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Introduction

A central goal of modern nuclear physics is to understand the structure of the proton and neutron directly from the dynamics of their quarks and gluons, governed by the theory of their interactions, quantum chromodynamics (QCD), and how nuclear interactions between protons and neutrons emerge from these dynamics.

ELECTRON-ION COLLIDER

In the 1960s, scientists at the Department of Energy (DOE) Stanford Linear Accelerator Center (SLAC) discovered that protons and neutrons, the building blocks of nuclei, are themselves made of smaller constituents—“quarks.” This remarkable structure was revealed by scattering electrons on protons and other nuclei, and indeed the SLAC 2-mile-long electron accelerator became the world’s most powerful “electron microscope,” peering inside neutrons and protons (see Box 1.1). To this day, electrons, as point-like particles apparently without internal structure, remain a clean and powerful probe of matter at the most basic level.

Understanding of nucleons—that is, protons and neutrons—and the larger family of hadrons—strongly interacting particles made of quarks and antiquarks—has advanced dramatically since the first SLAC experiments. Fractionally charged¹ quarks and antiquarks are held together in hadrons by the “color” force, whose

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¹ That is, fractions such as 1/3 and –2/3 of the charge of the electron.

carrier is the massless “gluon.” Quarks and gluons carry a color charge.² The fundamental “strong force,” which is also responsible for binding nucleons together in nuclei, is very different from the electromagnetic force holding atoms and molecules together, and is described theoretically by QCD, a remarkable but mathematically complicated generalization of ordinary electricity and magnetism. Discovering how the structure of nucleons arises from the dynamics of their quark and gluon constituents, and how interactions between protons and neutrons in nuclei arise from these dynamics, is a major goal of modern nuclear physics.

With deeper understanding of the building blocks of nucleons and their interactions, nuclear physicists are developing a view of nucleons and nuclei as collective many-body systems, not simply clouds of independent particles. In these systems, dynamical interactions among the components lead to new emergent phenomena—as has been seen over the years in condensed-matter systems—for example, weak attractive interactions among electrons leading to superconductivity. Viewing nucleons

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² “Color” refers to a generalization of electrical charge. As one forms an electrically neutral atom with equal numbers of positive and negative electric charges, one finds that it takes three different colors to produce a “color-neutral” nucleon.

and nuclei as complex, interacting, many-body systems gives rise to profound questions about the nature of ordinary matter. Three central issues are at the fore.

Gluons have no mass and quarks are nearly massless, but nucleons and nuclei are heavy, making up most of the visible mass of the universe. How do nucleons acquire mass? At a qualitative level, it is known that gluons and quark-antiquark pairs (called “sea quarks”) that exist inside nucleons are crucial to their properties. However, the precise arrangement, or states, of gluons and sea quarks inside the nucleon is not known, and the mechanism by which mass is generated remains only partially understood.

A second fundamental property of the nucleon is that it has internal angular momentum, or spin. How does the spin arise from its elementary quark and gluon constituents? The quarks within the nucleon are known to contribute only a fraction of the total spin.

Colored quarks and gluons form color-neutral bound states and, in particular, protons and neutrons. A remarkable feature of the strong force, crucial to an understanding of the world around us, is that neutrons and protons arrange themselves into composite objects, or nuclei. Nuclei are bound by residual color forces, mediated by gluons and sea quarks. What are the emergent properties of dense systems of gluons? What are their quantum states? How are they distributed in both position and momentum, and how are they correlated among themselves and with the quarks and antiquarks present?

To pursue the science needed to answer these questions will require peering into nucleons and nuclei with high energy electrons, as was done in the seminal SLAC experiments that first revealed the existence of the inner structure of the nucleon. One needs high energy in order to achieve the needed resolution, which in turn requires colliding a beam of electrons with a counter-moving beam of protons or nuclei in an electron-ion collider (EIC). To address the science questions above, such a machine must be capable of colliding a beam of “polarized”³ electrons of energies from 4 GeV up to possibly 20 GeV with a beam of polarized ions (complex nuclei) of energies from 30 GeV up to some 300 GeV at high “luminosity”—the measure of the rate at which collisions occur—approaching 10³⁴ cm^–2 s^–1. The high-energy electrons create both virtual⁴ photons and virtual quark-antiquark pairs in the collisions, and these virtual particles will precisely probe the target nucleons and ions, shedding light on their internal workings. The ability of the EIC to accelerate large ions as well as protons will also advance understanding of how nucleons are bound together by the color force to form nuclei. In addition to needing a collider to allow much larger energy collisions of electrons and nucleons than would be attainable with a fixed target accelerator, the center of mass of the

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³ Polarized particles have their angular momenta aligned in chosen directions, rather than being disordered.

