02 m in the vertical direction respectively, which can satisfy the luminosity design.And the maximum 𝛽 function value in the first focusing quadrupole magnet is around1000 m. It makes sure that this superconducting quadrupole magnet can be installed inthe central detector. Furthermore, in order to achieve higher luminosity, the dispersionat the IP should be zero to further reduce the beam transverse size. However, there is alarge dispersion on both sides of the IP to improve the detecting resolution. A dispersionsuppression section, which consists of two dipole magnets and two quadrupole magnets,will be installed upstream of the IP to make sure that the dispersion is zero at the IPwhile the dispersion at the forward detectors is large enough to provide high detectingresolution.The 𝛽 function values at the IP in the eRing are 0.2 m in the horizontal direction and0.06 m in the vertical direction, which satisfies the design of the luminosity. Furthermore,compared to the case of the pRing, the first focusing quadrupole magnet in the eRing iscloser to the IP, in order to separate the position at which the beam size is the largest inthe eRing from the corresponding position in the pRing. It makes it easier to separatethe beams at the IP. In the eRing, the maximum value of 𝛽 function in the first focusingquadrupole magnet is about 280 m as it is much closer to the IP. However, the fact thatthe first focusing quadrupole magnet in the eRing is much closer to the IP introduces ahuge advantage. Because the aperture required by electron beams is much smaller, thisquadrupole magnet can reduce the required installation space, which makes it possiblefor the central detector with end caps to detect all the reaction products more effectivelyand to avoid breaking the full-acceptance feature of the central detector.A superconducting dipole magnet with 1-meter length, 2.1 T maximum magneticfield, and 30 mrad deflection angle will be placed downstream of the IP in the pRing. Thedipole magnet will be able to provide large dispersion to enhance the detecting resolutionof the forward detectors installed behind it for small-angle products. Furthermore, thedipole magnet can separate the beams to make it more flexible for the optics design ofthe two collider rings. Behind the superconducting dipole magnet, there is a straightsection that contains only focusing quadrupole magnets, which can be used for theseparation of the small-angle reaction products and the installation of the small-angleforward detectors. The quadrupole magnet is followed by a dipole magnet providinga large deflecting angle to deflect the beam to the direction which is parallel with theeRing. The distance between the beamlines in the two collider rings is about 1 meter.Along with the following long straight section, this large dipole magnet can improve .6 Pre-research on key technologies –103/140– the detecting resolution for the ultra-small-angle reaction products. Besides, the neutralparticles will be not deflected when passing through this dipole magnet. To detect theneutral particles produced from the reaction, the detectors can be put in the direction ofthe extension line of the tilting straight section. Based on a system consisting of twodipole magnets, the forward reaction products of small angles and ultra-small angles inthe ion beams can be detected to almost 100%, which ensures the full-acceptance featureof the detector.In the eRing, a set of carefully-designed beamline segments are placed downstreamof the IP, for detecting the small-angle forward reaction products. With the horizontalbending dipole magnets, the electron beams will be deflected to a tilted direction withrespect to the eRing, and then deflected back to the parallel direction. Two sets ofdipole magnets (4 magnets in total) are placed symmetrically to cancel the dispersiongenerated by themselves and generate a smooth decrease of the 𝛽 function, which makesit convenient for the optics parameter matching upstream and downstream. The dipolemagnet closest to the IP is chosen to be the first dipole magnet of such a set of four. Itis followed by a long straight section, which can provide plenty of drifting space for thereaction products in the electron beams so that the reaction products can be observed bythe small-angle forward detectors. The straight section between the second and the thirddipole magnet is parallel to the long straight line of the interaction region. A polarimeter,based on the