Physics Opportunitieswith

e+A Collisionsat an

Electron Ion Collider

e+A White PaperEIC Collaboration

April 4, 2007

DISCLAIMER

This report was prepared as an account of work sponsored by an agency ofthe United States Government. Neither the United States Government nor anyagency thereof, nor any of their employees, not any of their contractors, subcon-tractors, or their employees, makes any warranty, express or implied, or assumesany legal liability or responsibility for the accuracy, completeness, or any thirdparty’s use or the results of such use of any information, apparatus, product, orprocess disclosed, or represents that its use would not infringe privately ownedrights. Reference herein to any specific commercial product, process, or serviceby trade name, trademark, manufacturer, or otherwise, does not necessarily con-stitute or imply its endoresement, recommendation, or favoring by the UnitedStates Government or any agency thereof or its contractors or subcontractors.The views and opinions of authors expressed herein do not necessarily state orreflect those of the United States Government or any agency thereof.

To the incoming virtual photon, the nucleus at very low x appears as a largewall of randomly oriented QCD color charge. The art on the cover is a depic-tion of a photon’s eye view of the nucleus. Original photograph by John Chase:http://www.flickr.com/photos/jahdakinebrah/301327284. Additional manip-ulation by David Morrison and Thomas Ullrich.

The EIC Collaboration*15C. Aidala 8J. Annand, 1J. Arrington, 24R. Averbeck, 3M. Baker, 24K. Boyle 26W. Brooks,26A. Bruell, 17A. Caldwell, 26J.P. Chen, 2R. Choudhury, 9E. Christy, 7B. Cole, 4D. De Flo-rian, 3R. Debbe 24A. Deshpande, 16K.Dow, 24A.Drees, 3J.C. Dunlop, 2D. Dutta, 26R. Ent,16R. Fatemi, 16W. Franklin, 26D. Gaskell, 14G. Garvey, 10M.Grosse-Perdekamp, 1K. Hafidi,16D. Hasell, 3T. Hemmick, 1R. Holt, 7E. Hughes, 20C. Hyde-Wright, 5G. Igo, 12K. Imai,8D. Ireland, 24B. Jacak, 13P. Jacobs, 26M. Jones, 8R. Kaiser, 15D. Kawall, 9C. Keppel, 6E. Kin-ney, 16M. Kohl, 2V. Kumar, 15K. Kumar, 19G. Kyle, 11J. Lajoie, 14M. Leitch, 25J. Lichten-stadt, 8K. Livingstone, 18W. Lorenzon, 13H. Matis, 10N. Makins, 16M. Miller, 16R. Milner,2A. Mohanty, 3D. Morrison, 24Y. Ning, 13G. Odyniec, 11C. Ogilvie, 2 L. Pant, 24V. Pan-tuyev, 19S. Pate, 24P. Paul, 10J.-C. Peng, 16R. Redwine, 1P. Reimer, 13H.-G.Ritter, 8G. Ros-ner, 23A. Sandacz, 6J. Seele, 10R. Seidl, 8B. Seitz, 2P. Shukla, 13E. Sichtermann, 16F. Simon,3P. Sorensen, 3P. Steinberg, 22M. Stratmann, 21M. Strikman, 16B. Surrow, 16E. Tsentalovich,9V. Tvaskis, 3T. Ullrich, 3R. Venugopalan, 3W. Vogelsang, 13H. Wieman, 13N. Xu, 3Z. Xu,7W. Zajc

1Argonne National Laboratory, Argonne, IL2Bhabha Atomic Research Centre, Mumbai, India3Brookhaven National Laboratory, Upton, NY4University of Buenos Aires, Argentina5University of California, Los Angeles, CA6University of Colorado, Boulder,CO7Columbia University, New York, NY8University of Glasgow, Scotland, United Kingdom9Hampton University, Hampton, VA10University of Illinois, Urbana-Champaign, IL11Iowa State University, Ames, IA12University of Kyoto, Japan13Lawrence Berkeley National Laboratory, Berkeley, CA14Los Alamos National Laboratory, Los Alamos, NM15University of Massachusetts, Amherst, MA16MIT, Cambridge, MA17Max Planck Institut fur Physik, Munich, Germany18University of Michigan Ann Arbor, MI19New Mexico State University, Las Cruces, NM20Old Dominion University, Norfolk, VA21Penn State University, PA22RIKEN, Wako, Japan23Soltan Institute for Nuclear Studies, Warsaw, Poland24SUNY, Stony Brook, NY25Tel Aviv University, Israel26Thomas Jefferson National Accelerator Facility, Newport News, VA

*with valuable contributions from: 11Alberto Accardi, Vadim Guzey (Ruhr-UniversitatBochum, Germany), 3Tuomas Lappi, 3Cyrille Marquet, and 11Jianwei Qiu.

Abstract

We outline the compelling physics case for e+A collisions at an Electron Ion Collider (EIC). With its widerange in energy, nuclear beams, high luminosity and clean collider environment, the EIC offers an unprece-dented opportunity for discovery and for the precision study of a novel universal regime of strong gluonfields in Quantum Chromodynamics (QCD). The EIC will measure, in a wide kinematic regime, the mo-mentum and space-time distribution of gluons and sea-quarks in nuclei, the scattering of fast, compactprobes in extended nuclear media and role of color neutral (Pomeron) excitations in scattering off nuclei.These measurements at the EIC will also deepen and corroborate our understanding of the formation andproperties of the strongly interacting Quark Gluon Plasma (QGP) in high energy heavy ion collisions atRHIC and the LHC.

Quantum Chromodynamics (QCD), thetheory of strong interactions, is a corner-stone of the standard model of physics.Approximately 99% of the mass of

baryonic matter in the universe can be attributedto QCD. This mass derives from “emergent phe-nomena” of the QCD vacuum that are not evidentfrom the Lagrangian. These phenomena includechiral symmetry breaking and confinement that arefundamental features of the strong interactions.

Lattice gauge theory and effective field theorieshave taught us that the rich and complex struc-ture of the QCD vacuum arises primarily from thedynamics of gluons with small contributions fromthe quark sea. Experiments probe the QCD vac-uum in a variety of ways. In electron-positron an-nihilation, we observe the response of the vacuumto the deposition of enormous amounts of energyinto minuscule space-time volumes. In hadron spec-troscopy, we observe the way in which configura-tions of quarks and gluons carve out and inhabitbubbles in the vacuum. In relativistic heavy ion col-lisions, we observe the evolution of the vacuum afterfirst heating a macroscopic (� 1 fm ) chunk of it totrillions of degrees Kelvin.

Precision measurements of deep inelastic scatter-ing (DIS) of leptons with hadrons study properties ofthe QCD vacuum that are manifest in the structure ofmatter at resolution scales of less than a femtometer.DIS experiments with nuclei can identify those fea-tures of the short distance structure of matter whichare common to all strongly interacting states. Thekinematic invariants in fully inclusive DIS are theBjorken variable x, the momentum transfer squaredQ2 > 0, the inelasticity y and s, the c.m. energysquared 1. For fixed y, x ∝ Q2/s; thus high ener-gies allow us to probe small values of x. DIS exper-iments of electrons off protons at the HERA colliderat DESY have shown that, for Q2 � Λ2

QCD (whereΛQCD ∼ 200 MeV), the gluon density grows rapidlywith decreasing x. For x < 0.01 the proton wavefunction is predominantly gluonic. DIS experimentswith nuclei have established that quark and gluondistributions in nuclei exhibit shadowing; they aremodified significantly relative to their distributionsin the nucleon wave function. However, in sharpcontrast to the proton, the gluonic structure of nu-clei is not known for x < 0.01. The nature of gluonshadowing is terra incognita in QCD at high energies.

We will discuss in the following how an ElectronIon Collider (EIC) can enhance our understandingof universal features of the dynamics of gluons innuclei.

At large x and at large Q2, the properties of quarksand gluons in the hadron are well described bythe linear evolution equations of perturbative QCD(pQCD). The rapid growth in gluon densities withdecreasing x is understood to follow from a self sim-ilar Bremsstrahlung cascade where harder (large x)parent gluons successively shed softer daughter glu-ons. Gluon saturation is a simple mechanism fornature to tame this growth. When the density ofgluons becomes large, softer gluons can recombineinto harder gluons. The competition between linearQCD Bremsstrahlung and non-linear gluon recom-bination causes the gluon distributions to saturateat small x. The onset of saturation and the prop-erties of the saturated phase are characterized by adynamical scale Q2

s which grows with increasing en-ergy (smaller x) and increasing nuclear size A.

The nucleus is an efficient amplifier of the univer-sal physics of high gluon densities. Simple consider-ations 2 suggest that Q2

s ∝ (A/x)1/3. Therefore DISwith large nuclei probes the same universal physicsas seen in DIS with protons at x’s at least two or-ders of magnitude lower (or equivalently an orderof magnitude larger

√s). Fig. 1 shows the satura-

tion scale for protons and nuclei as a function of x inrelation to the kinematic reach in x and Q2 of EIC.When Q2 � Q2

s , one is in the well understood “lin-ear” regime of QCD. For large nuclei there is a signif-icant window at small x where Q2

s � Q2 � Λ2QCD

and where one is in the domain of strong non-lineargluon fields.