⁴ The term “virtual” indicates that the created particles have only a momentary fleeting existence.

target and projectile system in a collider can be tuned to be approximately at rest in the laboratory,⁵ greatly simplifying analysis of scattering events, whereas in a fixed-target machine, the center of mass travels practically along the beam direction. Figure 2.4 in Chapter 2 illustrates how the physics reach of an EIC depends on the collider center-of-mass energy and luminosity.

The concept of an EIC—which the 2015 Nuclear Science Advisory Committee (NSAC) Nuclear Physics Long Range Plan⁶ identified as the highest-priority project for new construction in nuclear physics—builds upon a long heritage of electron scattering machines. In the postwar period, this heritage begins with the Illinois Betatron, the Hansen Experimental Physics Laboratory (HEPL) machine at Stanford University, then the SLAC 2-mile accelerator, and continuing with the more recent Hadron-Electron Ring Accelerator (HERA) electron-proton collider, which operated from 1991 to 2007 at the Deutsches Elektronen-Synchrotron (DESY) Lab in Hamburg, Germany, and the Continuous Electron Beam Accelerator Facility (CEBAF) at the Thomas Jefferson National Accelerator Facility (JLab) in Virginia, which has operated since 1995 (see Box 1.1). An EIC also builds on the polarized proton beam facility at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL), which has been in operation since 2002. However, an EIC would be much more capable and much more challenging to build than these earlier machines. The accelerator challenges are twofold: a high degree of polarization for both beams and high luminosity (almost three orders of magnitude beyond HERA). It would be the most sophisticated and challenging accelerator currently proposed for construction in the United States and would significantly advance accelerator science and technology here and around the world.

CONTEXT

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⁵ In an EIC the effective center-of-mass energy depends on the momentum of the struck parton and varies from collision to collision. What matters for the design of detectors is that the reaction products are kinematically separated.

⁶Reaching for the Horizon, 2015 DOE/NSF Long Range Plan for U.S. Nuclear Science.

⁷ Richard P. Feynman, The Feynman Lectures on Physics, Volume 1, Section 1-2, Addison-Wesley, Reading, MA, 1964.

Feynman’s enthusiasm about the importance of atoms may seem extravagant. However, the more one thinks about it, the more one is likely to agree. Pursuing the atomic hypothesis has led to the discovery of chemistry, thermodynamics, quantum mechanics, molecular biology, and so much more. Without an understanding of atoms, the technology that has created the lifestyle and world humans enjoy today would not be possible.

However, two big puzzles remain in understanding atoms as the building blocks of the physical world. The first is the full extent of the periodic table of chemical elements and how many isotopes each element has. The second is how two of the three building blocks of atoms—neutrons and protons—are themselves put together from quarks and then how they combine to form the nuclei of atoms. (The third atomic building block, the electron, is to the best of scientists’ knowledge fundamental.) Both of these questions in nuclear physics are ripe to be answered now.

The story of atoms begins with Democritus, who put forward the idea of fundamental, indivisible elements of matter circa 400 BCE. The modern term “atom” derives from atomos, the Greek word for indivisible. Humans have come a long way from Empedocles’s first attempt at identifying the basic building blocks—earth, fire, water, and air—and the alchemists, who saw an “application” of atomic theory, the transforming of lead into gold. Little could they realize that the applications of atomic theory would be far more transformational and rewarding.

Modern atomic theory dates back to John Dalton, who in the early 19th century laid out the basic rules of chemistry. Armed with atomic theory and a list of the chemical elements that would grow to 92 and beyond, chemists began to transform human existence by identifying and creating the myriad of substances that comprise the physical world. Today, molecular biologists and biophysicists continue the march into the living world, which is constructed from the very same chemical elements.

