Structure of longitudinal chromomagnetic fields in high energy collisions

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.

Hot spots and gluon field fluctuations as causes of eccentricity in small systems

We calculate eccentricities in high energy proton-nucleus collisions, by calculating correlation functions of the energy density field of the Glasma immediately after the collision event at proper time tau = 0. We separately consider the effects of color charge and geometrical hot spot fluctuations, analytically performing the averages over both in a dilute-dense limit. We show that geometric fluctuations of hot spots inside the proton are the dominant source of eccentricity whereas color charge fluctuations only give a negligible correction. The size and number of hot spots are the most important parameters characterizing the eccentricities.

Massive Quarks at One Loop in the Dipole Picture of Deep Inelastic Scattering

We calculate the light cone wave functions for a virtual photon to split into quark-antiquark states, including for the first time quark masses at one loop accuracy. These wave functions can be used to calculate cross sections for several precision probes of perturbative gluon saturation at the Electron-Ion Collider. Using these wave functions we derive, for the first time, the dipole picture DIS cross sections at one loop for longitudinal and transverse virtual photons including quark masses. The quark masses are renormalized in the pole mass scheme, satisfying constraints from the requirement of Lorentz invariance of the quark Dirac and Pauli form factors.

Multiplicity distributions and long range rapidity correlations

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).

Centrality-dependent forward J/ψ production in high energy proton-nucleus collisions

Forward $J/\psi$ production and suppression in high energy proton-nucleus collisions can be an important probe of gluon saturation. In an earlier work we studied this process in the Color Glass Condensate framework and showed that using the Glauber approach to extrapolate the dipole cross section of a proton to a nucleus leads to results closer to experimental data than previous calculations in this framework. Here we investigate the centrality dependence of the nuclear suppression in this model and show a comparison of our results with recent LHC data.

The ridge in proton-proton collisions at the LHC

We show that the key features of the CMS result on the ridge correlation seen for high multiplicity events in sqrt(s)=7TeV proton-proton collisions at the LHC can be understood in the Color Glass Condensate framework of high energy QCD. The same formalism underlies the explanation of the ridge events seen in A+A collisions at RHIC, albeit it is likely that flow effects may enhance the magnitude of the signal in the latter.

Use of a running coupling in the NLO calculation of forward hadron production

We address and solve a puzzle raised by a recent calculation [1] of the cross-section for particle production in proton-nucleus collisions to next-to-leading order: the numerical results show an un- reasonably large dependence upon the choice of a prescription for the QCD running coupling, which spoils the predictive power of the calculation. Specifically, the results obtained with a prescription formulated in the transverse coordinate space differ by one to two orders of magnitude from those obtained with a prescription in momentum space. We show that this discrepancy is an artefact of the interplay between the asymptotic freedom of QCD and the Fourier transform from coordinate space to mo…

Highly occupied gauge theories in 2 + 1 dimensions : a self-similar attractor

Motivated by the boost-invariant Glasma state in the initial stages in heavy-ion collisions, we perform classical-statistical simulations of SU(2) gauge theory in 2+1 dimensional space-time both with and without a scalar field in the adjoint representation. We show that irrespective of the details of the initial condition, the far-from-equilibrium evolution of these highly occupied systems approaches a unique universal attractor at high momenta that is the same for the gauge and scalar sectors. We extract the scaling exponents and the form of the distribution function close to this non-thermal fixed point. We find that the dynamics are governed by an energy cascade to higher momenta with sc…

Forward J/ψ production in pA collisions : centrality dependence

The nuclear suppression of forward J/ψ production in high energy proton-nucleus collisions can be used as a probe of gluon saturation at small x. In an earlier work we studied this suppression in minimum bias collisions in the Color Glass Condensate formalism, relying on the optical Glauber model to obtain the dipole cross section of the nucleus from the one of the proton fitted to HERA DIS data. Here we study how the impact parameter dependence of this model can be used to compare our results with recent LHC data on the centrality dependence of this suppression. peerReviewed

Nuclear modification of forward J/ψ production in proton-nucleus collisions at the LHC

We re-evaluate the nuclear suppression of forward J/ψ production at high energy in the Color Glass Condensate framework. We use the collinear approximation for the projectile proton probed at large x and an up to date dipole cross section fitted to HERA data to describe the target in proton-proton collisions. We show that using the Glauber approach to generalize the proton dipole cross section to the case of a nucleus target leads to a nuclear modification factor much closer to LHC data than previous estimates using the same framework.

Forward J /ψ production in proton-nucleus collisions at high energy

Inclusive production of J/ψ mesons, especially at forward rapidities, is an important probe of small-x gluons in protons and nuclei. In this paper we reevaluate 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 th…

Multigluon correlations in JIMWLK

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.

Long range rapidity correlations as seen in the STAR experiment

We analyze long range rapidity correlations observed in the STAR experiment at RHIC. Our goal is to extract properties of the two particle correlation matrix, accounting for the analysis method of the STAR experiment. We find a surprisingly large correlation strength for central collisions of gold nuclei at highest RHIC energies. We argue that such correlations cannot be the result of impact parameter fluctuations.

