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.

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Electron-Ion Collider: The next QCD frontier: Understanding the glue that binds us all

We provide a broad overview of the theoretical status and phenomenological applications of the Color Glass Condensate effective field theory describing universal properties of saturated gluons in hadron wavefunctions that are extracted from deeply inelastic scattering and hadron-hadron collision experiments at high energies.

The Color Glass Condensate

I briefly review the physical picture of the saturated gluons at small-x as a Colour Glass Condensate, and the effective theory which forms the basis of this picture.

The Colour Glass Condensate

Motivated by the vast string landscape, we consider the shear viscosity to entropy density ratio in conformal field theories dual to Einstein gravity with curvature square corrections. After field redefinitions these theories reduce to Gauss-Bonnet gravity, which has special properties that allow us to compute the shear viscosity nonperturbatively in the Gauss-Bonnet coupling. By tuning of the coupling, the value of the shear viscosity to entropy density ratio can be adjusted to any positive value from infinity down to zero, thus violating the conjectured viscosity bound. At linear order in the coupling, we also check consistency of four different methods to calculate the shear viscosity, and we find that all of them agree. We search for possible pathologies associated with this class of theories violating the viscosity bound.

Viscosity Bound Violation in Higher Derivative Gravity

A new set of equations for relativistic viscous hydrodynamics that captures both weak-coupling and strong-coupling physics to second order in gradients has been developed recently. We apply this framework to bulk physics at the Relativistic Heavy Ion Collider (RHIC), both for standard (Glauber-type) as well as for color-glass-condensate (CGC) initial conditions and show that the results do not depend strongly on the values for the second-order transport coefficients. Results for multiplicity, radial flow and elliptic flow are presented, and we quote the ratio of viscosity over entropy density for which our hydrodynamic model is consistent with experimental data. For CGC initial conditions, early thermalization does not seem to be required in order for hydrodynamics to describe charged hadron elliptic flow.

Conformal relativistic viscous hydrodynamics: Applications to RHIC results at s NN =200 GeV

In this work we simulate a viscous hydrodynamical model of noncentral Au-Au collisions in 2+1 dimensions, assuming longitudinal boost invariance The model fluid equations were proposed by Oettinger and Grmela [Grmela, M, and Oettinger, H C, Phys Rev E, 56, 6620 (1997)] Freeze-out is signaled when the viscous corrections become large relative to the ideal terms Then viscous corrections to the transverse momentum and differential elliptic flow spectra are calculated When viscous corrections to the thermal distribution function are not included, the effects of viscosity on elliptic flow are modest However, when these corrections are included, the elliptic flow is strongly modified at large p{sub T} We also investigate the stability of the viscous results by comparing the nonideal components of the stress tensor ({pi}{sup ij}) and their influence on the v{sub 2} spectrum to the expectation of the Navier-Stokes equations ({pi}{sup ij}=-{eta} ) We argue that when the stress tensor deviates from the Navier-Stokes form the dissipative corrections to spectra are too large for a hydrodynamic description to be reliable For typical Relativistic Heavy Ion Colloder initial conditions this happens for {eta}/s > or approx 03

Simulating elliptic flow with viscous hydrodynamics

We perform a detailed comparison of long-range rapidity correlations in the color glass condensate framework to high multiplicity dihadron data in proton-proton and proton-lead collisions from the CMS, ALICE and ATLAS experiments at the LHC. The overall good agreement thus far of the nontrivial systematics of theory with data is strongly suggestive of gluon saturation and the presence of subtle quantum interference effects between rapidity separated gluons. In particular, the yield of pairs collimated in their relative azimuthal angle $\ensuremath{\Delta}\ensuremath{\phi}\ensuremath{\sim}0$, is sensitive to the shape of unintegrated gluon distributions in the hadrons that are renormalization group evolved in rapidity from the beam rapidities to those of the measured hadrons. We present estimates for the collimated dihadron yield expected in central deuteron-gold collisions at the Relativistic Heavy Ion Collider.

Comparison of the color glass condensate to dihadron correlations in proton-proton and proton-nucleus collisions

The ridge in proton-proton collisions at the LHC

The azimuthal collimation of dihadrons with large rapidity separations in high multiplicity p+p collisions at the LHC is described in the color glass condensate (CGC) effective theory [A. Dumitru, K. Dusling, F. Gelis, J. Jalilian-Marian, T. Lappi, and R. Venugopalan, Phys. Lett. B 697, 21 (2011).] by N(c)(2) suppressed multiladder QCD diagrams that are enhanced α(S)(-8) due to gluon saturation in hadron wave functions. We show that quantitative computations in the CGC framework are in good agreement with data from the CMS experiment on per trigger dihadron yields and predict further systematics of these yields with varying trigger p(T) and charged hadron multiplicity. Radial flow generated by rescattering is strongly limited by the structure of the p+p dihadron correlations. In contrast, radial flow explains the systematics of identical measurements in heavy ion collisions.

Azimuthal collimation of long range rapidity correlations by strong color fields in high multiplicity hadron-hadron collisions.

The observation of long-range rapidity correlations among particles in high-multiplicity p–p and p–Pb collisions has created new opportunities for investigating novel high-density QCD phenomena in small colliding systems. We review experimental results related to the study of collective phenomena in small systems at RHIC and the LHC along with the related developments in theory and phenomenology. Perspectives on possible future directions for research are discussed with the aim of exploring emergent QCD phenomena.

Kevin Dusling

Papers

Simulating elliptic flow with viscous hydrodynamics

Comparison of the color glass condensate to dihadron correlations in proton-proton and proton-nucleus collisions

The ridge in proton-proton collisions at the LHC

Azimuthal collimation of long range rapidity correlations by strong color fields in high multiplicity hadron-hadron collisions.

Novel collective phenomena in high-energy proton–proton and proton–nucleus collisions