Electron Ion Collider:

The Next QCD Frontier

Understanding the glue that binds us all

White Paper Writing Committee

Elke C. AschenauerBrookhaven National Laboratory

William BrooksUniversidad Tecnica Federico Santa Maria

Abhay Deshpande1

Stony Brook University

Markus DiehlDeutsches Elektronen-Synchrotron DESY

Haiyan GaoDuke University

Roy HoltArgonne National Laboratory

Tanja HornThe Catholic University of America

Andrew HuttonThomas Jefferson National Accelerator Facility

Yuri KovchegovThe Ohio State University

Krishna KumarUniversity of Massachusetts, Amherst

Zein-Eddine Meziani1

Temple University

Alfred MuellerColumbia University

Jianwei Qiu1

Brookhaven National Laboratory

Michael Ramsey-MusolfUniversity of Wisconsin

Thomas RoserBrookhaven National Laboratory

1Co-Editor

1

Franck SabatieCommissariat a l’ Energie Atomique-Saclay

Ernst SichtermannLawrence Berkeley National Laboratory

Thomas UllrichBrookhaven National Laboratory

Werner VogelsangUniversity of Tubingen

Feng YuanLawrence Berkeley National Laboratory

Laboratories Management Representatives

Rolf EntThomas Jefferson National Accelerator Facility

Robert McKeownThomas Jefferson National Accelerator Facility

Thomas LudlamBrookhaven National Laboratory

Steven VigdorBrookhaven National Laboratory

2

Contents

1 Executive Summary: Exploring the Glue that Binds Us All 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Science Highlights of the Electron Ion Collider . . . . . . . . . . . . . . . . 3

1.2.1 Nucleon Spin and its 3D Structure and Tomography . . . . . . . . . 31.2.2 The Nucleus, a QCD Laboratory . . . . . . . . . . . . . . . . . . . . 71.2.3 Physics Possibilities at the Intensity Frontier . . . . . . . . . . . . . 10

1.3 The Electron Ion Collider and its Realization . . . . . . . . . . . . . . . . . 101.4 Physics Deliverables of the Stage I of EIC . . . . . . . . . . . . . . . . . . . 12

2 Spin and Three-Dimensional Structure of the Nucleon 142.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2 Longitudinal Spin of the Nucleon . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2.2 Status and Near Term Prospects . . . . . . . . . . . . . . . . . . . . 242.2.3 Open Questions and the Role of an EIC . . . . . . . . . . . . . . . . 27

2.3 Confined Motion of Partons in Nucleons: TMDs . . . . . . . . . . . . . . . 352.3.1 Introcution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.3.2 Opportunites for Measurements of TMDs at the EIC . . . . . . . . . 37

Semi-inclusive Deep Inelastic Scattering (SIDIS) . . . . . . . . . . . 38Access to the Gluon TMDs . . . . . . . . . . . . . . . . . . . . . . . 40

2.3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.4 Spatial Imaging of Quarks and Gluons . . . . . . . . . . . . . . . . . . . . . 44

2.4.1 Physics Motivations and Measurement Principle . . . . . . . . . . . 442.4.2 Processes and Observables . . . . . . . . . . . . . . . . . . . . . . . . 462.4.3 Parton Imaging Now and in the Next Decade . . . . . . . . . . . . . 482.4.4 Accelerator and Detector Requirements . . . . . . . . . . . . . . . . 502.4.5 Parton Imaging with the EIC . . . . . . . . . . . . . . . . . . . . . . 522.4.6 Opportunities with Nuclei . . . . . . . . . . . . . . . . . . . . . . . . 56

3 The Nucleus: A Laboratory for QCD 583.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.2 Physics of High Gluon Densities in Nuclei . . . . . . . . . . . . . . . . . . . 63

3.2.1 Gluon Saturation: a New Regime of QCD . . . . . . . . . . . . . . . 63Nonlinear Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Classical Gluon Fields and the Nuclear “Oomph” Factor . . . . . . . 66Map of High Energy QCD and the Saturation Scale . . . . . . . . . 68Nuclear Structure Functions . . . . . . . . . . . . . . . . . . . . . . . 71

3

Diffractive Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743.2.2 Key Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Structure Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Di-Hadron Correlations . . . . . . . . . . . . . . . . . . . . . . . . . 79Measurements of Diffractive Events . . . . . . . . . . . . . . . . . . . 82

3.3 Quarks and gluons in the nucleus . . . . . . . . . . . . . . . . . . . . . . . . 873.3.1 The distributions of quarks and gluons in a nucleus . . . . . . . . . . 873.3.2 Propagation of a fast moving color charge in QCD matter . . . . . . 903.3.3 Strong color fluctuations inside a large nucleus . . . . . . . . . . . . 93

3.4 Connections to pA, AA and Cosmic Ray Physics . . . . . . . . . . . . . . . 953.4.1 Connections to pA Physics . . . . . . . . . . . . . . . . . . . . . . . 953.4.2 Connections to Ultrarelativistic Heavy-Ion Physics . . . . . . . . . . 98

Initial Conditions in AA collisions . . . . . . . . . . . . . . . . . . . 99Energy Loss and Hadronization . . . . . . . . . . . . . . . . . . . . . 103

