Experimental and theoretical investigations of quarks and gluons in nucleons and nuclei,carried out over the last half a century, have resulted in the development of the fundamentaltheory of strong interactions known as Quantum Chromodynamics (QCD). In QCD the forcesamongst quarks and gluons result from the exchange of ”color” charges. Gluons, the carriers ofthe strong force, carry color, in contrast to their counterpart in electrodynamics (photons, whichdo not carry electric charge). This results in a unique situation that gluons can interact with eachother. These gluonic interactions amongst themselves and the quarks result in most of the massof the visible universe. It also leads to a little explored regime of matter where gluons dominatethe behavior and characteristics of matter. Hints of this regime have become manifest whennucleons or nuclei collide at nearly the speed of light, as they do in colliders such as HERA,RHIC and LHC. The quantitative study of matter in this new regime requires a new experimentalfacility: an Electron Ion Collider (EIC) with the center-of-mass (c.m.) energy of approximatelya hundred (or hundreds of) GeV.
New phenomenological tools developed during the last decade have enabled remarkable to-mographic images of the quarks and gluons inside protons and neutrons. These tools will befurther developed and utilized to study the valence quark dominated region of the nucleon at theupgraded 12 GeV CEBAF at JLab [1] and the COMPASS experiment [2] at CERN. Applyingthese new tools to study the gluon- and sea quark- dominated matter will require the the high-luminosity EIC, capable of c.m. energy of about hundred GeV. Some long standing questionssuch as the the origin and composition of the nucleon’s spin, will also be naturally addressed insuch a study and will require the EIC to have polarized hadron (and electron) beams.
If a future facility capable of electron-hadron collision energies of 1−2 TeV is considered (3-6 times higher than HERA at DESY), then the physics program at such a facility could include:precision QCD and Electroweak physics at the energy-frontier, physics of high parton densities(gluons in particular, described earlier), and searches for possible physics beyond the StandardModel. Such a scientific program would be complementary to that of the LHC. A situationsimilar to the complementary roles played by HERA and the Tevetron in the last decades.
1. Introduction
Deep inelastic scattering (DIS) has been a very effective technique in physics in the discovery andthe systematic study of the internal structure of matter. Three proposals for future experimenta-tion employing this technique for the next decade, currently under consideration, are presentedin this paper. We give a brief overview of each, and while their physics reach is wider, we presentsome highlights of physics motivation limited to the field of Quantum Chromodynamics.
Abstract
Abhay Deshpande (for the EIC Collaboration)Department of Physics and Astronomy, Stony Brook University, NY 11794-3800
Three proposals for the future Electron Ion Collider (EIC) are currently being developed:two in the US, and one in Europe. Two independent designs for a future EIC have evolvedin the United States [3, 4]. Both use the existing infrastructure and facilities available to theUS nuclear science community. At Brookhaven National Laboratory (BNL) the eRHIC design(Fig. 1, left) utilizes a new electron beam facility based on an Energy Recovery LINAC (ERL) tobe built inside the RHIC tunnel to collide with RHICs existing high-energy polarized proton andnuclear beams. At Jefferson Laboratory (JLab) the ELectron Ion Collider (ELIC) design (Fig. 1,right) employs a new electron and ion collider ring complex together with the 12 GeV upgradedCEBAF, now under construction, to achieve similar collision parameters. The EIC machine
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Figure 1: Left: The schematic of eRHIC at BNL, which would require construction of an electron beam facility (red)to collide with the RHIC blue beam at up to three interaction points. Right: The schematic of ELIC at JLab, whichwould require construction of the ELIC complex (red, black/grey) and its injector (green on the top) around the 12 GeVCEBAF.