Understanding saturation and AA collisions with an eA collider

The initial conditions in high energy nucleus-nucleus collisions are determined by the small momentum fraction part of the nuclear wavefunction. This is the regime of gluon saturation and the most direct way to experimentally study it would be deep inelastic scattering at a high energy electron ion collider (EIC). This talk discusses some of the connections between physics at the EIC and the initial stage of relativistic heavy ion collisions. We argue that measurements at an EIC will provide detailed high-precision information about the parameters for the initial conditions, transverse geometry and longitudinal correlations that will be crucial in understanding the initial stage of a heavy …

Ballistic protons in incoherent exclusive vector meson production as a measure of rare parton fluctuations at an Electron-Ion Collider

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 insensit…

Unequal rapidity correlators in the dilute limit of JIMWLK

We study unequal rapidity correlators in the stochastic Langevin picture of Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) evolution in the Color Glass Condensate effective field theory. We discuss a diagrammatic interpretation of the long-range correlators. By separately evolving the Wilson lines in the direct and complex conjugate amplitudes, we use the formalism to study two-particle production at large rapidity separations. We show that the evolution between the rapidities of the two produced particles can be expressed as a linear equation, even in the full nonlinear limit. We also show how the Langevin formalism for two-particle correlations reduces to a BFKL picture i…

Initial state azimuthal anisotropies in small collision systems

Strong multiparticle azimuthal correlations have recently been observed in high energy proton-nucleus collisions. While final state collective effects can be responsible for many of the observations, the domain structure in the classical color field of a high energy nucleus also naturally leads to such correlations. We describe recent calculations of 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. We find significant differences between Wilson lines from the MV model and from JIMWLK evolution. We also discuss the relation of this calculation to earlier work …

Single inclusive particle production at high energy from HERA data to proton-nucleus collisions

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 …

Broad excitations in a 2+1D overoccupied gluon plasma

Motivated by the initial stages of high-energy heavy-ion collisions, we study excitations of far-from-equilibrium 2+1 dimensional gauge theories using classical-statistical lattice simulations. We evolve field perturbations over a strongly overoccupied background undergoing self-similar evolution. While in 3+1D the excitations are described by hard-thermal loop theory, their structure in 2+1D is nontrivial and nonperturbative. These nonperturbative interactions lead to broad excitation peaks in spectral and statistical correlation functions. Their width is comparable to the frequency of soft excitations, demonstrating the absence of soft quasiparticles in these theories. Our results also su…

Proton hot spots and exclusive vector meson production

We explore consequences of the existence of gluonic hot spots inside the proton for coherent and incoherent exclusive vector meson production cross sections in deep inelastic scattering. By working in the dilute limit of the Color Glass Condensate framework to compute the cross sections for Gaussian hot spots of fluctuating color charges and employing a non-relativistic vector meson wave function, we are able to perform large parts of the calculation analytically. We find that the coherent cross section is sensitive to both the size of the target and the structure of the probe. The incoherent cross section is dominated by color fluctuations at small transverse momentum transfer ($t$), by pr…

Solving the NLO BK equation in coordinate space

We present results from a numerical solution of the next-to-leading order (NLO) BalitskyKovchegov (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.

Forward J/ψ production at high energy: Centrality dependence and mean transverse momentum

Forward rapidity $J/\psi$ meson production in proton-nucleus collisions can be an important constraint of descriptions of the small-$x$ nuclear wavefunction. In an earlier work we studied this process using a dipole cross section satisfying the Balitsky-Kovchegov equation, fit to HERA inclusive data and consistently extrapolated to the nuclear case using a standard Woods-Saxon distribution. In this paper we present further calculations of these cross sections, studying the mean transverse momentum of the meson and the dependence on collision centrality. We also extend the calculation to backward rapidities using nuclear parton distribution functions. We show that the parametrization is over…

Evolution of initial stage fluctuations in the glasma

We perform a calculation of the one- and two-point correlation functions of energy density and axial charge deposited in the glasma in the initial stage of a heavy ion collision at finite proper time. We do this by describing the initial stage of heavy ion collisions in terms of freely evolving classical fields whose dynamics obey the linearized Yang-Mills equations. Our approach allows us to systematically resum the contributions of high momentum modes that would make a power series expansion in proper time divergent. We evaluate the field correlators in the McLerran-Venugopalan model using the glasma graph approximation, but our approach for the time dependence can be applied to a general…

Forward dihadron correlations in the Gaussian approximation of JIMWLK

We compute forward dihadron azimuthal correlations in deuteron-gold collisions using a Gaussian approximation for the quadrupole operator. The double parton scattering contribution is found to be part of our dihadron calculation. We obtain a good description of the PHENIX data for the azimuthal-angle dependent away side peak and a relatively good estimate for the pedestal contribution.

Renormalization group evolution of multi-gluon correlators in high energy QCD

Many-body QCD in leading high energy Regge asymptotics is described by the Balitsky-JIMWLK hierarchy of renormalization group equations for the x evolution of multi-point Wilson line correlators. These correlators are universal and ubiquitous in final states in deeply inelastic scattering and hadronic collisions. For instance, recently measured di-hadron correlations at forward rapidity in deuteron-gold collisions at the Relativistic Heavy Ion Collider (RHIC) are sensitive to four and six point correlators of Wilson lines in the small x color fields of the dense nuclear target. We evaluate these correlators numerically by solving the functional Langevin equation that describes the Balitsky-…

On the gluon spectrum in the glasma

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.

Scattering and gluon emission in a color field : a light-front Hamiltonian approach

We develop a numerical method to nonperturbatively study scattering and gluon emission of a quark from a colored target using a light-front Hamiltonian approach. The target is described as a classical color field, as in the color glass condensate effective theory. The Fock space of the scattering system is restricted to the |q⟩+|qg⟩ sectors, but the time evolution of this truncated system is solved exactly. This method allows us to study the interplay between coherence and multiple scattering in gluon emission. It could be applied both to studying subeikonal effects in high-energy scattering and to understanding jet quenching in a hot plasma.

Small x physics and RHIC data

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.