3.4.3 Connections to Cosmic Ray Physics . . . . . . . . . . . . . . . . . . 105

4 Possibilities at the Luminosity Frontier: Physics Beyond the StandardModel 1074.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1074.2 Specific Opportunities in Electroweak Physics . . . . . . . . . . . . . . . . . 108

4.2.1 Charged Lepton Flavor Violation . . . . . . . . . . . . . . . . . . . . 1084.2.2 Precision Measurements of Weak Neutral Current Couplings . . . . 109

4.3 EIC Requirements for Electroweak Physics Measurements . . . . . . . . . . 112

5 The Accelerator Designs and Challenges 1135.1 eRHIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

5.1.1 eRHIC Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155.1.2 eRHIC Interaction Region . . . . . . . . . . . . . . . . . . . . . . . . 1175.1.3 eRHIC R&D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

5.2 MEIC: The Jefferson Lab Implementation . . . . . . . . . . . . . . . . . . . 1185.2.1 Jefferson Lab Staged Approach . . . . . . . . . . . . . . . . . . . . . 1185.2.2 Baseline Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

Ion Complex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122Collider Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122Interaction Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123Electron Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

6 The EIC Detector Requirements and Design Ideas 1256.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1256.2 Kinematic Coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

6.2.1 y Coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1256.2.2 Angle and Momentum Distributions . . . . . . . . . . . . . . . . . . 1266.2.3 Recoil Baryon Angles and t Resolution . . . . . . . . . . . . . . . . . 1296.2.4 Luminosity Measurement . . . . . . . . . . . . . . . . . . . . . . . . 1296.2.5 Hadron and Lepton Polarimetry . . . . . . . . . . . . . . . . . . . . 131

6.3 Detector and Interaction Region (IR) Layout . . . . . . . . . . . . . . . . . 1326.3.1 eRHIC Detector & IR Considerations and Technologies . . . . . . . 1326.3.2 Detector Design for MEIC/ELIC . . . . . . . . . . . . . . . . . . . . 134

4

Acknowledgment 139

References 140

5

Chapter 11

Executive Summary: Exploring the2

Glue that Binds Us All3

1.1 Introduction4

Nuclear science is concerned with the origin and structure of the core of the atom, the5

nucleus and the nucleons (protons and neutrons) within it, which account for essentially6

all of the mass of the visible universe. A half-century of investigations have revealed that7

nucleons are themselves composed of more basic constituents called quarks, bound together8

by the exchange of gluons, and have led to the development of the fundamental theory9

of strong interactions known as Quantum Chromo-Dynamics (QCD). Understanding these10

constituent interactions and the emergence of nucleons and nuclei from the properties and11

dynamics of quarks and gluons in QCD is a fundamental and compelling goal of nuclear12

science.13

QCD attributes the forces among quarks and gluons to their color charge. In contrast to14

the quantum electromagnetism, where the force carrying photons are electrically neutral,15

gluons carry color charge. This causes the gluons to interact with each other, generating16

nearly all the mass of the nucleon and leading to a little-explored regime of matter, where17

abundant gluons dominate its behavior. Hints of this regime become manifest when nucleons18

or nuclei collide at nearly the speed of light, as they do in colliders such as HERA, RHIC19

and LHC. The quantitative study of matter in this new regime requires a new experimental20

facility: an Electron Ion Collider (EIC).21

In the last decade, nuclear physicists have developed new phenomenological tools to en-22

able remarkable tomographic images of the quarks and gluons inside protons and neutrons.23

These tools will be further developed and utilized to study the valence quark dominated24

region of the nucleon at the upgraded 12 GeV CEBAF at JLab and COMPASS at CERN.25

Applying these new tools to study the matter dominated by gluons and sea quarks origi-26

nating from gluons will require the higher energy of an EIC.27

As one increases the energy of the electron-nucleon collision, the process probes regions28

of progressively higher gluon density. However, the density of gluons inside a nucleon must29

eventually saturate to avoid untamed growth in the strength of the nucleon-nucleon inter-30

action, which would violate the fundamental principle of unitarity. To date this saturated31

gluon density regime has not been clearly observed, but an EIC could enable detailed study32

of this remarkable aspect of matter. This pursuit will be facilitated by electron collisions33

with heavy nuclei, where coherent contributions from many nucleons effectively amplify the34

1

gluon density probed.35

The EIC was designated in the 2007 Nuclear Physics Long Range Plan as “embodying36

the vision for reaching the next QCD frontier” [1]. It would extend the QCD science37

programs in the U.S. established at both the CEBAF accelerator at JLab and RHIC at BNL38

in dramatic and fundamentally important ways. The most intellectually pressing questions39

that an EIC will address that relate to our detailed and fundamental understanding of QCD40

in this frontier environment are:41

• How are the sea quarks and gluons, and their spins distributed in space42

and momentum inside the nucleon? How are these quark and gluon distributions43

correlated with overall nucleon properties, such as its spin direction? What is the role44

of orbital motion of sea quarks and gluons in building the nucleon spin?45

• Where does the saturation of gluon densities set in? Is there a simple boundary46

that separates this region from that of more dilute quark-gluon matter? If so, how47

do the distributions of quarks and gluons change as one crosses the boundary? Does48

this saturation produce matter of universal properties in the nucleon and all nuclei49

viewed at nearly the speed of light?50

• How does the nuclear environment affect the distribution of quarks and51

gluons and their interactions in nuclei? How does the transverse spatial distri-52

bution of gluons compare to that in the nucleon? How does nuclear matter respond53

to a fast moving color charge passing through it? Is this response different for light54

and heavy quarks?55

Answers to these questions are essential for understanding the nature of visible matter.56