designs are aimed at achieving a) Highly polarized (∼ 70%) electron and nucleon beams, b)Ion beams from deuteron to the heaviest nuclei (Uranium or Lead), c) Variable center of massenergies from ∼ 20−100 GeV, upgradable to ∼150 GeV, d) High collision luminosity ∼1033−34
cm−2s−1, e) Possibilities of having more than one interaction region.The European proposal, the Large Hadron Electron Collider (LHeC) [5] entails adding a
60-140 GeV/c electron beam facility next to the existing LHC tunnel so as to collide electrons-protons and electron-nuclei at the c.m. of 1−2, and 0.7−1.2 TeV, respectively. Compared to theonly prior electron-proton collider, HERA, the LHeC would cover a kinematic region extendedby an order of magnitude in the negative four-momentum squared, Q2, and in the inverse Bjorkenx. The design luminosity is planned to be 1033cm−2sec−1. This machine will have polarizedelectrons colliding with unpolarized protons and nuclei. Two different designs for the electronbeam facility have been considered: the Ring design and the LINAC design. Currently theproponents favor the LINAC design, due to its possibility to reach higher energy, and the easeof realization at CERN. See the LHeC CDR[5] for more details regarding the physics and themachine design of the LHeC.
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3. Why is an EIC needed?
The most intellectually pressing questions that an EIC will address that relate to our detailedand fundamental understanding of QCD in this frontier environment are:
• How are the sea quarks and gluons, and their spins, distributed in space and momentuminside the nucleon? What is the role of orbital motion of sea quarks and gluons in buildingthe nucleon spin?
• Where does the saturation of gluon densities set in? Does this saturation produce matterof universal properties in the nucleon and all nuclei viewed at nearly the speed of light?
• How does the nuclear environment affect the distribution of quarks and gluons and theirinteractions in nuclei? How does nuclear matter respond to a fast moving color chargepassing through it?
Answers to these questions are essential for understanding the nature of visible matter. A DIS fa-cility that would address all the above questions would need to have high energy so that it reacheswell into the gluon-dominated region. As one increases the energy of the electron-nucleon col-lision, the process probes regions of progressively higher gluon density. However, the densityof gluons inside a nucleon must eventually saturate to avoid untamed growth in the strength ofthe nucleon-nucleon interaction.To date this saturated gluon density regime has not been clearlyobserved. This pursuit will be facilitated by electron collisions with heavy nuclei, where co-herent contributions from many nucleons effectively amplify the probed gluon density. Studyof correlations of sea quarks and gluon distributions with the nucleon spin will need polarizednucleon beams. The study of gluon saturation requires either nuclear beams of hundreds of GeVor multi-TeV proton beams available at the LHC. The EIC was designated in the 2007 NuclearPhysics Long Range Plan as “embodying the vision for reaching the next QCD frontier” [6]. Itwould extend the QCD science programs in the U.S. established at both the CEBAF acceleratorat JLab and RHIC at BNL in dramatic and fundamentally important ways. LHeC would do thesame with its high energy proton and lead beams. Because of its higher energy the physics goalsof the LHeC include precision QCD and Electroweak (EW) & beyond the Standard Model (SM)physics [5], which are not directly relevant to the interests of this conference.
4. EIC Physics Opportunities: If an EIC is built, what would we learn?
4.1. Nucleon Spin and its 3D Structure and Tomography
Several decades of experiments on deep inelastic scattering (DIS) of electron or muon beamsoff nucleons have taught us how quarks and gluons (collectively called partons) share the mo-mentum of a fast-moving nucleon. They have not, however, resolved the question of how par-tons share the nucleon’s spin and build up other nucleon intrinsic properties, such as its massand magnetic moment. The earlier studies were limited to providing the longitudinal momentumdistribution of quarks and gluons, a one-dimensional view of nucleon structure. The EIC is de-signed to yield much greater insight into the nucleon structure by facilitating multi-dimensionalmaps of the distributions of partons in space, momentum, spin, and flavor. The 12 GeV upgradeof CEBAF at JLab, and the COMPASS experiment at CERN will start on such studies in thekinematic region of the valence quarks. However, these programs will be dramatically extendedat the EIC to explore the role of the gluons and sea quarks in determining the hadron structure
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and properties. This will resolve crucial questions, such as whether a substantial “missing” por-tion of nucleon spin resides in the gluons. By providing high-energy probes of partons transversemomenta, the EIC should also illuminate the role of their orbital motion contributing to nucleonspin.