By the end of the 19th century, atomic theory was well developed and producing practical results. But a burning question remained: Are atoms real or just useful mathematical constructs, and what rules do they obey? Einstein’s study of Brownian motion—the random, thermal motions of atoms, molecules, and even larger clumps of matter—provided the first concrete confirmation that atoms actually exist and gave a reasonably accurate estimate of their masses: a single gram is comprised of some 6 × 10²³ atoms.

At the beginning of the 20th century, the understanding of the atom deepened further with experiments revealing that atoms comprise a tiny nucleus (size of order 10^–13 cm) containing neutrons and protons surrounded by a much larger cloud of electrons (size of order 10^–8 cm). Atoms themselves are made of three smaller building blocks. Around the same time, the discovery of quantum mechanics, the rules that govern the microscopic world, opened the door to understanding how atoms behave and can be manipulated.

The science of materials is based on how electrons interact when atoms combine to form molecules, all governed by the rules of quantum mechanics. Building upon this knowledge, chemists and physicists have been refining the abilities to understand materials and to create new ones. A new, related field arose, known as condensed matter (initially called solid-state) physics, and is concerned with the various phases of matter that exist, from conductors and insulators to crystalline states of matter to even more exotic phases of matter including superconductors and other macroscopic quantum states of matter. The ability to design and build materials almost atom by atom has opened yet another chapter in the saga began by Democritus: nanoscience and nano-engineering.

The discovery after World War II of hundreds of subatomic particles spawned a new investigation: elementary particle physics. As these studies revealed, neutrons and protons are not fundamental, but rather made of smaller quarks. Quarks may or may not be Democritus’s atomos. The quest for the ultimate indivisible pieces and the rules that govern them continues, with the most recent discovery being the Higgs boson. Today, the stakes are even higher, with ideas about how the fundamental particles and forces are related to the structure and origin of space-time, as well as to the birth and early evolution of the universe.

In the material world, two big questions remain about the atoms that are its building blocks. First, what is the full range of nuclei—and hence kinds of atoms—that can exist? Finding the range of nuclei that can exist far from stability is a primary aim of the Facility for Rare Isotope Beams (FRIB) being constructed at Michigan State University. The second question involves the nature of the two building blocks of the nucleus. The neutron is made of two “valence”-down quarks (charge 1/3 that of the electron) and one valence-up quark (charge −2/3 that of the electron), while the proton is made of two valence-up quarks and one valence-down quark. Simple enough. But there is a puzzle: the mass of the proton is about 100 times that of two up and one down quark; similarly, the mass of the neutron is about 80 times that of two down and one up.⁸ Furthermore, the three quarks within nucleons do not, as is mentioned below, account for their spins. What then accounts for the mass and spin of the neutron and of the proton?

The other components are gluons and the sea quarks—of all six types: up, down, strange, charmed, bottom, and top (see Box 1.2). However, a fundamental understanding of how gluons and sea quarks are distributed, both in space and

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⁸ The mass of a nucleus is slightly less—from about 0.1 percent typically to nearly 1 percent—than the sum of its component neutrons and protons. That mass defect or binding energy is the mass equivalent energy that is released when the nucleus is assembled; it is the origin of nuclear energy. Likewise, the mass of an atom is very, very slightly less—parts in a billion or smaller—than the sum of its component nucleus and electrons. This is the chemical binding energy that can be released in chemical reactions. The problem with the neutron and proton is just the opposite. Its mass is far greater than that of its constituents.

in momentum, within neutrons and protons, and how they determine the basic properties of neutrons and protons remains unanswered. Furthermore, how gluons and the color force then bind these nucleons into nuclei remains a mystery, as is the issue of whether or not there are more exotic states of matter made of gluons.

The primary aim of an EIC (see Box 1.3) is to understand how up and down quarks, sea quarks, and gluons create the building blocks of the nuclei of atoms, neutrons, and protons. Furthermore, although the question of the full extent of the periodic table of elements appears to be a separate one, knowledge gained from an EIC is likely to shed light on that big question as well, through a better understanding of how neutrons and protons in nuclei are held together by the color force.

Twenty-five hundred years after Democritus and the human quest for atomos, the indivisible constituents of matter, physicists are closing in on a fundamental understanding of the chemical elements that comprise the materials of the physical world. That understanding has already had enormous direct benefits in the design and manufacture of all kinds of materials, with many more benefits on the horizon. Along the way, this scientific adventure has spun off the fields of thermodynamics, quantum mechanics, molecular biology, nanoscience, and particle physics, all of which have had their own benefits to humankind and an understanding of the universe in which we live. Feynman’s extravagant claim may well have been an understatement.