An EIC is the ultimate machine to provide answers to these questions for the following57

reasons:58

• A collider is needed to provide kinematic reach well into the gluon-dominated regime;59

• Electron beams are needed to bring to bear the unmatched precision of the electro-60

magnetic interaction as a probe;61

• Polarized nucleon beams are needed to determine the correlations of sea quark and62

gluon distributions with the nucleon spin;63

• Heavy ion beams are needed to provide precocious access to the regime of saturated64

gluon densities and offer a precise dial in the study of propagation-length for color65

charges in nuclear matter.66

The EIC would be distinguished from all past, current, and contemplated facilities67

around the world by being at the intensity frontier with a versatile range of kinematics and68

beam polarizations, as well as beam species, allowing the above questions to be tackled69

at one facility. In particular, the EIC design exceeds the capabilities of HERA, the only70

electron-proton collider to date, by adding a) polarized proton and light-ion beams; b) a71

wide variety of heavy-ion beams; c) two to three orders of magnitude increase in luminosity72

to facilitate tomographic imaging; d) wide energy variability to enhance the sensitivity to73

gluon distributions. Realizing these challenging technical improvements will extend U.S.74

leadership in accelerator science and in nuclear science.75

2

The scientific goals and the machine parameters of the EIC were delineated in deliber-76

ations at a community-wide program held at the Institute for Nuclear Theory (INT) [2].77

The physics goals were set by identifying critical questions in QCD that remain unanswered78

despite the significant experimental and theoretical progress made over the past decade.79

This White Paper is prepared for the broader nuclear science community, and presents a80

summary of those scientific goals with a brief description of the golden measurements and81

accelerator and detector technology advances required to achieve them.82

1.2 Science Highlights of the Electron Ion Collider83

1.2.1 Nucleon Spin and its 3D Structure and Tomography84

Several decades of experiments on deep inelastic scattering (DIS) of electron or muon beams85

off nucleons have taught us about how quarks and gluons (collectively called partons) share86

the momentum of a fast-moving nucleon. They have not, however, resolved the question of87

how partons share the nucleon’s spin, and build up other nucleon intrinsic properties, such88

as its mass and magnetic moment. The earlier studies were limited to providing the lon-89

gitudinal momentum distribution of quarks and gluons, a one-dimensional view of nucleon90

structure. The EIC is designed to yield a much greater insight into the nucleon structure91

(Fig. 1.1, from left to right), by facilitating multi-dimensional maps of the distributions of92

partons in space, momentum (including momentum components transverse to the nucleon93

momentum), spin, and flavor.94

Figure 1.1: Evolution of our understanding of the nucleon spin structure. Left: in the 1980s,it was naively explained by the alignment of the spins of its constituent quarks. Right: currentpicture where valence quarks, sea quarks and gluons, and their possible orbital motion areexpected to contribute.

The 12 GeV upgrade of CEBAF at JLab will start on such studies in the kinematic95

region of the valence quarks, and a similar program will be carried out by COMPASS at96

CERN. However, these programs will be dramatically extended at the EIC to explore the97

role of the gluons and sea quarks in determining the hadron structure and properties. This98

will resolve crucial questions, such as whether a substantial “missing” portion of nucleon99

spin resides in the gluons. By providing high-energy probes of partons transverse momenta,100

the EIC should also illuminate the role of their orbital motion contributing to nucleon spin.101

3

The Spin and Flavor Structure of the Nucleon:102

An intensive and worldwide experimental program over the past two decades has shown that103

the spin of quarks and antiquarks is only responsible for ∼ 30% of the proton spin, while104

recent RHIC results indicate that the gluons’ spin contribution in the currently explored105

kinematic region is non-zero, but not yet sufficient to account for the missing 70%. The106

partons total helicity contribution to the proton spin is very sensitive to their minimum107

momentum fraction x accessible by the experiments. With the unique capability to reach108

two orders of magnitude lower in x and to span a wider range of momentum transfer Q109

than previously achieved, the EIC would offer the most powerful tool to precisely quantify110

how the spin of gluons and that of quarks of various flavors contribute to the protons spin.111

The EIC would realize this by colliding longitudinally polarized electrons and nucleons,112

with both inclusive and semi-inclusive DIS measurements. In the former, only the scattered113

electron is detected, while in the latter, an additional hadron created in the collisions is to114

be detected and identified.

x

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Current polarized DIS data:

CERN DESY JLab SLAC

Current polarized BNL-RHIC pp data:

PHENIX π0 STAR 1-jet

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-1

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data

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Figure 1.2: Left: The range in parton momentum fraction x vs. the square of the transferredmomentum by the electron to the proton Q2 accessible with the EIC in e-p collisions at twodifferent center-of-mass energies, compared to existing data. Right: The projected reductionin the uncertainties of the gluon’s helicity contribution ∆G vs. the quark helicity contribution∆Σ to the proton spin from the region of parton momentum fractions x > 0.001, that wouldbe achieved by the EIC for different center-of-mass energies.

