ForewordThe study of the fundamental structure of nuclear matter is a central thrust of physics research in the United States. As indicated in Frontiers of Nuclear Science, the 2007 Nuclear Science Advisory Committee long range plan, consideration of a future Electron-Ion Collider (EIC) is a priority and will likely be a significant focus of discussion at the next long range plan. We are therefore pleased to have supported the ten week program in fall 2010 at the Institute of Nuclear Theory which examined at length the science case for the EIC. This program was a major effort; it attracted the maximum allowable attendance over ten weeks.This report summarizes the current understanding of the physics and articulates important open questions that can be addressed by an EIC. It converges towards a set of "golden" experiments that illustrate both the science reach and the technical demands on such a facility, and thereby establishes a firm ground from which to launch the next phase in preparation for the upcoming long range plan discussions. We thank all the participants in this productive program. In particular, we would like to acknowledge the leadership and dedication of the five co-organizers of the program who are also the co-editors of this report.David Kaplan, Director, National Institute for Nuclear Theory Hugh Montgomery, Director, Thomas Jefferson National Accelerator Facility Steven Vigdor, Associate Lab Director, Brookhaven National Laboratory iii Preface This volume is based on a ten-week program on "Gluons and the quark sea at high energies", which took place at the Institute for Nuclear Theory (INT) in Seattle from September 13 to November 19, 2010. The principal aim of the program was to develop and sharpen the science case for an Electron-Ion Collider (EIC), a facility that will be able to collide electrons and positrons with polarized protons and with light to heavy nuclei at high energies, offering unprecedented possibilities for in-depth studies of quantum chromodynamics. Guiding questions were• What are the crucial science issues?• How do they fit within the overall goals for nuclear physics?• Why can't they be addressed adequately at existing facilities?• Will they still be interesting in the 2020's, when a suitable facility might be realized?The program started with a five-day workshop on "Perturbative and Non-Perturbative Aspects of QCD at Collider Energies", which was followed by eight weeks of regular program and a concluding four-day workshop on "The Science Case for an EIC".More than 120 theorists and experimentalists took part in the program over ten weeks. It was only possible to smoothly accommodate such a large number of participants because of the extraordinary efforts of the INT staff, to whom we extend our warm thanks and appreciation. We thank the INT Director, David Kaplan, for his strong support of the program and for covering a significant portion of the costs for printing this volume. We gratefully acknowledge additional financial support provided by BNL and JLab.The program w...

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The NLO corrections to the DIS structure functions F2 and FL (or equivalently the photon-target cross sections σ γ * T and σ γ * L ) at low xBj are obtained, as a generalization of the dipole factorization formula. For the first time, the contributions of both the qq and the qqg Fock states in the photon are directly calculated, using earlier results [1] for the qq light-front wave-functions at one loop inside a dressed virtual photon. Both the qq and the qqg contributions have UV divergences, which are shown to cancel each other, using conventional dimensional regularization as UV regulator. Finally, the resummation of high-energy logarithms on top of the NLO results for σ γ * T and σ γ * L is discussed.

The one-loop QCD corrections to the light-front wave-function for the quark-antiquark Fock state inside a transverse or longitudinal off-shell photon are explicitly calculated, both in full momentum space and in mixed space (a.k.a. dipole space). These results provide one of the main contributions to virtual NLO corrections to many DIS observables (inclusive or not) in the dipole factorization formalism at low Bjorken x.In a follow-up article, these one-loop corrections are combined with earlier results on the wavefunction for the quark-antiquark-gluon Fock state, in order to get the full set of NLO corrections to the DIS structure functions F2 and FL in the dipole factorization formalism, valid at low Bjorken x.At low Bjorken x (x Bj ), various deep inelastic scattering (DIS) observables can be studied using the dipole factorization formalism, in particular inclusive DIS structure functions [1,2] and diffractive DIS structure functions [3] as well as exclusive vector meson vector meson production [4] and deeply virtual Compton scattering. This formalism is motivated by light-front perturbation theory [1,5], which provides the light-front wave-functions (LFWF) for the fluctuation of the exchanged photon into a quark-antiquark dipole, and relies on the eikonal approximation, which allows to describe the interaction of the quark-antiquark dipole on the target, in the high-energy limit relevant for DIS at low x Bj . The dipole factorization has a remarkable versatility. Not only does it allow one to study in a unified way inclusive, diffractive and exclusive observables, but it allows one to include and study various dynamical effects from QCD. For that reason, a large part of the theoretical and phenomenological work in the literature related to the results (at low x Bj ) from the HERA collider are based on the dipole factorization.Pushing further the dipole picture, it has been possible to rederive in a more intuitive way [6-8] the BFKL equation [9][10][11], which allows one to resum large logarithms arising in perturbation theory for high-energy (or equivalently low x Bj ) semi-hard scattering processes between two dilute objects in QCD, within the leading logarithmic approximation (LL). Moreover, thanks to the use of the eikonal approximation, it is trivial to include coherent multiple scattering effects within the dipole factorization, via Wilson lines, in the case of a dense target. When such effects are relevant, one enters into the gluon saturation regime of QCD [12][13][14][15][16], also called Color Glass Condensate (CGC). In the presence of gluon saturation effects, the BFKL equation has to be replaced by a nonlinear evolution in order to perform the high-energy LL resummation, which is the B-JIMWLK evolution [17][18][19][20][21][22][23][24][25], or in a mean-field approximation the Balitsky-Kovchegov (BK) equation [17,26,27]. Using the dipole factorization in conjunction with the BK equation (modified to include running QCD coupling effects [28,29]), it has been possible to obtain successful fits [30][31...