## The Emerging QCD Frontier: The Electron Ion Collider 

### I. A New Experimental Quest to Study the Glue That Binds us All

Without gluons there would be no protons, no neutrons, and no atomic
nuclei. The exchange of gluons between quarks (particles with "color"
charge) mediates the color force that provides the internal binding in
all strongly interacting particles, just as the exchange of photons
between electrically charged particles mediates the electromagnetic
force that binds electrons to nuclei in atoms. But unlike photons,
gluons are much more than mere force carriers in QCD. The gluons
themselves have a color charge, and thus they interact among themselves.
The self-interactions of gluons determine all the unique features of QCD
and lead to a dominant abundance of gluons inside matter. Despite this
dominance, the properties of gluons in matter remain largely unexplored.
The world's premier accelerator facilities focused on QCD -- RHIC, CEBAF
and HERA -- have increasingly addressed selected aspects of gluon
behavior accessible to them. But getting to the heart of the matter --
unveiling the collective behavior of dense assemblies of gluons under
conditions where their self-interactions dominate -- will require a new
facility with capabilities well beyond those of any existing
accelerator.

The QCD equations governing the interactions among quarks and gluons are
easy to write down, but difficult to solve. This is especially so at
large length scales, where the interactions grow very strong, or at high
densities, where the theory becomes highly non-linear. Recent
breakthroughs have identified conditions of high density, but
sufficiently weak coupling, where the theory may be amenable to a
systematic solution, starting from a view of the dense assembly of
gluons as a very strong classical field. These developments suggest that
all hadrons and all nuclei should appear the same when viewed at
sufficiently high energy -- as a *universal* form of gluonic matter, of
saturated density, known as the Color Glass Condensate. Saturation of
the density -- a predicted result of the growing importance of gluon
recombination (two gluons merging into one) as the density increases --
is critical to avoid a theoretical catastrophe in which predicted high
energy scattering probabilities would exceed 100% if extrapolated
linearly from gluon properties measured to date. Hints of this
saturation have been extracted from measurements of electron-proton
collisions at HERA and of deuteron-nucleus and nucleus-nucleus
collisions at RHIC. Saturated gluon densities would have a profound
influence on heavy-ion collisions at the LHC. But a definitive search
for this universal gluonic matter, with a cleanly interpretable probe of
its properties, requires an Electron-Ion Collider (EIC).

Counter-intuitively, high-energy electron (or muon) beams provide the
best gluon microscope, by interacting primarily with individual
electrically charged quarks, in a process known as deep inelastic
scattering (DIS). When the struck quark emits a gluon, or arises from a
gluon conversion to a quark-antiquark pair, these QCD corrections modify
the precisely understood electromagnetic interaction of the electron and
quark in ways that allow us to infer the gluon properties. For this
inference to be precise, DIS must be studied over a broad range of
energies and scattering angles. Collider energies are needed to reach
the desired resolving power of the microscope. As explained below, the
density of gluons probed by the electron beam is amplified inside a
nucleus, as compared to a single proton. These features define the
specifications of an EIC of *high* and *variable energy,* with *beams of
heavy nuclei*, needed for robust access to the saturated gluon density
regime.

The addition of *spin-polarized proton and light-ion beams* to collide
with *polarized electrons and positrons* would give the EIC
unprecedented access to the spatial and spin structure of protons and
neutrons in the gluon-dominated region. Polarized DIS measurements would
be greatly extended in kinematic reach and precision, in comparison to
present-generation experiments with fixed polarized targets at CEBAF,
HERA, CERN and SLAC. Tomographic images of the nucleon's internal
landscape would be pushed far beyond the valence quark region to be
probed with 12 GeV electron beams at CEBAF. These extensions will be
critical to complete our picture of the origin of the nucleon's spin, by
providing new sensitivity to the orbital motion of sea quarks and to the
spin preferences of very soft (low momentum, highly abundant) gluons.

