Nuclear physics at the energy frontier: recent heavy ion results from the perspective of the Electron Ion Collider

Abstract

Quarks and gluons are the fundamental constituents of nucleons. Their interactions rather than their mass, is responsible for $99\%$ of the mass of all visible matter in the universe. Measuring the fundamental properties of matter has had a large impact on our understanding of the nucleon structure and it has given us decades of research and technological innovation. Despite the large number of discoveries made, many fundamental questions remain open and in need of a new and more precise generation of measurements. The future Electron Ion Collider (EIC) will be a machine dedicated to hadron structure research. It will study the content of protons and neutrons in a largely unexplored regime in which gluons are expected to dominate and eventually saturate. While the EIC will be the machine of choice to quantify this regime, recent surprising results from the heavy ion community begin to exhibit similar signatures as those expected from a regime dominated by gluons. Many of the heavy ion results that will be discussed in this document highlight the kinematic limitations of hadron-hadron and hadron-nucleus collisions. The reliability of using as a reference proton-proton (pp) and proton-Nucleus(pA) collisions to quantify and disentangle vacuum and Cold Nuclear Matter (CNM) effects from a Quark Gluon Plasma (QGP) may be under question. An selection of relevant pp and pA results which highlight the need of an EIC will be presented

Full text

Article
Nuclear physics at the energy frontier: recent heavy ion
results from the perspective of the Electron Ion Collider
Astrid Morreale 1,2 ,*
1Institute for Globally Distributed Open Research, Paris France ; astrid.morreale@igdore.org
2Center for Frontiers in Nuclear Science, New York, USA ; astrid.morreale@gmail.com
*Correspondence: astrid.morreale@igdore.org
Received: date; Accepted: date; Published: date
Abstract:
Quarks and gluons are the fundamental constituents of nucleons. Their interactions rather
than their mass, is responsible for 99% of the mass of all visible matter in the universe. Measuring the
fundamental properties of matter has had a large impact on our understanding of the nucleon structure
and it has given us decades of research and technological innovation. Despite the large number of
discoveries made, many fundamental questions remain open and in need of a new and more precise
generation of measurements. The future Electron Ion Collider (EIC) will be a machine dedicated to
hadron structure research. It will study the content of protons and neutrons in a largely unexplored
regime in which gluons are expected to dominate and eventually saturate. While the EIC will be the
machine of choice to quantify this regime, recent surprising results from the heavy ion community
begin to exhibit similar signatures as those expected from a regime dominated by gluons. Many of
the heavy ion results that will be discussed in this document highlight the kinematic limitations of
hadron-hadron and hadron-nucleus collisions. The reliability of using as a reference proton-proton (pp)
and proton-Nucleus(pA) collisions to quantify and disentangle vacuum and Cold Nuclear Matter (CNM)
effects from a Quark Gluon Plasma (QGP) may be under question. An selection of relevant pp and pA
results which highlight the need of an EIC will be presented.
Keywords: QGP; EIC; Gluon Saturation; nPDF; DIS; CNM
1. Introduction
Quarks and gluons, collectively called partons, are the fundamental constituents of protons, neutrons,
the atomic nucleus as well as other hadrons. Their interaction is governed by Quantum Chromodynamics
(QCD). Understanding QCD and in particular the confinement of quarks and gluons inside hadrons is
one of today’s greatest physics challenges. QCD is the theory of strong interactions and it is expected to
describe building blocks of visible matter and their binding in nuclei. While QCD is a well established
theory, it contains elements that cannot be calculated and rely mostly on experimental input.
1
As of today,
many fundamental aspects of the theory have not yet been quantified. These aspects include the quantified
contribution of partons (and their interactions) to the proton spin, or the mechanisms that permits us to
transition from point-like to non-point-like physics.
Since the discovery of quarks and gluons and the confirmation that they carried color and spin. QCD
and related sub-fields have continuously given us discoveries. One of which is the Quark Gluon Plasma
(QGP) formation. QGP was the discovery that there was a state of matter in which partons were no
1
While lattice calculations address these problem directly, results emerging from the lattice typically require large time scales.
The accuracy of the obtained results is largely correlated with the amount of computing power allocated to pursuing these
calculations.
Universe 2019,xx, 5; doi:10.3390/universexx010005 www.mdpi.com/journal/universe
arXiv:1904.02964v1 [nucl-ex] 5 Apr 2019

