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We present results from a numerical solution of the next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation in coordinate space in the large Nc limit. We show that the solution is not stable for initial conditions that are close to those used in phenomenological applications of the leading order equation. We identify the problematic terms in the NLO kernel as being related to large logarithms of a small parent dipole size, and also show that rewriting the equation in terms of the "conformal dipole" does not remove the problem. Our results qualitatively agree with expectations based on the behavior of the linear NLO BFKL equation., Comment: 6 pages, 4 figures. Talk by T.L. at DIS 2015, Dallas, TX, April 2015

We briefly review advances in understanding the initial stages of a heavy ion collision. In particular the focus is on moving from parametrizing the initial state to calculating its properties from QCD, consistently with the description of hard probes and dilute-dense scattering experiments. Modeling the event-by-event fluctuating nuclear geometry in initial state calculations has significantly improved in recent years. We also discuss prospects of directly seeing effects of particle correlations created in the initial state in the experimental observables., Comment: 6 pages, 3 figures. Plenary talk at Hard Probes 2015 conference, Montreal, QC, June/July 2015

We present the first numerical solution to the next to leading order Balitsky-Kovchegov (BK) equation in coordinate space in the large-$N_\mathrm{c}$ limit. In addition to the dipole operator we also solve the evolution of the "conformal dipole" for which the conformal invariance breaking double logarithmic term is absent from the evolution equation. The NLO corrections are shown to slow down the evolution. We show that the solution depends strongly on the details of the initial condition, and that the solution to the equation is not positive definite with all initial conditions relevant for phenomenological applications., Comment: 4 pages, 4 figures. Talk given by H.M. at the 7th International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions (Hard Probes 2015)

Recent experimental results have revealed a surprisingly rich structure of multiparticle azimuthal correlations in high energy proton-nucleus collisions. Final state collective effects can be responsible for many of the observed effects, but it has recently been argued that a part of these correlations are present already in the wavefunctions of the colliding particles. We evaluate the momentum space 2-particle cumulant azimuthal anisotropy coefficients v_n{2}, n=2,3,4 from fundamental representation Wilson line distributions describing the high energy nucleus. These would correspond to the flow coefficients in very forward proton nucleus scattering. We find significant differences beteen Wilson lines from the MV model and from JIMWLK evolution. The magnitude and transverse momentum dependence of the v_n{2} values suggest that the fluctuations present in the initial fields are a significant contribution to the observed anisotropies., Comment: 6 pages, 3 figures, ReVTEX V2: added references and labels on figures

Inclusive production of $J/\psi$ mesons, especially at forward rapidities, is an important probe of small-x gluons in protons and nuclei. In this paper we re-evaluate the production cross sections in the Color Glass Condensate framework, where the process is described by a large x gluon from the probe splitting into a quark pair and eikonally interacting with the target proton or nucleus. Using a standard collinear gluon distribution for the probe and an up to date dipole cross section fitted to HERA data to describe the target we achieve a rather good description of the cross section in proton-proton collisions, although with a rather large normalization uncertainty. More importantly, we show that generalizing the dipole cross section to nuclei in the Glauber approach results in a nuclear suppression of $J/\psi$ production that is much closer to the experimental data than claimed in previous literature., Comment: 8 pages, 10 figures, RevTeX. V2: small clarifications, 1 added figure, published in PRD

We present the first numerical solution to the next to leading order Balitsky-Kovchegov (BK) equation in coordinate space in the large-$N_\mathrm{c}$ limit. In addition to the dipole operator we also solve the evolution of the "conformal dipole" for which the conformal invariance breaking double logarithmic term is absent from the evolution equation. The NLO corrections are shown to slow down the evolution. We show that the solution depends strongly on the details of the initial condition, and that the solution to the equation is not positive definite with all initial conditions relevant for phenomenological applications., Comment: 8 pages, 10 figures. RevTeX. v2: references added, small clarifications to the text and Figs. 9 and 10, to be published in Phys. Rev. D

This document provides a summary of the discussions during the recent joint QCD Town Meeting at Temple University of the status of and future plans for the research program of the relativistic heavy-ion community. A list of compelling questions is formulated, and a number of recommendations outlining the greatest research opportunities and detailing the research priorities of the heavy-ion community, voted on and unanimously approved at the Town Meeting, are presented. They are supported by a broad discussion of the underlying physics and its relation to other subfields. Areas of overlapping interests with the "QCD and Hadron Structure" ("cold QCD") subcommunity, in particular the recommendation for the future construction of an Electron-Ion Collider, are emphasized. The agenda of activities of the "hot QCD" subcommunity at the Town Meeting is attached., Comment: 34 pages of text, 254 references,16 figures