The intensity of the chromo-electric and chromo-magnetic fields in the strong gluon field regime isof order O(1/αS), where the asymptotic freedomof QCD dictates that the fine structure constantαS(Q2

s ) � 1. These fields are therefore the strongestfields in nature! Remarkably, the weak coupling sug-gests that the onset and properties of this regimemay be computed systematically in a QCD frame-work. The high occupation numbers of gluons en-sures that their dynamics is classical and their pilingup at a characteristic momentum scale (QA

s ) is remi-niscent of a Bose–Einstein condensate. Further, kine-matic arguments suggest that the time scales of in-

1. For a brief primer on DIS kinematics, we refer the reader tothe text box on page 4

2. For an expanded discussion, see the text box on page 9.

Physics with an Electron Ion Collider 1

eRHIC e+Au, (20 GeV + 100 GeV/n)

eRHIC e+Au, (10 GeV + 100 GeV/n)

ELIC e+Ca, (7 GeV + 75 GeV/n)

EIC

1=y

Q 2s proton

Q 2s Ca (central)

Q 2s,q Au (central)

×9/4

Q2s,g

10-1

1

10

102

103

104

10-6

10-5

10-4

10-3

10-2

10-1

1

x

Q2

VeG (

2)

Figure 1: Kinematic acceptance in the (Q2, x) plane for the EIC.Shown are lines for two complementary concepts to realize EIC,eRHIC and ELIC (see page 14 for details). Lines showing thequark saturation scale Q2

s for protons, Ca, and Au nuclei aresuperposed on the kinematic acceptance. As indicated, the gluonsaturation scale in Au nuclei is larger by the color factor 9/4.

teractions of gluons are in practice time dilated wellbeyond characteristic time scales for gluon interac-tions. This slowing down is analogous to what hap-pens in spin glasses. These dynamical and kinematicconsiderations have led to a suggestion that the mat-ter in nuclear wave functions at high energies is uni-versal and can be described as a Color Glass Con-densate (CGC) [1, 2]. Alternative candidates for theappropriate degrees of freedom in QCD at high en-ergies include color neutral excitations with vacuumquantum numbers called Pomerons. These come insoft (non-perturbative) or hard (perturbative) vari-eties [3]. A wide range of measurements with EIC,which we shall discuss shortly, can distinguish be-tween predictions in the CGC (or other “unconven-tional” frameworks) and those following from thelinear evolution equations of pQCD.

The nucleus is also a powerful analyzer of physicsacross the full range of x, Q2 and A. In e+A collisionsat high energies, the virtual photon mediating theinteraction splits into a compact qq “dipole” whichscatters off the nuclear medium. The interaction ofthese fast, compact dipoles with an extended gluonmedium provides insight into how partons lose en-ergy, are absorbed, and how hadron formation ismodified in the presence of a colored medium. Vary-

Rg (

x,

Q2 =

5 G

eV

2)

x

LHCR

HIC

HKM

Sarcevic

Armesto

EKS98

Frankfurt

New hijing

10-5 10-4 10-3 10-2

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

Figure 2: Ratios of the Pb over proton gluon PDFs versus xfrom different models at Q2 = 5 GeV2. The RHIC and LHCranges shown cover x = Q/

√s at midrapidity. Figure taken

from [4].

ing x and Q2 enables one to study the transparencyor opacity of the medium relative to the propaga-tion of the dipoles. We will discuss novel features ofthese studies that are made feasible by the EIC.

The physics of universal strong gluon fields aswell as the response of compact probes in inter-actions with the gluonic medium are vital for adeeper understanding of the formation and ther-malization of the strongly interacting Quark GluonPlasma (QGP) currently being studied at RHIC andin the near future at the LHC. The plot shown inFig. 2 illustrates this connection. Extrapolations ofthe gluon distribution in Pb nuclei to x values rel-evant for LHC energies differ by a factor of three.These correspond to an order of magnitude uncer-tainty in the cross-sections for semi-hard final states.As we shall demonstrate, measurements of the nu-clear gluon distribution with EIC can strongly con-strain these cross-sections.

We can study the properties of the gluon domi-nated region in nuclei by performing the measure-ments necessary to address the following questions:

• What is momentum distribution of gluons(and sea quarks) in nuclei?

• What is the space-time distribution of gluons(and sea quarks) in nuclei?

2 Physics with an Electron Ion Collider

• What is the role of color neutral (Pomeron) ex-citations in scattering off nuclei?

• How do fast probes interact with an extendedgluonic medium?

Some of these measurements have analogs in e+pcollisions but have never been performed in nuclei;for these, e+A collisions will allow us to understanduniversal features of the physics of the nucleon andthe physics of nuclei. Other measurements have noanalog in e+p collisions and nuclei provide a com-pletely unique environment to explore these.

In the next section we outline some of the mea-surements that will be made available with an Elec-tron Ion Collider, and starting on page 12 we dis-cuss connections of these with measurements in p+Acollisions. We next discuss the relevance of specificmeasurements for heavy ion collisions. The final twosections sketch, respectively, the accelerator and de-tector concepts under consideration with emphasison e+A physics measurements.

Physics Program Overview

The gluon momentum distribution

The fully inclusive structure functions FA2 and FA

Loffer the most precise determination of quark andgluon distributions in nuclei. (A short discussion ofthese can be found in the text box on page 6.) Theformer is sensitive to the sum of quark and anti-quark momentum distributions in the nucleus; atsmall x, these are the sea quarks. The latter is sen-sitive to the gluon momentum distribution. Scal-ing violations of FA

2 (∂FA2 /∂ ln(Q2) 6= 0) with Q2

are also sensitive to the gluon distribution GA in thenucleus. In Fig. 3 we show projections from pQCDbased models with differing amounts of shadowingand from a saturation (CGC) model for the normal-ized (per nucleon) ratio of F2, in gold nuclei relativeto the deuteron, compared to the statistical precisionexpected for an integrated luminosity 3 of 4/A fb−1

for 10 GeV electrons on 100 GeV/n Au nuclei 4 Fig. 3shows that the quality of the data is sufficient to dis-tinguish differing model predictions. The gluon dis-tribution GA can be extracted from the longitudinalstructure function FA

L which is directly proportionalto the gluon distribution in the framework of pQCD.Independent extraction of FA

2 and FAL requires varia-

tion of the center of mass energy.

0.6

0.8

1

1.2

0.6

0.8

1

1.2

1 10 102

103

x=0.0006 x=0.006

x=0.02 x=0.2

nDS

EKS

FGS

CGC

1 10 102

103

104

EIC (10 GeV + 100 GeV/n), ∫Ldt = 4/A fb-1

F2 A

u/F

2 D

Q2 (GeV2)

Figure 3: The ratio of the structure function FAu2 in Au rela-

tive to the structure function FD2 in the deuteron as a function

of Q2 for several bins in x. The filled circles and error bars cor-respond respectively to the estimated kinematic reach in F2 andthe statistical uncertainties for a luminosity of 4/A fb−1 with theEIC. Here the acronym nDS, EKS and FGS correspond to differ-ent parameterizations of parton distributions at the initial scalefor pQCD evolution. The acronym CGC corresponds to a ColorGlass Condensate model prediction applicable at small x.

In Fig. 5, the normalized (per nucleon) ratio ofgluon distributions, in lead nuclei relative to thedeuteron, extracted from the longitudinal structureis shown for 10/A fb−1 data for DIS on Pb nuclei. Atsmall x, to good approximation, FA

L /FDL ∼ GA/GD.

Existing world data on the gluon structure functionis very sparse. The EIC will extend this kinematicrange by at least an order of magnitude in x and sig-nificantly enhance the precision of our knowledge ofgluon distributions.

We should note that the EIC, with luminosities of100 higher than that achieved at HERA and a widevariability in center of mass energies can increasethe precision of measurements of the gluon distribu-tions even in the proton. This is particularly relevantfor Q2 < 10 GeV2, where there are significant uncer-tainties in the proton gluon distribution.

3. To good approximation the integrated luminosity decreaseslinearly with increasing A. We therefore quote the integrated lu-minosity in units of A where appropriate.

4. There are various notations common in the literature to indi-cate the beam energy per nucleon. We use GeV/n.

Physics with an Electron Ion Collider 3

k

p, M W

q

k′

Figure 4: Kinematic quantities for the description of deep inelastic scattering. The quantities k and k′ are the four-momenta of the incoming and outgoing lepton with mass m, p is the four-momentum of a nucleon with mass M,and W is the mass of the recoiling system X. The exchanged particle is a γ, W±, or Z; it transfers four-momentumq = k− k′ to the nucleon.

High energy lepton-nucleon scattering plays a keyrole in determining the partonic structure of the nu-cleus (and nuclei). The process `(k) + N(p) →`′(k′) + X(p′) is illustrated in Fig. 4. The filled cir-cle in this figure represents the internal structure ofa nucleon (in a nucleus) which can be expressed interms of structure functions.The following variables provide a relativistic-invariant formulation of the unpolarized inelasticelectron-nucleon event kinematics:

s = (k + p)2 = Q2

xy + M2 + m2 ≈ 4E`EN is thesquare of the lepton-nucleon center of mass en-ergy.

x = Q2

2pq = Q2

2Mν in the parton model, is the fractionof the nucleon or nucleus momentum carried bythe struck parton. Note that for e+p 0 ≤ x ≤ 1while for e+A scattering 0 ≤ x ≤ A.

Q2 = −(k− k′)2 = −q2 ≈ 4E` E′` sin2(θ/2) where θis the lepton’s scattering angle with respect tothe lepton beam direction. Q2 is the negativesquare of the momentum transfer q and de-notes the virtuality of the exchanged gauge bo-son. The momentum transfer q determines thesize of the wavelength of the virtual boson andtherefore the object size which can be resolvedin the scattering process. Better resolution re-quires smaller wave lengths of the virtual bo-son and therefore larger momentum transfers.

