Multi-particle correlation observables in the Relativistic Heavy Ion Collider small system scan are computed in a framework that contains both initial state momentum anisotropies from the Color Glass Condensate effective theory and final state hydrodynamic evolution. The initial state is computed using the IP-Glasma model and coupled to viscous relativistic hydrodynamic simulations, which are followed by microscopic hadronic transport. All parameters of the calculation were previously constrained using experimental data on Au+Au collisions at the same center of mass energy. We find that the qualitative features of the experimental data, such as the system and centrality dependence of the charged hadron momentum anisotropy, can only be reproduced when final state interactions are present. On the other hand, we also demonstrate that the details of the initial state are crucially important for the quantitative description of observables in the studied small systems, as neglecting the initial transverse flow profile or the initial shear stress tensor, which contain information on the momentum anisotropy from the Color Glass Condensate, has dramatic effects on the produced final state anisotropy. We further show that the initial state momentum anisotropy is correlated with the observed elliptic flow in all small systems, with the effect increasing with decreasing multiplicity. We identify the precise measurement of $v_2$ in d+Au and Au+Au collisions at RHIC energy at the same multiplicity as a means to reveal effects of the initial state momentum anisotropy.
We evaluate the invariant cross section for production of dileptons in forward rapidities at RHIC and LHC, using the Color Glass Condensate formalism and present results for the nuclear modification factor $R_{d(p)A}$ as a function of dilepton invariant mass for the most central deuteron (proton)-nucleus collisions.
We summarize the theory and phenomenology of the Color Glass Condensate reviewed previously by E. Iancu and the author in hep-ph/0303204. In addition, we discuss some of the subsequent developments in the past year both in theory and in phenomenological applications.
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.
We investigate hydrodynamic evolution of the quark gluon plasma for the colour glass condensate type initial conditions. We solve full second-order viscous hydrodynamic equations in the longitudinal direction to find that non-boost invariant expansion leads to visible deformation on the initial rapidity distribution. The results indicate that hydrodynamic evolution with viscosity plays an important role in determining parameters for the initial distributions.
We consider dilepton production in high energy proton-nucleus (and very forward nucleus-nucleus) collisions. Treating the target nucleus as a Color Glass Condensate and describing the projectile proton (nucleus) as a collection of quarks and gluons as in the parton model, we calculate the differential cross section for dilepton production in quark-nucleus scattering and show that it is very sensitive to the saturation scale characterizing the target nucleus.
We show how the limiting fragmentation phenomenon can arise from the Color Glass Condensate model of high energy QCD. We consider the very forward rapidity region in relativistic heavy ion collisions and argue that in this region, nucleus-nucleus collisions are similar to proton-nucleus collisions (up to shadowing corrections). We then use the known results for proton-nucleus cross sections to show that it leads to the phenomenon of limiting fragmentation in the very forward region of heavy ion collisions as observed at RHIC.
We calculate the transverse correlation of fluctuations of the deposited energy density in nuclear collisions in the framework of the Gaussian color glass condensate model.
We compute the production of quark-antiquark pairs in high energy collisions between a small and a large projectile, as in proton-nucleus collisions, in the framework of the Color Glass Condensate. We derive a general expression for quark pair-production, which is not k_t-factorizable. However, k_t-factorization is recovered in the limit of large mass pairs or large quark--anti-quark momenta. Our results are amenable to a simple interpretation and suggest how multi-parton correlations at small x can be quantified in high-energy proton/deuteron-nucleus collisions.
In this review, I present the description of the early stages of heavy ion collisions at high energy in the Color Glass Condensate framework, from the pre-collision high energy nuclear wavefunction to the point where hydrodynamics may start becoming applicable.
In this talk, we discuss some general properties of particle production in a field theory coupled to strong time dependent sources, and techniques to compute the spectrum of the produced particles in such theories. We also discuss the application of these results to the description of hadron or heavy ion collisions in the Color Glass Condensate framework.