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longer confined to the boundaries of a hadron, but rather acted as free particles. Evidence of this new
state of matter was observed in heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) with
the discovery of a suppression of high transverse momentum hadrons, also called "jet quenching [
1
]. Jet
quenching is attributed to a decrease of the energy of the hard partons created during the first stages of a
high-energy heavy-ion collisions. The formation of the QGP is now understood as being responsible for
this loss of energy via interactions with its constituting hot and dense medium. Since its discovery we
have learned many of the interesting properties governing the QGP:
•The QGP behaves as a near-ideal Fermi liquid (almost no frictional resistance or viscosity) [2].
•The mean free path of partons in the QGP is comparable to inter-particle spacing [3].
•Experimental evidence points towards collective motion of particles during the QGP expansion [4].
While more precision measurements are needed, some revealing information has been obtained
regarding the QGP onset [
5
] as it is illustrated in Fig. 1from the STAR experiment. This figure
illustrates a classic QGP measurement: particle suppression in heavy ion collisions observed via the
central-to-peripheral nuclear modification factor ratio R
cp
, as a function of transverse momentum and
center of mass collision energy per nucleon-nucleon collision (
p(sNN )
). A smooth transition is seen as a
function of
p(sNN )
between enhancement and particle suppression, the latter a signature of the presence
of a QGP.
Figure 1.
Nuclear modification factor (R
CP
) of high-
pT
hadrons produced in central collisions relative to
those produced in peripheral collisions. A QGP onset is observed at collision energies
p(sNN )>
30
GeV
while an enhancement is observed at lower energies [5].
Despite the plethora of information we have obtained regarding the QGP, many questions remain
open. As an example we list: (1) How precisely does the plasma acquire its Fermi like fluid characteristics
(2) What are the processes in which color-charged quarks and gluons and colorless jets interact with a
nuclear medium (3) Is there a smooth transition for the physics involved in small systems to that of large
systems and (4) when does one transition from a regime of partons to a regime in which gluons dominate.
Indeed, recent puzzling results from proton-proton (pp) and proton-ion (pA) collisions seem to insist
we address the above.

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2. A new physics regime
The interaction between partons is usually described as a function of at least two quantities:
the momentum fraction
x
of the parent nucleon carried by the partons under consideration and the
energy/length scale
Q2
at which the interaction between partons is probed. These two quantities allow
one to identify several regimes for QCD, constituting what one calls the QCD landscape and illustrated on
Fig. 2(left). For a given
Q2
as we decrease towards smaller values of
x
the number of partons is increased.
While for a given
x
and as we decrease towards smaller values of
Q2
(reduce the resolution) the size
of partons increase. Now if we vary our kinematics towards small
x
and small
Q
one enters a regime
characterized by a large number of partons (gluons rather), with overlapping wave functions. This is the
phenomena that is known as gluon saturation.
Figure 2.
Left: The QCD landscape, the horizontal axis
Q2
represents the resolution of the probe while the
Y axis (
ln(
1
/x)
) is related to the parton density. Figure from [
6
]. Right: Parton distribution functions in the
proton plotted as functions of Bjorken x. Figure from [7]
For large values of
Q2
, the coupling constant
αs
is small and one expects scattering directly from
point-like bare color charges. pQCD can be then used to reliably predict the hard scattering of partons.
For small values of
Q2
, in a regime relevant for the description of nucleons and nuclei, one probes longer
length scales making QCD non perturbative and very little is thus calculable. For these small values of
Q2
the content of the nucleon in terms of partons is parameterized using parton distribution functions
(PDF) and more recently Generalized Parton Distribution functions (GPD) [
8
]. Parametrization of PDFs
typically requires experimental input (or direct calculations on the lattice.) For a given value of
Q2
and
decreasing values of
x
the density of gluons in the nucleon increases very rapidly (see Fig. 2right). Yet for
small enough values of
x
, and large enough values of
Q2
for
αs
to be considered small, it is expected that
this increase eventually saturates, giving rise to a new regime characterized by weakly-coupled but highly
correlated gluon matter called Color Glass Condensate (CGC).
A variety of recent Large Hadron Collider (LHC) results indicate that small systems such as pp and
pA exhibit signatures typically expected in larger heavy-ion systems (AA collisions) and resulting from
the presence of a QGP. A variety of theories exist which aim at providing explanation to these results some
which include (1) presence of a QGP already in these small systems and (2) universal properties of all
nuclei (small and large) in a gluon saturation regime. The first of these explanations requires a careful
disentangling of the initial state effects. This is not a trivial task since this is usually achieved using these