Q2 can be interpreted as the resolution powerof the scatter. The maximum possible value forQ2 is given by Q2

max = s.

y = q·pk·p = ν

E`is the fraction of the lepton’s energy

lost in the nucleon rest frame. It it thus also thefraction of the incoming electron energy (alsoknown as inelasticity) carried by the exchangeboson in the rest frame of the nucleon. In thiscase, y can also be written as ν/νmax. Note that0 ≤ y ≤ 1.

ν = q·pM = E` − E′` is the lepton’s energy loss in thenucleon rest frame. Here, E` and E′` are the ini-tial and final lepton energies in the nucleon restframe. The maximum energy transfer νmax isgiven by νmax = s/2M which amounts to 4-5 TeV at the highest EIC energies.

W2 = (p + q)2 = p′2 = M2 + 1−xx Q2 is the mass

squared of the system X recoiling against thescattered lepton. W can also be interpreted asthe center-of-mass energy of the gauge bosonnucleon system. Small values of x correspondto large values of the invariant mass W.

The relativistic invariant variables x, y, Q2, and s areconnected through the following relation: Q2 ' sxywhere electron and nucleon masses have been ig-nored.The process in Fig. 4 is called deep (Q2 � M2) in-elastic (W2 � M2) scattering (DIS).

Deep Inelastic Scattering

x

-410-3

10 -210 -110

)2

=5 G

eV

2(x

,QP

bg

R

0.4

0.6

0.8

1

1.2

xGraph

new HIJING

FGS

EKS98 CGC

Armesto

Sarcevic

HKM

nDS (NLO)

⟨Q2⟩→ 1.3 2.4 3.8 5.7 9.5 17 28 41 66 125

Figure 5: The ratio of gluon distributions in Pb nuclei to thosein deuterium extracted from the ratio of the respective longitu-dinal structure functions FL. The filled squares and error barscorrespond respectively to the projected kinematic reach and sta-tistical uncertainties for this measurement (for 10/A fb−1) withthe EIC. A large range of model predictions are shown whichdiffer widely in this kinematic region.

Measurements of the charm structure functionsFC

2 and FCL are sensitive to the photon-gluon fusion

process at high energies and will provide first dataon nuclear charm quark distributions at x < 0.1. Thehigh luminosities of EIC give estimates of 105 charmpairs for 5 fb−1 enabling precision charm studies.In Fig. 6, we show the p⊥, x, pseudo-rapidity ηand Q2 distributions from the pQCD computationsof Ref. [5] for e+p DIS compared to the kinematicrange and integrated luminosities for 20 weeks ofpeak running at HERA and the EIC. The factor 100higher luminosity allows us to test model predic-tions in a much wider kinematic range in e+p col-lisions at the EIC relative to HERA even though thec.m. energies (in e+p) are three times smaller. Charmmeasurements in most of this kinematic range areunavailable in nuclei, so measurements in nucleiof the distributions in Fig. 6 will provide qualita-tively new information of charm quark formationand propagation in nuclei. In the sections beginningon page 10 and also on page 13, we will discuss thephysics that can be learned from heavy quark mea-surements in e+A DIS and the possible implicationsfor heavy quark probes in heavy ion collisions. Wenote that inclusive charm measurements at x > 0.3are sensitive to the intrinsic charm component innuclei which dominates conventional (photon-gluonfusion) charm production mechanisms in this kine-matic region [8].

The photon–gluon fusion process results in semi-

pT(GeV/c)0 1 2 3 4 5 6 7 8 9

/A/d

pT (

nb/G

eV

)σ

d

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

)=3.8%π K→BR(D

log(x)

log(Q2)

-5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0

/A/d

log

(x)

(nb)

σd

0.2

0.4

0.6

0.8

1

1.2

1.4

η-3 -2 -1 0 1 2 3 4

(nb)

η/A

/dσ

d

0.2

0.4

0.6

0.8

1

1.2

1.4

0.5 1 1.5 2 2.5 3

) (n

b)

2/A

/dlo

g(Q

σd

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

HERA ep:

L=50pb-1, √s=297GeV

π K→ Dπ→±*

DEIC eA:L=5/A fb-1, √s=63GeV

Figure 6: Predictions for the distributions of charm mesons as afunction of p⊥, x, pseudo-rapidity η, and Q2 in a pQCD compu-tation [5] compared to the kinematic range and statistical preci-sion at HERA and EIC. The integrated luminosities correspondto 20 weeks of running at peak luminosity at the two collidersrespectively. The errors for HERA shown are consistent withthose published [6, 7]. The dot-dashed lines guide the projecteddivergence of the statistical errors at HERA at the stated inte-grated luminosity.

inclusive final states that are sensitive to the nucleargluon distributions. Noteworthy examples are di-jets channels. In the latter case, the QCD Comptonprocess also contributes. For further discussion inthe context of e+A studies, see Ref. [9].

Measurements of elastic vector meson productione+A −→ (ρ, φ, J/ψ)+A and Deeply Virtual ComptonScattering (DVCS) e+A −→ e+A + γ are extremelysensitive to the momentum distribution of gluons innuclei. The ratio, in a nucleus relative to the nucleon,of the forward cross-section for longitudinally polar-ized photons, is proportional in pQCD to the cor-responding ratio of gluon distributions squared [10].The Q2 dependence changes significantly in the non-linear saturation regime from 1/Q6 to 1/Q2 [11]. Aswe shall discuss further in the next section, mea-surements of exclusive final states are also very im-portant for extracting the space–time distributions ofglue.

Physics with an Electron Ion Collider 5

For Q2 < M2Z, where MZ is the Z boson mass, the cross sections for deep inelastic scattering on unpolarized

nucleons in Born approximation can be written in terms of the structure functions in the generic form:

d2σ

dxdQ2 =4πα2

xQ4

[(1− y +

y2

2

)F2(x, Q2)− y2

2FL(x, Q2)

]The structure function F2 is sensitive to the sum ofquark and anti-quark momentum distribution in thenucleon. The longitudinal structure function FL =F2 − 2xF1 starts to contribute to the cross-section atlarger values of y but is negligible at very small y val-ues. In the parton model, FL = 0, while in QCD, it isdirectly proportional to the gluon structure function,FL(x, Q2) ∝ αSxG(x, Q2), at low x.The double-differential cross-section and thereforethe event rate increases for Q2 → 0 and y → 0. Thekinematic variable y is given by: y ≈ 1− E′`/E`. Thelimit y → 0 is therefore equivalent to E′` → E`. Themeasured energy distribution of the scattered leptonat low Q2 is expected to exhibit a characteristic peakat the lepton beam energy E`.The figure shows the world data on the proton F2 asa function of Q2 for a wide range of fixed values ofx. Knowledge on FL is rather limited since it requiresmeasurements at varying

√s.

Besides the above expression for the differential e+Ncross-section in terms of the structure functions F1and F2 (or F2 and FL), one can interpret the cross-section as the product of a flux of virtual photonsand the total cross-section σ

γ∗Ntot for the scattering

of virtual photons on nucleons. This separation isonly valid if the virtual photon state is coherent overtimes large compared to the time it takes to interactwith the nucleus. The cross-section can now be writ-ten as the sum of the cross-section of transverselyand longitudinally polarized photons.

σγ∗Ntot = σT + σL

σT =4π2α

MKF1

σL =4π2α

K

[(1 +

Q2

4x2M2

)· 2xM

Q2 F2 −1M

F1

]≈ 4π2α

2xMKFL

where K is the flux factor K = ν− Q2/2M. The lastequation motivates why FL is called the longitudinalstructure function. FL is bounded to be in the rangeof 0 ≤ FL ≤ F2. At small values of x the total cross-section can be written as:

σγ∗Ntot ≈ 4π2α

Q2 F2(x, Q2).

The apparent scaling of the data with Q2 at large x inearly DIS data from SLAC was termed “Bjorken scal-ing” and motivated the parton model. Very strongviolations of this scaling, as predicted by pQCD, canbe seen at small x in Fig. 7.

HERA F2

0

1

2

3

4

5

1 10 102

103

104

105

F2

em -l

og

10(x

)

Q2(GeV

2)

ZEUS NLO QCD fit

H1 PDF 2000 fit

H1 94-00

H1 (prel.) 99/00

ZEUS 96/97

BCDMS

E665

NMC

x=6.32 10-5

x=0.000102x=0.000161

x=0.000253

x=0.0004x=0.0005

x=0.000632x=0.0008

x=0.0013

x=0.0021

x=0.0032

x=0.005

x=0.008

x=0.013

x=0.021

x=0.032

x=0.05

x=0.08

x=0.13

x=0.18

x=0.25

x=0.4

x=0.65

Figure 7: World data on the proton structure function F2as a function of Q2 for fixed values of x.

Cross-Sections and Structure Functions

The gluon space-time distribution

Much of our knowledge of the distribution of glu-ons is with regard to their momentum distributions.How is the glue distributed spatially in hadrons andnuclei? In the latter, we would like to know if the“gluon density profile” in the nucleus in the trans-verse impact parameter plane is one of small clumpsof glue or if its more uniform in impact parameter.The nature of the spatial distribution of glue pro-vides a unique handle on the physics of high partondensities and has important ramifications for a widerange of final states in hadronic and nuclear colli-sions.