115

Figure 1.2 (Right) shows the reduction in uncertainties of the contributions to the nu-116

cleon spin from the spin of the gluons, quarks and antiquarks, evaluated in the x range from117

0.001 to 1.0. This would be achieved by the EIC in its early stage of operation. At the later118

stage, the kinematic range could be further extended down to x ∼ 0.0001 reducing signif-119

icantly the uncertainty on the contributions from the unmeasured small-x region. While120

the central values of the helicity contributions in Fig. 1.2 are derived from existing data,121

they could change as new data become available in the low x region. The uncertainties122

calculated here are based on the state-of-the art theoretical treatment of all available world123

data related to the nucleon spin puzzle. Clearly, the EIC will make a huge impact on our124

knowledge of these quantities, unmatched by any other existing or anticipated facility. The125

reduced uncertainties would definitively resolve the question of whether parton spin prefer-126

ences alone can account for the overall proton spin, or whether additional contributions are127

needed from the orbital angular momentum of partons in the nucleon.128

4

The Confined Motion of Partons inside the Nucleon:129

The semi-inclusive DIS (SIDIS) measurements have two natural momentum scales: the130

large momentum transfer from the electron beam needed to achieve the desired spatial res-131

olution, and the momentum of the produced hadrons perpendicular to the direction of the132

momentum transfer, which prefers a small value sensitive to the motion of confined partons.133

Remarkable theoretical advances over the past decade have led to a rigorous framework134

where information on the confined motion of the partons inside a fast-moving nucleon is135

matched to transverse momentum dependent parton distributions (TMDs). In particular,136

TMDs are sensitive to correlations between the motion of partons and their spin, as well as137

the spin of the parent nucleon. These correlations can arise from spin-orbit coupling among138

the partons, about which very little is known to date. TMDs thus allow us to investigate139

the full three-dimensional dynamics of the proton, going well beyond the information about140

longitudional momentum contained in conventional parton distributions. With both elec-141

tron and nucleon beams polarized at collider energies, the EIC will dramatically advance142

our knowledge of the motion of confined gluons and sea quarks in ways not achievable at143

any existing or proposed facility.144

Figure 1.3 (Left) shows the transverse-momentum distribution of up quarks inside a145

proton moving in the z direction (out of the page) with its spin polarized in the y direc-146

tion. The color code indicates the probability of finding the up quarks. The anisotropy in147

transverse momentum is described by the Sivers distribution function, which is induced by148

the correlation between the proton’s spin direction and the motion of its quarks and gluons.149

While the figure is based on a preliminary extraction of this distribution from current ex-150

perimental data, nothing is known about the spin and momentum correlations of the gluons151

and sea quarks. The achievable statistical precision of the quark Sivers function from the152

EIC kinematics is also shown in Fig. 1.3 (Right). Currently no data exist for extracting153

such a picture in the gluon-dominated region in the proton. The EIC would be crucial to154

initiate and realize such a program.155

u quark

−0.5 0.5

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Figure 1.3: Left: Transverse-momentum distribution of up quark with longitudinal momentumfraction x = 0.1 in a transversely polarized proton moving in the z-direction, while polarized inthe y-direction. The color code indicates the probability of finding the up quarks. Right: Thetransverse-momentum profile of the up quark Sivers function at five x values accessible to theEIC, and corresponding statistical uncertainties.

5

The Tomography of the Nucleon - Spatial Imaging of Gluons and Sea Quarks:156

By choosing particular final states in electron-proton scattering, the EIC would probe the157

transverse spatial distribution of sea quarks and gluons in the fast-moving proton as a158

function of the parton’s longitudinal momentum fraction x. This spatial distribution yields159

a picture of the proton that is complementary to the one obtained from the transverse-160

momentum distribution of quarks and gluons, revealing aspects of proton structure that are161

intimately connected with the dynamics of QCD at large distances. With its broad range of162

collision energies, its high luminosity and nearly hermetic detectors, the EIC could image163

the proton with unprecedented detail and precision from small to large transverse distances.164

The accessible parton momentum fractions x extend from a region dominated by sea quarks165

and gluons to one where valence quarks become important, allowing a connection to the166

precise images expected from the 12 GeV upgrade at JLab and COMPASS at CERN. This167

is exemplified in Fig. 1.4, which shows the precision expected for the spatial distribution of168

gluons as measured in the exclusive process: electron + proton→ electron + J/Ψ + proton.169

The tomographic images obtained from cross sections and polarization asymmetries for170

exclusive processes are encoded in generalized parton distributions (GPDs) that unify the171

concepts of parton densities and of elastic form factors. They contain detailed information172

about spin-orbit correlations and the angular momentum carried by partons, including their173

spin and their orbital motion. The combined kinematic coverage of EIC and of the upgraded174

CEBAF as well as COMPASS is essential for extracting quark and gluon angular momentum175

contributions to the proton spin.

bT (fm)

xV

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trib

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stage-II,

∫Ldt =

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Figure 1.4: Projected precision of the transverse spatial distribution of gluons as obtained fromthe cross section of exclusive J/Ψ production. It includes statistical uncertainty and systematicuncertainties due to extrapolation into the unmeasured region of momentum transfer to thescattered proton. The distance of the gluon from the center of the proton is bT in femtometers,and the kinematic quantity xV = xB (1+M2

J/Ψ/Q2) determines the gluon’s momentum fraction.