Compton backscatter of the electron beams, will be placed in the extensionline of the straight section. Four dipole magnets will form a deflecting structure, whichensures the full-acceptance feature of the detector in the electron beams.To obtain higher luminosity with a large crossing angle at the IP, crab cavities willbe placed with a phase shift of 𝜋 / ± ◦ , which canfulfill the requirements of complete crabbing. As for the crab cavities in the eRing, thesame frequency used in the pRing is chosen but with a lower voltage, 3.6 MV, resultingfrom lower energy of electron beams. .6 Pre-research on key technologies –104/140– For the design presented above, the pre-research of the EicC accelerator facility andtesting of several related key technologies will be carried out on the existing facility HIAF.It mainly includes the atomic beam polarized ion sources (ABPIS), the photocathodepolarized electron gun, the high energy bunched beam electron cooler based on theenergy recovery linac (ERL), the Siberian snake, the spin rotator, a verification facilityof a figure-8 ring, and an elastic scattering polarimeter.The atomic beam polarized ion source (ABPIS) is the essential device for the pro-duction of the polarized proton beams (as well as the lighter polarized heavy ion beams).The study of the maximum polarization and the maximum intensity of such beams isone of the most important topics for the pre-research of the EicC accelerator facility. Inthe pre-research, the polarized ion source will be installed in the HIAF for online testingto find out if it meets the requirement of the EicC project.The technology of the photocathode polarized electron gun is relatively well-developed.However, there are still several subjects that need to be investigated thoroughly, such asthe control of the polarization direction, the optimization of the beam intensity, and thephotocathode lifetime. And it is necessary to study the related parameters of the pho-tocathode polarized electron gun, in order to determine the injection and accumulationschemes in the eRing. The photocathode polarized electron gun for the pre-researchof the EicC accelerator facility will be tested independently since there is no electronaccelerator in the HIAF.The high energy bunched beam electron cooler based on the energy recovery linac(ERL) is an indispensable device to achieve the required collision luminosity and thecollision lifetime in the EicC accelerator facility and will be developed in the stage of thepre-research. A verification facility of the high energy bunched beam electron cooler willbe installed in the BRing of the HIAF. The pre-research of the high energy bunched beamelectron cooler mainly includes three aspects. The first aspect is about the developmentof high- quality energy recovery linac (ERL). Compared to those energy recovery linacswhich are not used for electron cooling, the ERL employed for the EicC acceleratorfacility poses higher requirements on the electron beam quality, because the electronbeams should be kept sufficiently cold. In the pre-research, a prototype of ERL withlow energy will be built to provide electron beams for the experiment of the high energybunched beam electron cooling on the BRing of the HIAF, in which key technologiesand experience about the cavity design of the ERL, as well as the energy recovery, canbe developed and improved. The second aspect is about the design and implementationof a circulating ring. Since the electron beams generated from the electron gun cannot .6 Pre-research on key technologies –105/140– reach the beam current required by the high energy bunched beam electron cooling, theyneed to be recirculated in the circulating ring for 16 turns so that to reduce the ERLbeam current by 16 times. The third aspect is the development of the ultra-fast kickercavity. In the high energy bunched beam electron cooler based on the ERL, the electronbunches should be either injected from the main accelerating section to the circulatingring during the accumulation or extracted to the main accelerating section for energyrecovery. It is crucial that the kicker cavity is able to deflect several electron bunchesor even one electron bunch. There are many technical challenges for the design andproduction of such kicker cavities, which need to be examined and verified carefully inthe pre-research. Overall, the high energy bunched beam electron cooler based on theERL and developed in the pre-research stage of the EicC