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same small systems as a reference. The second explanation can be tested -with coarse precision and large
uncertainties- at current colliders. It is clear that a new generation of results such as those that will be
performed at the Electron Ion Collider ( EIC) will be extremely important to help quantify initial state
effects with better precision than what is currently achievable. Furthermore EIC measurements will be
pivotal to precisely pin-down the presence of new physics regimes ie. gluon saturation.
3. The Electron Ion Collider
One of the goals of the lepton-ion (eA) program at an EIC is to unveil the collective behavior of
densely packed gluons under conditions where their self-interactions dominate. With its high luminosity
and detector acceptance, as well as its span of available collision energies and ion species, the EIC will
probe the confined motion as well as the spatial distributions of quarks and gluons inside a nucleus at one
tenth of a femtometer resolution. The EIC will be able to detect soft gluons whose energy in the rest frame
of the nucleus is less than one tenth of the average binding energy needed to hold the nucleons together to
form the nucleus [
7
]. Thanks to eA collisions with large nuclei, the EIC will reach the saturation regime
faster than with ep collisions at similar cms energies (Fig. 3). This is due to the
x
and mass number (A)
dependence of the saturation scale Qswhich goes like:
Q2
s(x)∼A1/3(1/x)λ
The EIC will investigate the onset of saturation, explore its properties and reveal its dynamical behavior.
It will also provide a kinematically well defined reference to quantify cold nuclear matter effects. For
completeness it is noted that a similar accelerator proposal (LHeC) with complementary kinematic coverage
and physics programe is being evaluated by the European Strategy for Particle Physics [9,10].
Figure 3.
Theoretical expectations for the saturation scale as a function of Bjorken
x
for the proton along
with Ca and Au nuclei.
Q2
s∼
7
GeV2
is reached at
x=
10
−5
in e-p collisions at a
√s∼
1
TeV
while in e-Au
collisions, only
√s∼
60
GeV
is needed to achieve comparable gluon density and the same saturation scale.
Figure from [7]
The EIC is considered a key component for the future nuclear physics program in the US and as such
is among the key recommendations of the Nuclear Science Advisory Committee (NSAC) Long Range