The collision energies assumed for Stage-I and Stage-II are Ee = 5, 20 GeV and Ep = 100, 250GeV, respectively.

6

1.2.2 The Nucleus, a QCD Laboratory176

The nucleus is a QCD “molecule”, with a complex structure corresponding to bound states177

of nucleons. Understanding the emergence of nuclei from QCD is an ultimate long-term goal178

of nuclear physics. With its wide kinematic reach, as shown in Fig. 1.5 (Left), the capability179

to probe a variety of nuclei in both inclusive and semi-inclusive DIS measurements, the EIC180

would be the first experimental facility capable of exploring the internal 3-dimensional sea181

quark and gluon structure of a fast-moving nucleus. Furthermore, the nucleus itself would be182

an unprecedented QCD laboratory for discovering the collective behavior of gluonic matter183

at an unprecedented occupation number of gluons, and for studying the propagation of184

fast-moving color charge in a nuclear medium.185

1

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Measurements with A ≥ 56 (Fe):

eA/μA DIS (E-139, E-665, EMC, NMC)

νA DIS (CCFR, CDHSW, CHORUS, NuTeV)

DY (E772, E866)

perturbative

non-perturbative

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no

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ativ

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BK/JIMWLK

DGLAP

BFKL

Figure 1.5: Left: The range in parton momentum fraction x vs. the square of the transferredmomentum Q2 by the electron to the nucleus accessible to the EIC in e-A collisions at twodifferent center-of-mass energies, compared with the existing data. Right: The probe resolutionvs. energy landscape, indicating regions of non-perturbative and perturbative QCD, includingin the latter, low to high parton density, and the transition region between them.

QCD at Extreme Parton Densities:186

In QCD, the large soft-gluon density enables the non-linear process of gluon-gluon recom-187

bination to limit the density growth. Such a QCD self-regulation mechanism necessarily188

generates a dynamic scale from the interaction of high density massless gluons, known as189

the saturation scale, Qs, at which gluon splitting and recombination reach a balance. At190

this scale the density of gluons is expected to saturate, producing new and universal prop-191

erties of hadronic matter. The saturation scale Qs separates the condensed and saturated192

soft gluonic matter from the dilute but confined quarks and gluons in a hadron, as shown193

in Fig. 1.5 (Right).194

The existence of such a saturated soft gluon matter, often referred to as Color Glass195

Condensate (CGC), is a direct consequence of gluon self-interactions in QCD. It has been196

conjectured that the CGC of QCD has universal properties common to nucleons and all197

nuclei, which could be systematically computed if the dynamic saturation scale Qs is suffi-198

ciently large. However, such a semi-hard Qs is difficult to reach unambiguously in electron-199

7

proton scattering without a multi-TeV proton beam. Heavy ion beams at the EIC could200

provide precocious access to the saturation regime and the properties of the CGC because201

the virtual photon in forward lepton scattering probes matter coherently over a character-202

istic length proportional to 1/x, which can exceed the diameter of a Lorentz-contracted203

nucleus. Then, all gluons at the same impact parameter of the nucleus, enhanced by the204

nuclear diameter proportional to A1/3 with the atomic weight A, contribute to the probed205

density, reaching saturation at far lower energies than would be needed in electron-proton206

collisions. While HERA, RHIC and the LHC have only found hints of saturated gluonic207

matter, the EIC would be in a position to seal the case, completing the process started at208

those facilities.209

1 100

0.5

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1.5

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saturation model

stat. errors & syst. uncertainties enlarged (× 10)

Q2 = 5 GeV2

x = 3.3×10-3

eAu stage-I

Mx2 (GeV

2)

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1 2 3 4 5 6 7 8 9 10

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old

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on

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ton

e + p(Au) → e’ + p’(Au’) + V

φ no saturation

J/ψ no saturation

J/ψ saturation (bSat)

Experimental Cuts:

|η(Vdecay products)| < 4

p(Vdecay products) > 1 GeV/c

Coherent events only

stage-II, ∫Ldt = 10 fb-1/A

x < 0.01

Q2(GeV2)

Figure 1.6: Left: The ratio of diffractive over total cross section for DIS on gold normalizedto DIS on proton plotted for different values, M2

X, the mass square of hadrons produced inthe collisions for models assuming saturation and non-saturation. The grey bars are estimatedsystematic uncertainties. Right: The ratio of coherent diffractive cross section in e-Au toe-p collisions normalized by A4/3 plotted as a function of Q2, plotted for saturation and non-saturation models. The 1/Q is effectively the initial size of the quark-antiquark systems (φ andJ/Ψ) produced in the medium.

