DRAFT: EIC White Paper Executive Summary
Tuesday, April 14, 2020
Understanding the fundamental structure of matter/energy in the universe, and its evolution from its origin (the
Big Bang) to its current state, is among the most central goals of human scientific endeavor. Nuclear physics is concerned with what could be construed as a small part of that big picture — the roughly 5 percent of the universe’s total energy that is associated with atoms. But this small fraction happens to contain us — and everything we see and sense around us. And as is the case for the 95 percent of the universe’s energy associated with invisible dark energy and dark matter, many mysteries remain to be explored regarding the origin of the visible 5 percent.
At first glance, the structure of visible matter appears fairly simple: the mass of an atom is completely dominated by the mass of the nucleus, and it in turn by the mass of the nucleons (neutrons and protons) within it.
Experimental investigations in the second half of the last century revealed that nucleons are themselves composed of more fundamental constituents called quarks, bound together by gluons. But the sum of these pieces does not add up to the whole: the mass of a nucleon receives negligible contributions from the masses of its constituents, nearly massless (up and down) quarks and the massless gluons. The same is true for most quark-gluon bound states, collectively called “hadrons.” Thus, the combined substance of everything we see in the universe, including the most massive planets and stars, is a stunning manifestation of what John Wheeler called ‘mass without mass’ [1] — huge amounts of matter made of nearly massless building blocks.
It turns out that the mass of a nucleon, and hence of the visible universe, is dominated by the energy associated with the motion and the interaction of quarks and gluons — in particular, the self-interactions among gluons that are at the heart of the fundamental theory known as Quantum Chromo-Dynamics (QCD). QCD attributes the forces among quarks and gluons to their ‘color’ charge. It is by the self-interaction of the gluons, the colored
‘force carrier,’ that QCD distinguishes itself from Quantum Electrodynamics (QED), where the force carriers
(photons) carry no electric charge. These gluon properties give rise to Asymptotic Freedom – the idea that the closer these color charges are together, the weaker the strength of the color interaction responsible for binding quarks in ordinary matter. The discovery of this phenomenon in 1973 resulted in the 2004 Nobel Prize in Physics, and paved the way for using particle accelerators to study these interactions in particles accelerated to nearly the speed of light, where gluons would split and proliferate, and colliding them to compress their constituents to
“free” them from the color interaction.
The fact that a colored gluon can split into two `softer' gluons, which share the parent’s momentum, leads to a proliferation of soft gluons in the vicinity of any color charge (i.e., of a quark or a gluon) and to their dominant abundance within hadrons (the color-neutral particles composed of quarks and gluons). This proliferation, if untamed, would violate fundamental principles of high-energy nucleon-nucleon scattering. But it is indeed tamed in the presence of sufficiently high gluon density, by a QCD self-regulation mechanism, called `recombination' in which two gluons merge into one. The balance between gluon ``splitting'' and ``recombination'' is a natural feature of all matter, when viewed at the speed of light, as is the case in high-energy colliders such as the Relativistic
Heavy Ion Collider (RHIC) or the Large Hadron Collider (LHC). Previous experiments have provided a glimpse into this regime of high gluon density. But an Electron-Ion Collider (EIC) could provide a high-precision, highresolution probe to discover and explore the gluon-dominated matter within nucleons and nuclei. The proposed
EIC was designated in the 2007 Nuclear Physics Long Range Plan as “embodying the vision for reaching the next
QCD frontier.” It would extend the QCD science programs established at both the Thomas Jefferson National
Accelerator Facility’s CEBAF accelerator and RHIC at Brookhaven National Laboratory in dramatic and fundamentally important ways. At an EIC, electrons would serve as precision probes of the gluon structure of light-speed accelerated protons and heavy ions.

