Color Glass Condensate Research Articles

Inclusive J/ψ production in forward proton-proton and proton-lead collisions at high energy

We calculate the cross section for forward J/ψ production in proton-proton and minimum bias proton-lead collisions using the color glass condensate (CGC) and nonrelativistic QCD (NRQCD) formalism consistently with deep inelastic scattering data. The cross section for color singlet states is sensitive to a four-point correlator of Wilson lines for which we describe in the Gaussian approximation in the large-Nc limit. Furthermore, we quantify the importance of finite-Nc corrections to have a small ∼12% effect. In contrast with the generic NRQCD expectation, we show that the color singlet contribution is only 15% to the total cross section. We also compare our predictions for J/ψ production as well as for the nuclear modification ratio RpPb to LHCb and ALICE data. We find a good agreement at forward rapidities, except at low transverse momenta where the cross sections are overestimated. Published by the American Physical Society 2024

Holographic Gubser flow. A combined analytic and numerical study

Gubser flow is an evolution with cylindrical and boost symmetries, which can be best studied by mapping the future wedge of Minkowski space (R3,1) to dS3 × ℝ in a conformal relativistic theory. Here, we sharpen our previous analytic results and validate them via the first numerical exploration of the Gubser flow in a holographic conformal field theory.Remarkably, the leading generic behavior at large de Sitter time is free-streaming in transverse directions and the sub-leading behavior is that of a color glass condensate. We also show that Gubser flow can be smoothly glued to the vacuum outside the future Minkowski wedge generically given that the energy density vanishes faster than any power when extrapolated to early proper time or to large distances from the central axis. We find that at intermediate times the ratio of both the transverse and longitudinal pressures to the energy density converge approximately to a fixed point which is hydrodynamic only for large initial energy densities. We argue that our results suggest that the Gubser flow is better applied to collective behavior in jets rather than the full medium in the phenomenology of heavy ion collisions and can reveal new clues to the mechanism of confinement.

Incoherent diffractive production of jets in electron DIS off nuclei at high energy

We study incoherent diffractive production of two and three jets in electron-nucleus deep inelastic scattering (DIS) at small xBj using the color dipole picture and the effective theory of the color glass condensate (CGC). We consider color fluctuations in the CGC weight-function as the source of the nuclear break-up and the associated momentum transfer |t|. We focus on the regime in which the two jets are almost back-to-back in transverse space and have transverse momenta P⊥ much larger than both the momentum transfer and the saturation scale Qs. The cross section for producing such a hard dijet is parametrically dominated by large size fluctuations in the projectile wave-function that scatter strongly and for which a third, semihard, jet appears in the final state. The 2+1 jets cross section can be written in a factorized form in terms of incoherent quark and gluon diffractive transverse momentum distributions (DTMDs) when the third jet is explicit, or incoherent diffractive parton distribution functions (DPDFs) when the third jet is integrated over. We find that the DPDFs and the corresponding cross section saturate logarithmically when |t|≪Qs2, while they fall like 1/|t|2 in the regime Qs2≪|t|≪P⊥2. We further show that there is no angular correlation between the hard jet momentum and the momentum transfer. For typical EIC kinematics the 2 jets and 2+1 jets cross sections are of the same order. Published by the American Physical Society 2024

CGC and saturation approach: Impact-parameter dependent model of perturbative QCD and combined HERA data

In this paper we confront the color glass condensate and saturation approach of Contreras [Non-linear equation in the re-summed next-to-leading order of perturbative QCD: The leading twist approximation, ] with the experimental combined HERA data and obtain its parameters. The model includes two features that are in accordance with our theoretical knowledge of deep inelastic scattering. These consist of: (i) the use of analytical solution for the nonlinear Balitsky-Kovchegov evolution equation and () the exponential behavior of the saturation momentum on the impact parameter b-dependence, characterized by Qs∝exp(−mb) which reproduces the correct behavior of the scattering amplitude at large b in accord with Froissart theorem. The model results are then compared to data at small-x for the structure function of the proton F2, the longitudinal structure function FL, the charm structure function F2cc¯, the exclusive vector meson (J/ψ,ϕ,ρ) production and deeply virtual Compton scattering. We obtain a good agreement for the processes in a wide kinematic range of Q2 at small-x. Our results provide a strong guide for finding an approach, based on color glass condensate and saturation effective theory for high-energy QCD, to make reliable predictions from first principles and for forthcoming experiments like the Electron Ion Collider and the LHeC. Published by the American Physical Society 2024

Next-to-eikonal corrections to dijet production in Deep Inelastic Scattering in the dilute limit of the Color Glass Condensate