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Plan from 2015. It has further received a positive and encouraging report from the National Academy of
Sciences [11].
3.1. EIC requirements
•Large luminosity (1033 −1034cm−2s−1)
•Center of mass energy (30-140) GeV
•Hadron and electron beams with high longitudinal spin polarization
•Ion beams from D to the heaviest sable nuclei
•Large detector acceptance, in particular for small angle scattered hadrons
•large detector acceptance, in particular for small angle scattered hadrons
Optimized high luminosity and high acceptance running modes
3.2. EIC designs
The eRHIC design is based on an upgrade to the Relativistic Heavy Ion Collider (RHIC) located at
Brookhaven National Laboratory (BNL) in New York.
•New electron injector
•5-18 GeV electron energy
•Heavy ions up to 100 GeV /u
•√s: 20-140 GeV
•Peak luminosity ∼0.4x1034 cm−2s−1/A base design
•1.0x1034cm−2s−1/A with strong cooling
The JLEIC design is based on an upgrade to the Continuous Electron Beam Accelerator Facility
(CEBAF) located at the Jefferson Laboratory in Virginia.
•New hadron injector
•New figure eight collider configuration
•3-12 GeV electron energy
•Heavy ions up to 80 GeV/u that could be upgraded to 160 GeV/u
•√s: 20-100 GeV that could be upgraded to 140 GeV
•average luminosity per run ∼1034cm−2s−1/A
Both designs have science cases by themselves which require a robust integration with detector
designs. An ongoing "Generic Detector for an EIC" research and development peer reviewed program is
funded by the United States Department of Energy. Thanks to these funds an active effort exists in which a
variety of detector designs and technologies which meet EIC requirements are being explored and tested.
Two such examples are cited: the BeAST and JELIC detector R&D efforts. See [
12
] for a complete list of
these programs.
4. Physics at the energy frontier: selection of recent results
A short selection of unexpected heavy ion results measured at the LHC is presented. The presence
of a mini QGP in small hadronic system [
13
,
14
], has been proposed as an explanation. Other physics
mechanisms that do not involve QGP formation have also been proposed including the existence of a
gluon saturation regime [
15
,
16
]. For an interesting review on the subject see [
17
]. The selection presented
hereafter will highlight the need to better understand small colliding systems if we are to quantify
correctly QGP phenomena. The ep and eA collisions of the EIC will undoubtly contribute to an in-depth
understanding of these observations.

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4.1. QGP onset and strangeness enhancement
Strangeness enhancement was one of the first proposed signatures of the QGP [
18
] The QGP
expectation was that strange particle yields would be enhanced with respect to their yield in pp collision
and that the enhancement would follow a hierachy based on their strange quark contents, namely that
a particle with three strange quarks would be more enhance than one with two, and even more than a
particle with only one strange quark As predicted, strangeness enhancement was observed in AA collisions
at the SPS, RHIC and the LHC (left and middle panels of Fig. 4) [19].
Figure 4.
Left and middle: Ratio of strange yields in PbPb collisions with respect to pp collisions as a
function of participants. As it is observed in the figure, an enhancement with respect to pp is observed
which is larger for
Ω
(sss) than for
Ξ−
(dss) and
Λ
(uds). Rightmost: Ratio of strange yields to
π++π−
in pp, p-Pb a a function of average particle multiplicity. A smooth transition is observed as a function of
particle multiplicity connecting the small (pp) and larger (pPb) systems.
What is unexpected however, is the observation (Fig. 4right) that an enhancement of strange particles
(K,
Λ
,
Ω
) with respect to non strange yields (ie
π
) is also visible in the most violent high multiplicity pp
and p-Pb collisions 2.
The mechanisms responsible for the observed enhancement in these small systems might indicate
that such system may not be relied upon to discern cold from hot nuclear effects. While more experimental
insight is needed to interpret the the observed enhancement, it has been proposed that the presence of a
strong gluon field leading to the non-linear regime of gluon saturation [
7
] may explain these observations.
4.2. Heavy flavor vs Multiplicity
Heavy flavor probes are ideal to test QGP properties. The contribution of the QCD vacuum condensate
to the masses for the three light quark flavors (u, d, s) considerably exceeds the mass believed to be
generated by the Higgs fields. Charm and beauty masses on the other hand, are not expected to be affected
by this QCD vacuum (Fig. 5left) making them ideal probes of the QGP. The mass of the heavy quark itself
provides the hard scale for pQCD calculations. This is in contrast to light quarks which often have to rely
2
Multiplicity is the number of charged particles in the final state. In pPb and PbPb this quantity is related to the centrality of the
collision.