DRAFT: EIC White Paper Executive Summary
Tuesday, April 14, 2020
Among the most intellectually pressing questions an EIC is to address are:

Does the density of soft gluons saturate, producing matter of universal properties in all hadrons and nuclei viewed at light speed?
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How do the dominant gluons and the sea quarks they spawn, contribute to hadronic properties, such as the spin of a proton or neutron?
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How are gluons and quarks distributed in space and in momentum within the gluon-dominated regime in nucleons and nuclei?
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What governs the transition of quarks and gluons into hadrons?
The answers to these questions are crucial for understanding the nature of visible matter. The EIC would be distinguished from all past, current, and contemplated facilities around the world by being at both the intensity and the versatility frontier, allowing all the above questions to be addressed in one facility. In particular, the EIC design exceeds the capabilities of HERA, the only electron-proton collider to date, by adding a) polarized proton and light-ion beams; b) a wide variety of heavy ion beams; c) two to three orders of magnitude improvement in luminosity; d) wide energy variability.
The scientific goals and the machine parameters for the EIC were proposed in deliberations at a community wide program held at the Institute of Nuclear Theory (INT) [2]. The physics goals were set by identifying critical questions in QCD, which remain unanswered in spite of the great experimental and theoretical effort made over the past decade. This White Paper provides a brief description of those scientific goals, and a brief description of the golden measurement programs and accelerator and detector technology advances required to achieve them.
Realizing the EIC will also extend US leadership in nuclear and accelerator science, which have a proven track record of driving economic and technological advances in fields from computing to medicine, national security, energy technology and climate science
Several decades of experiments using deep inelastic scattering (DIS) of electron or muon beams to probe nucleon structure have taught us a lot about how quarks and gluons (collectively called partons) share the momentum of a light-speed nucleon. They have not, however, resolved the question of how partons contribute to the nucleon's spin. The earlier studies were also limited to provide a one-dimensional view of nucleon structure (Figure 1, left): the distribution of partons as a function of the fraction ( x ) they carry of the nucleon's momentum. The EIC is designed to yield much greater insight into nucleon structure by facilitating multi-dimensional maps (Figure 1, right) that include information on the distributions of partons in space, their momentum (including momentum components transverse to the nucleon momentum), spin and flavor.

DRAFT: EIC White Paper Executive Summary
Tuesday, April 14, 2020
Figure 1: FIGURE A PLACE HOLDER: (BNL Arts Department should suggest an alternate to this.) Evolution of our understanding of the nucleon spin: in the 1980’s being only contributed to by constituent quarks, 1990s/2000 needing contributions from gluons, and the orbital motion of quarks, to the present day picture where all constituents and their motion contribute resulting in a rich internal dynamics and a 3D structure of the nucleon.
The 12 GeV upgrade of CEBAF will start on such studies in the kinematic region of the valence quarks, but only experiments at the EIC would be able to explore the role of the dominant soft gluons and sea quarks in determining the hadron structure and its properties, and to resolve crucial questions, such as whether the substantial ``missing'' portion of nucleon spin resides in the soft gluons. And by probing transverse momentum, it should also illuminate the roles of parton orbital motion within the nucleon.
After an intensive and worldwide experimental program over the past two decades we have learned that quarks carry approximately 30 percent of the proton spin while recent RHIC results indicate that the gluons spin contribution in the currently explored kinematic region is clearly non-zero but not yet sufficient to account for the missing 70 precent. With the unique capabilities to reach two orders of magnitude smaller in parton momentum fraction x and a wide range of momentum exchange Q 2 , the EIC would offer the most powerful tool to precisely quantify how the spin of gluons and that of quarks of various flavors contribute to the proton’s spin. The EIC could achieve this by colliding longitudinally polarized electrons and nucleons, with both inclusive DIS measurements, where only the scattered electron is detected, and semi-inclusive DIS (SIDIS) measurements, where, in addition, a hadron created in the collisions is to be detected and identified.
Figure 2: Left: The range in parton momentum fraction x vs. resolution Q 2 (GeV 2 ) accessible to the EIC for different center- of-mass energy (√s) combinations (45 and 140 GeV) in comparison with the existing data. Right: The possible reduction in the measurement of the contribution from the gluon (  G) vs. that from quarks & antiquarks (  ) with the inclusive and semi-inclusive DIS experiment at the EIC is shown. The blue region indicates the uncertainty calculated in a next-toleading perturbative QCD analysis of all available data [3] and the red region indicates what could be achieved with the
EIC.
Figure 2 shows the possible reduction in uncertainties of the gluon’s and quark+antiquark’s contribution to the nucleon spin that could be achieved by the EIC as it turns on in its early phases of operation. The uncertainties calculated here are based on the state-of-the art knowledge theoretical treatment of all available date related to the nucleon spin puzzle in the world. Apparently, the EIC will make a huge early impact on our knowledge of these quantities, there is no other existing or anticipated facility comparable in its impact.