Heavy quark diffusion in an overoccupied gluon plasma

We extract the heavy-quark diffusion coefficient \kappa and the resulting momentum broadening in a far-from-equilibrium non-Abelian plasma. We find several features in the time dependence of the momentum broadening: a short initial rapid growth of , followed by linear growth with time due to Langevin-type dynamics and damped oscillations around this growth at the plasmon frequency. We show that these novel oscillations are not easily explained using perturbative techniques but result from an excess of gluons at low momenta. These oscillation are therefore a gauge invariant confirmation of the infrared enhancement we had previously observed in gauge-fixed correlation functions. We argue that…

Plasmon mass scale in two dimensional classical nonequilibrium gauge theory

We study the plasmon mass scale in weakly coupled strongly interacting nonabelian gauge theory in a two dimensional configuration that mimics the boost invariant initial color fields in a heavy ion collision. We numerically measure the plasmon mass scale using three different methods: a Hard Thermal Loop (HTL) expression involving the quasiparticle spectrum constructed from Coulomb gauge field correlators, an effective dispersion relation and the measurement of oscillations between electric and magnetic energies after introducing a spatially uniform perturbation to the electric field. We find that the hard thermal loop expression and the uniform electric field measurement are in rough agree…

Higher-order corrections to exclusive heavy vector meson production

We present results for higher-order corrections to exclusive $\mathrm{J}/\psi$ production. This includes the first relativistic correction of order $v^2$ in quark velocity, and next-to-leading order corrections in $\alpha_s$ for longitudinally polarized production. The relativistic corrections are found to be important for a good description of the HERA data, especially at small values of the photon virtuality. The next-to-leading order results for longitudinal production are evaluated numerically. We also demonstrate how the vector meson production provides complementary information to the structure functions for extracting the initial condition for the small-$x$ evolution of the dipole-pr…

Dipole picture and the nonrelativistic expansion

We study exclusive quarkonium production in the dipole picture at next-to-leading order (NLO) accuracy, using the non-relativistic expansion for the quarkonium wavefunction. This process offers one of the best ways to obtain information about gluon distributions at small $x$, in ultraperipheral heavy ion collisions and in deep inelastic scattering. The quarkonium light cone wave functions needed in the dipole picture have typically been available only at tree level, either in phenomenological models or in the nonrelativistic limit. In this paper, we discuss the compatibility of the dipole approach and the non-relativistic expansion and compute NLO relativistic corrections to the quarkonium …

Azimuthal harmonics of color fields in a high energy nucleus

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 W…

Spectral function for overoccupied gluodynamics from real-time lattice simulations

We study the spectral properties of a highly occupied non-Abelian non-equilibrium plasma appearing ubiquitously in weak coupling descriptions of QCD matter. The spectral function of this far-from-equilibrium plasma is measured by employing linear response theory in classical-statistical real-time lattice Yang-Mills simulations. We establish the existence of transversely and longitudinally polarized quasiparticles and obtain their dispersion relations, effective mass, plasmon frequency, damping rate and further structures in the spectral and statistical functions. Our new method can be interpreted as a non-perturbative generalization of hard thermal loop (HTL) effective theory. We see indica…

Incoherent diffractiveJ/Ψproduction in high-energy nuclear deep-inelastic scattering

We compute cross sections for incoherent diffractive $J/\ensuremath{\Psi}$ production in lepton-nucleus deep-inelastic scattering (DIS). The cross section is proportional to $A$ in the dilute limit and to ${A}^{1/3}$ in the black disk limit, with a large nuclear suppression due to saturation effects. The $t$ dependence of the cross section, if it can be measured accurately enough, is sensitive to the impact parameter profile of the gluons in the nucleus and their fluctuations, a quantity that determines the initial conditions of a relativistic heavy-ion collision. The nuclear suppression in incoherent diffraction shows how the transverse spatial distribution of the gluons in the nucleus gra…

Single inclusive forward hadron production at next-to-leading order

We discuss single inclusive hadron production from a high energy quark scattering off a strong target color field in the Color Glass Condensate formalism. Recent calculations of this process at the next-to-leading order accuracy have led to negative cross sections at large transverse momenta. We identify the origin of this problem as an oversubtraction of the rapidity divergence into the Balitsky-Kovchegov evolution equation for the target. We propose a new way to implement the kinematical restriction on the emitted gluons to overcome this difficulty.

Forward dihadron correlations in deuteron-gold collisions with a Gaussian approximation of JIMWLK

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 saturat…

Balitsky-Kovchegov equation at next-to-leading order accuracy with a resummation of large logarithms

We include resummation of large transverse logarithms into the next-to-leading order Balitsky-Kovchegov equation. The resummed NLO evolution equation is shown to be stable, the evolution speed being significantly reduced by higher order corrections. The contributions from $\alpha_s^2$ terms that are not enhanced by large logarithms are found to be numerically important close to phenomenologically relevant initial conditions.

Linearly polarized gluons and axial charge fluctuations in the glasma

We calculate of the one- and two-point correlation functions of the energy density and the divergence of the Chern-Simons current in the nonequilibrium Glasma state formed in a high-energy nuclear collision. We show that the latter depends on the difference of the total and linearly polarized gluon transverse momentum distributions. Since the divergence of the Chern-Simons current provides the source of axial charge, we infer information about the statistical properties of axial charge production at early times. We further develop a simple phenomenological model to characterize axial charge distributions in terms of distributions of the energy density.

Electron Ion Collider: The Next QCD Frontier - Understanding the glue that binds us all

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 a…

Theory overview of Heavy Ion collisions

This presentation discusses some recently active topics in the theoretical interpretation of high energy heavy ion collisions at the LHC and at RHIC. We argue that the standard paradigm for understanding the spacetime evolution of the bulk of the matter produced in the collision is provided by viscous relativistic hydrodynamics, which can be used to systematically extract properties of the QCD medium from experimental results. The initial conditions of this hydrodynamical evolution are increasingly well understood in terms of gluon saturation, and can be quantified using Classical Yang-Mills fields and QCD effective kinetic theory. Hard and electromagnetic probes of the plasma provide addit…

Color glass condensate at next-to-leading order meets HERA data

We perform the first dipole picture fit to HERA inclusive cross section data using the full next-to-leading order (NLO) impact factor combined with an improved Balitsky-Kovchegov evolution including the dominant effects beyond leading logarithmic accuracy at low $x$. We find that three different formulations of the evolution equation that have been proposed in the recent literature result in a very similar description of HERA data, and robust predictions for future deep inelastic scattering experiments. We find evidence pointing towards a significant nonperturbative contribution to the structure function for light quarks, which stresses the need to extend the NLO impact factor calculation t…

Diffractive vector meson production in ultraperipheral heavy ion collisions from the Color Glass Condensate

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.