A worldwide experimental program over the past two decades has shown that the spin ofquarks and antiquarks is only responsible for ∼ 30% of the proton spin. Recent RHIC resultsindicate that the gluons’ spin contribution in the currently explored kinematic region is non-zero, but not yet sufficient to account for the missing 70%. With the unique capability to reachtwo orders of magnitude lower in x and to span a wider range of momentum transfer Q thanpreviously achieved, the EIC would offer the most powerful tool to precisely quantify how thespin of gluons and that of quarks of various flavors contribute to the protons spin.
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Fig. 2 (Right) shows the reduction in uncertainties of the contributions to the nucleon spinfrom the spin of the gluons, quarks and antiquarks, evaluated in the x range from 0.001 to 1.0.This would be achieved by the EIC in its early stage of operation. At the later stage, the kinematicrange could be further extended down to x ∼ 0.0001 reducing significantly the uncertainty on thecontributions from the unmeasured small-x region.
Theoretical advances over the past decade have led to a rigorous framework where informa-tion on the confined motion of the partons inside a fast-moving nucleon is matched to transverse-momentum dependent parton distributions (TMDs). TMDs thus allow us to investigate the fullthree-dimensional dynamics of the proton, going well beyond the information about longitu-dional momentum contained in conventional parton distributions.
Fig. 3 (Left) shows the transverse-momentum distribution of up quarks inside a proton mov-ing in the z direction (out of the page) with its spin polarized in the y direction. The color codeindicates the probability of finding the up quarks. The anisotropy in transverse momentum isdescribed by the Sivers distribution function[3]. Nothing is known about the spin and momen-tum correlations of the gluons and sea quarks. The achievable statistical precision of the quarkSivers function from the EIC kinematics is shown in Fig. 3 (Right). Currently no data exist for
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Figure 3: Left: Transverse-momentum distribution of up quarks with longitudinal momentum fraction x = 0.1 in atransversely polarized proton moving in the z-direction, while polarized in the y-direction. The color code indicates theprobability of finding the up quarks. Right: The transverse-momentum profile of the up quark Sivers function at five xvalues accessible to the EIC, and corresponding statistical uncertainties.
extracting such a picture in the gluon-dominated region in the proton. The EIC would be crucialto initiate and realize such a program.
By choosing particular final states in electron-proton scattering, the EIC would probe thetransverse spatial distribution of sea quarks and gluons in the fast-moving proton as a functionof the parton’s longitudinal momentum fraction x. This spatial distribution yields a picture ofthe proton that is complementary to the one obtained from the TMDs of quarks and gluons, re-vealing aspects of proton structure that are intimately connected with the dynamics of QCD atlarge distances. The accessible parton momentum fractions x at the EIC extend from a regiondominated by sea quarks and gluons to one where valence quarks become important, allowinga connection to the precise images expected from the 12 GeV upgrade at JLab and COMPASSat CERN. This is exemplified in Fig. 4, which shows the precision expected for the spatial dis-tribution of gluons as measured in the exclusive process: electron + proton → electron + J/ψ+ proton. The tomographic images obtained from cross sections and polarization asymmetriesfor exclusive processes are encoded in generalized parton distributions (GPDs) that unify theconcepts of parton densities and of elastic form factors.
4.2. Nucleus as a QCD Laboratory
The nucleus is a QCD “molecule,” with a complex structure corresponding to bound statesof nucleons. Understanding the emergence of nuclei from QCD is an ultimate long-term goal ofnuclear physics. With its wide kinematic reach, as shown in Fig. 5 (Left), the capability to probea variety of nuclei in both inclusive and semi-inclusive DIS measurements, the EIC would be thefirst experimental facility capable of exploring the internal 3-dimensional sea quark and gluonstructure of a fast-moving nucleus. Furthermore, the nucleus itself would be an unprecedentedQCD laboratory for discovering the collective behavior of gluonic matter at an unprecedentedoccupation number of gluons, and for studying the propagation of fast-moving color charge in anuclear medium.