How do we extract information about the spatialdistribution of glue? The physics of DIS at small xcan be simply visualized in a frame where the vir-tual photon fluctuates into a quark anti-quark dipolethat subsequently scatters coherently on the hadronor nucleus. Combined use of the predictions of thisdipole picture for a) total cross-sections and b) thedifferential cross-section for the production of vec-tor mesons, enables one to estimate the differentialcross-section for the dipole to scatter elastically. TheFourier transform of the vector meson cross-section,as a function of the momentum transfer t along theproton line, allows one to estimate the scattering ma-trix for this amplitude. The optical theorem is thenemployed to extract the survival probability of smallsized dipoles of size d � 1 fm to propagate throughthe target at a given impact parameter b without in-teracting.

In pQCD, the survival probability of small sizeddipoles is close to 1. This pQCD prediction shouldbe contrasted with the survival probability in Fig. 8extracted from dipole models. The Munier et al. [12]curves correspond to results from the elastic produc-tion of ρ0 mesons. HERA data for this process arelimited and the curves result from differing extrap-olations to large t or small impact parameters. TheRogers et al. [13] curve uses data on elastic J/ψ pro-duction allowing reliable extrapolation to lower im-pact parameters; the agreement at large b of thesemodels is within 5%. At b = 0, the survival prob-ability of dipoles can be as low as 20% suggestingvery strong gluon fields localized at the center ofthe proton. A systematic dilution of the interac-tion strength (color transparency) is seen for largerb. Similar analyses for large nuclei give the survivalprobability of small sized (d = 0.3 fm) dipoles from60% at x = 10−2 to as low as 10% at x = 10−3.

Estimates of the quark saturation scale [14, 15]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

b (fm)

0

0.2

0.4

0.6

0.8

1

1.2

exp( − λ t) S. Munier et. al.

(1 / t3 ) S. Munier et. al

(1 / t6 ) S. Munier et. al.

Rogers et. al.

(1 -

Γ)2

x = 5.8 10-4, d = 0.32 fm

color opacity color transparency

Figure 8: The survival probability (1− Γ)2 of vector mesonsas a function of impact parameter b, extracted from HERA dataon elastic vector meson production on the proton. The Munieret al. curves are results extracted from data on ρ0 production ina limited region of momentum transfer t in the proton direction(see text). The Rogers et al. curve is for results extracted fromJ/ψ production.

extracted from the survival probability fit to dataare shown in the left panel of Fig. 9. Results areshown for two saturation model parameterizations.In the right panel, the distribution of impact pa-rameters contributing to the dipole cross-section isshown. The cross-section is dominated by medianb ∼ 0.4 fm, corresponding to rather small values ofthe saturation scale. Therefore saturation effects aredifficult to isolate for many processes in DIS off pro-tons at present energies.

In contrast, the b profile of nuclei is much moreuniform. The A dependence of the saturation scalecan be determined by convoluting the gluon im-pact parameter profile in the proton with the nu-clear density profile to fit the available inclusive nu-clear (structure function) data from fixed target ex-periments. As shown in Fig. 1, there is a significantenhancement in the saturation scale at b = 0 in thenucleus 5 relative to that in the proton for the medianb = 0.4 fm. A saturation model fit of HERA andNMC inclusive data to determine the A-dependencein large nuclei relative to light nuclei gives a nuclearenhancement of A0.38 [16] which is approximately10% larger than the back of the envelope estimateof A1/3. (See the text box on page 9 for further dis-cussion.) First measurements of elastic vector mesonfinal states at small x in nuclei will provide sensitivetests of the A-dependence of the saturation scale.

5. In large nuclei, the saturation scale for the “median” b valueis close to the value at b = 0. The situation is very different in theproton as evident from Fig. 9.

Physics with an Electron Ion Collider 7

b-Satb-CGC

1/x

QS 2 (

GeV

2)

10-1

1

102

103

104

105

106

b = 0 fm

0.2 fm

0.4 fm

0 0.2

1.75

1.5

1.25

1

0.75

0.5

0.25

00.4 0.6 0.8 1.41.21.0 1.6

b (fm)

Q2 = 0.4 GeV2

Q2 = 4 GeV2

Q2 = 40 GeV2

1/σ

γp d

σγp/d

b (

fm-1

)

Figure 9: Left: The b-dependent saturation scale in the proton as a function of 1/x extracted from two saturation model fits to theHERA data [14, 15]. Right: The dipole scattering cross-section off the nucleon is dominated by large b’s.

Deeply Virtual Compton Scattering (DVCS) onnuclear targets (e + A → e + A + γ) provides de-tailed information on the distribution and correla-tion of partons in nuclei (a 3D picture). Extract-ing information on DVCS is difficult because it in-terferes with the electromagnetic Bethe-Heitler pro-cess. However, in the 10 GeV+100 GeV/n EIC kine-matics, DVCS dominates Bethe-Heitler for a widerange of nuclei (from 40Ca to 208Pb); for example,for Q2 = 3 GeV2 and x ≥ 0.02. This choice ofkinematics allows clean studies of the nuclear DVCSamplitude (mostly its imaginary part) in the inter-esting transition region from nuclear shadowing toanti-shadowing. The integrated DVCS cross sectionis expected to increase as A4/3 (see below). Anotherpossibility would be to study the imaginary and realparts of the nuclear DVCS amplitude via the beam-spin and beam-charge (azimuthal) asymmetries, re-spectively, in the kinematics, when Q2 is a few GeV2

and 0.001 < x < 0.1. The former does not have asignificant x or A-dependence while the latter is ex-pected to have very rapid x-dependence and a sig-nificant A-dependence [17–20].

Coherent (nucleus stays intact) and incoherent(nucleus excites or breaks up) contributions are bothimportant in nuclear DVCS [21]. The coherent con-tribution is concentrated at small t and dies rapidlyaway as FA(t)2 (FA(t) is the nuclear form factor);the incoherent cross section is proportional to FN(t)(FN (t) is the nucleon e.m. form factor) and domi-nates at large t. The coherent DVCS cross section

in nuclei is proportional to the square of the off-forward gluon distribution per unit area. In the limitof Color Transparency (CT), this gives A2/3 timesa factor of A2/3 from the area resulting in an A-dependence for coherent DVCS of A4/3. In the ,Color Opacity (CO) limit, one gets a factor A2/3 lessfrom the area; the coherent DVCS cross-section inthis case goes as A2/3. Incoherent DVCS, in contrastto coherent DVCS, is proportional to the gluon dis-tribution per unit area, not its square. In the CT limit,multiplying with the area factor results in a linear Adependence for incoherent DVCS. In the CO limit,one again gets a factor A2/3 less thus changing theA-dependence of incoherent DVCS to A1/3.

Color neutral (Pomeron) excitations

Diffractive interactions result when the electronprobe in DIS interacts with a color neutral vacuumexcitation. This vacuum excitation, which in QCDmay be visualized as colorless combination of two ormore gluons, is often called the Pomeron. At HERA,an unexpected discovery was that 15% of the e+pcross-section is from diffractive final states. This isa striking result implying that a proton at rest re-mains intact one seventh of the time when struck bya 25 TeV electron. The effect is even more dramaticin nuclei. Several models of strong gluon fields innuclei suggest that large nuclei are intact ∼ 40% ofthe time, nearly saturating the quantum mechanicalblack disk bound of 50%.

8 Physics with an Electron Ion Collider

75

0.38

100

0.36

125

0.34

150

0.32

175 200

A

d lnQ

2 sA

/ d

lnA

1/x

QS 2 (

GeV

2)

1

0.1

10

102

103

104

105

106

Q2s,q

×9/4

Q2s,g

Ca (cen

tral)Au

(cen

tral)

proto

ns

Figure 10: Left: The A dependence of the saturation scale from the analysis of Ref. [16]. Right: The saturation scaleat b = 0 in Au and Ca nuclei compared to the median saturation scale in a proton [15].

From the uncertainity principle, the interaction ofan external QCD probe with a nuclear target ofatomic number A develops over longitudinal dis-tances l ∼ 1/2mN x , where mN is the nucleon mass.When l becomes larger than the nuclear diameter(∼ A1/3), or equivalently when x � A−1/3, theprobe cannot distinguish between nucleons locatedon the front and back edges of the nucleus. All par-tons within a transverse area 1/Q2, determined bythe momentum transfer Q across the target, partici-pate in the interaction coherently. A probe of trans-verse resolution 1/Q2 � 1/Λ2

QCD ∼ 1 fm2 will ex-perience large fluctuations of color charge propor-tional to the longitudinal extent of the nucleus alongits path. The corresponding “kick” to the probein a random walk through the nucleus is the satu-ration scale; one therefore expects (QA

s )2 ∝ A1/3.The saturation scale also grows because the num-ber of gluons in each nucleon along the probe’s pathlength increases with energy: a fit to HERA databased on the Golec-Biernat–Wusthoff (GBW) satura-tion model [22] gives (Qp

s )2 = Q20x−δ, where δ ≈ 0.3

and Q20 is a non-perturbative scale in the proton. A

simple pocket formula therefore to compare the sat-uration scale in heavy nuclei relative to the protonand in large nuclei relative to light nuclei is

(QAs )2 ≈ c Q2

0

(Ax

)1/3, (1)

where c is a dimensionless constant. An analysis us-ing the x-dependence of the GBW model and fits toNMC nuclear data also predicts the A-dependenceof the saturation scale [16]. The result is shown in

the left panel of Fig. 10. The power is shown to be≈ 10% larger than 1/3 in Eq. 1; the coefficient is es-timated to be c ≈ 0.5 for large nuclei.A more detailed analysis (going beyond the frame-work of the GBW model) of the x and A dependenceof the saturation scale was performed by Kowalskiand Teaney [15]. They extracted the b and x de-pendence of the saturation scale in the proton fromfits to the diffractive and exclusive HERA data-seeFig. 9 in text. This b-dependent profile in the nucleonwas then used to construct (using Glauber MonteCarlo methods) the b dependent quark saturationscale QA

s (x, b) in nuclei. Inclusive cross-sections innuclei are simply related to this saturation scale andKowalski and Teaney verified this result is consis-tent with NMC DIS data on nuclei. The quark satu-ration scale squared in Au and Ca nuclei relative tothe proton is shown in the right panel of Fig. 10; thegluon saturation scale squared is larger by a colorfactor of 9/4.The nuclear profile of large nuclei is nearly constantout to large b; that of the proton falls sharply. Themedian b for a proton is shown in the right panel ofFig. 9. As inclusive scattering is dominated by themedian impact parameter, it is therefore appropriateto compare the saturation scales in the center of thenucleus to the median b in the proton, as shown inFig. 10. The “oomph” factor of large nuclei is seento be quite significant. Measurements extracting thex, b and A dependence of the saturation scale pro-vide very useful information on the momentum andspace-time distribution of strong color fields in QCDat high energies [23].