project is expected to be ableto perform high energy bunched beam electron cooling experiments and online testingin the BRing, which will lay a solid technical foundation for the development of higherenergy bunched beam electron cooler in the EicC accelerator facility.The Siberian snake is a key device to avoid the depolarization resonances in theBRing. Technologically, it will be taken as a solenoid. Compared to dipole magnets, thesolenoid-shaped Siberian snake will not affect the closed orbit of the BRing. However, itsmagnetic field ramping rate can be far lower than the one of dipole magnets. The BRingwill be operated in a rapid cycling mode, in which the ramping rate of the magnetic fieldof the dipole magnets is about 12 T/s. There still exist quite a lot of technical difficultiesin the synchronization of the solenoid magnetic field with proton beam energy, whichneeds to be studied and optimized in detail. The solenoid-shaped Siberian snake forthe EicC accelerator facility will be firstly designed and built in the BRing. After thepolarized ion source developed in the pre-research is installed, an integration testing ofthe BRing performance will then be conducted to check whether the beam intensity andthe polarization of the BRing fulfill the criteria of the EicC project. So the booster ofthe EicC accelerator facility, i.e. the BRing, can be completed during the pre-researchstage.The spin rotator is an essential device for the adjustment of the polarization at the IP,as well as for the polarization direction matching between beamlines and accelerators ofthe EicC accelerator facility. There are three most important characteristics of the spinrotator, i.e. functioning well for different energies, rotating the polarization directionto arbitrary direction, and introducing no influence of the closed orbit. A spin rotatorfor the EicC accelerator is composed of two solenoids and two dipole magnets, withthe sequence of the solenoid-dipole magnet-solenoid-dipole magnet. It is important toverify that four parameters of magnetic fields for an arbitrary given rotation angle canbe always specified. To this end, a spin rotator will be designed and developed at the .6 Pre-research on key technologies –106/140– injection energy of the BRing, which can be used to perform online testing of the spinrotator design in the beamline for the injection of the BRing of the HIAF. Based on thesestudies, the design of the spin rotator will be further improved and eventually applied tothe EicC accelerator facility.There has been no synchrotron with a figure-8 structure in the world until now, and theproperty of a zero pure spin tune in such type of synchrotrons has not yet been verified.There is some free space reserved for the mirror ring next to the SRing in the designand construction process of the HIAF, which makes it possible to upgrade the SRinginto a figure-8 shaped synchrotron with less cost to test the effect of the depolarizationresonances on such synchrotrons. If the upgrade is completed smoothly during the pre-research stage and the main features (such as the maintenance of polarization and so on)are verified, the high-precision spectrometer ring SRing will become the first figure-8synchrotron that can store high intensity polarized proton beams in the world. Thiswork, which thus plays a crucial role in the whole pre-research of the EicC acceleratorfacility, will support the construction of the pRing with fruitful technical experience.Since there is no electron accelerator in the HIAF project, it is impossible to performthe testing of the polarization direction and polarimeter based on the Compton backscat-ter. For this reason, the test of the polarization direction and polarimeter based on theinternal target could be firstly performed. Typically, the polarimeter adopts the internalpolarized gaseous target, in which the polarization in every specified direction is mea-sured via recording the counting rate of the angle distribution of the Coulomb scattering,in which the direction with maximum polarization represents the polarization directionof the beams. In this measuring scheme, the transport of the low energy beam will begreatly affected, so it will stop the beams and is not an online measuring method. How-ever, for the beams of high energy, the measurement will end up with less effect on thebeam transport and become the online measuring method. The polarimeter is one of themost key devices for the polarization direction