Showing papers on "Color-glass condensate published in 2019"

Diffractive Dijet Production and Wigner Distributions from the Color Glass Condensate

Abstract: Experimental processes that are sensitive to parton Wigner distributions provide a powerful tool to advance our understanding of proton structure. In this work, we compute gluon Wigner and Husimi distributions of protons within the color glass condensate framework, which includes a spatially dependent McLerran-Venugopalan initial configuration and the explicit numerical solution of the Jalilian-Marian–Iancu–McLerran–Weigert–Leonidov–Kovner equations. We determine the leading anisotropy of the Wigner and Husimi distributions as a function of the angle between the impact parameter and transverse momentum. We study experimental signatures of these angular correlations at a proposed electron-ion collider by computing coherent diffractive dijet production cross sections in e+p collisions within the same framework. Specifically, we predict the elliptic modulation of the cross section as a function of the relative angle between the nucleon recoil and dijet transverse momentum for a wide kinematical range. We further predict its dependence on the collision energy, which is dominated by the growth of the proton with decreasing x.

Forward dihadron back-to-back correlations in p A collisions

Abstract: We study the disappearance of the away-side peak of the di-hadron correlation function in p+A vs p+p collisions at forward rapidities, when the scaterring process presents a manifest dilute-dense asymmetry. We improve the state-of-the-art description of this phenomenon in the framework of the color glass condensate (CGC), for hadrons produced nearly back to back. In that case, the gluon content of the saturated nuclear target can be described with transverse-momentum-dependent gluon distributions, whose small-x evolution we calculate numerically by solving the Balitsky-Kovchegov equation with running coupling corrections. We first show that our formalism provides a good description of the disappearance of the away-side azimuthal correlations in d+Au collisions observed at BNL Relativistic Heavy Ion Collider (RHIC) energies. Then, we predict the away-side peak of upcoming p+Au data at s=200 GeV to be suppressed by about a factor 2 with respect to p+p collisions, and we propose to study the rapidity dependence of that suppression as a complementary strong evidence of gluon saturation in experimental data.

CERN Large Hadron Collider system size scan predictions for PbPb, XeXe, ArAr, and OO with relativistic hydrodynamics

Abstract: In recent years the understanding of the limits of the smallest possible droplet of the quark gluon plasma has been called into question. Experimental results from both the Large Hadron Collider and the Relativistic Heavy Ion Collider have provided hints that the quark gluon plasma may be produced in systems as small as that formed in $p\mathrm{Pb}$ or $d\mathrm{Au}$ collisions. Yet alternative explanations still exist from correlations arising from quarks and gluons in a color glass condensate picture. In order to resolve these two scenarios, a system-size scan has been proposed at the Large Hadron Collider for collisions of ArAr and OO. Here we make predictions for a possible future run of ArAr and OO collisions at the Large Hadron Collider and study the system-size dependence of a variety of flow observables. We find that linear response (from the initial conditions to the final flow harmonics) becomes more dominant in smaller systems, whereas the $\text{linear}+\text{cubic}$ response can accurately predict multiparticle cumulants for a wide range of centralities in large systems.

Elliptic Flow of Heavy Quarkonia in pA Collisions.

Abstract: Using the dilute-dense factorization in the color glass condensate framework, we investigate the azimuthal angular correlation between a heavy quarkonium and a charged light hadron in proton-nucleus collisions. We extract the second harmonic v2, commonly known as the elliptic flow, with the light hadron as the reference. This particular azimuthal angular correlation between a heavy meson and a light hadron was first measured at the LHC recently. The experimental results indicate that the elliptic flows for heavy flavor mesons (J/ψ and D0) are almost as large as those for light hadrons. Our calculation demonstrates that this result can be naturally interpreted as an initial state effect due to the interaction between the incoming partons from the proton and the dense gluons inside the target nucleus. Since the heavy quarkonium v2 exhibits a weak mass dependence according to our calculation, we predict that the heavy quarkonium ϒ should have a similar elliptic flow as compared to that of the J/ψ, which can be tested in future measurements.

Non-eikonal corrections to multi-particle production in the Color Glass Condensate

Abstract: 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 implications on two particle correlations of these non-eikonal corrections that induce differences between the away- and near-side peaks.