Forward J / ψ and D meson nuclear suppression at the LHC

Abstract Using the color glass condensate formalism, we study the nuclear modification of forward J/ψ and D meson production in high energy proton-nucleus collisions at the LHC. We show that relying on the optical Glauber model to obtain the dipole cross section of the nucleus from the one of the proton fitted to HERA DIS data leads to a smaller nuclear suppression than in the first study of these processes in this formalism and a better agreement with experimental data.

Summary of Week VII

International audience; Week VII of the INT program 2018 “Probing Nucleons and Nuclei in High Energy Collisions” was dedicated to topics at the interface of the electron-ion collider (EIC), heavy ion and proton-nucleus collisions. The EIC will provide complementary tools to investigate and constrain the initial state in HIC collisions, as well as transport properties of QCD matter which can be extracted from observables that are sensitive to final states interactions such as pt-broadening and energy loss. The contributed talks and discussions covered a variety of physics topics from saturation physics and the origin of multi-particle correlations in HIC to jet quenching and the strong coupl…

Effect of sitting position on muscle activation and force generation in simulated sit ski double poling and on balance perturbation test

Tuomas Lappi (2014). Effect of sitting position on muscle activation and force generation in simulated sit-ski double poling and on balance perturbation test. Liikuntabiologian laitos, Jyväskylän yliopisto, Biomekaniikan Pro Gradu tutkielma, 98 s. Kelkkahiihto kuuluu vammaishiihtolajeihin, joita hallinnoi Kansainvälinen Paralympiakomitea (IPC). IPC ylläpitää kelkkahiihtäjien luokitteluprosessia joka pohjautuu hiihtäjän vammojen ominaisuuksiin ja suorituskykyyn kelkkahiihdossa. Luokittelujärjestelmän parametrit perustuvat lihasten ja nivelten toimintakykyyn, jota arvioidaan voimantuoton, liikkuvuuden sekä lääketieteellisen analyysin kautta. Vammojen yksilöllisen luonteen takia toiminnallisuu…

Does interferometry probe thermalization?

We carry out a systematic study of interferometry radii in ultrarelativistic heavy-ion collisions within a two-dimensional transport model. We compute the transverse radii R_o and R_s as a function of p_t for various values of the Knudsen number, which measures the degree of thermalization in the system. They converge to the hydrodynamical limit much more slowly (by a factor 3) than elliptic flow. This solves most of the HBT puzzle for central collisions: R_o/R_s is in the range 1.1-1.2 for realistic values of the Knudsen number, much closer to experimental data ($\simeq 1$) than the value 1.5 from hydrodynamical calculations. The p_t dependence of R_o and R_s, which is usually said to refl…

Multiparticle correlations in the Schwinger mechanism

We discuss the Schwinger mechanism in scalar QED and derive the multiplicity distribution of particles created under an external electric field using the LSZ reduction formula. Assuming that the electric field is spatially homogeneous, we find that the particles of different momenta are produced independently, and that the multiplicity distribution in one mode follows a Bose-Einstein distribution. We confirm the consistency of our results with an intuitive derivation by means of the Bogoliubov transformation on creation and annihilation operators. Finally we revisit a known solvable example of time-dependent electric fields to present exact and explicit expressions for demonstration.

Signatures of gluon saturation from structure-function measurements

We study experimentally observable signals for nonlinear QCD dynamics in deep inelastic scattering (DIS) at small Bjorken variable $x$ and moderate virtuality $Q^2$, by quantifying differences between the linear Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution and nonlinear evolution with the Balitsky-Kovchegov (BK) equation. To remove the effect of the parametrization freedom in the initial conditions of both equations, we first match the predictions for the DIS structure functions $F_2$ and $F_{\rm L}$ from both frameworks in a region in $x,Q^2$ where both frameworks should provide an accurate description of the relevant physics. The differences in the dynamics are then quanti…

Relativistic corrections to the vector meson light front wave function

We compute a light front wave function for heavy vector mesons based on long distance matrix elements constrained by decay width analyses in the Non Relativistic QCD framework. Our approach provides a systematic expansion of the wave function in quark velocity. The first relativistic correction included in our calculation is found to be significant, and crucial for a good description of the HERA exclusive $\mathrm{J}/\psi$ production data. When looking at cross section ratios between nuclear and proton targets, the wave function dependence does not cancel out exactly. In particular the fully non-relativistic limit is found not to be a reliable approximation even in this ratio. The important…

Forward hadron production in pA collisions beyond leading order

In this talk, we report our recent progress on pinning down the cause of negativity in the NLO single inclusive hadron production in pA collisions at forward rapidity.

On the implementation of NLO high energy factorization in single inclusive forward hadron production

Single inclusive particle production cross sections in high energy hadron collisions at forward rapidity are an important benchmark process for the CGC picture of small x QCD. Recent calculations of this process have not led to a stable perturbative expansion for this quantity at high transverse momenta. We consider the quark channel production cross section using the new rapidity factorization procedure proposed by Iancu et al. We show that for fixed coupling one does indeed obtain a physically meaningful cross section which is positive and reduces in a controlled way to previous leading order calculations. We also consider a running coupling that depends on the transverse momentum of the …

Tracing the origin of azimuthal gluon correlations in the color glass condensate

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 introduced color field domain model that captures key features of the observed azimuthal correlati…

Initial conditions of heavy ion collisions and small x

The Color Glass Condensate (CGC), describing the physics of the nonlinear gluonic interactions of QCD at high energy, provides a consistent first-principles framework to understand the initial conditions of heavy ion collisions. This talk reviews some aspects of the initial conditions at RHIC and discusses implications for LHC heavy ion phenomenology. The CGC provides a way compute bulk particle production and understand recent experimental observations of long range rapidity correlations in terms of the classical glasma field in the early stages of the collision.