and polarization control of the polarizedion source and the photocathode polarized electron gun. It is also the only equipmentthat can be employed to perform the polarization matching between accelerators andbeamlines, as well as to measure the depolarization resonances in the synchrotrons. Inthe pre-research of the EicC project, several internal target polarization direction andpolarimeters will be built and installed at the exit of the polarized ion source, at the exitof the photocathode polarized electron gun, at the exit of the spin rotator in the beamlinefor the injection of the BRing, in the BRing and in the high-precision spectrometer ringSRing and so on, to check whether the technical goals of the pre-research of the EicCaccelerator facility is fully satisfied.In conclusion, the pre-research of the EicC accelerator facility is crucial to ensure the .6 Pre-research on key technologies –107/140– design, construction, commissioning, and operation of the EicC accelerator facility tobe finished smoothly and successfully in the future. With that, the key technical barriersin the EicC project will be overcome, and their corresponding solutions and schemeswill be verified. hapter 4 Detector conceptual design Driven by the physics program of EicC, a conceptual design for a general purposespectrometer is presented in this chapter. The physics program includes investigatingthe nucleon spin structure, the nucleon 3-D structure with respect to TMDs and GPDs,and the study of exotics, etc., as detailed in previous chapters.Figure 4.1 shows the definition of the coordinate system, where the electron beampoints into the negative 𝑧 direction. The pseudo-rapidity axis is shown as the half-circle.The acceptance of the detector segments is only meant for illustration. Figure 4.1: Illustration of the coordinate system for EicC. Based on the EicC baseline design, a PYTHIA [445] simulation is performed. In theEicC baseline design, an electron beam energy is 3.5 GeV, proton beam energy of 20GeV, results in a center of mass energy of 16.7 GeV and a cross-section of 20.8 𝜇 b. Theluminosity is expected to be 𝐿 = × 𝑐𝑚 − 𝑠 − with an interaction rate of 83.2 kHz.The PYTHIA simulation shows the final state particles are concerntrated near 𝜂 = 1,with a particle density of 𝑑𝑁 / 𝑑𝜂𝑑𝑡 = × / 𝑠 . This yields a moderate event rate thathas to be considered in the design of detectors and the data acquisition system.For electron-ion collisions, the detection of the scattered electrons play an importantrole in most of the physics programs. As shown in Fig. 4.2, the isolines of energy,pseudo-rapidity, and inelasticity of the scattered electrons are drawn in the 𝑥 - 𝑄 space. .1 Detector performance requirements –109/140– Figure 4.2: Isolines of the scattered electron energy, pseudo-rapidity and inelasiticity. Here 𝑥 is the Bjorken variable and 𝑄 is the momentum transfer. The red lines showthe iso-lines of the energy of the scattered electrons. Inelastic scattering of electrons offprotons can be interpreted as elastic scattering of electrons off partons inside the proton.For 𝑥 = . 175 , which means that the parton carries the same momentum of 3.5 GeV asthe electron, elastic scattering will result in constant 3.5 GeV momentum of the scatteredelectron. This leads to the vertical line at 𝑥 = . 𝑥 < . 𝑄 and very forward goingelectrons at large rapidity. In contrast, on the right-hand side of the vertical line, with 𝑥 > . 𝑄 , the scattered electron is expected to be in the extreme forward direction(see the low 𝑄 region with 𝜂 = − 𝑒 𝑝 collisions. Among the final state particles, the scattered electrons provide crucial information tomost of the physics programs, in particular those focusing on the processes of DIS,SIDIS, DVCS, and so on. We have shown very instructive information from a generalbehavior analysis in Fig. 4.2. Here, with a detailed study, more information aboutthe kinematics of the scattered electrons can be obtained. In Fig. 4.3, distributions ofthe scattered electrons are shown for various 𝑄 bins. In these plots, the color scale .1 Detector performance requirements –110/140– Figure 4.3: Kinematics of the scattered election at various 𝑄 bins. reflects the cross-section. The distance from the center point denotes the magnitude ofthe scattered electron momentum, and the direction reflects the pseudo-rapidity. Theevents were generated with Pythia 6 [276]. Comparing the plots with various 𝑄 bins,it is noticed that with increasing 𝑄 , the