Nuclear “Oomph” Factor

In Fig. 11, we show results from a dipole modelprediction of diffractive effects in nuclei [24]. Themodel 6 includes the effects of linear small x evolu-tion for small dipoles (d < 1/Qs) and saturation ef-fects for larger sized dipoles (d > 1/Qs). The lattercan be turned off in the model and the curves (rightpanel) correspond to results with and without satu-ration effects. In the left panel, we see that the ratioof the diffractive to total structure function is largeand grows by about 30% from light to heavy nuclei.Very significantly, even though the nuclei are intact,the diffractively produced final states are semi-hardwith momenta ∼ (QA

s )2. They are therefore harderwith increasing nuclear size. In the right panel, thenormalized ratio of diffractive structure functions inheavy nuclei relative to light nuclei is shown as afunction 7 of the fraction of the nuclear momentumcarried by a Pomeron (xP) and as a function of β de-fined as β = x/xP.

Saturation/strong gluon field models predict aweak x dependence and a strong Q2 dependence ofthese ratios. They should be clearly distinguishablefrom non–perturbative (“soft” Pomeron) models ofdiffractive scattering [25]. In the pQCD framework,factorization theorems exist for diffractive DIS; asin inclusive DIS, diffractive parton distributions areintroduced at an initial hard scale and are evolvedto harder scales with the DGLAP equations. Aswe will discuss later, these factorization theoremsfor diffractive PDFs do not extend to hadronic colli-sions, indicating the breakdown of factorization the-orems for diffractive processes.

Model results suggest that multi-gluon correla-tions are enhanced in large nuclei. Can these be de-scribed in terms of universal quasi-particle degreesof freedom? Measurements of coherent diffractivescattering on nuclei are easier in the collider envi-ronment of EIC relative to fixed target experiments.These will provide definitive tests of strong gluonfield dynamics in QCD. Preliminary studies indicatethat such measurements are not statistics limited.

Diffractive measurements will be strongly system-atics limited so simple qualitative model predictionssuch as those discussed here can be substantiallyaffected when combined with the available accep-tance for such measurements. Realistic simulationsof diffractive final states are required to confirm thatthe qualitative differences between models can bedistinguished with the acceptance of EIC.

Hadronization and energy loss

In Deep Inelastic Scattering on nuclear targets (nDIS)one observes a suppression of hadron production[26–30] analogous to but weaker than the quench-ing in the inclusive hadron spectrum observed inheavy-ion collision at the Relativistic Heavy-IonCollider (RHIC) [31]. The cleanest environment toaddress nuclear modifications of hadron productionis nuclear DIS. It allows one to experimentally con-trol many kinematic variables; the nucleons act asfemtometer-scale detectors allowing one to experi-mentally study the propagation of a parton in this“cold nuclear matter” and its space-time evolutioninto the observed hadron. (See left panel of Fig. 12.)

Experimental data on hadron production in nDISare usually presented in terms of the ratio[27–30] ofthe single hadron multiplicity per DIS event on a tar-get of mass number A normalized to the multiplic-ity on a deuterium target. This ratio can be stud-ied as a function of the virtual photon energy ν, thevirtuality Q2, the hadron transverse momentum p⊥,and zh = p · ph/p · q. (p is the target 4-momentumdivided by A, ph the hadron 4-momentum and qthe virtual photon 4-momentum.) In the target restframe zh = Eh/ν is the fractional energy carried bya hadron with respect to the virtual photon energy.See Fig. 12 right.

The basic question to be answered is on whattime scale the color of the struck quark is neutral-ized, acquiring a large inelastic cross-section for in-teraction with the medium. 8 Energy loss mod-els [33–35] assume long color neutralization times,with “pre-hadron” formation outside the mediumand parton energy loss as the primary mechanismfor hadron suppression. Absorption models [32, 36–38] assume short color neutralization times with in-medium “pre-hadron” formation and absorption asthe primary mechanism. There are indications forshort formation times from HERMES data [28] andJLAB preliminary data [30]. As shown in the rightpanel of Fig. 12 however, more data for a wider en-ergy range is needed to clearly distinguish between

6. The model does not include impact parameter dependenceof the saturation scale in nuclei which can be expected to modifythe results. However, because we consider ratios, the qualitativefeatures illustrating the difference between linear and non-linearevolution will likely be robust.

7. See text box on page 15 for a brief primer on diffractive vari-ables.

8. Measurements of hadronic final states in nuclei will also al-low one to quantify the relative contribution of nuclear valenceand sea quark distributions.

10 Physics with an Electron Ion Collider

10-5

10-4

10-3

10-2

0

0.1

0.2

0.3

0.4

0.5

σdiff/σ

tot

x

A = 12

A = 40

A = 197

Q2 = 1

black disk bound

0 0.2 0.4 0.6 0.8β

0.1

0.15

0.2

0.25

0.3

xlP

= 0.0042Q

2 = 1

Au (linear evolution)

Au (saturation model)

Kugeratski, Goncalves, and Navarra, Eur.Phys.J. C46 (2006) 413

10-5

10-4

10-3

10-2

10-1

xlP

0.1

0.15

0.2

Rdi

ffA

u,D

(Q2 ,β

, xlP

) β = 0.062

Q = 1

Au (linear evolution)

Au (saturation model)

1.00

1.05

EIC (10 GeV + 100 GeV/n)∫Ldt = 5/A1 fb

-1 and 5/A2 fb-1

Figure 11: Left: A saturation model prediction [24] for the ratio of diffractive to total cross-sections as a function of x for fixed Q2

and several A. Right: The normalized ratio of diffractive structure functions in Au to deuterium nuclei is shown as a function ofthe variables xP and β at fixed Q2; the curves contrast model predictions of linear and non-linear QCD evolution effects. See textfor details. The statistical uncertainties are negligible relative to model predictions for EIC luminosities.

0.2 0.4 0.6

0.6

0.8

0.8

1

1

Zh

RMπ+

He

Ne

Kr

π+

HERMES

Kr final

He, Ne prelim.

absorption

energy loss

Figure 12: Left: In e+A collisions the hadronizing quark travels through the target nucleus. Center: In A+A collisions thehadronizing parton travels through the produced hot medium. Right: Ratio of π+ multiplicity in He, Ne and Kr to that indeuterium as measured by HERMES [28] and as compared to absorption model computations (solid) [32], and energy loss modelcomputations (dashed) [33].

the models. At the EIC, the range of photon ener-gies would be 10 GeV < ν < 1600 GeV compared toHERMES (2–25 GeV). It therefore offers more chan-nels to study hadronization inside and outside of thenucleus and reaches into a region relevant for theLHC.

Further progress requires an increase in the sta-tistical significance of the data to allow multi-differential measurements in all kinematic variables.

A novel feature of these studies at the EIC wouldbe measurements providing insight into the energyloss and hadronization of heavy quarks to formcharm and bottom mesons. Important measurementsalso include the study of baryon number transportin nuclei, nuclear modification of hadron p⊥ spec-tra and dihadron correlations to test and constrainhadronization mechanisms. All of these measure-ments (as we shall discuss in section 4) have analo-

Physics with an Electron Ion Collider 11

gous measurements in heavy ion collisions. One cantherefore in principle isolate hadronization effects inthe “cold” vacuum from how hadronization is mod-ified in a hot, excited vacuum.

The high luminosities of the EIC will allow ac-cess to rare signals and double differential measure-ments. Its high energies include and exceed mostfixed target facilities to date and its excellent lowx coverage provides increased production of heavyflavor (see section 2.2) and quarkonia. Finally, thecollider kinematics and associated detectors with ex-cellent hadron detection will allow for a comprehen-sive program to better understand how energy lossand hadronization occur in cold nuclear matter.

Connection to p+A Physics

Both p+A and e+A collisions can provide excellentinformation on the properties of gluons in the nu-clear wave functions because it is unlikely that a hotdense hadronic medium would be produced at cur-rently available p+A collision energies.

Deeply inelastic e+A collisions are dominated byone photon exchange; they have a better chance topreserve the properties of partons in the nuclearwave functions because there is no direct color in-teraction between e and A. The photon could inter-act with one parton to probe parton distributions, aswell as multiple partons coherently to probe multi-parton quantum correlations [39].