One-loop corrections to light cone wave functions: the dipole picture DIS cross section

We develop methods needed to perform loop calculations in light cone perturbation theory using a helicity basis, refining the method introduced in our earlier work. In particular this includes implementing a consistent way to contract the four-dimensional tensor structures from the helicity vectors with d-dimensional tensors arising from loop integrals, in a way that can be fully automatized. We demonstrate this explicitly by calculating the one-loop correction to the virtual photon to quark-antiquark dipole light cone wave function. This allows us to calculate the deep inelastic scattering cross section in the dipole formalism to next-to-leading order accuracy. Our results, obtained using …

Fermion and gluon spectral functions far from equilibrium

Motivated by the quark-gluon plasma, we develop a simulation method to obtain the spectral function of (Wilson) fermions non-perturbatively in a non-Abelian gauge theory with large gluon occupation numbers [arXiv:2106.11319]. We apply our method to a non-Abelian plasma close to its non-thermal fixed point, i.e., in a far-from-equilibrium self-similar regime, and find mostly very good agreement with perturbative hard loop (HTL) calculations. For the first time, we extract the full momentum dependence of the damping rate of fermionic collective excitations and compare our results to recent non-perturbative extractions of gluonic spectral functions in two and three spatial dimensions [arXiv:21…

Including resummation in the NLO BK equation

We include a resummation of large transverse momentum logarithms in the next-to-leading order (NLO) Balitsky-Kovchegov equation. The resummed evolution equation is shown to be stable, the evolution speed being significantly reduced by NLO corrections. The contributions from NLO terms that are not enhanced by large logarithms are found to be numerically important close to phenomenologically relevant initial conditions. We numerically determine the value for the constant in the resummed logarithm that includes a maximal part of the full NLO terms in the resummation.

Gluon spectrum in the glasma from JIMWLK evolution

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.

Plasmon mass scale in classical nonequilibrium gauge theory

Classical lattice Yang-Mills calculations provide a good way to understand different nonequilibrium phenomena in nonperturbatively overoccupied systems. Above the Debye scale the classical theory can be matched smoothly to kinetic theory. The aim of this work is to study the limits of this quasiparticle picture by determining the plasmon mass in classical real time Yang-Mills theory on a lattice in 3 spatial dimensions. We compare three methods to determine the plasmon mass: a hard thermal loop expression in terms of the particle distribution, an effective dispersion relation constructed from fields and their time derivatives, and by measuring oscillations between electric and magnetic fiel…

Predictions for cold nuclear matter effects in p+Pb collisions at s N N = 8.16 TeV

Small-x, Diffraction and Vector Mesons

This talk discusses recent progress in some topics relevant for deep inelastic scattering at small x. We discuss first differences and similarities between conventional collinear factorization and the dipole picture of deep inelastic scattering. Many of the recent theoretical advances at small x are related to taking calculations in the nonlinear saturation regime to next-to-leading order accuracy in the QCD coupling. On the experimental side significant recent progress has been made in exclusive and diffractive processes, in particular in ultraperipheral nucleus-nucleus collisions.

On the use of a running coupling in the calculation of forward hadron production at next-to-leading order

Factorization of the soft gluon divergence from the dipole picture deep inelastic scattering cross sections at next-to-leading order

We use a factorization scheme analogous to one proposed for single inclusive forward hadron production to factorize the soft gluon divergence present in the deep inelastic scattering cross sections in the dipole picture at next-to-leading order (NLO). We show numerically that in this carefully constructed scheme it is possible to obtain meaningful results for the DIS cross sections at NLO, and so we are able to quantitatively study the recently derived NLO corrections to the DIS cross sections. We find that the NLO corrections can be significant and sensitive to the details of the factorization scheme used for the resummation of the large logarithms into the BK evolution equation. In the ca…

Gluon correlations in the glasma

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).

Massive quarks in NLO dipole factorization for DIS : Longitudinal photon

In this work, we will present the first complete calculation of the one-loop longitudinal photon-to-quark-antiquark light cone wave function, with massive quarks. The quark masses are renormalized in the pole mass scheme. The result is used to calculate the next-to-leading order correction to the high energy Deep Inelastic Scattering longitudinal structure function on a dense target in the dipole factorization framework. For massless quarks the next-to-leading order correction was already known to be sizeable, and our result makes it possible to evaluate it also for massive quarks.

Next-to-leading order Balitsky-Kovchegov equation with resummation

We solve the Balitsky-Kovchegov evolution equation at next-to-leading order accuracy including a resummation of large single and double transverse momentum logarithms to all orders. We numerically determine an optimal value for the constant under the large transverse momentum logarithm that enables including a maximal amount of the full NLO result in the resummation. When this value is used the contribution from the $\alpha_s^2$ terms without large logarithms is found to be small at large saturation scales and at small dipoles. Close to initial conditions relevant for phenomenological applications these fixed order corrections are shown to be numerically important.

JIMWLK and beyond: From concepts to observables

Volume: 112 Host publication title: 6th International Conference on Physics Opportunities at an Electron-Ion Collider The Color Glass Condensate and its associated evolution equation, the JIMWLK equation have applications to many observables far beyond totally inclusive observables. The phenomenology is so rich that little has been done to explore beyond scaling behavior of correlators. We show first examples that exemplify the considerations necessary to access additional information both experimentally and theoretically and demonstrate that the Wilson line correlators appearing throughout make it imperative to consistently take into account that one is dealing with correlators of group el…

Are the Angular Correlations in pA Collisions due to a Glasmion or Bose Condensation ?