Figure 1.6 illustrates some of the dramatic predicted effects of gluon density saturation in210

electron-nucleus vs. electron-proton collisions at an EIC. The left frame considers coherent211

diffractive processes, defined to include all events in which the beam nucleus remains intact212

and there is a rapidity gap containing no produced particles. As shown in the figure, gluon213

saturation greatly enhances the fraction of the total cross section accounted for by such214

diffractive events. An early measurement of coherent diffraction in e+A collisions at the215

EIC would provide the first unambiguous evidence for gluon saturation.216

Figure 1.6 (Right) shows that gluon saturation is predicted to suppress vector meson217

production in e+A relative to e+p collisions at the EIC. The vector mesons result from218

quark-antiquark pair fluctuations of the virtual photon, which hadronize upon exchange of219

gluons with the beam proton or nucleus. The magnitude of the suppression depends on220

the size (or color dipole moment) of the quark-antiquark pair, being significantly larger for221

produced φ (red points) than for J/Ψ (blue) mesons. An EIC measurement of the processes222

8

in Fig. 1.6 (Right) would provide a powerful probe to explore the properties of the saturated223

gluon matter.224

Both the coherent diffractive and total DIS cross sections on nuclei are suppressed225

comparing to those on the proton in all saturation models. But, the suppression on the226

diffractive cross section is weaker than that on the total cross section leading to a dramatic227

enhancement in the double ratio as shown in Fig. 1.6 (Left).228

The Tomography of the Nucleus:229

With its capability to measure the diffractive and exclusive processes with a variety of ion230

beams, the EIC would also provide the first 3-dimensional images of sea quarks and gluons231

in a fast-moving nucleus with sub-femtometer resolution. For example, the EIC could232

obtain the spatial distribution of gluons in a nucleus by measuring the coherent diffractive233

production of J/Ψ in electron-nucleus scattering, similar to the case of electron-proton234

scattering shown in figure 1.4.235

Propagation of a Color Charge in QCD Matter:236

One of the key pieces of evidence for the discovery of quark-gluon plasma (QGP) at RHIC237

is jet quenching, manifested as a strong suppression of fast-moving hadrons produced in238

the very hot matter created in relativistic heavy ion collisions. The suppression is believed239

to be due to the energy loss of partons traversing the QGP. It has been puzzling that the240

production is nearly as much suppressed for heavy as for light mesons, even though a heavy241

quark is much less likely to lose its energy via medium-induced radiation of gluons. Some of242

the remaining mysteries surrounding heavy vs. light quark interactions in hot matter can243

be illuminated by EIC studies of related phenomena in cold nuclear matter. For example,244

the variety of ion beams available for electron-nucleus collisions at the EIC would provide245

a femtometer filter to test and to help determine the correct mechanism by which quarks246

and gluons lose energy and hadronize in nuclear matter (see schematic in Fig. 1.7 (Left)).247

Figure 1.7 (Right) shows the ratio of number of produced mesons in electron-nucleus248

and electron-deuteron collisions for pion (light mesons) and D0-mesons (heavy mesons) at249

both low and high virtual photon energy ν, as a function of z - the momentum fraction of250

the virtual photon taken by the observed meson. The calculation of the lines and blue circle251

symbols assumes the mesons are formed outside of the nucleus, as shown in the top sketch252

of Fig. 1.7 (Left), while the square symbols are simulated according to a model where a253

color neutral pre-hadron was formed inside the nucleus, like in the bottom sketch of Fig. 1.7254

(Left). The location of measurements within the shaded area would provide the first direct255

information on when the mesons are formed. Unlike the suppression expected for pion256

production at all z, the ratio of heavy meson production could be larger than unity due to257

very different hadronization properties of heavy mesons. The discovery of such a dramatic258

difference in multiplicity ratios between light and heavy mesons at the EIC would shed light259

on the hadronization process and on what governs the transition from quarks to hadrons.260

The Distribution of Quarks and Gluons in the Nucleus:261

The EMC experiment at CERN and experiments in the following two decades clearly re-262

vealed that the distribution of quarks in a fast-moving nucleus is not a simple superposition263

of their distributions within nucleons. Instead, the ratio of nuclear over nucleon structure264

functions follows a non-trivial function of Bjorken x, deviating significantly from unity, with265

a suppression (often referred to as nuclear shadowing) as x decreases. Amazingly, there is as266

of yet no knowledge whether the same holds true for gluons. With its much wider kinematic267

reach in both x and Q, the EIC could measure the suppression of the structure functions to268

a much lower value of x, approaching the region of gluon saturation. In addition, the EIC269

9

h

h

γ∗

γ∗

0.30

0.50

0.70

0.90

1.10

1.30

1.50

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io o

f par

ticle

s pr

oduc

ed in

lea

d o

ve

r p

roto

n D0 mesons (lower energy)

Pions (lower energy)

D0 mesons (higher energy)

Pions (higher energy)

Wang, pions (lower energy)

Wang, pions (higher energy)

0.01 < y < 0.85, x > 0.1, 10 fb-1

Higher energy : 25 GeV2< Q

2< 45 GeV

2, 140 GeV < < 150 GeV

Lower energy : 8 GeV2< Q

2<12 GeV

2, 32.5 GeV< < 37.5 GeV

1- D0systematic

uncertainty

1- pion systematicuncertainty

v

v

0.0 0.2 0.4 0.6 0.8 1.0Z

Figure 1.7: Left: Schematic illustrating the interaction of a parton moving through coldnuclear matter: the hadron is formed outside (top) or inside (bottom) the nucleus. Right:Ratio of semi-inclusive cross section for producing a pion (red) composed of light quarks, and aD0 meson (blue) composed of heavy quarks in e-Lead collisions to e-deuteron collisions, plottedas function of z, the ratio of the momentum carried by the produced hadron to that of thevirtual photon (γ∗), as shown in the plots on the Left.