DRAFT: EIC White Paper Executive Summary
Tuesday, April 14, 2020
The SIDIS measurements have two natural momentum scales: the large momentum transfer from the electron beam needed to achieve the desired spatial resolution, and the momentum of the produced hadrons transverse to the direction of the momentum transfer, which has a small value sensitive to the motion of confined partons.
Remarkable theoretical advances over the past decade have led to a rigorous framework to match the information on confined motion of the partons inside a fast moving nucleon to transverse-momentum-dependent parton distributions (TMDs). In particular, TMDs are sensitive to correlations between the spin of the hadron and the motion of its partons, as well as between the spin of the parton and the motion of its fragmented hadrons. These correlations can arise from spin-orbit coupling among the partons, about which we know very little to date. By polarizing both electron and nucleon beams at collider energies, EIC will dramatically advance our knowledge of the motion of confined parton, gluon and sea quarks in ways not achievable at any existing or proposed facility.
Figure 3 shows the transverse momentum distribution probabilities of the up and down quarks in x and y (spatial) direction, inside a transversely polarized proton (moving in the z direction while polarized in the x direction).
While this is an intuitive model prediction for quarks, nothing is known about the spin and momentum correlations of the gluons and sea quarks. Measuring such distributions for the same would be a gateway to a fundamentally different approach to investigating the internal structure and dynamics of the proton. Currently no data exists for extracting such a picture in the gluon-dominated region in the proton. The EIC would be crucial to initiate and realize such a program.
Figure 3: The transverse momentum distributions of up (left) and down (right) quarks in a transversely polarized proton moving in z direction while polarized in x direction. This is a model prediction calculation.
By choosing particular final states in electron-proton and electron-nucleus scattering, the EIC would be able to selectively probe the transverse spatial distribution of sea quarks and gluons as a function of the parton's longitudinal momentum fraction x . Generalized parton distributions (GPDs) are the momentum space density distributions that encode this tomographic information. Such tomographic images promise insight into the dynamics of confinement of partons within nucleons and nuclei. The integral over the momentum fraction x of specific quark and gluon GPDs gives the total angular momentum carried by quarks and gluons, respectively.
With its unprecedented luminosity and kinematic reach, the EIC could provide the first tomographic images of sea quarks and gluons in a proton, as shown in Figure 4. In combination with valence quark GPDs measured at the upgraded CEBAF, the EIC could provide meaningful constraints on the quark orbital angular momentum contribution to the proton's spin.

DRAFT: EIC White Paper Executive Summary
Tuesday, April 14, 2020
Figure 4: PLACE HOLDER: (JQ sent an email to MD with a request, will follow up) A single figure with overlapping b for the range of values of x from minimum to maximum shown in this plot is being requested. The distribution of gluons as function of distance b Fermi from the center of the proton extracted from measurements of J/  production cross section.
Nucleus is known to be made of nucleons, which are fundamental bound states of quarks and gluons in QCD.
Understanding the emergence of nuclei from QCD is an ultimate long-term goal of nuclear physics. With its wide kinematic reach, as shown in Fig. 5 (left), the capability to perform both inclusive and semi-inclusive DIS measurements, and the control over the nuclear species, the EIC would be the first experimental facility capable of exploring the internal 3-dimensional sea quark and gluon structure of a fast moving nucleus, and thus enable new understanding of the nuclei at a sub-femtometter scale. More importantly, the nucleus at the EIC itself could be a unprecedented QCD laboratory for studying the propagation of a fast moving color charge in QCD matter, and for discovering the properties of condensed gluons at an extreme high gluon density and exploring the dynamical balance between the “splitting” and “recombining” of gluons and the generation of a dynamical scale from massless gluon self-interactions.
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Figure 5: Left: The resolution (Q 2 ) vs. the parton momentum fraction (x) landscape of available data for e-nucleus collisions past and current experiments and the kinematic reach for the EIC for its different center of mass energies. The significant extension afforded by the collider over the past fixed target experiment is apparent. Right: (place holder)
Current knowledge of the ratio of nuclear gluon distribution over nucleon gluon distribution as a function of gluon momentum fraction x, plotted with various commonly used parameterizations (new plot with 10 -4 < x < 0.1), along with error bars placed on the R g
=1 line that could be achieved by the EIC.