We show that the numerical solution of the classical SU(3) Yang-Mills equations of motion in the McLerran-Venugopalan model for gluon production in central heavy ion collisions leads to a suppresion at low $p_t$ and an enhancement at the intermediate $p_t$ region as compared to peripheral heavy ion and pp collisions at the same energy. Our results are compared to previous, Color Glass Condensate inspired calculations of gluon production in heavy ion collisions. We revisit the predictions of the Color Glass Condensate model for $pA$ ($dA$) collisions in Leading Order and show that quantum evolu…
We study the Drell-Yan production cross section and structure functions in proton (deuteron)-nucleus collisions using the Color Glass Condensate formalism. The nucleus is treated in the Color Glass Condensate framework which includes both higher twist effects due to the inclusion of multiple scatterings and leading twist pQCD shadowing due to the small x resummation, while the proton (or deuteron) is treated within the DGLAP improved parton model. In particular, the Drell-Yan structure functions are used in order to investigate the Lam-Tung relation at small x, which is known to be identically…
The net-baryon production at forward rapidities is investigated considering the Color Glass Condensate formalism. We assume that at large energies the coherence of the projectile quarks is lost and that the leading baryon production mechanism changes from recombination to independent fragmentation. The phenomenological implications for net-baryon production in $pp/pA/AA$ collisions are analysed and predictions for LHC energies are presented.
In a model of relativistic heavy ion collisions wherein the unconfined quark-gluon plasma is condensed into glass, we derive the Vogel-Fulcher-Tammann cooling law. This law is well known to hold true in condensed matter glasses. The high energy plasma is initially created in a very hot negative temperature state and cools down to the Hagedorn glass temperature at an ever decreasing rate. The cooling rate is largely determined by the QCD string tension derived from hadronic Regge trajectories. The ultimately slow relaxation time is a defining characteristic of a color glass condensate.
We perform a detailed comparison of long range rapidity correlations in the Color Glass Condensate framework to high multiplicity di-hadron 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 non-trivial 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 $Δϕ\sim 0$, is sensitive to the shape of unintegrated glu…
We perform a quantitative analysis of the nuclear modification factor in deuteron--gold collisions R(dAu) within the Color Glass Condensate approach, and compare our results with the recent data from RHIC experiments. Our model leads to Cronin enhancement at mid-rapidity, while at forward rapidities it predicts strong suppression of R(dAu) at all pT due to low-x evolution. We demonstrate that our results are consistent with the data for dAu charged hadron spectra, R(dAu) and R(CP) recently reported for rapidities in the interval eta=0--3.2 by the BRAHMS experiment at RHIC. We also make a predi…
We present a review of parton saturation/Color Glass Condensate physics in the context of deuteron-gold ($d+Au$) collisions at RHIC. Color Glass Condensate physics is a universal description of all high energy hadronic and nuclear interactions. It comprises classical (McLerran-Venugopalan model and Glauber-Mueller rescatterings) and quantum evolution (JIMWLK and BK equations) effects both in small-$x$ hadronic and nuclear wave functions and in the high energy scattering processes. Proton-nucleus (or $d+A$) collisions present a unique opportunity to study Color Glass Condensate predictions, sin…
We consider the J/Psi production in proton (deuteron) -- nucleus collisions at high energies. We argue that the production mechanism in this case is different from that in pp collisions due to gluon saturation in the nucleus and formation of the Color Glass Condensate. At forward rapidities (in the proton fragmentation region), the production of J/Psi is increasingly suppressed both as a function of rapidity and centrality. On the other hand, at backward rapidities at RHIC (in the fragmentation region of the nucleus) the coherent effects lead to a modest enhancement of the production cross sec…
The eccentricity in coordinate-space at midrapidity of the overlap zone in high-energy heavy-ion collisions predicted by the $k_\perp$-factorization formalism is generically larger than expected from scaling with the number of participants. We provide a simple qualitative explanation of the effect which shows that it is not caused predominantly by edge effects. We also show that it is quite insensitive to ``details'' of the unintegrated gluon distribution functions such as the presence of leading-twist shadowing and of an extended geometric scaling window. The larger eccentricity increases the…
We review the Color Glass Condensate effective theory, that describes the gluon content of a high energy hadron or nucleus, in the saturation regime. The emphasis is put on applications to high energy heavy ion collisions. After describing initial state factorization, we discuss the Glasma phase, that precedes the formation of an equilibrated quark-gluon plasma. We end this review with a presentation of recent developments in the study of the isotropization and thermalization of the quark-gluon plasma.