could for the first time reliably quantify the nuclear gluon distribution over a wide range of270

momentum fraction x.271

1.2.3 Physics Possibilities at the Intensity Frontier272

The subfield of Fundamental Symmetries in nuclear physics has an established history of273

key discoveries, enabled by either the introduction of new technologies or the increase in274

energy and luminosity of accelerator facilities. While the EIC is primarily being proposed for275

exploring new frontiers in QCD, it offers a unique new combination of experimental probes276

potentially interesting to the investigations in Fundamental Symmetries. For example,277

the availability of polarized beams at high energy and high luminosity, combined with a278

state-of-the-art hermetic detector, could extend Standard Model tests of the running of279

the weak-coupling constant far beyond the reach of the JLab12 parity violation program,280

namely toward the Z-pole scale previously probed at LEP and SLC.281

1.3 The Electron Ion Collider and its Realization282

Two independent designs for a future EIC have evolved in the US. Both use the existing283

infrastructure and facilities available to the US nuclear science community. At Brookhaven284

National Laboratory (BNL) the eRHIC design (Figure 1.8, top) utilizes a new electron beam285

facility based on an Energy Recovery LINAC (ERL) to be built inside the RHIC tunnel to286

collide with RHICs existing high-energy polarized proton and nuclear beams. At Jefferson287

Laboratory (JLab) the ELectron Ion Collider (ELIC) design (Figure 1.8, bottom) employs288

10

a new electron and ion collider ring complex together with the 12 GeV upgraded CEBAF,289

now under construction, to achieve similar collision parameters.290

eSTAR

ePH

EN

IX

30 GeV

30 GeV

100 m

Lina

c 2.

45 G

eV

Linac 2.45 GeV

Coh

eren

t e-c

oole

r

Polarized

e-gun

Beam

dump

0.60 GeV

5.50 GeV

10.4 GeV

15.3 GeV

20.2 GeV

25.1 GeV

30.0 GeV

3.05 GeV

7.95 GeV

12.85 GeV

17.75 GeV

22.65 GeV

27.55 GeV

0.6 GeV

0.6 GeV

27.55 GeV

New

detector

Figure 1.8: Top: The schematic of eRHIC at BNL: require construction of an electron beamfacility (red) to collide with the RHIC blue beam at up to three interaction points. Botton:The schematic of ELIC at JLab: require construction of the ELIC complex (red, black/grey) andits injector (green on the top) around the 12 GeV CEBAF.

The EIC machine designs are aimed at achieving291

• Highly polarized (∼ 70%) electron and nucleon beams292

11

• Ion beams from deuteron to the heaviest nuclei (Uranium or Lead)293

• Variable Center of mass energies from ∼ 20− ∼100 GeV, upgradable to ∼150 GeV294

• Collision luminosity ∼1033−34 cm−2s−1295

• Possibilities of having more than one interaction region296

The EIC requirements will push the accelerator designs to the limits of current tech-297

nology, and will therefore need significant R&D. Cooling of the hadron beam is essential to298

attain the luminosities demanded by the science. Development of coherent electron cooling299

is now underway at BNL, while the JLab design is based on conventional electron cooling300

techniques, but proposes to use bunched electron beams for the first time.301

An energy recovery linac at the highest possible energy and intensity are key to the302

realization of eRHIC at BNL, and this technology is also important for electron cooling in303

ELIC at JLab. The eRHIC design at BNL also requires a high intensity polarized electron304

source, that would be an order of magnitude higher in intensity than the current state of305

the art, while the ELIC design at JLab, will utilize a novel figure-8 storage ring design for306

both electrons and ions.307

The physics-driven requirements on the EIC accelerator parameters and extreme de-308

mands on the kinematic coverage for measurements, makes integration of the detector into309

the accelerator a particularly challenging feature of the design. Lessons learned from past ex-310

perience at HERA have been considered while designing the EIC interaction region. Driven311

by the demand for high precision on particle detection and identification of final state par-312

ticles in both e-p and e-A programs, modern particle detector systems will be at the heart313

of the EIC. In order to keep the detector costs manageable, R&D efforts are under way314

on various novel ideas for: compact (fiber sampling & crystal) calorimetry, tracking (NaI315

coated GEMs, GEM size & geometries), particle identification (compact DIRC, dual ra-316

diator RICH & novel TPC) and high radiation tolerance for electronics. Meeting these317

R&D challenges will keep the U.S. nuclear science community at the cutting edge in both318

accelerator and detector technology.319

1.4 Physics Deliverables of the Stage I of EIC320

A staged realization of the EIC is being planned for both the eRHIC and ELIC designs.321