Many observables in p+A collisions require gluonsto contribute at the leading order in partonic scat-tering. Thus p+A collisions provide more direct in-formation on the response of a nuclear medium toa gluon probe. However, soft color interactions be-tween p and A before the hard collision takes placehas the potential to alter the nuclear wave functionand destroy the universality of parton properties[40]. Such soft interactions contribute to physical ob-servables as a correction at order 1/Q4 or higher [41–43]. These power corrections cannot be expressed interms of universal parton properties in the nuclearwave functions thereby breaking QCD factorization.

The breakdown of factorization has already beenobserved in comparisons of diffractive final statesin e+p collisions at HERA and p+p collisions at theTevatron. At HERA, diffractive parton distributionfunctions are extracted from fits to diffractive cross-section data; these diffractive pdf’s, used as input ina factorized approach to compute diffractive di-jetdata at the Tevatron, overestimate the cross-section

by at least an order of magnitude. This result canbe seen in Fig. 13. One can therefore expect diffractivemeasurements in e+A collisions at EIC to be qualitativelydifferent from those in p+A diffractive final states at theLHC.

0.1 1

0.1

1

10

100

CDF data

ET

Jet1,2> 7 GeV

0.035 < ξ < 0.095

| t | < 1.0 GeV2

H1 fit-2

H1 fit-3

( Q2= 75 GeV

2 )

β

F∼D JJ (

β)

H1 2002 σrD QCD Fit (prel.)

Figure 13: Diffractive di-jet data in p+p collisions at the Teva-tron (data points in yellow band) compared to curves show-ing predictions from fits to e+p diffractive structure functiondata [44]. The discrepancy between theory and experimentdemonstrates strong breaking of factorization for diffractive fi-nal states.

Due to the very large reach in x and M2, p+A colli-sions at the LHC have significant discovery potentialfor the physics of strong color fields in QCD. How-ever, due to uncertainties relating to convolutionsover parton distributions in the proton probe, finalstate fragmentation effects and factorization break-ing contributions, the results can be cleanly inter-preted only for M2 � Q2

s where the strong fieldeffects will be weaker. 9 As discussed previously(see Fig. 1 and related text), saturation effects inthe strong field regime of Q2

s > Q2 will be acces-sible in e+A collisions. Genuine discovery of thephysics of this novel regime will require comple-mentary hadronic and leptonic probes.

9. Similar considerations will also complicate extraction of lead-ing twist gluon distributions in nuclei.

12 Physics with an Electron Ion Collider

Connections to RHIC and LHC

Measurements over the last six years in heavy ioncollision experiments at RHIC indicate the formationof a strongly coupled plasma of quarks and gluons(sQGP). Striking results include the strong collectiveflow of all mesons and baryons (of particular note isthe strong flow even of heavy charm quarks) and theopaqueness of the hot and dense medium to hadronjets up to p⊥ ∼ 20 GeV. This sQGP behaves like a“near-perfect fluid” with a ratio of shear viscosity toentropy approaching zero [31, 45]. To fully exploreand quantify the properties of this system, upgradesof the collider and detectors at RHIC are planned.p+p p+A and A+A experiments at the LHC will pro-vide substantially higher energies.

While evidence of collective behavior is com-pelling, there is still no quantitative framework tounderstand all the stages in the expansion of the hotand dense matter. We outline here how EIC can con-tribute to a better understanding of the dynamics ofheavy ion collision-from the initial formation of par-tonic matter in bulk to jet quenching and hadroniza-tion that probe the properties of the sQGP.

Initial Conditions for the sQGP Understandingthe dynamical mechanisms that lead to rapid equi-libration in heavy ion collisions is perhaps the ma-jor outstanding issue of the RHIC program. Hydro-dynamic modeling of RHIC data suggests that thesystem achieves nearly complete thermalization nolater than 1 fm/c after the initial impact of the twonuclei. These hydrodynamic models are very sen-sitive to the initial pre-equilibrium properties of thematter (often called “Glasma”) formed immediatelyafter the collision of the two nuclei. The proper-ties of these nuclear wave functions will be stud-ied in great detail in e+A collisions. They thereforepromise a better understanding of the initial stateand its evolution into the sQGP. Specifically, the sat-uration scale Qs, which can be independently ex-tracted in e+A collisions, sets the scale for the for-mation and thermalization of strong gluon fieldsfrom the CGC wave functions [46–49]. Beyond es-tablishing the multiplicity and initial energy den-sity, these gluon fields may contribute to instability-driven thermalization [50]. To extract the param-eters of the system’s evolution, the initial state ofthe system before hydrodynamic evolution must beknown precisely: saturation effects may have a largeimpact on extracted hydrodynamic parameters[51].

Experiments at the EIC are crucial for the precise de-termination of the properties of the system at RHIC.

Energy Loss and Hadronization in Hot MatterThe use of hard probes to study the properties of hotmatter in heavy ion collisions is moving into the pre-cision stage with high luminosities at RHIC and highenergies at the LHC. The strong suppression of highpT hadrons observed in RHIC collisions has a natu-ral interpretation in terms of partonic energy loss viainduced gluon radiation in the high-density matter.The initial parton distributions (which determine theincoming flux) play a crucial role in quantitativelyextracting the amount of energy lost. These distri-butions are strongly modified in nuclei, with shad-owing and saturation at low x and the EMC effectat moderate x. To calibrate the nuclear parton dis-tributions, GA(x, Q2) must be well constrained forx ≥ 10−2 at RHIC, and x ≥ 10−4 at the LHC forQ2 ∼1–10 GeV2. Fig. 2 shows that the current uncer-tainties, especially at the LHC, are large, leading todifferences in the final transverse energy flow by fac-tors of 2–4 and an order of magnitude uncertainty insemi–hard cross-sections[4]. At the same time, RHICdata on π0 production in deuteron-gold collisions athigh p⊥ and on photon production in A+A collisionsat high p⊥ suggest non-trivial modifications of par-ton distributions at x > 0.1. Precision measurementsin the kinematic regime relevant to the RHIC mea-surements are essential for using hard probes to di-agnose the active degrees of freedom of the sQGP.

While the RHIC data is broadly explained by theattenuation of quarks and gluons in a hot medium,quantitative studies require that the role of the coldnuclear medium on partons and hadrons be wellunderstood. HERMES DIS data confirm that theenergy loss and pT-broadening of formed hadronsproduced in e+A collisions are small, but the lumi-nosity at HERMES is too low to study the attenu-ation of charm or bottom quarks. In hot matter atRHIC, the surprisingly large energy loss of heavypartons poses major challenges to theory [52]; con-jectures about the role of collisional energy loss andpre–hadron absorption in the attenuation of heavyquarks can be tested, for the first time, in cold mat-ter with EIC. Further, the wide range of photon en-ergies at an Electron Ion Collider 10 GeV < ν <1600 GeV compared to HERMES (2–25 GeV) offersmore channels to study hadronization inside andoutside of the nucleus and to test the factorization(e+A/p+A/e+p/p+p) of the fragmentation of par-

Physics with an Electron Ion Collider 13

tons into hadrons, especially with processes involv-ing heavy quarks. The wide photon energy avail-able at the EIC is especially relevant as a cold matterbenchmark for final states in A+A collisions at theLHC, where the typical energies of jets will be wellabove the maximal values available at HERMES.

Saturation Effects in the Forward Region atRHIC and at Midrapidity at LHC Yields of moder-ate pT particles (2–4 GeV) in the forward region (η ≈3.2) of d+Au collisions at RHIC show a systematicsuppression as the deuteron passes through thickerregions of the Au nucleus, as shown in Fig. 14.These particles correspond to partons of very lowx ≈ O(10−3 − 10−4), suggestive of the relevanceof saturation effects, especially with the large val-ues of (Q2

s ≈2.5–5 GeV2) in this region. These val-ues are comparable to those at mid-rapidity at theLHC. The theory curves shown correspond to dif-ferent model assumptions. In the forward region atthe LHC (y = 3), one expects saturation momentaof order Q2

s = 10 GeV2. The establishment of satu-ration effects via measurements of GA(x, Q2) at theEIC will be vital to interpret measurements in theforward region at RHIC and at all rapidities at theLHC.

)c (GeV/T

p0 1 2 3 4 5

dAu

R

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

BRAHMS data

pQCD+shadow [Guzey et al.]

pQCD+shadow [Accardi]

CGC [Tuchin et al.], no isospin corr.

CGC [Jalilian-Marian], no isospin corr.

d+Au → h−+X, √sNN = 200 GeV, η = 3.2

Figure 14: Nuclear modification factor RdAu, which is the ra-tio between differential yield in d+Au collisions and differentialcross-section in p+p collisions, scaled by the number of binarycollisions, for negative charged hadrons at forward pseudorapid-ity.

Collider Concepts

The requirements for an e+A collider are driven bythe need to access the relevant region in x and Q2

that will allow us to explore saturation phenomenain great detail. This region is defined by our cur-rent understanding of Qs(x, Q2) depicted in Fig. 1. Amachine that would reach sufficiently large Q ≈ Qsvalues in e+p collision would require energies thatare beyond current budget constraints. However,as pointed out in the text box on page 9, at fixedx, Qs scales approximately with A1/3. Ions withlarge masses thus allows us to reach into the satura-tion regime at sufficiently large Q values, which willensure the validity of perturbative calculations. Tofully explore the physics capabilities in e+A, doubledifferential measurements at varying

√s are manda-

tory. This can be only achieved if the providedbeams have large luminosities.