Simple power counting arguments in the dilute-dense framework of the Color Glass Condensate (CGC) Effective Field Theory predict that even and odd azimuthal anisotropy harmonics of two-particle correlations in proton-nucleus collisions at the LHC will respectively satisfy v^2_{2n} ~ N_{ch}^0 and v^2_{2n+1} ~ N_{ch}, where N_{ch} denotes the number of charged particles. We show that these expectations are borne out qualitatively, and even quantitatively, within systematic uncertainties, for v_2 and v_4 in comparisons with data from the ATLAS collaboration. We also observe that ATLAS data for th…
We present a good description of recent experimental data on forward di-hadron azimuthal correlations measured in deuteron-gold collisions at RHIC, where monojet production has been observed. Our approach is based on the Color Glass Condensate effective theory for the small-x degrees of freedom of the nuclear wave function, including the use of non-linear evolution equations with running QCD coupling. Our analysis provides further evidence for the presence of saturation effects in RHIC data.
The forthcoming LHC measurement of hadron multiplicity in proton-nucleus collisions is a crucial test of the k_t factorization and gluon saturation based models. Here, we provide quantitative predictions for the pseudorapidity distribution of charged particles produced in minimum bias proton-nucleus collisions at the LHC based on the idea of gluon saturation in the color-glass condensate framework. Our formulation gives good descriptions of the LHC and RHIC data for the charged-hadron multiplicities in both proton-proton and nucleus-nucleus collisions, and also the deep inelastic scattering at…
We compute quark-antiquark pair production in the context of the Color Glass Condensate model for central heavy-ion collisions. The calculation is performed analytically to leading order in the density of hard sources present in the projectiles, and is applicable to quarks with a mass large compared to the saturation momentum. The formulas derived in this paper are compared to expressions derived in the framework of collinearly factorized perturbative QCD and in kt factorization models. We comment on the breaking of kt factorization which occurs beyond leading order in our approach.
We discuss baryon stopping in the Color Glass Condensate description of high energy scattering. We consider the scattering of a distribution of valence quarks on an ultra-relativistic sheet of colored charge. We compute the distribution of scattered quarks from a composite projectile, and calculate the baryon currents before and after the collisions and on an event by event basis. We obtain simple analytic estimates of the baryon number compression and rapidity shifts, which in the idealized case of plane wave scattering, produce results that agree with considerations of Anishetty-Koehler-McLe…
The impact parameter (b) dependence on the saturation scale, in the framework of the Color Glass Condensate (b-CGC) dipole model, is investigated from the configurational point of view. During the calculations and analysis of the quantum nuclear states, the critical points of stability in the configurational entropy setup are computed, matching the experimental parameters that define the onset of the quantum regime in the b-CGC in the literature with very good accuracy. This new approach is crucial and important for understanding the stability of quantum systems in study of deep inelastic scat…
We consider one loop corrections to single inclusive particle production in parton-nucleus scattering at high energies, treating the target nucleus as a Color Glass Condensate. We prove by explicit computation that in the leading log Q^2 approximation, these corrections lead to collinear factorization and DGLAP evolution of the projectile parton distribution and hadron fragmentation functions. At leading logarithmic level, and in single-inclusive cross sections, only two-point functions of Wilson lines in the adjoint and fundamental representations (Mueller's dipoles) arise, which can be obtai…
We develop a Monte-Carlo event generator based on combination of a parton production formula including the effects of parton saturation (called the DHJ formula) and hadronization process due to the Lund string fragmentation model. This event generator is designed for the description of hadron productions at forward rapidities and in a wide transverse momentum range in high-energy proton-proton collisions. We analyze transverse momentum spectra of charged hadrons as well as identified particles; pion, kaon, (anti-)proton at RHIC energy, and ultra-forward neutral pion spectra from LHCf experimen…