SCIENCE OPPORTUNITIES

An EIC is needed to address the picture of nucleons and nuclei as complex interacting many-body systems, and in particular to address three immediate and profound questions about neutrons and protons and how they are assembled to form the nuclei of atoms:

• How does the mass of the nucleon arise? In other words, how do the constituents of the nucleon, the valence quarks, the sea quarks, and the gluons, and importantly their interactions, lead to a mass some 100 times larger than the sum of the three constituent quarks alone? Physicists are used to the mass of a bound system—a nucleus made of neutrons and protons, an atom made of a nucleus and electrons or even two black holes bound together by gravity—having a mass less than the sum of its parts. The difference is the binding energy of the system. In a nucleon, the opposite is true: half of the mass exists in the gluons that hold it together. How do gluons provide this mass? (See Figure 2.1 in Chapter 2.)
• How does the spin of the nucleon arise? Spin, or internal angular momentum, is one of the basic properties of a neutron or proton, central both to understanding atoms and their practical applications such as magnetic

resonance imaging (MRI). While nucleons are made of three quarks, each with spin ½ (technically ħ/2, where ħ is Planck’s constant), the spins of these quarks constitute only a small fraction of the nucleon’s spin, the rest seemingly carried by the gluon spins, the sea quarks, and the orbital motion of the quarks and gluons. (See Figures 1.1 and 2.6.)

• What are the emergent properties of dense systems of gluons? The color force mediated by gluons is fundamentally different from the electromagnetic force that binds atoms and molecules. In particular, the force between quarks strengthens as the objects get farther apart, and quarks are permanently confined in neutrons and protons. Two questions concerning the gluons arise when nucleons are combined into nuclei: How is the gluon field modified in a nucleus to accommodate the binding of nucleons? And does a novel regime of nuclear physics emerge in the high-energy limit, a regime in which the complicated structure of the nucleus is radically simplified, leading to a state in which the whole nucleus becomes a dense gluon system?

These three questions are simple to state and yet are of paramount importance in completing an understanding of the building blocks of the physical world—atoms. The answers to all three questions involve a better understanding of the gluons within nucleons and nuclei, and nucleons and nuclei as collective many-

body systems more generally. The following sections discuss in more detail how an EIC would better enable the exploration of the gluon content of nucleons and nuclei and answer these questions. Box 1.3 summarizes the key physics ideas mentioned here.

How Does the Mass of the Nucleon Arise?

In broad-brush terms, the answer to this question is that most of the mass of a nucleon is accounted for by the gluons, the sea quarks, and the kinetic energy of the valence quarks within it, but the details are poorly understood. There is evidence that the largest fraction of the mass is contributed by gluons (see Figure 2.1), but the gluon is not electrically charged, and the energy stored in the gluon field is a form of invisible energy. The role of the gluon field energy has been inferred indirectly, but never directly measured.

An EIC will address this gap in the understanding of fundamental aspects of the nucleon in several ways. First, an EIC will map the gluon distribution in the proton, both in space and in momentum, with unprecedented precision, using the new technique of parton tomography described in Chapter 2. Traditional DIS measurements provide information on only the fraction of the longitudinal momentum carried by the various components of the nucleon—that is, the momentum component in the direction of the momentum transferred by the electron to the target. Tomography measurements allow two additional properties of the constituents to be measured: transverse distance x_T (perpendicular to the direction of the transferred momentum) and transverse momentum k_T. Studying the interplay of quark and gluon distributions in the proton would allow us to see gluons at work. Tomography provides a series of images of the proton in the transverse plane, labeled by the longitudinal momentum fraction of the parton. Scanning through these pictures, starting from the valence quark regime, will enable the determination of where and how gluons and sea quarks appear and whether the gluon distribution has a compact core, smaller than the electric charge radius of the proton, or whether the gluon distribution is extended. A variant of tomography would study transverse motion rather than transverse position. These images can be used to analyze the coupling between spin and orbital angular momentum.