With these considerations, one can define the fol-lowing requirements for an e+A collider:

• The machine needs to provide collisions of atleast

√s > 60 GeV to go well beyond the range

explored in past fixed target experiments. Thehigher the energy, the longer the lever-arm inQ2 and the greater the low-x reach.

• The machine must be able to provide ion beamsat different energies. Measurements at various√

s are mandatory for the study of many rel-evant distributions such as FL. Note that it iskinematically better for any experimental setupto lower the ion beam energy then the electronenergy.

• The machine must provide a wide range of ions.For saturation physics studies beams of veryhigh mass numbers (A ≥ Au) are vital.

• To collect sufficient statistics luminosities withL > 1030 cm−2s−1 are required.

Since the 2001 Long Range Plan, there has beensignificant progress in the design of EIC acceleratorconcepts. There are two complementary conceptsto realize EIC: (i) eRHIC, to construct an electronbeam (either ring or linac) to collide with the exist-ing RHIC ion complex and (ii) ELIC, to construct anion complex to collide with the upgraded CEBAF ac-celerator.

In the next two sections we describe the currentdesign of both concepts.

14 Physics with an Electron Ion Collider

k

p, M

MX

q

gap

k′

p′

Figure 15: Kinematic quantities for the descriptionof diffractive event.

Diffractive scattering, or Pomeron physics, has made aspectacular comeback with the observation of an unex-pectedly large cross-section for diffractive events at theHERA e+p collider. At HERA, hard diffractive events,`(k) + N(p) → `′(k′) + N(p′) + X, were observed wherethe proton remained intact and the virtual photon frag-mented into a hard final state producing a large rapiditygap between the projectile and target devoid of particles.These events are indicative of a color singlet exchange inthe t-channel between the virtual photon and the pro-ton over several units in rapidity. This color singlet ex-change has historically been called the Pomeron wherethe Pomeron had a specific interpretation in Regge the-ory. Here we will use it to denote the kinematics of thecolor singlet exchange without specifying the dynamics.An illustration of the hard diffractive event is shown inFig. 15.The kinematic variables are similar to those for DIS withthe following additions:

t = (p− p′)2 is the square of the momentum transfer at the hadronic vertex.

M2X = (p− p′ + k− k′)2 is the diffractive mass of the final state,

β = Q2

M2x−t+Q2 is the momentum fraction of the struck parton with respect to the Pomeron, and

xP = x/β is the momentum fraction of the Pomeron with respect to the hadron.

In pQCD, the probability of a rapidity gap is exponentially suppressed as a function of the gap size ∆η ≈ln(1/xP). At HERA though, gaps of several units in rapidity are relatively unsuppressed; one finds thatroughly 15% of the cross-section corresponds to hard diffractive events with invariant masses MX > 3 GeV.The remarkable nature of this result is transparent in the proton rest frame: a 25 TeV electron slams intothe proton and ≈ 15% of the time, the proton is unaffected, even though the interaction causes the virtualphoton to fragment into a hard final state. The interesting question in diffraction is the nature of the colorsinglet object (the “Pomeron”) within the proton that interacts with the virtual photon. This interactionprobes, in a novel fashion, the nature of confining interactions within hadrons.The cross-section can be formulated analogously to inclusive DIS by defining the diffractive structure func-tions FD

2 and FDL as

d4σ

dxdQ2dβdt=

4πα2

β2Q4

[(1− y +

y2

2

)FD,4

2 (x, Q2, β, t)− y2

2FD,4

L (x, Q2, β, t)]

In practice, detector specifics may limit measurements of diffractive events to those where the outgoinghadron is not tagged (without determining t) requiring instead a large rapidity gap in the detector. Thecross-section, formulated in terms of the structure function FD,3, measures a larger cross-section than ex-pected from simple integration, FD,3 >

∫FD,4dt because events are included where the outgoing hadron

has broken up. The EIC will require careful instrumentation of forward detectors to detect intact nuclei andmeasure the t-dependence of diffractive events.

Diffractive Deep Inelastic Scattering

eRHIC

Two accelerator design options for eRHIC were de-veloped in parallel and presented in detail in the2004 Zeroth-Order Design Report[53]. At present,the most promising design option is based on theaddition of a superconducting energy recovery linac(ERL) to the existing RHIC ion machine. The linacwill provide the electron beam for the collisionswith ions or protons, circulating in one of the RHICrings. The general layout of the machine is shown inFig. 16.

PHENIX

STAR

e-cooling

Four e-beam passes e

+ storage ring

5 GeV 1/4 RHIC circumference

Main ERL (3.9 GeV per pass)

Low energy e-beam pass

Figure 16: Design layout of the eRHIC collider based on theEnergy Recovery Linac.

The main features of the electron machine include:

• The electron beam passes the main ERL fivetimes during the acceleration, with the maxi-mum energy gain per pass of 3.9 GeV. The finalelectron beam energy range is from 3 to 20 GeV.

• After collisions the electron beam is deceleratedin the same linac. The energy recovered fromthe beam is used for the acceleration of subse-quent electron bunches.

• The electron beam is produced by a polarizedelectron source and has 80% polarization de-gree. If needed, an unpolarized electron sourcecan be used providing higher electron beam in-tensity.

• To provide a positron beam, a conversion sys-tem for the positron production may be addedand a compact storage ring, at one quarter of theRHIC circumference, may be built for positronaccumulation, storage and self-polarization.

• As many as four electron-ion interaction pointsare possible.

Another configuration is being studied (notshown) in which the whole electron ERL is locatedinside the RHIC tunnel. The advantage of this con-figuration is the reduced cost of the conventionalconstruction. Table 1 shows the beam parametersand luminosities for e+Au collisions for highest andlowest energy setups. The luminosity integral perweek is based on the average luminosity since ittakes into account the luminosity deterioration dur-ing the course of the store and the time spent be-tween stores. Due to those factors the expected av-erage luminosity is a factor three smaller than thepeak luminosity. The luminosity is proportional tothe energy of ions and does not depend on the en-ergy of electrons. R&D for the high current polarizedelectron source is needed to achieve the design lumi-nosities in the ERL-based option. This R&D is not re-quired for unpolarized electron beam. Another op-tion of the eRHIC accelerator design under consid-eration is based on the addition of an electron stor-age ring instead of the linac. A pair of recirculat-ing linacs of 2 GeV each provide polarized electronsor unpolarized positrons of 5 to 10 GeV which arestacked into a storage ring up to currents of 0.5–1 A.The positrons get polarized during the storage. Thestorage ring has one-third of the circumference ofRHIC and a race-track shape with two long straightsections, one of which intersects the RHIC ring atsingle interaction point. The storage ring design ismore mature than the ERL- based design but theachievable luminosity has additional limitations dueto the deterioration of electron beam quality in thebeam-beam interactions and the interaction regiondesign issues. The design luminosities of e+Au colli-sion for the e-ring based design is 5–10 times smaller,depending on the energy setup, than for the ERL-based design. Some upgrades have to be realizedin the RHIC ion ring in order to achieve the designluminosities. Electron cooling will be required toachieve the design transverse emittances. The sameelectron cooling system which is presently under de-velopment for RHIC-II will be used for eRHIC. Thenumber of ion bunches in RHIC should be increasedto 166 instead of presently achieved 111.

ELIC

Accelerator physicists at Jefferson Lab are pursuingan ELectron-Ion Collider, ELIC [54], which uses theCEBAF linear accelerator and requires the construc-tion of an ion storage ring.

16 Physics with an Electron Ion Collider

High Energy Setup Low Energy SetupAu e Au e

Energy, GeV (or GeV/n) 100 20 50 3Number of bunches 166 166Bunch spacing (ns) 71 71 71 71Bunch intensity (1011) 1.1 1.2 1.1 1.2Beam current (mA) 180 260 180 26095% normalized emittance (π mm mrad) 2.4 115 2.4 115Rms emittance (nm) 3.7 0.5 7.5 3.3β x/y (cm) 26 200 26 60Beam-beam parameters (x/y) 0.015 1.0 0.015 1.0Rms bunch length (cm) 20 0.7 20 1.8

Peak Luminosity/n (1033 cm−2s−1) 2.9 1.5Luminosity integral/week /n (pb−1) 580 290

Table 1: Luminosities and main beam parameters for e+Au collisions at eRHIC.

Ion Ion Energy EA Luminosity at Ee = 7 GeV Luminosity at Ee = 3 GeV(GeV/n) (cm−2s−1) and EA/5 (cm−2s−1)

Proton 150 7.8 · 1034 6.7 · 1033

Deuteron 75 1.6 · 1035 1.3 · 1034

3H+1 50 2.3 · 1035 2.0 · 1034

3He+2 100 1.2 · 1035 1.0 · 1034

4He+2 75 1.6 · 1035 1.3 · 1034

12C+6 75 1.6 · 1035 1.3 · 1034

40Ca+20 75 1.6 · 1035 1.3 · 1034

Table 2: ELIC luminosities per nucleon for e+A collisions.

ELIC is envisioned as a future upgrade of CEBAF,beyond the planned 12 GeV Upgrade for fixed targetexperiments. The CEBAF accelerator with the exist-ing polarized electron source will be used as a fullenergy injector into an electron storage ring, capa-ble of delivering the required electron beam energy,current, and polarization. The addition of a positronsource to the CEBAF injector, will allow a positronbeam to be accelerated in CEBAF, accumulated andpolarized in the electron storage ring, and used incollisions with ions (and possibly electrons), with lu-minosity similar as for electron/ion collisions. Anion complex with a green-field design optimized todirectly address the science program of ELIC, willbe used to generate, accelerate, and store polarizedlight ions and unpolarized medium to heavy ions,and will be a major addition to the CEBAF facility.