The Color Glass Condensate density matrix: Lindblad evolution, entanglement entropy and Wigner functional

Abstract: We introduce the notion of the Color Glass Condensate (CGC) density matrix $\hat\rho$. This generalizes the concept of probability density for the distribution of the color charges in the hadronic wave function and is consistent with understanding the CGC as an effective theory after integration of part of the hadronic degrees of freedom. We derive the evolution equations for the density matrix and show that the JIMWLK evolution equation arises here as the evolution of diagonal matrix elements of $\hat\rho$ in the color charge density basis. We analyze the behavior of this density matrix under high energy evolution and show that its purity decreases with energy. We show that the evolution equation for the density matrix has the celebrated Kossakowsky-Lindblad form describing the non-unitary evolution of the density matrix of an open system. Additionally, we consider the dilute limit and demonstrate that, at large rapidity, the entanglement entropy of the density matrix grows linearly with rapidity according to $d S_e / d y = \gamma$, where $\gamma$ is the leading BFKL eigenvalue. We also discuss the evolution of $\hat\rho$ in the saturated regime and relate it to the Levin-Tuchin law and find that the entropy again grows linearly with rapidity, but at a slower rate. By analyzing the dense and dilute regimes of the full density matrix we are able to establish a duality between the regimes. Finally we introduce the Wigner functional derived from this density matrix and discuss how it can be used to determine the distribution of color currents, which may be instrumental in understanding dynamical features of QCD at high energy.

TMD factorization for dijets + photon production from the dilute-dense CGC framework

Abstract: We calculate the production of a photon and two jets at forward rapidity in proton-nucleus collisions, within the hybrid dilute-dense framework in the Color Glass Condensate (CGC) formalism. After obtaining the cross section for both the quark- and gluon-initiated channels, we consider the correlation limit, in which the vector sum of the transverse momenta of the three outgoing particles is small with respect to the individual transverse momenta. In this limit, the cross section simplifies considerably and can be written in a factorized form, sensitive to various unpolarized and linearly-polarized transverse-momentum-dependent gluon distribution functions (gluon TMDs). Thus, we demonstrate for the first time that the emergence of a TMD factorization formula in the correlation limit, from CGC expressions, holds beyond the previously-considered simpler 2→2processes.

The Color Glass Condensate density matrix: Lindblad evolution, entanglement entropy and Wigner functional

Abstract: We introduce the notion of the Color Glass Condensate (CGC) density matrix $$ \widehat{\rho} $$ . This generalizes the concept of probability density for the distribution of the color charges in the hadronic wave function and is consistent with understanding the CGC as an effective theory after integration of part of the hadronic degrees of freedom. We derive the evolution equations for the density matrix and show that the JIMWLK evolution equation arises here as the evolution of diagonal matrix elements of ρ in the color charge density basis. We analyze the behavior of this density matrix under high energy evolution and show that its purity decreases with energy. We show that the evolution equation for the density matrix has the celebrated Kossakowsky-Lindblad form describing the non-unitary evolution of the density matrix of an open system. Additionally, we consider the dilute limit and demonstrate that, at large rapidity, the entanglement entropy of the density matrix grows linearly with rapidity according to $$ \frac{d}{dy}{S}_e=\gamma $$ , where γ is the leading BFKL eigenvalue. We also discuss the evolution of $$ \widehat{\rho} $$ in the saturated regime and relate it to the Levin-Tuchin law and find that the entropy again grows linearly with rapidity, but at a slower rate. By analyzing the dense and dilute regimes of the full density matrix we are able to establish a duality between the regimes. Finally we introduce the Wigner functional derived from this density matrix and discuss how it can be used to determine the distribution of color currents, which may be instrumental in understanding dynamical features of QCD at high energy.

Spacetime picture of baryon stopping in the color-glass condensate

Abstract: 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 ultrarelativistic 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-McLerran [Phys. Rev. D 22, 2793 (1980)].

Effect of non-eikonal corrections on azimuthal asymmetries in the color glass condensate

Abstract: 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 increasing collision energy and becomes negligible at the energies of the Large Hadron Collider, it is found to be sizeable up to top energies at the Relativistic Heavy Ion Collider.

Quark jets scattering from a gluon field: From saturation to high p t

Abstract: We continue our studies of possible generalization of the color glass condensate effective theory of high energy QCD to include the high ${p}_{t}$ (or equivalently large $x$) QCD dynamics as proposed in [Phys Rev D 96, 074020 (2017)] Here, we consider scattering of a quark from both the small and large $x$ gluon degrees of freedom in a proton or nucleus target and derive the full scattering amplitude by including the interactions between the small and large $x$ gluons of the target We thus generalize the standard eikonal approximation for parton scattering, which can now be deflected by a large angle (and therefore have large ${p}_{t}$) and also lose a significant fraction of its longitudinal momentum (unlike the eikonal approximation) The corresponding production cross section can thus serve as the starting point toward the derivation of a general evolution equation that would contain the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equation at large ${Q}^{2}$ and the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner evolution equation at small $x$ This amplitude can also be used to construct the quark Feynman propagator, which is the first ingredient needed to generalize the color glass condensate effective theory of high energy QCD to include the high ${p}_{t}$ dynamics We outline how it can be used to compute observables in the large $x$ (high ${p}_{t}$) kinematic region where the standard color glass condensate formalism breaks down