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on the
pT
of the final state hadron. In addition low
pT
production of charmonia at forward rapidity (where
smaller values of xcan be reached) is expected to be sensitive to gluon saturation.
Figure 5.
Left: Masses of the six quark flavors. The masses generated by electroweak symmetry breaking
(current quark masses) are shown in blue; the additional masses of the light quark flavors generated by
spontaneous chiral symmetry breaking in QCD (constituent quark masses) are shown in yellow [
20
]. Right:
Relative J/
ψ
production yields as a function of the relative number of charged particles per unit of rapidity.
The blue line corresponds it of a power law function to the data.
Recent results from the ALICE experiment at the LHC show an event activity dependence of inclusive
J/ψ
and D mesons. The relative charmonium production yield as a function of the per-event relative
charged particle multiplicity shows an increase that is faster than linear in pp collisions (Fig. 5right).
Figure 6(middle) shows a similar measurement performed in pPb collisions a negative (Pb-going
side), mid and forward rapidity (p-going side). The positive rapidity measurement corresponds to small
x
values (
∼
10
−5
) , a range in which gluon saturation may be present. The observation of similar charged
particle multiplicity dependence (Fig. 6left) for both open and hidden charm points that hadronization
may be of lesser importance.
Figure 6.
Left: average inclusive
J/Ψ
(closed black and open blue markers), D meson (red closed markers)
dependence on charged particle multiplicity in pp collisions and central rapidity. Middle: inclusive forward
and backward rapidity
J/ψ
’s dependence on charged particle multiplicity in p-Pb collisions [
21
]. Right:
CGC comparisons [15] to recent J/ψmultiplicity results in pp collisions.
One plausible physics explanation for the previous results is the existence of a gluon saturation regime
as it has been discussed in the introduction of this document. In Fig. 6(right) a CCG [
15
] which includes

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gluon saturation effects is compared to ALICE measurements in pp collisions. The calculation describes
the data.
4.3. Hydrodynamic flow
One of the properties of the QGP is that it behaves like a perfect fluid with nearly zero viscosity. This
near zero viscosity has been quantified by the correlated momentum anisotropies among the particles
produced in the heavy collisions which result from a common velocity field pattern. This pattern is now
identified as collective flow [
22
]. Among the flow phenomena, two types are highlighted in this document:
(1) Radial flow which typically affects the shape of low
pT
spectra and (2) Elliptic Flow
v2
: which is the
second coefficient of the Fourier decomposition of particle’s momentum azimuthal distributions. This
decomposition quantifies the anisotropic particle density which emerges from two nuclei interacting in
semi central collisions. A non zero
v2
implies early thermalization of the medium and it is considered a
signature of the QGP.
Baryon to meson ratios obtained in Pb-Pb collisions as shown in Fig. 7illustrates the effect of radial
flow. Radial flow will push hadrons from low
pT
towards intermediate
pT
. The effect is expected
to be stronger for baryons than for mesons, resulting in a bump in the baryon-to-meson ratio (here
proton-to-pions), which depends on the centrality of the collision. Until recently, this was well understood
in heavy-ion collisions. What is unexpected however, is the observation of a similar effect in pp and pPb
collisions as shown in Fig. 8. The results would naively imply that thermalization is occurring already in
these small systems.
Figure 7.
Proton to pion ratio in PbPb collisions as a function of
pT
at two
√sNN
and six centrality classes.

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Figure 8.
Proton to pion ratio as a function of
pT
in pp (left), pPb (middle) and PbPb (right) collisions. The
measurements are classified as a function of charged particle multiplicity.
Light meson flow
v2
results in PbPb and reported by the ALICE collaboration are shown in Fig. 9(top
figures). At low
pT
, as it is the case for many other flow results, the trend is understood as being consistent
with a collective expansion within the QGP and has been successfully explained by hydrodynamic
models [
23
]. At high
pT
constituent quark number scaling takes over (dressed quarks), all mesons fall
together and baryons climb above by
∼
1
/
3. What is intriguing on the other hand is that similar signatures
are observed in pPb (Fig. 9bottom and Fig. 10 ) and pp collisions (Fig. 10 bottom right ). Effects than
can cause the current observations are either due to initial state effects (saturation), or final state effects
(expansion and/or thermal equilibrium). More recently, quantum entanglement has been suggested as
a possible explanation [
24
] and well as double parton scattering coupled with the elliptic gluon Wigner
distributions [
25
]. This phenomena could be elucidated with a variety of probes at the EIC’s lepton-nucleon
program, including diffractive measurements of dijet production.