Figure 17 displays the conceptual layout of ELICat CEBAF. The three major constituents of ELIC are:the electron/positron complex, the ion complex withelectron cooling, and the four interaction regions.

The electron/positron complex is designed to de-liver electron beam in the energy range of 3 GeV

to 9 GeV, average beam current for collisions be-tween 1 A to 3 A, and longitudinal polarization atthe IP’s of 80%. This electron/positron complexcomprises two major facilities: the CEBAF accelera-tor upgraded to 12 GeV and an electron storage ringwhich will have to be constructed. CEBAF is a su-perconducting RF recirculating linac operating at theRF frequency of 1500 MHz. The 12 GeV Upgradeof CEBAF will allow energy gain of 11 GeV in fiverecirculations. Longitudinally polarized electronsare generated from CEBAF’s polarized DC photo-injector and accelerated to the desired top energy of3 to 9 GeV in multiple recirculations through CEBAF.They are then injected into a figure-8 shaped elec-tron storage ring, where they are accumulated usingstacking by synchrotron radiation damping.

The ion complex is designed to deliver protons inthe energy range of 30 to 225 GeV and average cur-rent of 0.3 to 1 A, and light to heavy ions with max-imum energy of approximately 100 GeV/n. It con-sists of polarized ion sources, a 200 MeV to 400 MeVlinac, a pre-booster up to 3 GeV/c, and a 225 GeV,1 A storage ring. The ion source is designed to pro-

Physics with an Electron Ion Collider 17

AB

C

Dx

x

xx

source

Linac 200 MeV

Electron Cooling

IR

IR

Snake

Snake

Figure 17: ELIC schematic layout.

duce polarized light ion species: p, d, 3He and Li,and unpolarized light to heavy ion species up to Pb.

The electron ring (arcs) is used as the main, 15 to30 GeV/u booster for the ion beam. The ion storagering serves as the collider ring with four interactionregions. As depicted in Fig. 17, the electron and ionstorage rings are designed as figure-8 shaped dou-ble rings and are housed in the same tunnel, withthe ion ring below the electron ring. The rings con-sist of two identical arcs connected by two crossingstraight beam line sections. The choice of figure-8shape eliminates the issue of spin maintenance at ac-celeration and allows one to easily arrange the de-sired spin orientation and flipping for all the ionspecies at all energies.

A critical component of the ion complex is a15 MeV to 112.5 MeV ERL-based continuous elec-tron cooling facility, which is anticipated to providelow emittance and simultaneously very short ionbunches.

The interaction region of ELIC is designed to ac-commodate up to four detectors simultaneously, atfour collision points located symmetrically aroundthe centers of the figure-8 colliders, along each ofthe two crossing straights. After beam stackingand accumulation is complete, the two storage ringsare switched to the collider mode, where electronbunches are bent vertically to collide with the ionbunches. Table 2 summarizes the design peak lumi-

nosity per nucleon for e+A collisions at two differentenergy setups for the electron-ion collider at CEBAF.Luminosity calculations for the highest energy se-tups, and heavier nuclei are presently under devel-opment. Peak luminosity at the 1035 cm−2s−1 levelper interaction point appears feasible for 75 GeV/nions colliding on 7 GeV electrons. ELIC is designedto be compatible with simultaneous operation of the12 GeV CEBAF for fixed target program, and its po-tential extension to 24 GeV.

Experimental Concepts

A new EIC facility will require the design and con-struction of a new optimized detector profiting fromthe experience gained from the H1 and ZEUS detec-tors operated at the HERA collider at DESY. The de-tails of the design will be closely coupled to the de-sign of the interaction region, and thus to the ma-chine development work in general.

The following minimal requirements on a futureEIC detector can be made:

• Measure precisely the energy and angle of thescattered electron (Kinematics of DIS reaction)

• Measure hadronic final state (Kinematics of DISreaction, jet studies, flavor tagging, fragmenta-tion studies, particle ID system for heavy flavorphysics and K/π separation)

• Missing transverse energy measurement(Events involving neutrinos in the final state,electroweak physics)

In addition to those demands on a central detector,the following forward and rear detector systems arecrucial:

• Zero-degree photon detector to control radia-tive corrections and measure Bremsstrahlungphotons for luminosity measurements (absoluteand relative with respect to different e+p spincombinations)

• Tag electrons under small angles (< 1◦) tostudy the non-perturbative and perturbativeQCD transition region

• Tagging of forward particles (Diffraction andnuclear fragments)

18 Physics with an Electron Ion Collider

EIC (eA) event topology

Ee=10 GeV, En/A=100 GeV/n

10-2

10-1

1

10

102

103

104

10-6

10-5

10-4

10-3

10-2

10-1

1

x

Q2

e

e

Au

h

eRHIC (20+100) GeV

eRHIC (10+100) GeV

EIC (eAu)

1=y

Lines of constant

electron angle

Lines of constant

hadron angle

177° (η = -3.64)

178° (η = -3.13)

179° (η = -4.74)

10° (η = 2.44)

5° (η = 3.13)

2° (η = 4.05)

proton

Au (central)

Q2s

10-1

1

10

102

103

104

10-6

10-5

10-4

10-3

10-2

10-1

1x

Q2

VeG(

2)

θEe

EpF

Ee′

γ

Figure 18: Kinematic Q2-x plane for Ee = 10 (20) GeV and EA = 100 GeV. Left: Shown are the lines of constant electron scatteringangles (blue) for θ = 177◦, 178◦, and 179◦, as well as the hadron/jet scattering angles γ = 2◦, 5◦, and 10◦. Note that for manymeasurements (e.g. F2) the reconstruction of the event kinematic at low-x is best done using the scattered electron, while at large xthe reconstruction of the final hadronic state is more precise (Jacquet-Blondel method). Right: shows the direction and energy of thescattered electron and current jet. The scale is taken with respect to the incoming electron and proton beams shown on the upperleft corner [55].

Fig. 18 shows the kinematic Q2 − x plane for Ee= 10 GeV (20 GeV) and EA = 100 GeV with the di-rection and energy of the scattered electron and cur-rent jet for several (Q2, x) points. In the low-Q2 /low-x region both the scattered electron and currentjet are found mainly in the rear direction with ener-gies well below 10 GeV. Good electron/hadron sepa-ration is essential. As x grows, the current jet movesforward with larger energies and is clearly separatedfrom the scattered electron at low-Q2. At high-Q2

/ high-x both the current jet and the scattered elec-tron are found mainly in the barrel and forward di-rection with energies much larger than 10 GeV (elec-tron) and 100 GeV (current-jet).

Optimizing all of these requirements is a chal-lenging task. Two detector concepts have beenconsidered so far. One, which focuses on therear/forward acceptance (Fig. 19) and thus on low-x/high-x physics, which emerges out of the HERA-III detector studies [56]. This detector concept isbased on a compact system of tracking and cen-tral electromagnetic calorimetry inside a magneticdipole field and calorimetric end-walls outside. For-ward produced charged particles are bent into thedetector volume which extends the rapidity cover-age compared to existing detectors.

The design shown in Fig. 20 is a wide acceptancedetector similar to the current HERA collider exper-iments H1 and ZEUS [55]. The physics program de-mands high luminosity and focusing machine ele-ments in a ring-ring configuration have to be as closeas possible to the interaction region while preserv-ing good central detector acceptance. The hermeticinner and outer tracking system and the electromag-netic section of the barrel calorimeter is surroundedby an axial magnetic field. The forward calorime-ter is divided into hadronic and electromagnetic sec-tions. The rear and barrel electromagnetic calorime-ter consists of segmented towers, e.g., a W-Si type.This would result in a compact configuration. A fu-ture EIC facility with only one interaction region willbe challenged to combine both of the above detectorconcepts to maximize its physics reach.

Physics with an Electron Ion Collider 19

Positron Hemisphere

EM calorimeter end-wall at -360cm

EM barrel calorimeter

covering z = ±70cmEM catcher calorimeterat z = -110cm

EM catcher calorimeterat z = +110cm

Proton HemisphereEM and hadron calorimeterend-wall at +360cm-3.8 m 0 +3.8 m 5.2 m

EM endwall

hadronic

endwall

+ 0.8 m

- 0.8 mcalorimetry

tracking

magnetic field

e p

Figure 19: Concept of a detector layout focusing on forward physics. Left: Conceptual layout of the detector with a 7m long dipolefield and an interaction region without machine elements extending from -3.8 m to +5.2 m. Right: Schematic overview over thedetector components within ≈ ±5 m of the interaction point. The silicon planes are visible inside the yellow tracking volume. Thecalorimeter system consisting of a central barrel, a catcher ring on each side and end-walls is depicted in blue and green. From [56].

Figure 20: Schematic layout of a design focusing on a wide acceptance detector system similar to the current HERA colliderexperiments H1 and ZEUS to allow for the maximum possible Q2 range. Depicted is the side view of the GEANT detectorimplementation as part of the ELECTRA simulation and reconstruction package. A deep-inelastic scattering event resulting froma LEPTO simulation is overlayed with Q2 = 361 GeV2 and x = 0.45. From [55].

20 Physics with an Electron Ion Collider

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22 Physics with an Electron Ion Collider