Results and measurement programs at the world's existing QCD
laboratories point to the physics accessible at an EIC as the next QCD
frontier. EIC measurements will be critical in answering one of the
overarching questions for our field: **What is the role of gluons and
gluon self-interactions in nucleons and nuclei?** Self-interacting force
carriers exist in interaction theories other than QCD (e.g., for the
weak force and various hypothesized forces beyond the Standard Model),
but without comparable opportunities to discover unique manifestations
of those self-interactions in matter. EIC experiments would also yield
missing links needed to answer two other overarching questions: **What
is the internal landscape of the nucleons? What governs the transition
of quarks and gluons into pions and nucleons?**

### II. The Electron Ion Collider

The detailed requirements for the machine complex and detectors at an
EIC are driven by the need to access the relevant kinematic region that
will allow us to explore gluon saturation phenomena and image the gluons
in the nucleon and nuclei with great precision. These considerations
constrain the basic design parameters to be a 3 to at least 10 GeV
energy electron beam colliding with a nucleon beam of energy between 25
and 250 GeV or with nuclear beams ranging from 20 to 100 GeV/nucleon.

While the HERA collider at DESY provided electron-proton collisions at
even higher energies, the performance needed at EIC relies on three
major advances over HERA: (1) Beams of heavy nuclei, at least up to
gold, are essential to access the gluon saturation regime under
conditions of sufficiently weak QCD coupling, and to test the
universality of the Color Glass Condensate. (2) Collision rates
exceeding those at HERA by at least two orders of magnitude are required
for precise and definitive measurements of the gluon distributions of
interest, especially with the complete outgoing particle detection
needed for tomographic imaging. (3) Polarized light-ion beams, in
addition to the polarized electrons available at HERA, are mandatory to
address the central question of the nucleon's spin structure in the
gluon-dominated region.

A new EIC facility will require the design and construction of new
optimized detectors profiting from the experience gained from those
operated at DESY. A central collider detector providing momentum and
energy measurements and particle identification for both leptons and
hadrons will be essential. Special purpose detectors that provide
extreme forward/backward coverage are also required.

There are currently two complementary concepts to realize an EIC: eRHIC,
to construct an electron beam to collide with the existing RHIC ion
complex and ELIC, to construct an ion complex to collide with the
upgraded CEBAF accelerator. Both rely on new accelerator and detector
technology, and on allocation of suitable R&D resources for their
expeditious development. Over the next five years we anticipate
sufficient R&D to choose the implementation that optimizes scientific
impact and cost. In parallel with the technical developments, continuing
progress on the theoretical treatment of saturated gluonic matter is
needed to ensure that a future facility incorporate capabilities
suitable to answer the most critical scientific questions.

### III. The Physics Program at an Electron ion Collider

**Saturation of Gluon Densities and the Color Glass Condensate**. A
major discovery of the last decade is the dominant role of gluons in
nucleons viewed by a high-energy probe. The density of gluons grows
extremely rapidly as one probes gluons carrying progressively smaller
fractions *x* of a proton's overall momentum. This growth reflects a QCD
cascade in which higher-momentum (harder) parent gluons successively
split into two or more lower-momentum (softer) daughter gluons. But this
growth cannot continue unabated without eventually violating fundamental
rules of physics. Physicists expect the growth to be tamed because at
sufficiently high gluon densities softer gluons will again recombine
into harder ones. The competition between the splitting and
recombination processes should lead to a saturation of gluon densities
at small *x*. Recent theoretical breakthroughs suggest that this
saturation regime is characterized by new physics that can be best
studied at an EIC.

The onset of saturation depends not only on the gluon's momentum
fraction *x*, but also on the spatial resolution with which the nucleon
is probed. As the momentum kick *Q* imparted by a beam electron to the
struck parton is decreased, the resolution of structure details in the
plane transverse to the beam direction gets coarser. This increases the
sensitivity to the recombination of gluons. This sensitivity also
increases when the target nucleons are contained within a heavy nucleus,
where many closely spaced nucleons along the beam path can conspire to
contribute gluons to the recombination cause, amplifying the gluon
density. The predicted result of these multiple dependences is a
*saturation scale Q*~s~^2^ (A/*x*)^1/3^ that grows with increasing
nuclear mass number A and with decreasing gluon momentum fraction *x*
(see Fig. 1). When the probe has much finer spatial resolution, *Q*^2^
\>\> *Q*~s~^2^, the physics is described by the well-studied linear
regime of QCD, dominated by gluon splitting. But as *Q*^2^ decreases
below *Q*~s~^2^ one enters the novel non-linear regime of saturated
gluonic matter