We take hydrodynamic initial conditions in relativistic heavy ion collisions from the Color Glass Condensate (CGC) picture through the kT factorization formula. Gluon distributions produced from the CGC are found to provide good initial conditions for the hydrodynamic simulations in Au + Au collisions at Relativistic Heavy Ion Collider (RHIC) energies. We reproduce the centrality, rapidity, and energy dependences of multiplicity within this approach. We also investigate the energy loss of high pT partons in the dense thermalized medium created from colliding two CGC's. We find that our results…
The dipole-nucleus forward scattering amplitude rules the onset of the gluon anomalous dimension, in the Color-Glass Condensate regime. In this model, the onset of quantum regime is here derived as a critical stable point in the nuclear configurational entropy, matching the fitted experimental data in the literature with accuracy of 1%. It corroborates with the informational entropy paradigm in high energy nuclear physics.
A current goal of relativistic heavy ion collisions experiments is the search for a Color Glass Condensate as the limiting state of QCD matter at very high density. In viscous hydrodynamics simulations, a standard Glauber initial condition leads to estimate $4πη/s \sim 1$, while a Color Glass Condensate modeling leads to at least a factor of 2 larger $η/s$. Within a kinetic theory approach based on a relativistic Boltzmann-like transport simulation, we point out that the out-of-equilibrium initial distribution proper of a Color Glass Condensate reduces the efficiency in building-up the ellipti…
The Color Glass Condensate formalism and its application to high energy heavy ion collisions at RHIC are discussed. We argue that the RHIC data supports the view that the Color Glass Condensate provides the initial conditions for gold-gold collisions at RHIC while final state (Quark Gluon Plasma) effects are responsible for the high $p_t$ suppression in mid rapidity. At forward rapidities in deuteron-gold collisions, however, Color Glass Condensate is the underlying physics of the observed suppression of the particle spectra and their centrality dependence.
In this talk, we report on our results about the computation of the elliptic flow of the quark-gluon-plasma produced in relativistic heavy ion collisions, simulating the expansion of the fireball by solving the relativistic Boltzmann equation for the parton distribution function tuned at a fixed shear viscosity to entropy density ratio $η/s$. We emphasize the role of saturation in the initial gluon spectrum modelling the shattering of the color glass condensate, causing the initial distribution to be out of equilibrium. We find that the saturation reduces the efficiency in building-up the elli…
We report on a first NLO computation of photon production in p+A collisions at collider energies within the Color Glass Condensate framework, significantly extending previous LO results. At central rapidites, our result is the dominant contribution and probes multi-gluon correlators in nuclei. At high photon momenta, the result is directly sensitive to the nuclear gluon distribution. The NLO result contains two processes, the annihilation process and the process with $q\bar{q}$ pair and a photon in the final state. We provide a numerical evaluation of the photon spectrum from the annihilation …
The power-law tail of high-pt pi^\pm spectra observed in forward d+Au collisions at RHIC can be attributed to the power-law decrease of the dipole forward scattering amplitude appearing in the color glass condensate (CGC) approach. Forward particle production probes the small-x gluon distribution of the target nucleus where its anomalous dimension is rather flat (gamma = 0.6 \sim 0.8) for moderately high pt (\lsim 5 GeV), and where the leading-twist DGLAP approximation is not valid. In the same framework, we examine p and \bar{p} production using baryon fragmentation functions parameterized in…
In this letter we update our predictions for exclusive $J/Ψ$ and $Υ$ photoproduction in proton-proton and nucleus - nucleus collisions at the Run 2 LHC energies obtained with the color dipole formalism and considering the impact parameter Color Glass Condensate model (bCGC) for the forward dipole - target scattering amplitude. A comparison with the LHCb data on rapidity distributions and photon - hadron cross sections is presented. Our results demonstrate that the current data can be quite well described by the bCGC model, which takes into account nonlinear effects in the QCD dynamics and repr…