An EIC would not only determine the distribution of gluons but also measure the distribution of gluonic energy density and pressure in the proton. These measurements would directly inform our understanding of the origin of mass and constrain models of the gluon field inside the nucleon—for example, models based on flux tubes or solitonic solutions.

Two key features of an EIC enable measurements of gluons. The first is large kinematic coverage, which provides multiple independent avenues for accessing gluons, as explained in Chapter 2. The second is large luminosity, which is impor-

tant for identifying specific final states in DIS. It is this information that can be used to obtain tomographic images.

How Does the Spin of the Nucleon Arise?

The spin of a nucleon is an important property; through the electric charges of quarks, spin allows protons and neutrons to behave as tiny magnets. The magnetic axis is aligned with the spin axis, and external radio frequency fields can drive resonant spin transitions. This is the basis of MRI imaging and many other applications. It is remarkable that scientists do not know in detail the origin of the proton (or neutron) spin.

The proton has spin ½, and in a simple quark picture the total spin arises from three valence quarks of spin ½ that combine to form a total spin ½. While this naïve picture qualitatively describes the observed magnetic moment of the proton, it fails quantitatively. In particular, experiments at SLAC, the European Organization for Nuclear Research (CERN), and HERA have shown that the sum of all quark spins in the nucleon accounts for only about one-third of the total spin of the proton. The remainder of the proton spin must reside in orbital angular momentum or gluon spin (gluons have spin 1, twice that of the quarks; see Figure 1.1).

An EIC can comprehensively explore these contributions. The orbital angular momentum of quarks and gluons can be extracted using the transverse position information contained in the tomographic measurements, discussed at length in Chapter 2. Measurements of the gluon-spin contribution to the spin of the proton are based on the idea that the gluon can transfer its polarization to a quark-antiquark pair, which can be probed using polarized electrons.

What Are the Emergent Properties of Dense Systems of Gluons?

Nuclear physics exhibits one remarkable limit where simplicity emerges. Despite the extraordinary complexity of QCD—the strength and presence of interactions among all quarks and gluons—at ordinary densities and low temperature, nuclei can be accurately modeled as collections of colorless composite particles—nucleons—interacting through long-range forces understood as arising from the exchange of mesons. An EIC would seek to explore a second regime where great simplicity may emerge, despite the inherent complexity of QCD: In this regime, quarks are predicted to behave as a nearly static source of a gluon field that reaches a limiting density, producing “dense gluonic matter.” At an EIC, this regime would manifest itself in terms of DIS reactions on nuclei that cannot be understood in terms of approximately independent nucleons. Box 1.2 describes the similarities between how the electromagnetic force binds neutral atoms into molecules and how the color force binds colorless nucleons into nuclei. Because the color force

is so profoundly different than the electromagnetic force, there are also big differences and deep mysteries to be understood, including how quark distributions are modified in nuclei, how the gluons are distributed, and how gluons bind nucleons into nuclei.

Physicists understand well why atoms retain their individual identities in molecules, but not why nucleons retain their identities within nuclei. In fact, nuclear matter can have simpler states where nucleons do not retain their individual identities, as in the quark matter seen in ultrarelativistic heavy ion collisions, and inferred in massive neutron stars.

In addition, nucleons and nuclei differ from atoms and molecules because they contain so many gluons, a fact discovered at the HERA facility, whose implications are still not well understood.

This abundance of gluons provides the opportunity to address fundamental questions about nucleons and nuclei. As HERA found, the number of gluons grows significantly in the small x, high-energy limit. This means that gluons must overlap in the plane transverse to the electron-ion collision. The most interesting case is when this limit can be achieved at high resolution (high Q²), so that the number of gluons that can be packed into the transverse area of a proton or nucleus is large. An EIC of sufficiently large energy would be able to reach this limit. Under such conditions, a quantum state of “cold dense gluonic matter”⁹ is posited to exist. Such a state is possibly analogous to Bose-Einstein condensates of clouds of cold atoms created in atomic physics laboratories.

An EIC would be able to reach unprecedented gluon densities by using the concentrated gluon fields of large nuclei. Relativistic length contraction implies that the number of gluons per transverse area is proportional to the radius of the nucleus, which is itself proportional to the one-third power of the nuclear mass number A. Although an EIC would operate at lower energies than HERA (which collided beams of electrons and protons), an EIC would achieve higher gluon densities because it can accelerate ions with high atomic weight.