In QCD, the large soft-gluon density enables the non-linear process of gluon-gluon recombi-nation to limit the density growth. Such a QCD self-regulation mechanism necessarily generatesa dynamic scale from the interaction of high density massless gluons, known as the saturation
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Figure 4: Projected precision of the transverse spatial distribution of gluons as obtained from the cross section ofexclusive J/ψ production. It includes statistical uncertainty and systematic uncertainties due to extrapolation into theunmeasured region of momentum transfer to the scattered proton. The distance of the gluon from the center of the protonis bT in femtometers, and the kinematic quantity xV = xB (1+M2
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scale, Qs, at which gluon splitting and recombination reach a balance. At this scale the densityof gluons is expected to saturate, producing new and universal properties of hadronic matter. Thesaturation scale Qs separates the condensed and saturated soft gluonic matter from the dilute butconfined quarks and gluons in a hadron, as shown in Fig. 5 (Right).
The existence of such a state of saturated, soft gluon matter, often referred to as Color GlassCondensate (CGC), is a direct consequence of gluon self-interactions in QCD. It has been con-jectured that the CGC of QCD has universal properties common to nucleons and all nuclei,which could be systematically computed if the dynamic saturation scale Qs is sufficiently large.However, such a semi-hard Qs is difficult to reach unambiguously in electron-proton scatter-ing without a multi-TeV proton beam, which is only possible at the LHeC (proposal mentionedabove). Heavy ion beams at the EIC could allow access to the saturation regime because the vir-tual photon in forward lepton scattering probes matter (coherently) over a characteristic length
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proportional to 1/x, which would exceed the diameter of a Lorentz-contracted nucleus. All glu-ons at the same impact parameter of the nucleus, enhanced by the nuclear diameter proportionalto A1/3 with the atomic weight A, would contribute to the probed density, reaching saturation atfar lower energies than would be needed in electron-proton collisions. While HERA, RHIC andthe LHC have only seen hints of saturated gluonic matter, the EICs (including the LHeC) wouldbe in a position to seal the case.
Figure 6: Left: The ratio of diffractive over total cross section for DIS on gold normalized to DIS on proton plottedfor different values, M2
X, the mass square of hadrons produced in the collisions for models assuming saturation and non-saturation. The grey bars are estimated systematic uncertainties. Right: The ratio of coherent diffractive cross section ine-Au to e-p collisions normalized by A4/3 plotted as a function of Q2, plotted for saturation and non-saturation models.The 1/Q is effectively the initial size of the quark-antiquark systems (φ and J/psi) produced in the medium.
Fig. 6 illustrates some of the dramatic predicted effects of gluon density saturation in electron-nucleus vs. electron-proton collisions at an EIC. The left frame considers coherent diffractiveprocesses: the gluon saturation greatly enhances the fraction of the total cross section accountedfor by such diffractive events. An early measurement of coherent diffraction in e+A collisions atthe EIC would provide the first unambiguous evidence for gluon saturation.
Fig. 6 (Right) shows that gluon saturation is predicted to suppress vector meson production ine+A relative to e+p collisions at the EIC. The magnitude of the suppression depends on the size(or color dipole moment) of the quark-antiquark pair, being significantly larger for produced φ(red points) than for J/ψ (blue) mesons. An EIC measurement of the processes in Fig. 6 (Right)would provide a powerful probe to explore the properties of the saturated gluon matter.
Both the coherent diffractive and total DIS cross sections on nuclei are suppressed comparingto those on the proton in all saturation models. But, the suppression on the diffractive crosssection is weaker than that on the total cross section leading to a dramatic enhancement in thedouble ratio as shown in Fig. 6 (Left).