We analyze the effects of next-to-eikonal corrections on dijet production in Deep Inelastic Scattering off nuclear targets in the framework of the Color Glass Condensate. They require the knowledge of correlators of fields in the target beyond those computed in the standard McLerran-Venugopalan model, specifically those between transverse and boost-enhanced components, and of the recoil of the fields. We neglect the latter, while for the former we develop a linear model valid for large nuclei. We considered the unpolarized cross sections for dijet production in the approximation of a homogenous dilute nucleus, obtaining simple analytic expressions for the cross sections at next-to-eikonal accuracy, valid in the limit of total dijet momentum and dijet momentum imbalance larger than the saturation scale of the nucleus. We perform a numerical study of the results at energies of the Electron Ion Collider, finding O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(10%) effects in the cross sections at large total momentum. We also analyze the azimuthal asymmetries between total momentum and imbalance, finding that non-eikonal corrections induce odd azimuthal harmonics for the situation of jets with equal momentum fractions from the virtual photon, where they are absent in the eikonal approximation. Finally, in the eikonal approximation we have compared the results of our analytic expansion valid in the dilute limit of the target, and the full Color Glass Condensate results in the McLerran-Venugopalan model and their correlation limit. Our analytic expressions match the correlation limit ones in the region where both should be simultaneously valid and reproduce very well the full Color Glass Condensate results in its validity region.

TMD factorisation for diffractive jets in photon-nucleus interactions

Using the colour dipole picture and the colour glass condensate effective theory, we study the diffractive production of two or three jets via coherent photon-nucleus interactions at high energy. We consider the hard regime where the photon virtuality and/or the transverse momenta of the produced jets are much larger than the saturation momentum Qs of the nuclear target. We show that, despite this hardness, the leading-twist contributions are controlled by relatively large parton configurations, with transverse sizes R ~ 1/Qs, which undergo strong scattering and probe gluon saturation. We demonstrate that these leading-twist contributions admit transverse-momentum dependent (TMD) factorisation, in terms of quark and gluon diffractive TMD distribution functions, for which we obtain explicit expressions from first principles. We go beyond our previous work by evaluating the contributions involving the quark diffractive distributions and by establishing that their DGLAP evolution emerges via controlled calculations within the colour dipole picture. We find the same expression for the quark diffractive TMD in two different processes (semi-inclusive diffraction and the diffractive production of quark-gluon dijets), thus demonstrating its universality.

Bayesian quantification of strongly interacting matter with color glass condensate initial conditions

Bayesian quantification of strongly interacting matter with color glass condensate initial conditions

Energy-momentum tensor of the dilute (3+1)D glasma

We present a succinct formulation of the energy-momentum tensor of the glasma characterizing the initial color fields in relativistic heavy-ion collisions in the color glass condensate effective theory. We derive concise expressions for the (3+1)D dynamical evolution of symmetric nuclear collisions in the weak field approximation employing a generalized McLerran-Venugopalan model with nontrivial longitudinal correlations. Utilizing Monte Carlo integration, we calculate in unprecedented detail non-trivial rapidity profiles of early time observables at RHIC and LHC energies, including transverse energy densities and eccentricities. For our setup with broken boost invariance, we carefully discuss the placement of the origin of the Milne frame and interpret the components of the energy-momentum tensor. We find longitudinal flow that deviates from standard Bjorken flow in the (3+1)D case and provide a geometric interpretation of this effect. Furthermore, we observe a universal shape in the flanks of the rapidity profiles regardless of collision energy and predict that limiting fragmentation should also hold at LHC energies. Published by the American Physical Society 2024

D0 meson production in pp collisions at large Qs2

The impact of the nonlinear effects in the QCD on the observables is directly related to the magnitude of the saturation scale Qs, which is predicted to increase with the energy, rapidity, and multiplicity. In this paper, we investigate the D0 meson production in pp collisions at forward rapidities and/or high multiplicities considering the color glass condensate (CGC) formalism and the solutions of the running coupling Balitsky-Kovchegov equation. The contributions of gluon- and charm-initiated processes are taken into account, and a comparison with the current LHCb data is performed. The impact of an intrinsic charm component in the proton’s wave function is also estimated. Predictions for the self-normalized yields of D0 mesons as a function of the multiplicity of coproduced charged hadrons are presented, considering pp collisions at s=13 TeV and different values of the meson rapidity. A comparison with the predictions for the kaon and isolated photon production is performed. Our results indicate that a future experimental analysis of the D0 meson production at forward rapidities and high multiplicities can be useful to probe the CGC formalism and to disentangle the contribution of initial—and final—state effects. Published by the American Physical Society 2024

ρ -meson spectroscopy and diffractive production using the holographic light-front Schrödinger equation and the ’t Hooft equation