A good part of high-energy scattering can be understood in terms of “diffraction” of the projectile by the target. Diffraction is well known in optics, where light waves bend around the edge of an obstruction, producing an interference pattern on a screen placed behind the object. One of the remarkable predictions is that at a high-energy EIC, such events would constitute a significant fraction of the total number of events, and a classical diffraction pattern would be observed—periodic oscillations of the scattering rate as a function of the scattering angle (see Figure 2.9). Analyzing diffractive events would provide a wealth of information about dense gluon matter, the strength of the color field, fluctuations in the color

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⁹ “Cold” in the sense that the matter has no thermal motion, only quantum zero-point energy.

field of the proton and of nuclei, and the interaction of color dipoles with the gluon field of the target.

ACCELERATOR TECHNOLOGY

Building an EIC capable of fully exploring the physics described above is by no means an easy task. The machine must collide electrons with protons and other atomic nuclei (ions) over a range of energies. There must be enough collisions for the experiment to gather adequate data to elucidate or settle the known physics questions, and other questions that may emerge, in a reasonable time. A collider’s ability to squeeze many particles of two beams into a tiny volume where they collide defines its luminosity. The luminosity ultimately required of an EIC is comparable to those of the highest performing colliders built to date, such as the Large Hadron Collider (LHC) at CERN and the B-meson factories at SLAC and High Energy Accelerator Research Organization (KEK).

Furthermore, given the crucial role of spin, both beams must be polarized. That is to say, the spins of the individual particles in each beam must be made to line up with each other, overcoming their natural tendency to point “every which way” at random.

To achieve these goals, a host of techniques in accelerator physics and technology must be brought to bear. Only a few are mentioned here. State-of-the-art superconducting radio frequency (SRF) cavities will accelerate high-intensity beams efficiently. Further specialized radio frequency (RF) cavities will rotate the beams as they collide to optimize their overlap. Elaborate interaction region designs must squeeze two very different beams simultaneously into the tiny collision volume using advanced superconducting magnet designs. The hadron beams must be compressed in volume by sophisticated new “beam cooling” techniques that involve subtle interaction with yet other electron beams. Polarized beams require polarized particle sources, special magnets, and a further level of mastery of beam physics to preserve the polarization through the acceleration process to the collisions. Polarized colliding stored beams have been achieved before only at HERA (polarized e⁺/e^– on unpolarized protons) and at RHIC (both proton beams polarized).

These and numerous other accelerator physics and technology challenges are discussed in more detail in Chapters 4 and 5. Not only would development of an EIC advance accelerator science and technology in nuclear science, it would benefit other fields of accelerator-based science and society. The accelerator physics and technology advances required for an EIC will, importantly, have the potential to extend the capabilities of many particle accelerators built for other purposes, from medicine through materials science to elementary particle physics.

Fortunately, an EIC does not have to be built from scratch—significant parts of the accelerators, their injector complexes, and other infrastructure already exist at

two locations in the United States. BNL already has the hadron rings of RHIC, which could be converted to an EIC by the addition of a suitable electron accelerator and storage ring and further upgrades. JLab, conversely, has an electron accelerator but would need to add the hadron injectors and storage ring and an electron storage ring. This has resulted in two somewhat different designs for an EIC, both of which push the limits of present technology. While neither the technical assessment nor the choice between these designs was a task of the present report, the committee found it appropriate to summarize them to illustrate how such benefits might accrue from the construction of an EIC.

Experience at all the world’s major accelerator laboratories has demonstrated the value of building not only on existing hardware (going back over 60 years in long-established labs like BNL and CERN), but on the less visible collective expertise of the beam physicists, engineers (magnets, RF, vacuum, controls, civil, etc.), and operators among the laboratory staff. Construction of an EIC would sustain and develop this precious national asset and help the United States to maintain a leading role in international accelerator-based science.

Chapter 2 lays out in detail the basic science that could be achieved at an EIC. Chapter 3 describes the role of an EIC within the context of U.S. and international nuclear physics. Chapter 4 presents the accelerator challenges of building an EIC, and Chapter 5 compares a future U.S. EIC to current and future facilities both in the United States and internationally. Chapter 6 summarizes the impact of an EIC on other fields of physics, and Chapter 7 summarizes the conclusions and findings of this report.