Gluons are among the class of particles known as *bosons* that are
permitted by quantum physics to have more than one particle in the same
state. In fact, the occupancy of gluons in the saturation regime is
proportional to the inverse of the QCD coupling strength. When *Q*~s~^2^
is large, this coupling is weak, and therefore the occupancy is large
and the behavior of the gluon ensemble is nearly classical. In this
limit, theorists predict that one should gain access to a fascinating
facet of *all* matter: a dense swarm of gluons, wherein the individual
gluons interact weakly but collectively form a coherent classical color
field whose intensity may be the *strongest allowed in nature*! This
predicted universal facet of matter has much in common with
Bose-Einstein condensates (whose study led to the 2001 Nobel Prize in
Physics) and with glassy materials, and has thus been labeled the *Color
Glass Condensate,* CGC.

  -----------------------------------------------------------------------
  ![](media/image1.png){width="3.4770833333333333in"
  height="3.064583333333333in"}

  ***Figure 1**: Regimes of hadronic matter in QCD at high energies, as a
  function of the resolving momentum transfer of the electron, Q^2^, the
  relative momentum fraction of the gluon in the nucleus,* *x, and the
  atomic number of the nuclei probed, A. The multi-colored surface
  indicates the saturation scale Q~s~^2^ as a function of x and A. The
  saturation regime (Q^2^\<Q~s~^2^) that is kinematically accessible by
  the EIC is depicted in blue. For very large Q^2^ matter exists in the
  form of a parton gas, while the confining regime of QCD is
  characterized by very low Q^2^ values. The higher Q~s~^2^ (large A),
  the larger the accessible Q^2^ range of the Color Glass Condensate and
  the more nearly classical its expected behavior. Acceptance at Q≈Q~s~
  is not essential, coverage of the region at Q\<Q~s~ is. The beam
  energies of the EIC would allow robust study of the saturation regime
  for gluons carrying as little as 0.01% of the nucleus' momentum.*
  -----------------------------------------------------------------------

To reach CGC conditions one needs a suitable combination of high beam
energy (small *x*) and heavy ion (large A) beams to collide with the
probing electrons. A hypothetical observer co-moving with the electron
will see a tidal wave of gluons from protons and neutrons along the
entire depth of the nucleus. Using heavy nuclei as an *amplifier* of
gluon densities allows us to reach this regime with 10 times lower beam
energy than would be needed in an electron-proton collider.

The regimes probed in atomic nuclei at high energies are shown in Fig. 1
as a function of the resolving momentum *Q*^2^ of the probe, the gluon
momentum fraction *x* and the atomic number A. As suggested by the
figure, the Color Glass regime is expected to be universal across all
atomic nuclei and for resolving momenta below the saturation scale. The
use of large nuclei and high energies together opens a wide window to
explore, with unmatched precision, this novel regime. The figure also
shows that the CGC regime of strong gluon fields lies adjacent to the
confining regime of QCD, where the interactions among individual gluons
grow very strong. The transition between the two regimes may hold the
key to understanding the confining dynamics at the heart of all matter.

Is there, in fact, a universal saturation scale, as suggested by QCD
theory? Are the properties of the gluon-dominated matter beyond this
scale truly the same in neutrons, protons and all nuclei? Do such
universal properties explain remarkable patterns in particle production
via strong interactions that have so far defied quantitative
understanding? The discovery of the CGC would represent a major
breakthrough in our understanding of QCD and nuclear matter. We turn
next to the EIC measurement programs key to such a discovery.

**A Precise Image of Gluons in Nucleons and Nuclei.** The energy
dependence of the high energy scattering process of electrons from
nucleons and nuclei renders an indirect but precise measure of gluons
through the evolution with energy scale of quark properties. Application
of this technique established the massive wall of gluons found in HERA
data when one probes protons with increasing spatial resolution.
However, at the moderate resolutions and very small gluon momenta of the
saturation region, the situation is much less understood. The
conventional linear QCD analysis of energy evolution is expected to
break down here, and its application to HERA data yields puzzling
results.