We show that in proton-lead (p+Pb) collisions at the LHC, the Color Glass Condensate (CGC) and hydrodynamics lead to qualitatively different behavior of the average transverse momentum, <p_T>, with the particles rapidity. In hydrodynamics, the <p_T> decreases as one goes from zero rapidity, y=0, to the proton fragmentation region since the number of particles decreases. In contrast, in the CGC the saturation momentum increases as one goes from y=0 to the proton fragmentation region, and so the <p_T> increases. At the LHC, the difference between the two models may be large enough to be tested e…
I review the problem of parton saturation and its implications through three in principal different approaches, but somewhat related: saturation in a geometrical approach, QCD saturation through the Color Glass Condensate and perturbative Pomeron approach with initial conditions. I also make some comments about how that could be related to a Quark Gluon Plasma formation.
We demonstrate that the striking systematics of two-particle azimuthal Fourier harmonics $v_2$ and $v_3$ in ultrarelativistic collisions of protons, deuterons and helium-3 ions off gold nuclei measured by the PHENIX Collaboration [arXiv:1805.02973] at the Relativistic Heavy Ion Collider (RHIC) is reproduced in the Color Glass Condensate (CGC) effective field theory. This contradicts the claim in [arXiv:1805.02973] that their data rules out initial state based explanations. The underlying systematics of the effect, as discussed previously in [arXiv:1705.00745,arXiv:1706.06260,arXiv:1801.09704],…
We perform a numerical study of higher order saturation corrections to the dilute-dense approximation for multi-particle production in high-energy hadronic collisions in the framework of the Color Glass Condensate. We compare semi-analytical results obtained by performing a leading order expansion in the dilute field of the projectile with numerical simulations of the full Classical Yang-Mills dynamics for a number of phenomenologically relevant observables. By varying the saturation momentum of the target and the projectile, we establish the regime of validity of the dilute-dense approximatio…
We study gluon production in high energy proton-nucleus collisions in the semi-classical framework of the Color Glass Condensate. We develop a general formalism to compute gluon fields in covariant gauge to lowest order in the classical field of the proton and to all orders in the classical field of the nucleus. The use of the covariant gauge makes the diagrammatic interpretation of the solution more transparnt. k_t-factorization holds to this order for gluon production -- Our results for the gluon distribution are equivalent to the prior diagrammatic analysis of Kovchegov and Mueller. We also…
In this brief note, we determine the fluctuations of the initial eccentricity in heavy-ion collisions caused by fluctuations of the nucleon configurations. This is done via a Monte-Carlo implementation of a Color Glass Condensate $k_t$-factorization approach. The eccentricity fluctuations are found to nearly saturate elliptic flow fluctuations measured recently at RHIC. Extrapolations to LHC energies are shown.
At very high energies or small values of Bjorken x, the density of partons, per unit transverse area, in hadronic wavefunctions becomes very large leading to a saturation of partonic distributions. When the scale corresponding to the density per unit transverse area, the saturation scale Q_s, becomes large (Q_s\gg Λ_{QCD}), the coupling constant becomes weak (α_S(Q_s)\ll 1) which suggests that the high energy limit of QCD may be studied using weak coupling techniques. This simple idea can be formalized in an effective theory, the Color Glass Condensate (CGC), which describes the behavior of th…
The CMS experiment at the Large Hadron Collider has recently presented data on the average transverse momentum of protons, kaons and pions as a function of particle multiplicity. We relate the particle multiplicity to saturation momentum using recently published computations of the interaction radius determined from the theory of the Color Glass Condensate. We show that the pp and the pA experimental data scale in terms of these saturation momenta. Computing transverse momentum spectra for identified particles using Boltzmann-type distributions and relating different associated multiplicities …
The color memory effect is the non-abelian gauge theory analog of the gravitational memory effect, in which the passage of color radiation induces a net relative SU(3) color rotation of a pair of nearby quarks. It is proposed that this effect can be measured in the Regge limit of deeply inelastic scattering at electron-ion colliders.