DRAFT: EIC White Paper Executive Summary
Tuesday, April 14, 2020
Are the quarks and gluons in a nucleus confined within the individual nucleons, or does the nuclear environment significantly affect their distribution? The EMC experiment at CERN and experiments in the following two decades clearly revealed that the distribution of quarks in a fast moving nucleus, with respect to longitudinal momentum fraction x , is not a simple superposition of their distributions within nucleons. For the first time, the
EIC with the inclusive and semi-inclusive DIS measurements could reliably quantify the nuclear gluon distribution, which is currently unknown, for a wide range of momentum fraction x , as shown in Fig. 5(Right).
With its unprecedented luminosity, the EIC could provide the first imaging of three-dimensional sea quark and gluon structure of a fast moving nucleus with sub-femtometer resolution.
The discovery of the quark-gluon plasma (QGP) at the relativistic heavy ion collider (RHIC) at Brookhaven
National Lab provided a gateway to study the dynamics taking place few microseconds after the Big Bang. One of the key evidences of the discovery was the strong suppression of fast moving hadrons produced in the relativistic heavy ion collisions (jet quenching), which is believed to be due to the energy loss of fast moving partons following their multiple interactions with the medium, the QGP. However, it has been puzzling that heavy meson production seems to be as suppressed as much as the light meson, although a heavy quark is much less likely to loose its energy via medium induced radiation. By facilitating studies on how struck partons propagate through cold nuclear matter and evolve into hadrons, as sketched in Fig. 6(Left), the EIC would provide independent and complimentary information essential for understanding the response of nuclear medium to a colored fast moving (heavy or light) quark at high energies. EIC will thus provide the best testing ground for studying the multiple scattering and energy loss mechanism in QCD.
Figure 6: Left: Interactions of the parton moving through cold nuclear matter. Right: Ratio of semi-inclusive cross section for producing a pion (red), composed of light quarks, and a D 0 meson (blue) composed of heavy quarks in electron-Lead collisions to the same produced in electron-deuteron as function of z, the momentum fraction of the exchanging photon carried by the observed meson. Statistical uncertainties are shown in each case.
Figure 6 (Right) shows the predictions for the ratio of semi-inclusive meson production in electron-nucleus and electron-deuteron collisions for both light meson-pion (red square symbols) and heavy meson-D 0 (blue circle symbols) at the EIC with two virtual photon energies, 35 GeV (red) and 145 (blue) GeV, respectively. Although the heavy charm quark is expected to loose much less energy via radiation than the light quark, the suppression is similar for both heavy and light mesons in the large z region. The steep fall of the heavy quark fragmentation with increasing z could be a possible explanation. However, unlike the suppression expected in the case of pion production, the nuclear production of a heavy meson could be enhanced at low z . Study of such effects in light and heavy meson production over a broad z range would be possible with the EIC. The discovery of such a