Improvement for color glass condensate factorization: Single hadron production in p A collisions at next-to-leading order

Abstract: High-order calculation at the semihard scale in high-energy collisions is very important, but a satisfactory calculation framework is still missing. We propose a systematic method to regularize the rapidity divergence in color glass condensate (CGC) factorization, which makes higher-order calculation rigorous and straightforward. By applying this method to the single hadron production in the $pA$ collision, we find the kinematic constraint effect introduced by hand in previous works comes out automatically, but with different values. The difference is crucial for our next-to-leading-order result to have a smaller theoretical uncertainty compared with leading-order result, which makes the high-order calculation in CGC factorization be useful. As a byproduct, the negativity problem found in the literature can also be overcome in our framework by properly choosing the factorization scale.

Initial correlations of the Glasma energy-momentum tensor

Abstract: We present an analytical calculation of the covariance of the energy-momentum tensor associated to the gluon field produced in ultra-relativistic heavy ion collisions at early times, the Glasma. This object involves the two-point and single-point correlators of the energy-momentum tensor (〈Tμν (x⊥)Tσρ(y⊥)〉 and 〈Tμν (x⊥)〉, respectively) at proper time τ = 0+. Our approach is based on the Color Glass Condensate effective theory, which allows us to map the fluctuations of the valence color sources in the colliding nuclei to those of the energy-momentum tensor of the produced gluon fields via the solution of the classical equations of motion in the presence of external currents. The color sources in the two colliding nuclei are characterized by Gaussian correlations, albeit in more generality than in the McLerran-Venugopalan model, allowing for non-trivial impact parameter and transverse dependence of the two-point correlator. We compare our results to those obtained under the Glasma Graph approximation, finding agreement in the limit of short transverse separations. However, important differences arise at larger transverse separations, where our result displays a slower fall-off than the Glasma Graph result (1/r2 vs. 1/r4 power-law decay), indicating that the color screening of the correlations in the transverse plane occurs at distances larger than 1/Qs by a logarithmic factor sensitive to the infrared. In the Glasma flux tube picture, this implies that the color domains are larger than originally estimated.

Fluctuations in heavy-ion collisions generated by QCD interactions in the color glass condensate effective theory

Abstract: Since their discovery, fluctuations in the initial state of heavy-ion collisions have been understood as originating mostly from the random positions of nucleons within the colliding nuclei. We consider an alternative approach where all the focus is on fluctuations generated by QCD interactions that we evaluate at leading logarithmic accuracy in the color glass condensate effective theory. We validate our approach using BNL Relativistic Heavy Ion Collider (RHIC) and CERN Large Hadron Collider (LHC) data on anisotropic flow. In particular, we show that, compared to standard Glauber-inspired calculations, our formalism provides a better description of the centrality dependence of the ratio of elliptic flow and triangular flow. It also naturally explains the evolution of elliptic flow fluctuations between RHIC and LHC energies.

Large baryon densities achievable in high-energy heavy-ion collisions outside the central rapidity region

Abstract: Nuclei are nearly transparent to each other when they collide at high energy, but the collisions do produce high energy density matter in the central rapidity region where most experimental measurements are made. What happens to the receding nuclear fireballs? We calculate the energy loss of the nuclei using the color glass condensate model. We then use a simple space-time picture of the collision to calculate the baryon and energy densities of the receding fireballs. For central collisions of large nuclei at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider we find baryon densities more than ten times that of normal nuclear matter. These results provide initial conditions for subsequent hydrodynamic evolution and could test the equation of state at very high baryon densities.

TMD gluon distributions for multiparton processes

Abstract: We derive gauge invariant operators entering definitions of the Transverse Momentum Dependent (TMD) gluon distributions, for all five and six parton processes. Our calculations utilize color decomposition of amplitudes in the color flow basis. In addition, we find the general result for multi-gluon process (with arbitrary number of gluons) at large $$N_{c}$$ . On phenomenological ground our results may be used for multi-jet production in the small-x regime, where the TMD gluon distributions can be derived from the Color Glass Condensate effective theory.