In nuclei, the region of gluons for *x* \< 0.01 is *terra incognita* and
measurements at an EIC will be the first. Figure 2 shows projections of
EIC measurements of the ratio of gluon distributions for a lead nucleus
relative to that for deuterium. The saturated gluon densities associated
with the CGC and those anticipated in linear QCD approaches (labeled as
HKM and FGS here) are shown. By combining measurements such as those in
Fig. 2 for a variety of nuclear beams with different masses A, one can
search directly for a universal scaling behavior that collapses all the
data onto a single curve as a function of *Q*^2^/*Q*~s~^2^. Such scaling
would demonstrate the universality of the CGC and directly determine how
the saturation scale depends on *x* and A.

  -----------------------------------------------------------------------
  ![](media/image2.png){width="3.245833333333333in"
  height="2.433333333333333in"}

  ***Figure 2**: The ratio of gluon distributions in lead relative to
  deuterium as determined from projected measurements with an EIC, as a
  function of gluon momentum fraction x. HKM and FGS represent QCD
  parameterizations of existing data extrapolated linearly to small x.
  The curve labeled Color Glass Condensate is a saturation model
  prediction. Domains relevant to nucleus-nucleus collisions at RHIC and
  the LHC are shown.*
  -----------------------------------------------------------------------

The deep inelastic scattering measurements determine how the gluons are
distributed in momentum inside nuclei. It is also important to see how
they are distributed in space; *e.g.*, are the conditions for saturation
achieved first in localized regions within the nucleus? The spatial
distribution can be probed when the scattering electron produces a
single high-energy photon, or a meson with the same quantum numbers as
the photon, without exciting the target nucleus. The results would
provide insight into the role of strong color fields in binding nuclei
and in more complex processes of multiple particle production.

Strong gluon fields also enhance the probability for a high-energy probe
to interact gently with the nucleus by exchanging a colorless particle
comprising multiple gluons -- a particle sometimes called the Pomeron.
Indeed, experiments at the HERA collider produced the striking discovery
that a proton at rest remains intact in roughly one-seventh of its
collisions with electrons of energy roughly 25,000 times the proton rest
mass. Several models suggest that the amplified gluon fields in heavy
nuclei may cause the nucleus to remain intact nearly 30-40% of the time
in EIC collisions. This would be truly astounding if confirmed
experimentally at an EIC. Measurements for such events place strong
demands on EIC detector design.

  -----------------------------------------------------------------------
  ![](media/image3.png){width="3.2194444444444446in"
  height="3.7979166666666666in"}

  ***Figure 3**: The world database of polarized deep inelastic
  scattering results for the proton, from SLAC experiments E143 and E155,
  CERN-SMC, and DESY-HERMES. The curves (and error bands) are from a
  global QCD fit by Boetcher and Bluemlein. The blue-shaded area
  represents the enlarged (x,Q^2^) area accessible by an EIC. The insert
  shows one example of the consequent physics reach, comparing projected
  data as a function of x in one Q^2^ bin for about one year of EIC
  running with theoretical predictions based on global QCD fits to the
  present world data under differing assumptions for gluon spin
  preferences.*
  -----------------------------------------------------------------------

**The Spin Structure of the Proton**. As described in Chap. \<?"Hadron
Structure"\>, deep inelastic scattering of high-energy electrons and
muons from fixed polarized targets have shown that spin alignment of
quarks and antiquarks surprisingly accounts for only about 30% of the
nucleon's spin. The remainder must be due to the spin of the gluons
and/or the orbital motion of the constituents (quarks and gluons). EIC
with its unique high luminosity, highly polarized electron and nucleon
capabilities, and its extensive energy span, will allow access to quark
and gluon spin contributions at substantially lower momentum fractions
*x* than current and forthcoming experiments at RHIC, DESY, CERN and
JLab.

We currently know much less about the spin preferences than about the
number density of low-momentum gluons in a nucleon because there has
been no polarized electron---polarized nucleon collider. EIC deep
inelastic scattering measurements would rectify the situation, expanding
the kinematic coverage as indicated in Fig. 3. The insert shows
quantitative projections for EIC results in comparison with model
predictions that make different assumptions regarding the sign and
magnitude of the gluon spin contribution to the proton spin. Data from
polarized proton collisions at RHIC are now beginning to establish
preferences among these particular four models at *x* \> 0.03, but will
not be able to constrain the shape of the gluon spin distribution at
lower *x*, where the density of gluons rapidly increases.