DRAFT: EIC White Paper Executive Summary
Tuesday, April 14, 2020 dramatic difference in multiplicity ratios (Figure 6, Right) at the EIC would shed light on the hadronization process and what governs the transition from quarks and gluons to hadrons.
The discovery of the sharp growth of gluon density in a nucleon when gluon momentum fraction x decreases, by
HERA, opened a gateway to a world effort of studying QCD at an extreme gluon density and searching for a new domain of QCD matter of saturated gluons. A continuing growth in the number of soft gluons would lead at high energies to violation of the unitarity bound of hadronic cross sections. The large soft gluon density leads naturally in QCD to the process of gluon-gluon recombination, tending to reduce the number of gluons, see Fig. 7 (left).
The non-linear gluon self-interaction in QCD necessarily generate a dynamic scale from the interaction of high density massless gluons, known as the saturation scale, Q s
, at which gluon radiation and fusion reach a balance so that both the density of gluons and the effective QCD coupling strength
 s
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Figure 7: Left: Map of high energy QCD in resolution (Q 2 ) vs. energy (Y) plane. The high gluon density saturation region is shown. Middle and Right: show ratios of cross-section ratios of e-Gold vs. e-p for J/  and  production with (red) and without (black) the saturation, and with the statistical uncertainties possible with measurements at the EIC. (Can we combine middle and right plots in to one? At the same scale, it would show a more dramatic effect of the size difference)
The existence of such a saturated soft gluon matter, often referred to as Color Glass Condensate, is a direct consequence of the QCD dynamics. The dynamic saturation scale Q s
may be impossible to reach in electronproton scattering without a multi-TeV proton beam. However, heavy ion beams provide precocious access to the saturation regime because the virtual photon in forward lepton scattering probes matter coherently over a characteristic length proportional to 1/ x , which can exceed the nuclear diameter. Then all the gluons at a given impact parameter within the nucleus contribute to the probed density, reaching saturation at far lower energies than would be needed in electron-proton collisions. While HERA, RHIC and LHC have all found evidence for saturated gluonic matter, the EIC would have the potential to seal the case, completing the discovery process started at those facilities.
Figure 7 (middle and right) shows the nuclear over nucleon cross section ratio of vector meson production for the light (phi) and heavy (J/psi) mesons as a function of initial size of the quark-antiquark pair that hadronizes into the observed vector meson. QCD calculation of vector meson production with and without the gluon saturation reach lead to two dramatically different manifestations, one of suppression and of enhancement, respectively. The effect is amplified by the size of the produced vector mesons. Such measurement at the EIC would provide unambiguous evidence for the discovery of a new and novel QCD matter of saturated gluons.

DRAFT: EIC White Paper Executive Summary
Tuesday, April 14, 2020
The subfield of Fundamental Symmetries (FS) in nuclear physics has an established history of key discoveries, enabled by either the introduction of new technologies or increases in energy and luminosity of accelerator facilities. While the EIC is primarily being proposed for exploring new frontiers in QCD, it offers a unique new combination of experimental probes potentially interesting to the investigations in FS. For example, the availability of polarized beams at high energy and high luminosity, combined with a state-of-the-art hermetic detector, could extend Standard Model tests of the running of the weak-coupling constant far beyond the reach of the JLab12 parity violation program, toward the Z-pole scale previously probed at LEP and SLC
Two independent designs for a future EIC have evolved in the US. Both use the existing infrastructure and facilities available to the US nuclear science community. At Brookhaven National Laboratory (BNL) the eRHIC design (Figure 3, left) uses a new electron beam facility based on an Energy Recovery LINAC (ERL) to be built inside the RHIC tunnel to collide with RHIC’s existing high-energy polarized proton and heavy ion beams. At
Jefferson Laboratory (JLab) the ELectron Ion Collider (ELIC) design (Figure 3, right) employs a new electron and ion collider ring complex together with the 12 GeV upgraded CEBAF, now under construction, to achieve similar collision parameters.
The EIC machine designs are aimed at achieving:
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Highly polarized (> 70%) electron and nucleon beams
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Ion beams from deuteron to the heaviest nuclei (uranium or lead)
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Variable center of mass energy ranges from ~20-150 GeV
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Collision luminosity ~10 33-34 cm -2 s -1
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Possibilities of having more than one interaction region
The EIC accelerator design requirements will push the machine designs to the forefront of accelerator technology, requiring significant R&D. The cooling of the hadron beam is essential to attain the luminosities demanded by the science. The development of coherent electron cooling (CEC) is now underway at BNL, while conventional electron cooling techniques, pushed to the highest possible RF-power, are being tried in the JLab design.
Figure 8: Left: The schematic of eRHIC at BNL: will require construction of the electron beam facility (indicated in RED) to collide with the RHIC blue beam at three interaction points. Right: The schematic of the ELIC at JLab: will require construction of the ELIC complex (red and black in the center) and its injector (shown in green, top right) next to the 12
GeV CEBAF
The success of high-power Energy Recovery LINACs (ERLs) is essential for the realization of the EIC. The eRHIC design at BNL also requires a polarized electron source producing beam intensities an order of magnitude