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Figure 9.
Top figures: elliptic flow
v2
in PbPb collisions as a function of
pT
in two centrality classes and
four particle species. Bottom figure: Elliptic flow v2in pPb collsions.
Figure 10.
Left panel:
v2
flow as a function of
pT
of charm and strange hadrons in high-multiplicity pPb
collisions at
√spA =
8.16
TeV
(CMS Collaboration [
26
]). Right panel:
v2
as a function of
pT
in pp collisions
at √s=13TeV (ATLAS Collaboration [27].)
4.4. Nuclear modification factor and energy loss in the medium
The nuclear modification factor
RAA
is an observable used to quantify the effect of the nuclear
medium on particle production.
RAA
consists of measuring invariant spectra as a function of p
T
of

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particles produced in heavy ion collisions and compared to reference data (pp) at the same energy and
scaled by the number of binary collisions. RAA is defined as:
RAA =AA
scaled pp =d2NAA/d pTdy
<Ncoll >d2Npp/dpTdy
Values greater than unity would be an indication of production enhancement, while values less than unity
will indicate particle suppression in the QGP.
While partons are expected to loose energy when propagating through the dense QGP medium it is
also expected that the amount of energy loss will depend on the parton type and the medium properties.
A large number of results such as those in Fig. 11 indicate that the amount of suppression observed in
heavy ion collisions is irrelevant of particle mass (or quark content) at high enough pT.
Figure 11.
Left: Prompt D-meson R
AA
as a function of p
T
compared to the nuclear modification factors of
charged pions and charged particles in the 0-10% centrality class [
28
]. Right: R
AA
of neutral and charged
pions, kaons and eta meson [29]
RAA
results could largely benefit from independent measurements at the EIC. Measurements such as
those illustrated in Fig. 12 will study the response of the nuclear medium to a fast moving quark [
6
,
7
] and
allow proper understanding of hadronization mechanisms.

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Figure 12. Left:
Hadronization schematic illustrating the interaction of a parton moving through cold
nuclear matter: the hadron is formed outside (top) or inside (bottom) the nucleus.
Right:
Ratio of
semi-inclusive cross section for producing a pion (red) composed of light quarks, and a D0 meson (blue)
composed of heavy quarks in e-Lead collisions to e-deuteron collisions, plotted as function of z, the ratio of
the momentum carried by the produced hadron to that of the virtual photon (
γ∗
), as shown in the plots on
the left. Figures and descriptions taken from [7]
4.5. Nuclear parton distribution functions
Finally, a careful evaluation of initial state effects such as nuclear modifications of Parton Distribution
Functions (nPDFs) is also needed in order to correctly quantify hot nuclear effects present.
nPDFs refers to the difference observed between nuclear (bound nucleons) PDFs and and free nucleons
PDFs (proton, neutron). The nuclear modification of PDFs is due to the interactions between partons from
different nucleons. As such, precise measurements of nPDFs are essential in order to understand cold
nuclear matter effects that may be convoluted with current heavy ion results. Fig. 13 illustrates (in grey)
the uncertainty of gluons distributions in the lead nucleus which is rather large at both low and high
x
.
Measurements that aim at at improving the precision on nPDF are proposed key measurements of the
EIC [6].

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Figure 13. Left:
The ratio R
Pb
g
, from EPPS16
∗
, of gluon distributions in a lead nucleus relative to the
proton, for two different momentum transfers Q
2
possible at the EIC. The grey band represents the current
theoretical uncertainty. The orange (blue hatched) band includes the EIC simulated inclusive (charm quark)
reduced cross-section data. The lower panel in each plot shows the reduction factor in the uncertainty with
respect to the baseline fit. Figures and details taken from [6]
5. Conclusions
QCD studies have given us decades of discoveries. Many open questions remain on how does
the transition from a small system to a dense system takes place: this information is needed to fully
understand the properties of the QGP. The current document has given a selection of results that may be
better understood and quantified with a new generation of lepton-nucleon experiments at the EIC.
Acknowledgments:
The author thanks the Center for Frontiers on Nuclear Science for funding support which enabled
promoting the topics outlined in this document.
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