scattered electrons are less boosted to negativepseudo-rapidity. For physics requiring 𝑄 larger than 1 GeV (such as SIDIS or DVCS),a detector coverage of 𝜂 > − 𝜋 − (red), 𝐾 − (green), ¯ 𝑝 (blue), proton(grey), 𝑒 − (black), and 𝛾 (purple) at a given pseudo-rapiditybin are shown. By comparing the yields of these particles, it is noticed that the numberof final state pions is about 1-2 orders of magnitude larger than those of kaons andanti-protons. The momenta of hadrons in other 𝜂 regions are also investigated. At apseudo-rapidity smaller than 1, the momenta of final state hadrons are expected to besmaller than 6 GeV, while at large pseudo-rapidity ( 𝜂 > .1 Detector performance requirements –111/140– - 10 1 10 p(GeV) E n t r i es g - e - p - Kpp Figure 4.4: Momentum distributions for the final state 𝜋 − (red), 𝐾 − (green), ¯ 𝑝 (blue), pro-ton(grey), 𝑒 − (black), and 𝛾 (purple) at a given pseudo-rapidity bin 2 < 𝜂 < direction are observed. This is consistent with the previous Pythia simulation. TheseSIDIS processes set very basic requirements for the central detector. Figure 4.6 showsthe distributions of the scattered electrons, protons, and photons in the DVCS process.Here, the detection of extremely forward going protons in the DVCS process needsspecial consideration. A dedicated device, Roman Pot [446], can be installed to detectthese small-angle protons. Furthermore, the final state neutrons are important for somephysics programs, such as the meson structure function measurements, in which a neutronis found at extreme forward angles near the proton beam. This indicates that a specialneutron detection is needed for EicC to carry out this physics program. These small-angle neutrons can be detected with zero-degree calorimeters after the analysing dipolein the far ion-forward region. In the meson structure section, the Kaon structure functionis mentioned. With the Sullivan process, the Kaon structure function can be measured,in which a forward Lambda baryon needs to be reconstructed. With the current detectordesign, the proton and pion from Lambda decay could be partly detected by the forwarddetectors. Detailed studies on the detection efficiency and background level are neededto provide guidance to optimize the detector design and to make clear statement on thephysics potential.In EicC, exotic hadron production is one of the important physics highlights. Fig-ure 2.22 shows the distributions of various pentaquarks in EicC. To reconstruct thesepentaquarks, the final state particles, such as protons and lepton pairs from 𝐽 / 𝜓 ( Υ ), or .1 Detector performance requirements –112/140– 20 40 60 80 100 120 140 160 180 (Degree) ele q ( G e V ) e l e P (Degree) p q P p ( G e V ) 20 40 60 80 100 120 140 160 180 (Degree) ele q ( G e V ) e l e P (Degree) K q ( G e V ) K P Figure 4.5: Distribution of the scattered electrons and charged pions (the upper two plots) andKaons (the lower two plots) in SIDIS processes. 𝑄 > is applied. γ P050100150 ( deg r ee ) γ θ − − − − − 20 GeV × ep 3.5 e’ P050100150 ( deg r ee ) e ’ θ − − − − − 20 GeV × ep 3.5 p P0123456 ( deg r ee ) p θ − − − − − 20 GeV × ep 3.5 Figure 4.6: Distributions of the scattered electrons, protons and photons in the DVCS process. charged pions, kaons, photons for reconstruction of open-charm (open-bottom) hadrons,are under investigation. For a collider such as EicC, the precise knowledge of the beam luminosity is essentialfor any type of cross-section measurements. For electron-proton collisions, e.g. atHERA, the luminosity can be continuously monitored via the bremsstrahlung process, 𝑒 𝑝 → 𝑒 𝑝𝛾 . This is a pure QED process where the cross-section is large and well known( 0.2%). The luminosity can be quickly and precisely measured from the photon rateat very small angles by using a calorimeter system installed next to the beamline in the .2 Detector conceptual design –113/140– electron direction. The cross-section of the bremsstrahlung process also depends on thebeam polarization.The precise investigation of nucleon structure in the sea quark region, includingone-dimensional and three-dimensional tomography of the nucleon spin-flavor structurein both the momentum and spatial spaces is one of the featured physics highlights ofEicC. For any of these spin related measurements, the final results always need to benormalized to the beam polarization. Since an unprecedented statistical precision is ex-pected from the proposed high luminosity of EicC, the precision of the beam