DRAFT: EIC White Paper Executive Summary
Tuesday, April 14, 2020 beyond the current state of the art, while the ELIC design at JLab, utilizes a novel figure-8 storage ring design for electrons and ions and relies on attaining unprecedentedly small hadron beam bunch dimensions.
The physics driven requirements on the EIC accelerator parameters and the extreme demands on the kinematic coverage for measurements makes integration of the detector into the accelerator particularly challenging. feature of the design. Lessons learned from past experience at HERA have been considered while designing the EIC interaction region. Driven by the demand for high precision on particle detection and identification of final state particles in both electron-proton and electron-heavy ion programs, state-of-the-art particle detector systems will be at the heart of the EIC. In order to keep the detector costs manageable, R&D efforts are under way on various novel ideas for, compact (fiber sampling and crystal) calorimetry; tracking (NaI coated GEMs, GEM size and geometries); particle identification (compact DIRC, dual radiator RICH and novel TPC) and high radiation tolerance for electronics. Meeting these R&D challenges will keep the U.S. nuclear science community at the cutting edge in both accelerator and detector technology.
A staged realization of the EIC is being planned for both eRHIC and ELIC designs. The first stage is anticipated to have up to approximately 60-100 GeV in center-of-mass-energy, with polarized nucleon and electron beams, a wide range of heavy ion beams for nuclear DIS, and a luminosity for electron-proton collisions greater than 10 33 cm -2 s -1 . With such a facility, the EIC physics program would have an excellent start including, but not limited to, the following deliverables:

Inclusive and semi-inclusive DIS measurements with polarized electron-nucleon collisions would enable precise measurement of the polarized gluon distribution, as well as flavor-separated quark and anti-quark distributions all down to x values around 10 -4 .

Collisions of polarized electrons with transversely polarized nucleons, coupled with excellent particle identification, would enable measurements of transverse momenta of the quarks over the widest range of momentum transfer ever possible, and it would also enable the first transverse gluon momentum measurement.
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At the highest luminosities a unique spatial imaging program would become possible -- for sea quarks via
 deeply virtual Compton scattering (DVCS) and for gluons via coherent vector meson production.
Inclusive DIS measurements at x values down to 10 -3 on a wide range in nuclear species would enable an unprecedented systematic study and extraction of nuclear parton distributions, and in particular of the presently unknown nuclear soft gluon distribution, of which we currently have essentially no knowledge.

Tagging mesons produced in DIS in the nuclei would enable a systematic study of the parton propagation in cold nuclear matter, both for light and heavy quarks.

Starting to understand the onset of saturation via inclusive and diffractive cross section measurements, and investigations of the saturation scale, as a function of nuclear size, and energy, are critical first steps towards the ultimate study of low -x saturation physics and the gluonic state of matter known as the Color
Glass Condensate. This program would start with EIC's Stage 1.
Fig. 4 illustrates the physics potential of the EIC as it a function of its center of mass and integrated luminosity.
Both machine designs under consideration are intended to provide clear paths toward later increases in center-ofmass energy to extend the reach for gluon saturation studies and Standard Model tests.

DRAFT: EIC White Paper Executive Summary
Tuesday, April 14, 2020
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Figure 9: The landscape of EIC Physics shown with approximate √s vs. integrated luminosity (fb -1 ).
The Relativistic Heavy Ion Collider (RHIC) at BNL has revolutionized our understanding of hot and dense QCD matter through its discovery of the strongly coupled quark-gluon plasma that existed a few microseconds after the birth of the universe. Unprecedented studies of the nucleon and nuclear structure including the nucleon spin, and the nucleon's tomographic images in the valence quark region have been, and will be, possible with the high luminosity fixed target experiments at Jefferson Laboratory using the 6 and 12 GeV CEBAF, respectively. The
EIC promises to propel both programs to the next QCD frontier, by exploring dense QCD matter in confinement.
The EIC will hence enable the US to continue its leadership role in the study of nuclear science through the quest for understanding the unique gluon-dominated nature of the visible matter in the universe.
References:
[1] J. A. Wheeler, Geometrodynamics, Academic, New York, 1962, p25; F. Wilczek, Mass Without Mass I,
Physics Today, November 1999
[2] D. Beoer et al., Gluons and sea quarks at high energy: distributions, polaraization and tomography, arXiv:
1108.1713; INT-PUB-11-034, BNL-96164-2011, JLAB-PHY-11-1373