Experiments at the LHC have recently reported results on the angular asymmetry coefficients $v_n[m]$, for various angular moments $n$ and orders of cumulants $m$, in high multiplicity p+Pb collisions. These coefficients are large, and have both even and odd moments. We discuss here some of the implications of these results for our understanding of the initial state of the collision (Color Glass Condensate) and for the evolution in the final state (Glasma and thermalized Quark Gluon Plasma). We show the Color Glass Condensate predicts large even moments, $v_n$ with $n$ an even integer. Odd moments are generated by final state interactions or fragmentation. For a multi-particle determination …

Initial state in heavy ion collisions

Abstract 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.

On the use of a running coupling in the calculation of forward hadron production at next-to-leading order

We study a puzzle raised recently regarding the running coupling prescription used in the calculation of forward particle production in proton-nucleus collisions at next-to-leading order: using a coordinate space prescription which is consistent with the one used in the high energy evolution of the target leads to results which can be two orders of magnitude larger than the ones obtained with a momentum space prescription. We show that this is an artefact of the Fourier transform involved when passing between coordinate and momentum space and propose a new coordinate space prescription which avoids this problem.

Forward rapidity isolated photon production in proton-nucleus collisions

We calculate isolated photon production at forward rapidities in proton-nucleus collisions in the Color Glass Condensate framework. Our calculation uses dipole cross sections solved from the running coupling Balitsky-Kovchegov equation with an initial condition fit to deep inelastic scattering data and extended to nuclei with an optical Glauber procedure that introduces no additional parameters beyond the basic nuclear geometry. We present predictions for future forward RHIC and LHC measurements. The predictions are also compared to updated results for the nuclear modification factors for pion production, Drell-Yan dileptons and $J/\psi$ mesons in the same forward kinematics, consistently c…

Small-$x$ Physics in the Dipole Picture at NLO Accuracy

International audience; We review recent progress in NLO calculations for dilute-dense processes in the CGC picture. In particular, we focus here on recent steps in understanding high energy renormalization group evolution (BK/JIMWLK), the total DIS cross section at small x and forward particle production in proton-nucleus collisions at next-to-leading order.

Time evolution of linearized gauge field fluctuations on a real-time lattice

Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Due to instabilities, small quantum fluctuations on top of the classical background may significantly affect the dynamics of the system. In this paper we argue for the need for a numerical calculation of a system of classical gauge fields and small linearized fluctuations in a way that keeps the separation between the two manifest. We derive and test an explicit algorithm to solve these equations on the lattice, maintaining gauge invariance and Gauss's law.

Dipole amplitude with uncertainty estimate from HERA data and applications in Color Glass Condensate phenomenology

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 RpA that approaches unity at large transverse momentum, independently of the center-of-mas…

Solving the Balitsky-Kovchegov equation at next to leading order accuracy

We solve the Balitsky-Kovchegov small-x evolution equation in coordinate space. We find that the solution to the equation is unstable when using an initial condition relevant for phenomenological applications at leading order. The problematic behavior is shown to be due to a large double logarithmic contribution. The same problem is found when the evolution of the “conformal dipole” is solved, even though the double logarithmic term is then absent from the evolution equation.

The one loop gluon emission light cone wave function

Light cone perturbation theory has become an essential tool to calculate cross sections for various small-$x$ dilute-dense processes such as deep inelastic scattering and forward proton-proton and proton-nucleus collisions. Here we set out to do one loop calculations in an explicit helicity basis in the four dimensional helicity scheme. As a first process we calculate light cone wave function for one gluon emission to one-loop order in Hamiltonian perturbation theory on the light front. We regulate ultraviolet divergences with transverse dimensional regularization and soft divergences with using a cut-off on longitudinal momentum. We show that when all the renormalization constants are comb…

Heavy quark momentum diffusion coefficient in 3D gluon plasma

We study the heavy-quark momentum diffusion coefficient in far from equilibrium gluon plasma in a self-similar regime using real-time lattice techniques. We use 3 methods for the extraction: an unequal time electric field 2-point correlator integrated over the time difference, a spectral reconstruction (SR) method based on the measured equal time electric field correlator and a kinetic theory (KT) formula. The time-evolution of the momentum diffusion coefficient extracted using all methods is consistent with an approximate $t^{\frac{-1}{2}}$ power law. We also study the extracted diffusion coefficient as a function of the upper limit of the time integration and observe that including the in…

Massive quarks in NLO dipole factorization for DIS : Transverse photon

We calculate the light cone wave functions for the QCD Fock components in a transverse virtual photon necessary for applications at next-to-leading order in the QCD coupling, including quark masses. We present a detailed calculation of both the one loop wave function for the quark-antiquark Fock component and the tree level wave function for the quark-antiquark-gluon Fock component. The quark masses are renormalized in the pole mass scheme, satisfying constraints from the requirement of Lorentz invariance. In particular the quark Pauli form factor at NLO is recovered from the on-shell limit of the quark-antiquark Fock component. We use our result to calculate the next-to-leading order corre…

Implementing consistent NLO factorization in single inclusive forward hadron production

Single inclusive forward hadron production in high-energy hadron collisions can provide an important test of the Color Glass Condensate picture at small $x$. Recent studies of this process at next-to-leading order have led to problematic results, with cross sections becoming negative at large transverse momenta. We study a new formulation of this quantity proposed recently by Iancu et al. We show that it leads to physical results up to large transverse momenta at fixed coupling. Taking into account running coupling effects in a way that is consistent with existing DIS calculations still poses a challenge.

Proposal for a running coupling JIMWLK equation

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.

Particle Production in the Color Class Condensate: from electron-proton DIS to proton-nucleus collisions

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…

Centrality dependence of forward J/ψ suppression in high energy proton–nucleus collisions

The production of forward $J/\psi$ mesons in proton-nucleus collisions can provide important information on gluon saturation. In a previous work we studied this process in the Color Glass Condensate framework, describing the target using a dipole cross section fitted to HERA inclusive data and extrapolated to the case of a nuclear target using the optical Glauber model. In this work we study the centrality dependence of the nuclear suppression in this model and compare our results with recent LHC data for this observable.