We determine the mass spectroscopy and light-front wave functions (LFWFs) of the ρ-meson by solving the holographic Schrödinger equation of light-front chiral QCD along with the ’t Hooft equation of (1+1)-dimensional QCD in the large Nc limit. Subsequently, we utilize the obtained LFWFs in conjunction with the color glass condensate dipole cross section to calculate the cross sections for the diffractive ρ-meson electroproduction. Our spectroscopic results align well with the experimental data. Predictions for the diffractive cross sections demonstrate good consistency with the available experimental data at different energies from H1 and ZEUS collaborations. Additionally, we show that the resulting LFWFs for the ρ-meson can effectively describe various properties, including its decay constant, distribution amplitudes, electromagnetic form factors, charge radius, magnetic and quadrupole moments. Comparative analyses are conducted with experimental measurements and the available theoretical predictions. Published by the American Physical Society 2024

Semi-inclusive single-jet production in DIS at next-to-leading order in the Color Glass Condensate

Within the Color Glass Condensate (CGC) effective field theory, we derive the next-to-leading order (NLO) cross-section for the single-jet semi-inclusive cross-section in deep inelastic scattering (DIS) at small x, for both longitudinally and transversely polarized virtual photons. We provide analytic expressions, valid at finite Nc and suitable for numerical evaluation, for both the cross-section differential in rapidity and transverse momentum and the cross-section differential in rapidity only. Our NLO formulae demonstrate that the very forward rapidity regime is plagued by large double logarithmic corrections coming from phase space constraints on soft gluons close to the kinematic threshold for jet production. A joint resummation of small-x and threshold logarithms at single logarithmic accuracy is proposed to remedy the instability of the cross-section in this regime. By integrating over the single-jet phase space, we recover known results for the NLO DIS structure functions at small x, previously obtained using the optical theorem.

Transverse energy-energy correlators in the color-glass condensate at the electron-ion collider

We investigate the transverse energy-energy correlators (TEEC) in the small-x regime at the upcoming Electron-Ion Collider (EIC). Focusing on the back-to-back production of electron-hadron pairs in both ep and eA collisions, we establish a factorization formula given in terms of the hard function, quark distributions, soft functions, and TEEC jet functions, where the gluon saturation effect is incorporated. Numerical results for TEEC in both ep and eA collisions are presented, together with the nuclear modification factor RA. Our analysis reveals that TEEC observables in deep inelastic scattering provide a valuable approach for probing gluon saturation phenomena. Our findings underscore the significance of measuring TEEC at the EIC, emphasizing its efficacy in advancing our understanding of gluon saturation and nuclear modifications in high-energy collisions. Published by the American Physical Society 2024

Diffractive deep inelastic scattering at NLO in the dipole picture

We compute the transverse and longitudinal diffractive structure functions to full next-to-leading order accuracy in the dipole picture of deep inelastic scattering. Our calculation uses the standard light-cone perturbation theory method for the partonic content of the virtual photon, together with the Color Glass Condensate description of the target color field. Our result includes as a subset the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q\\overline{q }g$$\\end{document} contribution calculated earlier. We show that there is a rapidity divergence that can be factorized into the BK/JIMWLK evolution of the target Wilson lines, and that all other divergences cancel.

Inclusive photoproduction of charmonia-bottomonia pairs

In this article we analyze the inclusive photoproduction of heavy charmonia-bottomonia pairs in the color glass condensate framework and demonstrate that the cross section of the process is sensitive to dipole and quadrupole forward scattering amplitudes (2- and 4-point correlators of Wilson lines). Using the phenomenological parametrizations of these amplitudes, we estimate numerically the production cross sections in the kinematics of the forthcoming Electron Ion Collider and the ultraperipheral collisions at the LHC. We found that the contribution controlled by the quadrupole amplitude is dominant, and for this reason, the suggested channel can be used as a gateway for studies of this nonperturbative object. Published by the American Physical Society 2024

McDIPPER: A novel saturation-based 3+1D initial-state model for heavy ion collisions

We present a new three-dimensional resolved model for the initial state of ultrarelativistic heavy-ion collisions, based on the k⊥-factorized color glass condensate (CGC) hybrid approach. The framework responds to the need for a rapidity-resolved initial-state Monte Carlo event generator which can deposit the relevant conserved charges (energy, charge, and baryon densities) both in the midrapidity and forward (backward) regions of the collision. This event-by-event generator computes the gluon and (anti-) quark phase-space densities using the IP-Sat model, from where the relevant conserved charges can be computed directly. In the present work we have included the leading-order contributions to the light flavor parton densities. As a feature, the model can be systematically improved in the future by adding next-to-leading-order calculations (in the CGC hybrid framework) and extending to lower energies by including subeikonal corrections to the channels included. We present relevant observables, such as the eccentricities and flow decorrelation, as tests of this new approach. Published by the American Physical Society 2024