We argue that the proton multiplicities measured in Roman pot detectors at an electron ion collider can be used to determine centrality classes in incoherent diffractive scattering. Incoherent diffraction probes the fluctuations in the interaction strengths of multi-parton Fock states in the nuclear wavefunctions. In particular, the saturation scale that characterizes this multi-parton dynamics is significantly larger in central events relative to minimum bias events. As an application, we study the centrality dependence of incoherent diffractive vector meson production. We identify an observable which is simultaneously very sensitive to centrality triggered parton fluctuations and insensitive to details of the model., Comment: 5 pages, 4 figures, RevTEX V2: small clarifications, to be published in PRL

The initial stage of a heavy ion collision is dominated by nonperturbatively strong chromoelectric and -magnetic fields. The spatial Wilson loop provides a gauge invariant observable to probe the dynamics of the longitudinal chromomagnetic field. We discuss recent results from a real time lattice calculation of the area-dependence of the expectation value of the spatial Wilson loop. We show that at relatively early times after the collision, a universal scaling as a function of the area emerges at large distances for very different initial conditions, with a nontrivial critical exponent. A similar behavior has earlier been seen in calculations of the gluon transverse momentum spectrum, which becomes independent of the initial spectrum of gauge fields. We also show the distribution of eigenvalues of the spatial Wilson loop and the fluctuations of its real and imaginary parts., Comment: 4 pages, 3 figures, talk by TL at the Quark Matter 2014 conference, Darmstadt, Germany, May 19-24

We compute cross sections for incoherent and coherent diffractive J/$\Psi$ and $\Psi(2S)$ production in ultraperipheral heavy ion collisions. The dipole models used in these calculations are obtained by fitting the HERA deep inelastic scattering data and compared with available electron-proton diffraction measurements. We obtain a reasonably good description of the available ALICE data. We find that the normalization of the ultraperipheral cross section has large model dependence, but the rapidity dependence is more tightly constrained., Comment: 6 pages, 4 figures. Talk given by H.M. at XXII. International Workshop on Deep-Inelastic Scattering and Related Subjects

We determine the initial condition for the small-$x$ evolution equation (BK) from the HERA deep inelastic scattering data using a new parametrization that also keeps the unintegrated gluon distribution positive. The obtained dipole amplitude and its uncertainty estimate can be used to compute single inclusive particle production in proton-proton and proton-nucleus collisions. We argue that one has to use consistently the proton transverse area measured in DIS and the total inelastic cross section when calculating the single inclusive cross section. This leads to a midrapidity nuclear modification factor $R_{pA}$ that approaches unity at large transverse momentum, independently of the center-of-mass energy., Comment: 6 pages, 4 figures. Talk given by H.M. at XXII. International Workshop on Deep-Inelastic Scattering and Related Subjects

We compute expectation values of spatial Wilson loops in the forward light cone of high-energy collisions. We consider ensembles of gauge field configurations generated from a classical Gaussian effective action as well as solutions of high-energy renormalization group evolution with fixed and running coupling. The initial fields correspond to a color field condensate exhibiting domain-like structure over distance scales of order the saturation scale. At later times universal scaling emerges at large distances for all ensembles, with a nontrivial critical exponent. Finally, we compare the results for the Wilson loop to the two-point correlator of magnetic fields., Comment: RevTeX, 7 pages, 8 figures. V2: minor clarifications in text, Fig 6 revised

We compute single inclusive hadron production in proton-proton and proton-nucleus collisions consistently within the CGC framework. The parameters in the calculations are obtained from electron-proton DIS and standard nuclear geometry. We obtain a good description of the DIS data without an anomalous dimension in the initial condition of the BK evolution and get a good agreement with the available single inclusive proton-proton and proton-nucleus data., Comment: 4 pages, 4 figures, talk given at the 6th International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions (Hard Probes 2013), November 4-8, 2013 (Cape Town, South Africa)

In the CGC framework the initial stages of a heavy ion collision at high energy are described as "glasma" field configurations. The initial condition for these evolving fields depends, in the CGC effective theory, on a probability distribution for color charges. The energy dependence of this distribution can be calculated from the JIMWLK renormalization group equation. We discuss recent work on a practical implementation of the running coupling constant in the Langevin method of solving the JIMWLK equation., Comment: 4 pages, 4 figures, talk by T.L. at the 6th International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions (Hard Probes 2013), November 4-8, 2013 (Cape Town, South Africa)