With polarized deuteron or 3-Helium beams at an EIC, electrons could
also be scattered by polarized neutrons, allowing a precision test of
the fundamental Bjorken sum rule, which relates the proton and neutron
spin structure via the axial weak coupling strength measured in neutron
beta-decay. Corrections to this relation are known to higher order in
the strong coupling constant ~s~(*Q^2^*) than any other quantity in QCD.
This measurement could very well provide the best determination of
~s~(*Q^2^*) away from the CERN measurements at the *Z*-particle mass,
and thus constrain the evolution of the strong force with energy to high
precision.

Various avenues have emerged to investigate the contribution of orbital
angular momentum to the proton spin. One of them is the study of
correlations of the transverse momentum of a quark in the nucleon with
the nucleon spin transverse to its momentum. Such correlations have been
found to cause surprisingly large left-right asymmetries for the
final-state hadrons produced in the scattering process. Measurements at
an EIC would allow quantitative investigation of how quarks and
antiquarks of different flavor are orbiting in protons and neutrons. An
alternative approach will utilize reactions to probe Generalized Parton
Distributions (GPDs), to which we turn next.

**The Complete Image: Measurements of Generalized Parton
Distributions.** GPDs may be viewed as functions describing
distributions of a nucleon's constituents in position and momentum
simultaneously. They represent the closest analog to a classical phase
space density allowed by the uncertainty principle. The concept of GPDs
has revolutionized the way scientists visualize nucleon structure, in
the form of either two-dimensional tomographic images (analogous to CT
scans in medical imaging) or genuinely six-dimensional space-momentum
images.

Measurements of GPDs are possible in select high-energy processes. The
experimental study of these rare processes requires high luminosities.
While initial maps of GPDs in the valence-quark region will be carried
out with the 12 GeV upgrade at JLab, the EIC would allow unique access
to the gluon, sea-quark and antiquark GPDs, through study of reactions
in which an electron scattering also produces a single photon or hadron
(e.g., pion, kaon or *J*/ particle). The production probabilities encode
information about the spatial distribution of the nucleon's
constituents. Precise EIC measurements over a wide kinematic range would
probe whether gluons are clumped in the nucleon, or are uniformly
distributed. Such spatial gluon distributions could be measured for
varying gluon momenta. In a nucleus, this could be correlated with the
hunt for gluon saturation in localized spatial regions. From the trends
in measured GPDs, one could invoke the so-called Ji sum rule to infer
the orbital contributions of sea quarks and antiquarks to the nucleon
spin, thus testing nucleon structure models in which a proton spends
part of its time as a fluctuation into a neutron and an orbiting
positively charged pion.

**The Formation of Hadronic Final States from Light Quarks and Massless
Gluons.** High-energy scattering from nucleons in a collider environment
lends itself specifically to study how the creation of matter from
energy is realized in QCD when an essentially massless (but colored)
quark or gluon evolves into massive (and color-neutral) hadrons. We have
known since the work of Einstein that matter can be created out of pure
energy, a concept that is at the root of modern physics, but full
understanding of this process remains lacking. The availability of a
high-luminosity *polarized* electron-ion collider, using high-efficiency
detectors with good particle identification, will facilitate experiments
to measure new features of this *fragmentation* process, such as its
dependence on quark flavor, spin orientation, and motion, and on passage
through nuclear matter. It is already apparent now, from measurements in
electron-positron collisions and in fixed-target electron scattering,
that correlations exist between the momentum components of hadron
fragments transverse to the jet axis and any quark spin preference
transverse to its momentum. In addition to systematic exploration of
these initial hints at EIC, it may be possible for selected final-state
hadrons - e.g., -mesons - reconstructed from their decay daughters to
correlate their own spin preferences with the spin orientation of the
fragmenting quark. Such measurements are likely to launch a new stage in
modeling how quarks accrete colored partners from the vacuum or the
debris of the high-energy collision to form colorless hadrons.