The first stage is anticipated to have up to ∼ 60− 100 GeV in center-of-mass-energy, with322

polarized nucleon and electron beams, a wide range of heavy ion beams for nuclear DIS, and323

a luminosity for electron-proton collisions approaching 1034 cm−2s−1. With such a facility,324

the EIC physics program would have an excellent start toward addressing the following325

fundamental questions with key measurements:326

• The proton spin: Within just a few months of operation, the EIC would be able327

to deliver decisive measurements, no other facility in the world could achieve, on how328

much the intrinsic spin of quarks and gluons contribute to the proton spin as shown329

in Fig. 1.2 (Right).330

• The motion of quarks and gluons in the proton: Semi-inclusive measurements331

with polarized beams would enable us to selectively probe with precision the correla-332

tion between the spin of a fast moving proton and the confined transverse motion of333

both quarks and gluons within. Images in momentum space as shown in Fig. 1.3 are334

12

simply unattainable without the polarized electron and proton beams of the proposed335

EIC.336

• The tomographic images of the proton: By measuring exclusive processes, the337

EIC with its unprecedented luminosity and detector coverage would create detailed338

images of the proton gluonic matter distribution as shown in Fig. 1.4, as well as the339

images of sea quarks. Such measurements would reveal aspects of proton structure340

that are intimately connected with QCD dynamics at large distances.341

• QCD matter at an extreme gluon density: By measuring the diffractive cross342

sections together with the total DIS cross sections in electron-proton and electron-343

nucleus collisions as shown in Fig. 1.6, the EIC would provide the first unambiguous344

evidence for the novel QCD matter of saturated gluons. The EIC is poised to explore345

with precision the new field of the collective dynamics of saturated gluons at high346

energies.347

• Quark hadronization: By measuring pion and D0 meson production in both electron-348

proton and electron-nucleus collisions, the EIC would provide the first measurement349

of the quark mass dependence of the hadronization along with the response of nuclear350

matter to a fast moving quark.351

The Relativistic Heavy Ion Collider (RHIC) at BNL has revolutionized our understand-352

ing of hot and dense QCD matter through its discovery of the strongly coupled quark-gluon353

plasma that existed a few microseconds after the birth of the universe. Unprecedented354

studies of the nucleon and nuclear structure including the nucleon spin, and the nucleon’s355

tomographic images in the valence quark region have been, and will be, possible with the356

high luminosity fixed target experiments at Jefferson Laboratory using the 6 and 12 GeV357

CEBAF, respectively. The EIC promises to propel both programs to the next QCD frontier,358

by unraveling the three dimensional sea quark and gluon structure of the visible matter.359

Further, the EIC will probe the existence of the universal saturated gluon matter and has360

the capability to explore it in detail. The EIC will thus enable the US to continue its361

leadership role in nuclear science research through the quest for understanding the unique362

gluon-dominated nature of visible matter in the universe.363

13

Acknowledgment3778

This document is a result of a community wide effort. We particularly thank the fol-3779

lowing colleagues for their contributions to the preparation of this document:3780

J. L. Albacete (IPNO, Universite Paris-Sud 11, CNRS/IN2P3)3781

M. Anselmino (Torino University & INFN)3782

N. Armesto (University of Santiago de Campostella)3783

A. Bacchetta (University of Pavia)3784

T. Burton (Brookhaven National Lab)3785

N.-B. Chang(Shandong University)3786

W.-T. Deng (Frankfurt U., FIAS & Shandong University)3787

A. Dumitru (Baruch College, CUNY)3788

R. Dupre (CEA, Centre de Saclay)3789

S. Fazio (Brookhaven National Lab)3790

V. Guzey (Jefferson Lab)3791

H. Hakobyan(Universidad Tecnica Federico Santa Maria)3792

Y. Hao (Brookhaven National Lab)3793

D. Hasch (INFN, Frascatti)3794

M. Huang(Duke University)3795

C. Hyde (Old Dominion University)3796

B. Kopeliovich (Universidad Tecnica Federico Santa Maria)3797

K. Kumericki (University of Zagreb)3798

M. Lamont (Brookhaven National Lab)3799

T. Lappi (University of Jyvaskyla)3800

J.-H. Lee (Brookhaven National Lab)3801

Y. Lee (Brookhaven National Lab)3802

E. M. Levin (Tel Aviv University & Universidad Tecnica Federico Santa Marıa)3803

F.-L. Lin (Brookhaven National Lab)3804

V. Litvinenko (Brookhaven National Lab)3805

C. Marquet (CERN)3806

A. Metz (Temple University)3807

V. S. Morozov (Jefferson Lab)3808

D. Muller (Ruhr-University Bochum)3809

P. Nadel-Turonski (Jefferson Lab)3810

A. Prokudin (Jefferson Lab)3811

V. Ptitsyn, (Brookhaven National Lab)3812

X. Qian (Caltech)3813

R. Sassot (University de Buenos Aires)3814

G. Schnell (University of Basque Country, Bilbao)3815

P. Schweitzer (University of Connecticut)3816

M. Stratmann (Brookhaven National Lab)3817

M. Sullivan (SLAC)3818

S. Taneja (Stony Brook University & Dalhousie University)3819

T. Toll (Brookhaven National Lab)3820

D. Trbojevic (Brookhaven National Lab)3821

R. Venugopalan (Brookhaven National Lab)3822

138

X. N. Wang (Lawrence Berkeley National Lab & Central China Normal University)3823

B.-W. Xiao (Central China Normal University)3824

Y.-H. Zhang (Jefferson Lab)3825

L. Zheng (Brookhaven National Lab)3826

139

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