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.

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Filling a gap in the current literature, this book is the first entirely dedicated to high energy quantum chromodynamics (QCD) including parton saturation and the color glass condensate (CGC). It presents groundbreaking progress on the subject and describes many problems at the forefront of research, bringing postgraduate students, theorists and interested experimentalists up to date with the current state of research in this field. The material is presented in a pedagogical way, with numerous examples and exercises. Discussion ranges from the quasi-classical McLerran–Venugopalan model to the linear BFKL and nonlinear BK/JIMWLK small-x evolution equations. The authors adopt both a theoretical and an experimental outlook, and present the physics of strong interactions in a universal way, making it useful for physicists from various subcommunities of high energy and nuclear physics, and applicable to processes studied at all high energy accelerators around the world. A selection of color figures is available online at www.cambridge.org/9780521112574.

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.

In this paper a solution is given to the nonlinear equation which describes the evolution of the parton cascade in the case of the high parton density. The related physics is discussed as well as some applications to heavy ion-ion collisions. *

We argue that the suppression of high p t hadrons discovered recently in heavy ion collisions at RHIC may be a consequence of saturation in the Color Glass Condensate. We qualitatively and semi-quantitatively describe the data, in particular, the dependence upon the number of nucleon participants. We show that if parton saturation sets in at sufficiently small energy, then in nucleus-nucleus collisions at RHIC and LHC energies the cross sections of semi-hard processes should scale approximately with the number of participants, N part . Our results provide a possible explanation of both the absence of apparent jet quenching at SPS energies and its presence at RHIC. Under the same assumption we predict that in semi-central and central pA (dA) collisions at collider energies the dependence of semi-hard processes on the number of participating nucleons of the nucleus will change to ∼ (N A part ) 1/2 . The forthcoming data on dA collisions will provide a crucial test of this description.

We derive a simple analytical scaling function which embodies the predictions of high density QCD on the energy, centrality, rapidity, and atomic number dependences of hadron multiplicities in nuclear collisions. Both centrality and rapidity dependences of hadron multiplicity in $Au-Au$ collisions as measured at RHIC at $\sqrt{s}= 130 {GeV}$ are well described in this approach. The centrality and rapidity dependences of hadron multiplicity at $\sqrt{s}= 200 \ {GeV}$ run at RHIC are predicted; the variation of these dependences with energy appear different from other approaches, and can be used as an important test of the ideas based on parton saturation and classical Chromo-Dynamics.Comment: 15 pages, 7 figures; final journal version - 3 typos corrected, discussion extende

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