**Connection to Other Fields.** EIC measurements will provide critical
input to two dramatic aspects of heavy-ion collisions at RHIC and at the
LHC. The strong flow observed suggests that the hot fireball formed in a
central heavy ion collisions thermalizes into a nearly perfect liquid in
the remarkably short time interval of \~310^-24^ seconds! Does this
rapid equilibration result from "shattering" the Color Glass Condensate
in the incident nuclei? EIC measurements of the saturation scale as a
function of energy, nuclear size, and position within the nucleus will
test this idea further against data at both RHIC and LHC. The observed
strong suppression of high-momentum hadrons in the final state of RHIC
collisions has been interpreted as evidence of the rapid loss of energy
of quarks and gluons traversing the hot, gluon-rich matter. However,
recent observations of the strong attenuation of heavy quarks are
difficult to explain quantitatively in this scenario. Our understanding
of parton energy loss in hot matter can be enhanced significantly by
studying similar processes in "cold matter". The EIC will enormously
expand the energy range of previous fixed target measurements, allowing
for the first time the study of attenuation of heavy-quark mesons in
cold nuclear matter.

A detailed study of collective phenomena in cold QCD matter facilitates
comparison with more familiar collective behavior in condensed (QED)
matter systems. In addition to the close analogy to Bose-Einstein
condensation, saturated gluons also have stochastic properties analogous
to that of glassy ("spin glass") systems in condensed matter physics.
Further, the behavior of QCD cross sections as they approach saturation
are equivalent to that of a wide class of statistical reaction diffusion
systems from physics to biology. These connections should blossom as the
CGC properties become better delineated.

High energy studies with polarized electron and proton beams seek to
uncover the origin of the proton's spin in terms of the underlying quark
and gluon fields. Spin is a fundamental quantum mechanical property of
sub-atomic particles that underlies all of chemistry and explains
magnetism. The nuclear physics of spin-½ protons and neutrons explains
the origin of the chemical elements and their properties. As a practical
consequence, the medical diagnostic technique of magnetic resonance
imaging (MRI) is based on the manipulation of nuclear spins in a
patient's body. Resolving how spin arises in QCD would settle how an
important aspect of nature works at a fundamental level.

### IV. Outlook

The Electron-Ion Collider embodies the vision of our field for reaching
the next QCD frontier: the study of the glue which binds all atomic
nuclei. A high luminosity EIC with center-of-mass energy in the range
from 30 to 100 GeV with polarized nucleon beams and the full mass range
of nuclear beams could be sited either at Brookhaven National Laboratory
or at Thomas Jefferson National Accelerator Facility. EIC is the natural
evolution of the JLab 12 GeV upgrade, which will be focused on the role
of valence quarks, and of the RHIC II upgrade, which will complete the
study of the hot, dense matter discovered in RHIC's heavy ion collisions
and will allow a first look at the gluon contribution to proton spin.
Precision measurements with the EIC, directly interpretable within the
framework of QCD, will open a new window to the regime dominated by
direct manifestations of the defining feature of QCD: the
self-interactions of gluons. These self-interactions lie at the heart of
nucleon and nuclear structure and are expected to be essential to the
understanding of high energy heavy ion collisions.

To develop the most compelling case for EIC in a timely way it is clear
that over the next five years significant progress must be made in the
design of the accelerator and the optimized suite of detectors. It will
be important to converge on one, optimized design for the accelerator.
This can only happen after essential R&D is completed in a number of
areas including: cooling of high-energy hadron beams, high intensity
polarized electron sources, and high energy high current Energy Recovery
Linacs. This R&D effort should be carried out so as to leverage existing
expertise and capabilities at laboratories and universities. R&D for a
high energy EIC will maintain U.S. leadership in an area with important
societal applications. The design of collider detectors integrated into
the accelerator will also be a high priority requiring detailed physics
simulations as well as detector R&D.

Theoretical developments have been essential in shaping the scientific
arguments for EIC, have attracted a growing number of young physicists
and have sparked one of the most active areas in all of theoretical high
energy physics. The coming years should see new insights into the
universal character of gluon fields when viewed in hadrons at high
energies. In addition, first-principles QCD calculations using lattice
techniques are expected to provide increasingly realistic predictions to
be tested with data. It is essential that theoretical support for EIC
related physics is maintained at a healthy level in the coming years.

When realized, EIC will be a unique facility to study QCD complementary
to next generation accelerators either under construction or planned in
Europe and Asia. Thus, EIC has attracted significant interest from
physicists around the world, which can be nurtured by timely allocation
of resources for continuing R&D and theoretical progress. It is natural
and important that future EIC planning ensure a strong international
participation.