Energy dependent nuclear suppression from gluon saturation in exclusive vector meson production

We calculate exclusive J/ψ photoproduction at high energies in the color glass condensate approach. The results are compared to the center-of-mass energy dependent γ+A→J/ψ+A cross sections extracted from measurements in ultraperipheral heavy ion collisions at RHIC and LHC. We predict strong saturation-driven nuclear suppression at high energies, while LHC data prefer even stronger suppression. We explore effects of nucleon shaped fluctuations and show that the most recent measurement of the |t|-differential incoherent J/ψ cross section prefers large event-by-event fluctuations of the nucleon substructure in heavy nuclei, comparable to that found for a free proton. Published by the American Physical Society 2024

Inferring the initial condition for the Balitsky-Kovchegov equation

We apply Bayesian inference to determine the posterior likelihood distribution for the parameters describing the initial condition of the small-x Balitsky-Kovchegov evolution equation at leading logarithmic accuracy. The HERA structure function data is found to constrain most of the model parameters well. In particular, we find that the HERA data prefers an anomalous dimension γ≈1 unlike in previous fits where γ>1 which led to, e.g., the unintegrated gluon distribution and the quark-target cross sections not being positive definite. The determined posterior distribution can be used to propagate the uncertainties in the nonperturbative initial condition when calculating any other observable in the color glass condensate framework. We demonstrate this explicitly for the inclusive quark production cross section in proton-proton collisions and by calculating predictions for the nuclear modification factor for the F2 structure function in the EIC and LHeC/FCC-he kinematics. Published by the American Physical Society 2024

Direct quarkonium-plus-gluon production in DIS in the color glass condensate

We compute the differential cross-section for direct quarkonium production accompanied by a gluon in high-energy deep inelastic scattering (DIS) at small-x. We employ the Non-Relativistic QCD factorization framework, focusing on the S-wave contribution to the formation of the quarkonium, and including both color singlet and octet contributions. Our short distance coefficients for the production of the heavy quark pair are obtained within the Color Glass Condensate effective field theory. Our results pave the way towards the next-to-leading order computation of direct quarkonium in DIS, as well as the study of azimuthal correlations of direct quarkonium and jet.

Probing valence quark width of the proton in deeply virtual Compton scattering at high energies* *Supported by the National Natural Science Foundation of China (12165004), the Basic and Applied Basic Research Project of Guangzhou Science and Technology Bureau (202201011324), the Education Department of Guizhou Province, China (QJJ[2022]016) and the National Key Research and Development Program of China (2018YFE0104700, CCNU18ZDPY04)

We use the refined hot spot model to study the valence quark shape of the proton with the deeply virtual Compton scattering at high energies in the color glass condensate framework. To investigate the individual valence quark shape, a novel treatment of the valence quark width is employed. We calculate the cross-sections for coherent and incoherent deeply virtual Compton scattering using, for the first time, different widths ( and ) for the profile density distributions of the up and down quarks instead of using the same width as in the literature. We find that the cross-sections calculated with at each collision energy are consistent with each other, which is in agreement with theoretical expectations, whereas those computed with show some discrepancies. This outcome implies that the up quark might emit more gluons than the down quark, leading to at high energy. The impact of energy on the outcome is estimated. Our results show that as the collision energy increases, the aforementioned discrepancies are not only significantly broadened, but also shift to a relatively smaller momentum transfer range at the future Electron-Ion Collider (EIC) and Large Hadron Electron Collider (LHeC) energies, which indicates that the EIC and LHeC can provide an unprecedented chance to access the shape of the valence quark of the proton.

Complete next-to-leading order calculation of single inclusive π0 production in forward proton-nucleus collisions

We present the first fully consistent calculation of inclusive π0 production at forward rapidities at next-to-leading order (NLO) accuracy in proton-lead collisions at s=8.16 TeV within the color glass condensate approach. The center-of-mass energy dependence is determined by the Balitsky-Kovchegov equation with the initial condition constrained at NLO accuracy by the proton structure function measurements. We find that the LHCb data further constrain this nonperturbative input, and that both the NLO corrections to the evolution equation and to the impact factor have significant effects on the nuclear modification factor RpPb. The complete NLO calculation is shown to be in qualitative agreement with the LHCb data, and the predictions are found to be sensitive to the details of the applied deep inelastic scattering (DIS) fit. These results demonstrate the need to perform global analyses of DIS and LHC data in order to probe gluon saturation phenomena at precision level at very small momentum fraction x. Published by the American Physical Society 2024