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Abstract. This White Paper presents the science case of an Electron-Ion Collider (EIC), focused on the structure and interactions of gluon-dominated matter, with the intent to articulate it to the broader nuclear science community. It was commissioned by the managements of Brookhaven National Laboratory (BNL) and Thomas Jefferson National Accelerator Facility (JLab) with the objective of presenting a summary of scientific opportunities and goals of the EIC as a follow-up to the 2007 NSAC Long Range plan. This document is a culmination of a community-wide effort in nuclear science following a series of workshops on EIC physics over the past decades and, in particular, the focused ten-week program on "Gluons and quark sea at high energies" at the Institute for Nuclear Theory in Fall 2010. It contains a brief description of a few golden physics measurements along with accelerator and detector concepts required to achieve them. It has been benefited profoundly from inputs by the users' communities of BNL and JLab. This White Paper offers the promise to propel the QCD science program in the US, established with the CEBAF accelerator at JLab and the RHIC collider at BNL, to the next QCD frontier. Preamble Editors' note for the second editionThe first edition of this White Paper was released in 2012. In the current (second) edition, the science case for the EIC is further sharpened in view of the recent data from BNL, CERN and JLab experiments and the lessons learnt from them. Additional improvements were made by taking into account suggestions from the larger nuclear physics community including those made at the EIC Users Group meeting at Stony Brook University in July 2014, and the QCD Town Meeting at Temple University in September 2014.Abhay Deshpande, Zein-Eddine Meziani and Jian-Wei Qiu November 2014 Editors' note for the third edition Since the 2nd release of this White Paper, the NSAC's Long Range Plan (2015) was successfully completed. The EIC is a major recommendation of the US nuclear science community. In the current release (version 3) we have fixed some minor remaining errors in the text, and have added a few new references. While the core science case for the EIC remains the same, the machine designs of both options, the eRHIC at BNL and the JLEIC at JLab keep evolving. In this 3rd release of the EIC White Paper instead of making substantial changes to the machine design sections (5.1 and 5.2), we give references to the most recent machine design documents.

This White Paper presents the science case of an Electron-Ion Collider (EIC), focused on the structure and interactions of gluon-dominated matter, with the intent to articulate it to the broader nuclear science community. It was commissioned by the managements of Brookhaven National Laboratory (BNL) and Thomas Jefferson National Accelerator Facility (JLab) with the objective of presenting a summary of scientific opportunities and goals of the EIC as a follow-up to the 2007 NSAC Long Range plan. This document is a culmination of a community-wide effort in nuclear science following a series of workshops on EIC physics over the past decades and, in particular, the focused ten-week program on "Gluons and quark sea at high energies" at the Institute for Nuclear Theory in Fall 2010. It contains a brief description of a few golden physics measurements along with accelerator and detector concepts required to achieve them. It has been benefited profoundly from inputs by the users' communities of BNL and JLab. This White Paper offers the promise to propel the QCD science program in the U.S., established with the CEBAF accelerator at JLab and the RHIC collider at BNL, to the next QCD frontier. Editors' Note for the Second EditionThe first edition of this White Paper was released in 2012. In the current (second) edition, the science case for the EIC is further sharpened in view of the recent data from BNL, CERN and JLab experiments and the lessons learnt from them. Additional improvements were made by taking into account suggestions from the larger nuclear physics community including those made at the EIC Users Group meeting at Stony Brook University in July 2014, and the QCD Town Meeting at Temple University in September 2014.

We propose a method to evaluate hadronic matrix elements of QCD gluon operators in the instanton vacuum. We construct the ground state of the interacting instanton ensemble for non-zero $\vartheta$--angle using a variational principle. A method to study the $\vartheta$--dependence of observables on the lattice is suggested. We then derive the effective fermion action, which allows to calculate hadronic correlation functions in a $1/N_c$--expansion (Nambu--Jona-Lasinio type effective fermion theory). Gluon operators are systematically represented as effective fermion operators. Physical matrix elements are obtained after integrating the correlation functions over fluctuations of the numbers of instantons. The influence of the fermion determinant on the topological susceptibility is taken into account. Our effective description gives matrix elements fully consistent with the trace and $U(1)_A$ anomalies. The approach allows to consistently evaluate the nucleon matrix elements of various gluon and mixed quark--gluon operators in a chiral soliton picture of the nucleon.Comment: 40 pp. The discussion of the value of g_A^0 and of ref.[36] has been updated. A trivial error in formulas of section 5 has been corrected. This is the final version to appear in Nucl. Phys.

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...