We study single inclusive hadron production in proton-proton and proton-nucleus collisions in the CGC framework. The parameters in the calculation are obtained by fitting electron-proton deep inelastic scattering data. The obtained dipole-proton amplitude is generalized to dipole-nucleus scattering without any additional nuclear parameters other than the Woods-Saxon distribution. We show that it is possible to use an initial condition without an anomalous dimension and still obtain a good description of the HERA inclusive cross section and LHC single particle production measurements. We argue that one must consistently use the proton transverse area as measured by a high virtuality probe in DIS also for the single inclusive cross section in proton-proton and proton-nucleus collisions, and obtain a nuclear modification factor $R_{pA}$ that at midrapidity approaches unity at large momenta and at all energies., Comment: 8 pages, 8 figures. Talk by H.M. at the International Conference on the Initial Stages in High-Energy Nuclear Collisions (IS2013), Spain, September 8-14 2013. Conference proceedings article

We study single inclusive hadron production in proton-proton and proton-nucleus collisions in the CGC framework. The parameters in the calculation are determined solely by standard nuclear geometry and by electron-proton deep inelastic scattering data, which is fit using the running coupling BK equation. We show that it is possible to obtain a good fit of the HERA inclusive cross section also without an anomalous dimension in the initial condition. We argue that one must consistently use the proton transverse area as measured by a high virtuality probe in DIS also for the single inclusive cross section in proton-proton and proton-nucleus collisions. We show that this leads to a midrapidity nuclear modification ratio R_pA that approaches unity at high transverse momentum independently of sqrt(s), in contrast to most CGC calculations in the literature. We also present predictions for future forward R_pA measurements at the LHC., Comment: 13 pages, 18 figures. RevTeX

We discuss coherent and incoherent photoproduction of $J/\Psi$ vector mesons in high energy heavy ion collisions. In a dipole picture for the photon both can be naturally related to the dipole cross section that is also probed in inclusive DIS. We compare results of a particular calculation to ALICE data., Comment: Presented at EDS Blois 2013 (arXiv:1309.5705)

We discuss applications of the JIMWLK renormalization group equation to multigluon correlations in high energy collisions. This includes recent progress in computing the energy dependence of higher point Wilson line correlators from the JIMWLK renormalization group equation. We find that the large Nc approximation used so far in the phenomenological literature is not very accurate. On the other hand a Gaussian finite Nc approximation is surprisingly close to the full result. We also discuss correlations at large rapidity separations, relevant for the "ridge" correlations observed in experiments., Comment: 4 pages, 3 figures, talk given at the 5th international Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions (Hard Probes 2012), May 27th - June 1st, Cagliari (Italy) V2: typo corrections

We propose a new method to implement the running coupling constant in the JIMWLK equation, imposing the scale dependence on the correlation function of the random noise in the Langevin formulation. We interpret this scale choice as the transverse momentum of the emitted gluon in one step of the evolution and show that it is related to the "Balitsky" prescription for the BK equation. This slows down the evolution speed of a practical solution of the JIMWLK equation, bringing it closer to the x-dependence inferred from fits to HERA data. We further study our proposal by a numerical comparison of the BK and JIMWLK equations., Comment: 13 pages, 11 figures, RevTeX

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 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, and it benefited from inputs from 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., Comment: The Second Edition, 164 pages

Multiparticle correlations, such as forward dihadron correlations in pA collisions, are an important probe of the strong color fields that dominate the initial stages of a heavy ion collision. We describe recent progress in understanding two-particle correlations in the dilute-dense system, e.g. at forward rapidity in deuteron-gold collisions. This requires evaluating higher point Wilson line correlators from the JIMWLK equation, which we find well described by a Gaussian approximation. We then calculate the dihadron correlation, including both the "elastic" and "inelastic" contributions, and show that our result includes the double parton scattering contribution., Comment: 4 pages, 5 figures, talk by T.L. at Quark Matter 2012, Washington DC, August 13-18 2012