Predictions for cold nuclear matter effects in p+Pb collisions at sNN=8.16 TeV

Predictions for cold nuclear matter effects on charged hadrons, identified light hadrons, quarkonium and heavy flavor hadrons, Drell–Yan dileptons, jets, photons, gauge bosons and top quark pairs produced in p +Pb collisions at sNN=8.16 TeV are compiled and, where possible, compared to each other. Predictions of the normalized ratios of p +Pb to p+p cross sections are also presented for most of the observables, providing new insights into the expected role of cold nuclear matter effects. In particular, the role of nuclear parton distribution functions on particle production can now be probed over a wider range of phase space than ever before.

Dipole model at Next-to-Leading Order meets HERA data

Deep inelastic scattering (DIS) total cross section data at small-x as measured by the HERA experiments is well described by Balitsky-Kovchegov (BK) evolution in the leading order dipole picture. Recently the full Next-to-Leading Order (NLO) dipole picture total cross sections have become available for DIS, and a working factorization scheme has been devised which subtracts the soft gluon divergence present at NLO. We report our recently published work in which we make the first comparisons of the NLO DIS total cross sections to HERA data. The non-perturbative initial condition to BK evolution is fixed by fitting the HERA reduced cross section data. As the NLO results for the DIS total cros…

Particle production from the Color Glass Condensate: proton-nucleus collisions in light of the HERA data

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.

Deep inelastic scattering in the dipole picture at next-to-leading order

We study quantitatively the importance of the recently derived NLO corrections to the DIS structure functions at small x in the dipole formalism. We show that these corrections can be significant and depend on the factorization scheme used to resum large logarithms of energy into renormalization group evolution with the BK equation. This feature is similar to what has recently been observed for single inclusive forward hadron production. Using a factorization scheme consistent with the one recently proposed for the single inclusive cross section, we show that it is possible to obtain meaningful results for the DIS cross sections.

Jet momentum broadening during initial stages in heavy-ion collisions

We study the jet quenching parameter $\hat q$ in the initial pre-equilibrium stages of heavy-ion collisions using the QCD kinetic theory description of the anisotropic quark-gluon plasma. This allows us to smoothly close the gap in the literature between the early glasma stage of the collision and the onset of hydrodynamics. We find that the pre-hydrodynamic evolution of $\hat q$ during the bottom-up kinetic scenario shows little sensitivity to the initial conditions, jet energies and models of the transverse momentum cutoff. We also observe that, similarly to the glasma case, the jet quenching parameter is enhanced along the beam axis as compared to the transverse direction during most of …

Unequal rapidity correlators in the dilute limit of the JIMWLK evolution

We study unequal rapidity correlators in the stochastic Langevin picture of Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) evolution in the color glass condensate effective field theory. We discuss a diagrammatic interpretation of the long-range con elators. By separately evolving the Wilson lines in the direct and complex conjugate amplitudes, we use the formalism to study two-particle production at large rapidity separations. We show that the evolution between the rapidities of the two produced particles can be expressed as a linear equation, even in the full nonlinear limit. We also show how the Langevin formalism for two-particle correlations reduces to a Balitsky-Fadin…

Long range rapidity correlations and the ridge in A+A collisions

We discuss results for n-gluon correlations that form the basis of the Glasma flux tube picture of early times in heavy ion collisions. Our formalism is valid to all orders in perturbation theory at leading logarithmic accuracy in x and includes both QCD bremsstrahlung and the many body screening and recombination effects that are important at large parton densities. Long range rapidity correlations, as seen in the near-side ridge in heavy ion collisions, are a chronometer of these early time strong color field dynamics. They also contain information on how radial flow develops in heavy ion collisions.

Isolated photon production in proton-nucleus collisions at forward rapidity

We calculate isolated photon production at forward rapidities in proton-nucleus collisions in the Color Glass Condensate framework. Our calculation uses dipole cross sections solved from the running coupling Balitsky-Kovchegov equation with an initial condition fit to deep inelastic scattering data. For comparison, we also update the results for the nuclear modification factor for pion production in the same kinematics. We present predictions for future forward RHIC and LHC measurements at $\sqrt{s_{NN}}=200$ GeV and $\sqrt{s_{NN}}=8$ TeV.

Plasmon mass scale and quantum fluctuations of classical fields on a real time lattice

Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Above the Debye scale the classical Yang-Mills (CYM) theory can be matched smoothly to kinetic theory. First we study the limits of the quasiparticle picture of the CYM fields by determining the plasmon mass of the system using 3 different methods. Then we argue that one needs a numerical calculation of a system of classical gauge fields and small linearized fluctuations which correspond to quantum fluctuations, in a way that keeps the separation between the two manifest. We demonstra…

Single inclusive hadron production in pA collisions at NLO

We study single inclusive forward hadron production in high energy proton-nucleus collisions at next-to-leading order in the Color Glass Condensate framework. Recent studies have shown that the next-to-leading order corrections to this process are large and negative at large transverse momentum, leading to negative cross sections. We propose to overcome this difficulty by introducing an explicit rapidity factorization scale when subtracting the rapidity divergence into the evolution of the target.

JIMWLK evolution of the odderon

We study the effects of a parity-odd "odderon" correlation in JIMWLK renormalization group evolution at high energy. Firstly we show that in the eikonal picture where the scattering is described by Wilson lines, one obtains a strict mathematical upper limit for the magnitude of the odderon amplitude compared to the parity even pomeron one. This limit increases with N_c, approaching infinity in the infinite N_c limit. We use a systematic extension of the Gaussian approximation including both 2- and 3-point correlations which enables us to close the system of equations even at finite N_c. In the large-N_c limit we recover an evolution equation derived earlier. By solving this equation numeric…

Initial conditions in AA and pA collisions

A full understanding of the spacetime evolution of the QCD matter created in a heavy ion collision requires understanding the properties of the initial stages. In the weak coupling picture these are dominated by classical gluon fields, whose properties can also be studied via the scattering of dilute probes off a high energy hadron or nucleus. A particular challenge is understanding small systems, where LHC data is also showing signs of collective behavior. We discuss some recent results of on the initial matter production and thermalization in heavy ion collisions, in particular in the gluon saturation framework.

