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...

In the framework of quantum chromodynamics (QCD), parton distribution functions (PDFs) quantify how the momentum and spin of a hadron are divided among its quark and gluon constituents. Two main approaches exist to determine PDFs. The first approach, based on QCD factorization theorems, realizes a QCD analysis of a suitable set of hard-scattering measurements, often using a variety of hadronic observables. The second approach, based on first-principle operator definitions of PDFs, uses lattice QCD to compute directly some PDF-related quantities, such as their moments. Motivated by recent progress in both approaches, in this document we present an overview of lattice-QCD and globalanalysis techniques used to determine unpolarized and polarized proton PDFs and their moments. We provide benchmark numbers to validate present and future lattice-QCD calculations and we illustrate how they could be used to reduce the PDF uncertainties in current unpolarized and polarized global analyses. This document represents a first step towards establishing a common language between the two communities, to foster dialogue and to further improve our knowledge of PDFs.The detailed understanding of the inner structure of nucleons is an active research field with phenomenological implications in high-energy, hadron, nuclear and astroparticle physics. Within quantum chromodynamics (QCD), information on this structure -specifically on how the nucleon's momentum and spin are divided among quarks and gluons -is encoded in parton distribution functions (PDFs).There exist two main methods to determine PDFs. 1 The first method is the global QCD analysis [3][4][5][6][7][8][9][10][11][12]. It is based on QCD factorization of physical observables, i.e. the fact that a class of hard-scattering cross-sections can be expressed as a convolution between short-distance, perturbative, matrix elements and long-distance, nonperturbative, PDFs. By combining a variety of available hard-scattering experimental data with state-of-the-art perturbative calculations, complete PDF sets, including the gluon and various combinations of quark flavors, are currently determined for protons, in both the unpolarized [13][14][15][16][17] and the polarized [18][19][20][21] case.Recent progress in global QCD analyses has been driven, on the one hand, by the increasing availability of a wealth of high-precision measurements from Jefferson Lab, HERA, RHIC, the Tevatron and the LHC and, on the other hand, by the advancement in perturbative calculations of QCD and electroweak (EW) higher-order corrections. Parton distributions are now determined with unprecedented precision, in many cases at the few-percent level. A paradigmatic illustration of this progress is provided by both the unpolarized and polarized gluon PDFs, which were affected by rather large uncertainties until recently, due to the limited experimental information available. In the unpolarized case, the gluon PDF is now constrained quite accurately from small to large x thanks to the inclusion of processes such a...

We study the structure of generalized parton distributions (GPDs) in spin 0 nuclei within a microscopic approach for nuclear dynamics. GPDs can be used on one side as tools to unravel the deep inelastic transverse structure of nuclei in terms of both transverse spatial and transverse momentum degrees of freedom. On the other, one can obtain information on GPDs themselves by observing how they become modified in the nuclear environment. We derive the structure of the nuclear deeply virtual Compton scattering tensor and generalized parton distributions at leading order in Q in a field-theoretical framework. The nuclear generalized parton distributions are calculated using a two-step process-the convolution approach-where the scattering process happens from a quark inside a nucleon, itself inside a nucleus, disregarding final state interactions with both the nuclear and nucleon debris. We point out that details of the nuclear long-range interactions, such as two-body currents, can be disregarded compared to the deep inelastic induced modifications of the bound GPDs. We show how the pattern of nuclear modifications predicted, and in particular the deviations of off-shell effects from the longitudinal convolution provide clear signals to be sought in experimental measurements. Finally, we find interesting relationships by studying Mellin moments in nuclei: in particular we predict the A dependence for the D term of GPDs within a microscopic approach and the behavior with t of the total momentum carried by quarks in a nucleus. The latter provides an important element for the evaluation of nuclear hadronization phenomena that are vital for interpreting current and future data at RHIC, HERMES, and Jefferson Lab.

We present a physically motivated parametrization of the chiral-even generalized parton distributions in the non-singlet sector obtained from a global analysis using a set of available experimental data. Our analysis is valid in the kinematical region of intermediate Bjorken x and for Q 2 in the multi-GeV region which is accessible at present and currently planned facilities. Relevant data included in our fit are from the nucleon elastic form factors measurements, and from deep inelastic scattering experiments. Additional information provided by lattice calculations of the higher moments of generalized parton distributions, is also considered. Recently extracted observables from Deeply Virtual Compton Scattering on the nucleon are reproduced by our fit.

We propose a physically motivated parametrization for the unpolarized generalized parton distributions. At zero value of the skewness variable, ζ, the parametrization is constrained by simultaneously fitting the experimental data on both the nucleon elastic form factors and the deep inelastic structure functions. A rich phenomenology can be addressed based on this parametrization. In particular, we track the behavior of the average: i) interparton distances as a function of the momentum fraction, X, ii) X as a function of the four-momentum transfer, t; iii) the intrinsic transverse momentum k ⊥ as a function of X. We discuss the extension of our parametrization to ζ = 0 where additional constraints are provided by higher moments of the generalized parton distributions obtained from ab initio lattice QCD calculations.

Exclusive o electroproduction from nucleons is suggested for extracting the tensor charge and other quantities related to transversity from experimental data. This process isolates C-parity odd and chiral-odd combinations of t-channel exchange quantum numbers. In a hadronic picture it connects the meson production amplitudes to C-odd Regge exchanges with final state interactions. In a description based on partonic degrees of freedom, the helicity structure for this C-odd process relates to the quark helicity flip, or chiral-odd generalized parton distributions. This differs markedly from deeply virtual Compton scattering, and both vector meson and charged electroproduction, where the axial charge can enter the amplitudes. Contrarily, the tensor charge enters the o process. The connection through the helicity description of the process to both the partonic and hadronic perspectives is studied and exploited in model calculations to indicate how the tensor charge and other transversity parameters can be related to cross section and spin asymmetry measurements over a broad range of kinematics.

Abstract. We review the phenomenological framework for accessing Generalized Parton Distributions (GPDs) using measurements of Deeply Virtual Compton Scattering (DVCS) from a proton target. We describe various GPD models and fitting procedures, emphasizing specific challenges posed both by the internal structure and properties of the GPD functions and by their relation to observables. Bearing in mind forthcoming data of unprecedented accuracy, we give a set of recommendations to better define the pathway for a precise extraction of GPDs from experiment.

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