With its capability to measure the diffractive and exclusive processes with a variety of ionbeams, the EIC would also provide the first 3-dimensional images of sea quarks and gluons ina fast-moving nucleus with sub-femtometer resolution [3]. Furthermore, mysteries surroundingheavy vs. light quark interactions in hot QCD matter discovered at RHIC can be illuminated withthe EIC through studies in cold nuclear matter [7].
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4.3. Physics Possibilities at the Intensity FrontierWhile the US EIC is primarily being proposed for exploring new frontiers in QCD, it offers
a unique new combination of experimental probes potentially interesting to the investigationsin Fundamental Symmetries. For example, the availability of polarized beams at high energyand high luminosity, combined with a state-of-the-art hermetic detector, could extend StandardModel tests of the running of the weak-coupling constant [4] far beyond the reach of the JLab12parity violation program[1].The LHeC at CERN, will not have polarized beams, but will beable to do such experimental measurements at high energies directly, including possible directsearches for lepto-quarks and other Beyond the SM entities [5].
5. EIC: Path to Realization & Prospects
A staged realization of the EIC is being planned for both the eRHIC and ELIC designs. Thefirst stage is anticipated to have up to ∼ 60 − 100 GeV in center-of-mass-energy, with polarizednucleon and electron beams, a wide range of heavy ion beams for nuclear DIS, and a luminosityfor electron-proton collisions approaching 1034 cm−2s−1. The US EIC would be distinguishedfrom all past, current, and future facilities around the world by being at the intensity frontierwith a versatile range of kinematics and beam polarizations, as well as beam species, allowingthe above questions to be tackled at one facility. In particular, the US EIC design exceeds thecapabilities of HERA, the only electron-proton collider to date, by adding a) polarized protonand light-ion beams; b) a wide variety of heavy-ion beams; c) two to three orders of magni-tude increase in luminosity to facilitate tomographic imaging; and d) wide energy variability toenhance the sensitivity to gluon distributions. The EIC promises to propel the RHIC and thefixed target experimental program at Jefferson Lab, to the next QCD frontier, by unraveling thethree-dimensional sea quark and gluon structure of visible matter, and enable a detailed study ofa universal state of saturated gluon matter should it exist. The EIC proposals at BNL and JLabwill thus enable the US to continue its leadership role in nuclear science research through thequest for understanding the unique gluon-dominated nature of visible matter in the universe.
Acknowledgement
AD gratefully acknowledges the contribution of 500+ authors of the [4] and the co-authorsof the EIC White Paper [3]: Z.-E. Meziani, J. Qiu, E. C. Aschenauer, W. Brooks, M. Diehl, H.Gao, R. Holt, T. Horn, A. Hutton, Y. Kovchegov, K. Kumar, A. Mueller, M. Ramesy-Musolf, T.Roser, F. Sabatie E. Sichtermann, T. Ullrich, W. Vogelsang, F. Yuan. Support and discussionswith R. Ent, T. Ludlam, R. McKeown, & S. Vigdor were indispensable.
References
[1] The 12 GeV Upgrade of CEBAF & its Physics; https://www.jlab.org/12GeV/[2] COMPASS Experiment at CERN; http://arxiv.org/abs/hep-ex/0703049 & http://wwwcompass.cern.ch/[3] The Glue that Binds Us All, A white paper on Electron Ion Collider prepared for the NSAC’s future Long Range
Plan, http://skipper.physics.sunysb.edu/ abhay/eicwp12/draft/EIC-WhitePaper-11252012.pdf, November 2012[4] D. Boer et al., Gluons and quarks sea at high energies: distributions, polarization, tomography, The INT Report on
EIC Science, arXiv:1108.1713v2[5] Conceptual Design Report LHeC, arXiv: 1206.2913v1; see also http://cern.ch/lhec[6] NSAC Long Range Plan 2007: http://science.energy.gov/ /media/np/nsac/pdf/docs/NuclearScienceHighRes.pdf[7] C. Marquett, these proceedings.
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