We compute dihadron correlations in forward deuteron-gold or proton-gold collisions. The running coupling BK equation is used to calculate the energy dependence of the dipole cross sections and extended to higher point Wilson line correlators using a factorized Gaussian approximation. Unlike some earlier works we include both the "inelastic" and "elastic" contributions to the dihadron cross section. We show that the double parton scattering contribution is included in our calculation and obtain both an away side peak that roughly agrees with experimental observations and an estimate for the azimuthal angle-independent pedestal. We find that nonlinear effects for momenta close to the saturation scale are clearly visible in the away side peak structure., Comment: 15 pages, 12 figures, RevTeX. v2: Published in Nucl. Phys. A

A natural framework to understand the energy dependence of bulk observables from lower energy experiments to the LHC is provided by the Color Glass Condensate, which leads to a "geometrical scaling" in terms of an energy dependent saturation scale Q_s. The measured charged multiplicity, however, seems to grow faster (~\sqrt{s}^0.3) in nucleus-nucleus collisions than it does for protons (~\sqrt{s}^0.2), violating the expectation from geometric scaling. We argue that this difference between pp and AA collisions can be understood from the effect of DGLAP evolution on the value of the saturation scale, and is consistent with gluon saturation observations at HERA., Comment: RevTeX, 8 pages, 4 figures. V2: modified discussion of fragmentation, published in EPJC

The JIMWLK equation with a "daughter dipole" running coupling is solved numerically starting from an initial condition given by the McLerran-Venugopalan model. The resulting Wilson line configurations are then used to compute the spectrum of gluons comprising the glasma inital state of a high energy heavy ion collision. The development of a geometrical scaling region makes the spectrum of produced gluons harder. Thus the ratio of the mean gluon transverse momentum to the saturation scale grows with energy. Also the total gluon multiplicity increases with energy slightly faster than the saturation scale squared., Comment: 7 pages, 8 figures, RevTeX. V2: typo corrections, corrected fig 1. Published in PLB

This report 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 in Seattle in Fall 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. This report is organized around four major themes: i) the spin and flavor structure of the proton, ii) three-dimensional structure of nucleons and nuclei in momentum and configuration space, iii) QCD matter in nuclei, and iv) Electroweak physics and the search for physics beyond the Standard Model. Beginning with an executive summary, the report contains tables of key measurements, chapter overviews for each of the major scientific themes, and detailed individual contributions on various aspects of the scientific opportunities presented by an EIC., Comment: 547 pages, A report on the joint BNL/INT/Jlab program on the science case for an Electron-Ion Collider, September 13 to November 19, 2010, Institute for Nuclear Theory, Seattle; v2 with minor changes, matches printed version

The physics of the initial conditions of heavy ion collisions is dominated by the nonlinear gluonic interactions of QCD. These lead to the concepts of parton saturation and the Color Glass Condensate (CGC). We discuss recent progress in calculating multi-gluon correlations in this framework, prompted by the observation that these correlations are in fact easier to compute in a dense system (nucleus-nucleus) than a dilute one (proton-proton)., Comment: 7 pages, 4 figures, talk at "Saturation, the CGC and the Glasma: What have we learned from RHIC?" RBRC workshop, May 2010

We study the gluon distribution in nucleus-nucleus collisions in the framework of the Color-Glass-Condensate. Approximate analytical solutions are compared to numerical solutions of the non-linear Yang-Mills equations. We find that the full numerical solution can be well approximated by taking the full initial condition of the fields in Coulomb gauge and using a linearized solution for the time evolution. We also compare kt-factorized approximations to the full solution., Comment: 13 pages, 12 figures, RevTeX

This is a review of applications of the Color Glass Condensate to the phenomenology of relativistic heavy ion collisions. The initial stages of the collision can be understood in terms of the nonperturbatively strong nonlinear glasma color fields. We discuss how the CGC framework can and has been used to compute properties of the initial conditions of AA collisions. In particular this has led to recent progress in understanding multiparticle correlations, which can provide a directly observable signal of the properties of the initial stage of the collision process., Comment: Review, 45 pages, 19 figures, IJMPE style

The physics of the initial conditions of heavy ion collisions is dominated by the nonlinear gluonic interactions of QCD. These lead to the concepts of parton saturation and the Color Glass Condensate (CGC). We discuss recent progress in calculating multi-gluon correlations in this framework, prompted by the observation that these correlations are in fact easier to compute in a dense system (nucleus-nucleus) than a dilute one (proton-proton)., Comment: 8 pages, 5 figures, talk at the Symposium on High Energy Strong Interactions 2010 (HESI 2010), Yukawa Institute for Theoretical Physics, Kyoto, Japan, August 9-13, 2010