RHIC data and small x physics

This is a short review of some RHIC results that have been most important for the small x physics community. We discuss saturation effects in deuteron-gold collisions, particle production in gold-gold collisions and some effects of the large "glasma" field configurations in the early stages of the collision.

Structure of chromomagnetic fields in the glasma

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, whic…

Next-to-leading order Balitsky-Kovchegov equation beyond large Nc

We calculate finite-Nc corrections to the next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation. We find analytical expressions for the necessary correlators of six Wilson lines in terms of the two-point function using the Gaussian approximation. In a suitable basis, the problem reduces from the diagonalization of a six-by-six matrix to the diagonalization of a three-by-three matrix, which can easily be done analytically. We study numerically the effects of these finite-Nc corrections on the NLO BK equation. In general, we find that the finite-Nc corrections are smaller than the expected 1/N2c∼10%. The corrections may be large for individual correlators, but have less of an influence…

Light-front wavefunctions of mesons by design

AbstractWe develop a mechanism to build the light-front wavefunctions (LFWFs) of meson bound states on a small-sized basis function representation. Unlike in a standard Hamiltonian formalism, the Hamiltonian in this method is implicit, and the information of the system is carried directly by the functional form and adjustable parameters of the LFWFs. In this work, we model the LFWFs for four charmonium states, $$\eta _c$$ η c , $$J/\psi $$ J / ψ , $$\psi '$$ ψ ′ , and $$\psi (3770)$$ ψ ( 3770 ) as superpositions of orthonormal basis functions. We choose the basis functions as eigenfunctions of an effective Hamiltonian, which has a longitudinal confining potential in addition to the transver…

Ultraperipheral collisions and low-x physics

Ultraperipheral collisions at the LHC and RHIC offer the highest currently available energy for photon-nucleon and photon-nucleus collisions. Thus they are a valuable tool for studying the gluonic structure of hadrons and nuclei at small $x$. We discuss recent theoretical work towards understanding such exclusive processes at NLO accuracy in QCD perturbation theory. These theoretical advances are also immediately relevant for understanding the physics of deep inelastic scattering at small $x$. We also discuss experimental results in ultraperipheral collisions, most prominently for exclusive vector meson production.

Probing spectral properties of the QGP with real-time lattice simulations

We present a new method to obtain spectral properties of a non-Abelian gauge theory in the region where occupation numbers are high. The method to measure the (single-particle) spectral function is based on linear response theory and classical-statistical lattice simulations. Although we apply it to a system far from equilibrium in a self-similar regime, the extracted spectral function can be understood within the hard thermal loop (HTL) formalism and can thus be connected to thermal equilibrium at high temperatures. This allows us to obtain quantities like the lifetime of quasiparticles that are beyond the leading order and difficult to compute within HTL. The approach has the potential to…

Forward J/ψ production at high energy: Centrality dependence and mean transverse momentum

Forward rapidity J=ψ meson production in proton-nucleus collisions can be an important constraint of descriptions of the small-x nuclear wave function. In an earlier work we studied this process using a dipole cross section satisfying the Balitsky-Kovchegov equation, fit to HERA inclusive data and consistently extrapolated to the nuclear case using a standard Woods-Saxon distribution. In this paper we present further calculations of these cross sections, studying the mean transverse momentum of the meson and the dependence on collision centrality. We also extend the calculation to backward rapidities using nuclear parton distribution functions. We show that the parametrization is overall ra…

Finite Nc corrections in the Balitsky-Kovchegov equation at next-to-leading order

Publisher Copyright: © owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). We study the finite-Nc corrections to the next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation. This contains correlators of six Wilson lines, which we express in terms of the two-point function using the Gaussian approximation. Numerically, the effects of these finite-Nc corrections on the NLO BK equation are found to be smaller than the expected 1/Nc2 ∼ 10%. Corrections may be large for individual correlators, but have less of an influence on the shape of the amplitude as a function of the dipole size. There is a…

Effects of partial thermalization on HBT interferometry

Hydrodynamical models have generally failed to describe interferometry radii measured at RHIC. In order to investigate this ``HBT puzzle'', we carry out a systematic study of HBT radii in ultrarelativistic heavy-ion collisions within a two-dimensional transport model. We compute the transverse radii $R_o$ and $R_s$ as functions of $p_t$ for various values of the Knudsen number, which measures the degree of thermalization in the system. For realistic values of the Knudsen number estimated from $v_2$ data, we obtain $R_o/R_s \simeq 1.2$, much closer to data than standard hydrodynamical results. Femtoscopic observables vary little with the degree of thermalization. Azimuthal oscillations of th…

Long range two-particle rapidity correlations in collisions from high energy QCD evolution

Long range rapidity correlations in A+A collisions are sensitive to strong color field dynamics at early times after the collision. These can be computed in a factorization formalism \cite{GelisLV5} which expresses the $n$-gluon inclusive spectrum at arbitrary rapidity separations in terms of the multi-parton correlations in the nuclear wavefunctions. This formalism includes all radiative and rescattering contributions, to leading accuracy in $\alpha_s\Delta Y$, where $\Delta Y$ is the rapidity separation between either one of the measured gluons and a projectile, or between the measured gluons themselves. In this paper, we use a mean field approximation for the evolution of the nuclear wav…

Spectral function for overoccupied gluodynamics from classical lattice simulations

We study the spectral properties of an overoccupied gluonic system far from equilibrium. Using classical Yang-Mills simulations and linear response theory, we determine the statistical and spectral functions. We measure dispersion relations and damping rates of transversally and longitudinally polarized excitations in the gluonic plasma, and also study further structures in the spectral function.

Forward particle correlations in the color glass condensate

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.