polarizationmeasurement becomes very demanding. For the electron beam, the polarization can bemeasured from different QED processes, e.g., the electron-photon Compton scatteringand the electron-electron Møller scattering. The spin dependent cross-section and theanalyzing power of these processes can be precisely obtained from QED calculations.Together with the known polarization of the polarimeter targets, the beam polarizationcan thus be extracted. Taking CEBAF at Jefferson Lab, for instance, there are three typesof electron beam polarimeter which are Mott [447], Møller [448], and Compton [449],respectively, providing polarization measurements as precise as 1% at different positionsalong the beamline. The Compton polarimeter uses a highly polarized and high powerlaser as the scattering target which is noninvasive to the electron beam so that it cancontinuously monitor the beam polarization. The Mott and Møller polarimeters use goldand iron foils, respectively, as the scattering targets which have very high rates and areable to perform precise measurements in a short period of time.For the proton beam, the polarization can be measured from elastic proton-proton orproton-nucleus scattering, where large transverse spin asymmetries are expected. Forexample, at RHIC two types of polarimeter are used to perform proton beam polarizationmeasurements. One of them, the 𝑝 -Carbon polarimeter [450], uses carbon fibers as thescattering target with large scattering rates, periodically measuring the polarization.Another one is the H-jet polarimeter [451], which continuously performs noninvasivepolarization measurements, just analogous to the Compton polarimeter for the electronbeam. The proton beam polarization at RHIC can be measured with a precision at the ∼ 3% level. In the previous section, we showed the requirements derived from the key physicsprograms at EicC. A summary table is given in Fig. 4.7, in which the physics requirementsare listed in terms of momentum or energy reach at different pseudo-rapidity coverage.For example, the hadron separation power at 4 GeV is sufficient for the 𝑒 -Endcap region. .2 Detector conceptual design –114/140– However, hadrons with momenta up to 15 GeV are expected for the ion-Endcap region.These differences indicate that different detection techniques need to be adopted in thedetector design. Figure 4.7: Physics requirements for EicC. As a high luminosity machine, EicC could reduce the statistical uncertainty downto a few percent for many measurements. To cope with the small statistical uncertainty,we need a matching systematic error, which requires a good detector. For example, atracking detector with a tracking resolution of a few percent is necessary. In Fig. 4.7,a momentum resolution of 1% for the central coverage and 2% for small angles aremarked based on experiences from similar experiments. For the first conceptual design,we divide the EicC detector into the central detector and forward detectors. The centraldetector consists of the barrel part and two endcaps, and it will be constructed around asolenoid. Four main detection components include:(1) Vertex detector, for detecting the primary and secondary vertices. MAPS [452]based vertex detectors have been used in many experiments and can be consideredfor EicC.(2) Tracking detector, for the momentum reconstruction of charged particles. TPC [453],GEM [454], or Straw Tube detectors [455] can be considered for EicC.(3) Particle identification detectors, such as Time-of-Flight (TOF) detectors and .2 Detector conceptual design –115/140– p(GeV) / p p s m m =150 f r s N=30, L=0.6m, B = 1.0 TeslaB = 1.5 TeslaB = 2.0 Tesla Figure 4.8: Momentum resolution for tracking detectors at different magnetic fields. Cerenkov detectors.(4) Calorimeter, including electro-magnetic calorimeter and hadron calorimeters.For the tracking detector, a momentum resolution of roughly 1% at 1 GeV withenergy deposition ( 𝑑𝐸 / 𝑑𝑥 ) measurement is widely used in many experiments [456, 457].For the central rapidity coverage, the tracking detector is usually installed inside asolenoid magnet. As one of the key components of the central spectrometer, the solenoidmagnet provides the bending power for charged particles inside a tracking detector.Figure 4.8 shows the impact of different magnet fields to the momentum resolutionwith the other parameters fixed. A solenoid magnet of 1 to 2 Tesla, well used in manyexperiments [456, 458] with adequate power to allow for