Multiparticle Production at Mid-Rapidity in the Color-Glass Condensate

Abstract: In this paper, we compute a number of cross sections for the production of multiple particles at mid-rapidity in the semi-dilute / dense regime of the color-glass condensate (CGC) effective field theory. In particular, we present new results for the production of two quark-antiquark pairs (whether the same or different flavors) and for the production of one quark-antiquark pair and a gluon. We also demonstrate the existence of a simple mapping which transforms the cross section to produce a quark-antiquark pair into the corresponding cross section to produce a gluon, which we use to obtain various results and to cross-check them against the literature. We also discuss hadronization effects in the heavy flavor sector, writing explicit expressions for the production of various combinations of D and $$ \overline{D} $$ mesons, J/ψ mesons, and light hadrons. The various multiparticle cross sections presented here contain a wealth of information and can be used to study heavy flavor production, charge-dependent correlations, and “collective” flow phenomena arising from initial-state dynamics.

Non-eikonal corrections to multi-particle production in the Color Glass Condensate

Abstract: 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 implications on two particle correlations of these non-eikonal corrections that induce differences between the away- and near-side peaks.

Simulations of the glasma in 3+1D

Abstract: The Glasma is a gluonic state of matter which can be created in collisions of relativistic heavy ions and is a precursor to the quark-gluon plasma. The existence of this state is a prediction of the color glass condensate (CGC) effective theory. In many applications of the CGC framework, the boost invariant approximation is employed. It assumes that the longitudinal extent of the nuclei can be approximated as infinitesimally thin. Consequently, the Glasma produced from such a collision is boost invariant and can be effectively described in 2+1D. Therefore, observables of the boost invariant Glasma are by construction independent of rapidity. The main goal of this thesis is to develop a numerical method for the non-boost-invariant setting where nuclei are assumed to be thin, but of finite longitudinal extent. This is in conflict with a number of simplifications that are used in the boost invariant case. In particular, one has to describe the collisions in 3+1D in the laboratory or center-of-mass frame. The change of frame forces the explicit inclusion of the color charges of nuclei. The new method is tested using an extension of the McLerran-Venugopalan model which includes a parameter for longitudinal thickness. It reproduces the boost invariant setting as a limiting case. Studying the pressure components of the Glasma, one finds the pressure anisotropy remains large. The energy density of the Glasma depends on rapidity due to the explicit breaking of boost invariance. The width of the observed rapidity profiles is controlled by the collision energy and can be shown to roughly agree with experimental data. Finally, a new numerical scheme for real-time lattice gauge theory is developed which provides higher numerical stability than the previous method. This new scheme is shown to be gauge-covariant and conserves the Gauss constraint even for large time steps.

Effect of non-eikonal corrections on azimuthal asymmetries in the Color Glass Condensate

Abstract: 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 increasing collision energy and becomes negligible at the energies of the Large Hadron Collider, it is found to be sizeable up to top energies at the Relativistic Heavy Ion Collider.

Memory effect in Yang-Mills theory

Abstract: We study the empirical realization of the memory effect in Yang-Mills theory, especially in view of the classical vs quantum nature of the theory. Gauge invariant analysis of memory in classical $\mathrm{U}(1)$ electrodynamics and its observation by total change of transverse momentum of a charge is reviewed. Gauge fixing leads to a determination of a gauge transformation at infinity. An example of Yang-Mills memory then is obtained by reinterpreting known results on interactions of a quark and a large high energy nucleus in the theory of color glass condensate. The memory signal is again a kick in transverse momentum, but it is only obtained in quantum theory after fixing the gauge, after summing over an ensemble of classical processes.

Update of a multiphase transport model with modern parton distribution functions and nuclear shadowing

Abstract: A multiphase transport (AMPT) model has been successful in explaining a wide range of observables in relativistic heavy ion collisions. In this work, we implement a newer set of free proton parton distribution functions and an impact parameter-dependent nuclear shadowing in the AMPT model. After refitting the parameters of the two-component initial condition model to the experimental data on $pp$ and $p\overline{p}$ total and inelastic cross sections from $\sqrt{s}\ensuremath{\sim}$ 4 GeV to 13 TeV, we study particle productions in $pp$ and $AA$ collisions. We show that the updated AMPT model with string melting can reasonably describe the overall particle yields and transverse momentum spectra for both $pp$ and $AA$ collisions at RHIC and LHC energies after we introduce a nuclear scaling of the minijet transverse momentum cutoff for $AA$ collisions at LHC energies that is motivated by the color glass condensate. Since heavy flavor and $\mathrm{high}\ensuremath{-}{p}_{\mathrm{T}}$ particles are produced by perturbative-QCD processes and thus directly depend on parton distribution functions of nuclei, the updated AMPT model is expected to provide a more reliable description of these observables.