We provide quantitative predictions for the rapidity, centrality and energy dependencies of inclusive charged-hadron productions for the forthcoming LHC measurements in nucleus-nucleus collisions based on the idea of gluon saturation in the color-glass condensate framework. Our formulation gives very good descriptions of the first data from the LHC for the inclusive charged-hadron production in proton-proton collisions, the deep inelastic scattering at HERA at small Bjorken-x, and the hadron multiplicities in nucleus-nucleus collisions at RHIC.
We examine the origins of azimuthal correlations observed in high energy proton-nucleus collisions by considering the simple example of the scattering of uncorrelated partons off color fields in a large nucleus. We demonstrate how the physics of fluctuating color fields in the color glass condensate (CGC) effective theory generates these azimuthal multiparticle correlations and compute the corresponding Fourier coefficients v_n within different CGC approximation schemes. We discuss in detail the qualitative and quantitative differences between the different schemes. We will show how a recently…
We analyse the azimuthal structure of two gluon correlations in the Color Glass Condensate including those effects that result from relaxing the shockwave approximation for the target. Working in the Glasma graph approach suitable for collisions between dilute systems, we compute numerically the azimuthal distributions and show that both even and odd harmonics appear. We study their dependence on model parameters, energy of the collision, pseudorapidity and transverse momentum of the produced particles, and length of the target. While the contribution from non-eikonal corrections vanishes with…
We consider the non-eikonal corrections to particle production in the Color Glass Condensate stemming from the relaxation of the shockwave approximation for the target that acquires a finite longitudinal dimension. We derive a modified expression of the Lipatov vertex which takes into account this finite target width. This expression is employed to compute single, double and triple gluon production in the Glasma graph limit valid for the scattering of two dilute objects, at all orders in the expansion in the number of colors. We justify and generalize previous results, and discuss the possible…
We compute cross sections for incoherent and coherent diffractive J/$Ψ$ and $Ψ(2S)$ 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.
With the tremendous accomplishments of RHIC and the LHC experiments and the advent of the future Electron-Ion Collider on the horizon, the quest for compelling evidence of the color glass condensate (CGC) has become one of the most aspiring goals in the high energy Quantum Chromodynamics research. Pursuing this question requires developing the precision test of the CGC formalism. By systematically implementing the threshold resummation, we significantly improve the stability of the next-to-leading-order calculation in CGC for forward rapidity hadron productions in $pp$ and $pA$ collisions, esp…
We investigate the contribution of inelastic and elastic processes to single inclusive hadron production in proton-proton and proton (deuteron)-nucleus collisions at RHIC and the LHC. Using the hybrid formulation which includes both elastic and inelastic contributions, supplemented with the running-coupling Balitsky-Kovchegov equation, we get a good description of RHIC data. It is shown that inclusion of the inelastic terms makes the transverse momentum dependence of the production cross section steeper in the mid-rapidity region but does not affect the cross section in the very forward region…
We present our work on the simulation of the early stages of heavy-ion collisions with finite longitudinal thickness in the laboratory frame in 3+1 dimensions. In particular we study the effects of nuclear thickness on the production of a glasma state in the McLerran-Venugopalan model within the color glass condensate framework. A finite thickness enables us to describe nuclei at lower energies, but forces us to abandon boost-invariance. As a consequence, random classical color sources within the nuclei have to be included in the simulation, which is achieved by using the colored particle-in-c…