a good momentum resolutionand less challenging in manufacturing, is fine for EicC. For the small-angle coverage inthe central spectrometer, certain layers of position-sensitive detectors can be adopted,such as the GEM disks or silicon detectors.One challenge for the EicC detector is the hadron identification, especially in theion forward direction where the hadrons may have large momenta up to 15 GeV. Aseries of detectors may serve the particle identifications. The energy deposition ( 𝑑𝐸 / 𝑑𝑥 )measurements from tracking detectors could provide particle identification in the regionof low momenta around a few hundred MeV. A TOF detector with a time resolution ofa few tens of picoseconds and a flight distance of about 2-3 meters (the forward region)could extend the particle identification up to a few GeV. To reach large momenta up to .2 Detector conceptual design –116/140– Figure 4.9: 𝜋 / 𝐾 separation power with a Cherenkov detector of different refractive indices. 15 GeV, a Cherenkov detector [459] with a small refractive index ( 𝑛 = . 𝑛 = . 02 could achieve a 3 𝜎 separation of the 𝜋 / 𝐾 mesons up to almost 15 GeV. ACherenkov detector with a further small refractive index, such as 𝑛 = . 𝐶 𝐹 ,covering high momentum range as shown with the green lines in Fig. 4.9, is unnecessaryin EicC. For the other regions, where the hadron momenta are smaller than 6 GeV, acompact DIRC (Detection of Internally Reflected Cherenkov light) detector [460, 461]could be used. As the red lines shown in Fig. 4.9, with a 1 mrad (round filled dot)Cherenkov angle resolution, the 𝜋 /K separation power at 3 𝜎 for a DIRC detector of 𝑛 = . 47 could reach up to 6 GeV.For EM-Calorimeters, different types of calorimeters should be adopted at differentrapidity coverage. A typical configuration could be sampling calorimeters for most ofthe regions, featuring relatively low-performance at a low price, and costly homogenouscrystal calorimeters for small region at the 𝑒 -Endcap side. A compromise betweenphysics and budget needs to be found in the deployment of lower price and higher-quality calorimeters in different regions.A conceptual design of the EicC detector is shown in Fig. 4.10. In the currentconceptual design, forward detectors are also considered at small angles. These detectorsare crucial to many important physics programs of EicC. As a doubly polarized highluminosity machine, the polarization and luminosity measurement are important and aredesigned with integration to the forward detectors. Starting from the conceptual design, .2 Detector conceptual design –117/140– the detector requirements for each sub-detector will be derived iteratively with detectorand physics simulations.As a general-purpose spectrometer, the EicC detector design is facing difficultiesand challenges. Detector R&D will be started at the early stage, including the R&D ofCherenkov detector, tracking detector, calorimeters, super-conducting solenoid, the dataacquisition system, etc. Acknowledgement In 2018, we started the process of writing an EicC White Paper in order to, on onehand, unite the Chinese QCD and hadron physics community and, on the other hand, toestablish an electron-ion collider whose somewhat lower center-of-mass energy servesto complement the US EIC physics program. It would not have been possible for us tocomplete this document within two-and-a-half years without generous assistance frommany colleagues all over the world. We are grateful for support from the Institute ofModern Physics; and sincerely thank S. J. Brodsky, J.-P. Chen, A. Deshpande, H. Y.Gao, S. Goloskokov, T. Horn, X. D. Ji, S. Joosten, V. Kubarovsky, Z. E. Meziani, J.W. Qiu, E. Sichtermann, Z. H. Ye, F. Yuan, Y. S. Yuan, J. X. Zhang, X. B. Zhao, Z.W. Zhao and F. Zimmermann for helpful discussions and valuable advice. We wouldalso like to thank the referees from Frontiers of Physics journal for their critical readingof the early version of the document and constructive suggestions. During the studiesnecessary for the preparation of this document, we were granted access to an arrayof software packages written by others, including DJANGOH, DSSV14, eSTARlight,LAGER, LHAPDF, MILOU, NNPDF, PARTONS, and Pythia. .2 Detector conceptual design –118/140– Figure 4.10: Conceptual design of the EicC detector. ibliography [1] Charles Seife. Illuminating the dark universe. Science , 302(5653):2038–2039, 2003.[2] Steven Weinberg. A Model of Leptons. 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