The goal of the INT workshop on Physics at a High Energy Electron Ion Collider was to explore the physics case for an Electron Ion Collider (EIC), A "medium energy" proposal for the collider would provide high luminosity collisions (10³³/cm²/sec or greater) of 4 to 5 GeV electron beams on polarized proton beams with energies ranging from 60 to 250 GeV and light and heavy nuclei with energies up to 100 GeV/nucleon. A "high energy" version would contain electron beams of 10 to 20 GeV. The EIC would have energies above those of the current Jlab, COMPASS and earlier fixed target deeply inelastic scattering (DIS) facilities (SLAC, NMC, E665) but below those of the recently decommissioned HERA facility at DESY in Germany and the proposed LHeC project at CERN. It would have unique capabilities-in addition to the highest luminosities achieved for an electron-proton collider, it would be the world's first electron-nucleus collider, and the first polarized electron-polarized proton collider.

The workshop began with an overview by George Sterman of outstanding problems in QCD that can be addressed by an EIC. He stressed the importance of factorization in extracting universal QCD physics of fundamental importance. While detailed questions about QCD dynamics require high luminosities, reliably extracting this physics requires high energies as well, thereby providing powerful motivation for a high energy, high luminosity collider. The physics overview was was followed by talks discussing the accelerator and detector capabilities of the EIC, the suite of possible DIS measurements, other proposed DIS facilities (Jlab12 GeV, ENC@FAIR and LHeC) and physics puzzles and open questions resulting from measurements at existing facilities (Jlab 6 GeV, RHIC heavy ion and spin experiments). These survey and overview talks were followed by an extensive discussion session chaired by Hugh Montgomery (Jlab) and Steve Vigdor (BNL) on the prospects and challenges in realizing an EIC in the United States in the next decade.

The days following the first day of survey talks and discussion on the status, prospects and promise of an EIC were focused on articulating the physics case for such a machine. Because the EIC will access gluon and sea quark degrees of freedom with precision, the focus was on what one can learn about momentum and spatial distributions of gluons and sea quarks, their flavor and spin content, the importance of multi-parton correlations and the dynamics of parton propagation in QCD media.

Parton distribution functions (pdfs) are universal quantities that carry fundamental information on the momentum distribution of quarks and gluons inside hadrons and nuclei. A review of their status was presented by Blumlein, who highlighted the impressive program of higher order computations in perturbative QCD that in some instances have been carried out to four loop order. The pdfs remain highly unconstrained at large x (the momentum fraction of the proton carried by the parton) even up to very large momentum transfers; at small x, significant uncertainties exist at lower momentum transfers. A significant part of both these kinematic regions are covered by the EIC, data from which could impact pdf global analyses. Polarized pdfs, which tell us about the probability of having quarks and gluons in the proton with their spins aligned either in the direction of or opposite to the proton spin, have much greater uncertainties primarily because of the relative paucity of DIS data. In his talk on the subject, Stratmann stressed the need for a global QCD fit with projected EIC data to quantify their impact.

For nuclear pdfs, there is NO data on gluon pdfs in the small x regime (momentum fractions less than 0.01 of the momentum of a nucleon in the nucleus); EIC measurements will provide first measurements of nuclear gluon pdfs. Nuclear pdfs are of intrinsic importance because they tell us the degree to which nuclei are not simply collections of nucleons, and that quark and gluon distributions are modified in a nuclear medium. Such deviations, at large x, were called the EMC effect, which is still not fully understood. At small x, these deviations, called "shadowing" are also not understood; for gluons, the amount of shadowing is not known at all. Parton distribution functions are defined and extracted within a leading twist framework in QCD, which ignores multi-parton "higher twist" contributions that are suppressed by powers of the momentum transfer. These effects are likely enhanced in nuclei and are not quantified; diffractive parton distributions measured at HERA predict the magnitude of leading twist shadowing in nuclei and thereby constrain higher twist contributions.

At small x, higher twist contributions may be as large as leading twist contributions resulting in a complete break down of linear QCD evolution. This phenomenon is known as gluon saturation. In the infinite momentum frame, partons in this regime have high occupation numbers (or strong color fields). Reggeon field theory and the Color Glass Condensate are effective theoretical descriptions of saturated gluon matter--whether these are equivalent descriptions is still an open question. Saturation effects, which are enhanced in nuclei, are best probed in semi-inclusive, diffractive and exclusive final states. With regard to the last, an interesting idea was presented by Kowalski to use exclusive J/Ψ photo-production off nuclei to explore with precision the role of partonic degrees of freedom in short range nuclear forces.

A high luminosity EIC makes it possible to extract information about leading twist generalized parton distributions (gpds). They carry important information which may allow one to construct a spatial "tomography" of the distribution of partons in a hadron. In polarized hadrons, they provide information on the orbital motion of quarks and gluons. A key question to be addressed is how this tomographic data provides specific insight into the QCD structure of final states in hadronic collisions (for instance, at the LHC). In semi-inclusive DIS, how the spatial distortions of polarized quarks in unpolarized hadrons (or vice versa) translate into momentum space asymmetries can be quantified into terms of unintegrated transverse momentum dependent distributions (tmds). While these carry crucial information on QCD final state interactions, important questions remain regarding the universality of these distributions.

At large x and momentum transfers, hard final states (leading hadrons, jets, heavy quarks,photons,...) in nuclei carry important information about the response of the QCD medium to these probes and on the in-medium modification of hadronization. Because the medium in e+A collisions is cold, its effect on hard probes provides an essential calibration of the effects of a hot medium (produced in heavy ion collisions) on the same. As emphasized by Accardi, the EIC will vastly increase the scope of these studies beyond those of prior fixed target e+A experiments. While nearly all of the program focused on what one can learn about QCD with an EIC, talks by Kumar, Marciano and Ramsey-Musolf explored the possibility of an electroweak and beyond the standard model program with EIC. Detailed studies of the energy and luminosity requirements for these are underway.

In summary, the wide range of talks at the workshop suggested that the EIC is a powerful machine with unique features which has to potential to uncover new physics and challenge existing wisdom. The Fall 2010 program at the INT, which is devoted to the topics discussed at the workshop, will help articulate in greater depth the science case for an Electron Ion Collider.