Color Glass Condensate Research Articles

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

Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small x: Complete NLO Results and Predictions.

We compute the back-to-back dijet cross section in deep inelastic scattering at small x to next-to-leading order (NLO) in the color glass condensate effective field theory. Our result can be factorized into a convolution of the Weizsäcker-Williams gluon transverse-momentum-dependent distribution function (WW gluon TMD) with a universal soft factor and an NLO coefficient function. The soft factor includes both double and single logarithms in the ratio of the relative transverse momentum P_{⊥} of the dijet pair to the dijet momentum imbalance q_{⊥}; its renormalization group (RG) evolution is resummed into the Sudakov factor. Likewise, the WW TMD obeys a nonlinear RG equation in x that is kinematically constrained to satisfy both the lifetime and rapidity ordering of the projectile. Exact analytical expressions are obtained for the NLO coefficient function of transversely and longitudinally polarized photons. Our results allow for the first quantitative separation of the dynamics of Sudakov suppression from that of gluon saturation. They can be extended to other final states and provide a framework for precision tests of novel QCD many-body dynamics at the Electron-Ion Collider.

Particle Production in pA Collisions at Mid-Rapidity in the Color Glass Condensate

Particle correlations in small collisions systems, like proton–nucleus, lie at the core of the discussion about whether quark–gluon plasma is produced in small systems. Both initial and final state explanations have been essayed to describe such correlations. In this work, we focus on the initial state explanations provided by the quantum effects in the initial wave function of the incoming hadrons, in the framework of the Color Glass Condensate effective theory. We describe the formalism indicating the different inputs required for phenomenological applications. We compare the results from two different models, finding that the results for azimuthal harmonics agree qualitatively, but show quantitative differences, particularly at transverse momenta above the saturation scale.

Forward production of a Drell-Yan pair and a jet at small x at next-to-leading order

We perform the analytical next-to-leading order calculation of the process p + A γ∗ + jet + X, at forward rapidities and low x. These kinematics justify a hybrid approach, where a quark from the ‘projectile’ proton scatters off the gluon distribution of the ‘target’, which can be a nucleus or a highly boosted proton. By using the Color Glass Condensate effective theory approach, this gluon distribution is allowed to be so dense that the quark undergoes multiple scattering. Moreover, large high-energy logarithms in the ratio of the hard scale and the center-of-mass energy are resummed by the Balitsky, Kovchegov, Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner or BK-JIMWLK evolution equations. We demonstrate that all ultraviolet divergences encountered in the calculation cancel, while the high-energy divergences are absorbed into BK-JIMWLK. The remaining singularities are collinear in nature and can be either absorbed into the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution of the incoming quark, when they stem from initial-state radiation, or else can be treated by a jet function in case they are caused by final-state emissions. The resulting cross section is completely finite and expressed in function of only a small set of color operators.

Wee partons in QCD and gravity: Double copy and universality

We discuss a quantitative “double copy” between radiation from shockwave collisions in Einstein gravity and in QCD. The correspondence extends to 2 → N amplitudes in Regge asymptotics. The classicalization and unitarization of these amplitudes at maximal occupancy, corresponding to black hole and Color Glass Condensate (CGC) states respectively, are described by the emergent Goldstone dynamics of wee partons. We outline some consequences of the universal dynamics on both sides of the correspondence.

Pursuing the precision study for Color Glass Condensate framework in forward single hadron productions

The forward single hadron production process is an important benchmark process for investigating the emergent properties of gluon saturation or the dense gluon system. We present our recent work [1] in which we improve the prediction accuracy of the next-to-leading order calculation of forward single hadron productions in high-p⊥ regions by implementing the threshold resummations in the Color Glass Condensate framework. Our resummed formula provides accurate descriptions of all related data across a range of energies from RHIC to the LHC. This work sheds light on the path for precision study of Color Glass Condensate based on experimental data.

Probing nuclear structure at the Electron-Ion Collider and in ultra-peripheral nuclear collisions

Within the Color Glass Condensate framework, we demonstrate that exclusive vector meson production at high energy is sensitive to the geometric deformation of the target nucleus and subnucleon scale fluctuations. Deformation of the nucleus enhances the incoherent cross section in the small |t| region. Subnucleon scale fluctuations increase the incoherent cross section in the large |t| region. In ultra-peripheral collisions (UPCs), larger deformation leads to a wider distribution of the minimal impact parameter Bmin required to produce a UPC. This, together with larger incoherent cross sections for larger deformation, results in smaller extracted radii. Our results demonstrate great potential for future studies of nuclear structure in UPCs and electron-ion collisions.

Probing quark transverse momentum distributions in the color glass condensate: Quark-gluon dijets in deep inelastic scattering at next-to-eikonal accuracy

Probing quark transverse momentum distributions in the color glass condensate: Quark-gluon dijets in deep inelastic scattering at next-to-eikonal accuracy

Low projectile density contributions in the dilute-dense CGC framework for two-particle correlations

At leading-order, the standard dilute-dense Color Glass Condensate formula used for two-particle correlations in proton-nucleus collisions, whose symmetries prevent the generation of odd azimuthal anisotropy harmonics, is the dilute projectile limit of the dense-dense formalism. However, when the projectile is genuinely dilute, the complete formulation contains additional contributions at the same leading order in the strong coupling constant. In this work we investigate those low projectile density contributions that are relevant when the particles are produced at forward rapidities. We find that they are responsible for non-zero odd harmonics which are negative, in qualitative agreement with recent experimental measurements at the Relativistic Heavy-Ion Collider.

Searching for saturation in forward dijet production at the LHC

We review recent results for forward jests at the LHC and EIC as obtained within small-x Improved Transverse Momentum Dependent factorization (ITMD). In addition to elementary overview of various approaches to perturbative QCD at high energy, including High Energy Factorization, Color Glass Condensate and ITMD, we describe the Monte Carlo implementation and discuss the existing and unpublished phenomenological results for forward dijets.

Measurement of the non-prompt D-meson fraction as a function of multiplicity in proton-proton collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV

The fractions of non-prompt (i.e. originating from beauty-hadron decays) D0 and D+ mesons with respect to the inclusive yield are measured as a function of the charged-particle multiplicity in proton-proton collisions at a centre-of-mass energy of s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV with the ALICE detector at the LHC. The results are reported in intervals of transverse momentum (pT) and integrated in the range 1 < pT< 24 GeV/c. The fraction of non-prompt D0 and D+ mesons is found to increase slightly as a function of pT in all the measured multiplicity intervals, while no significant dependence on the charged-particle multiplicity is observed. In order to investigate the production and hadronisation mechanisms of charm and beauty quarks, the results are compared to PYTHIA 8 as well as EPOS 3 and EPOS 4 Monte Carlo simulations, and to calculations based on the colour glass condensate including three-pomeron fusion.

Forward gamma +jet production in proton-proton and proton-lead collisions at LHC within the FoCal calorimeter acceptance

Using the small-x improved transverse momentum dependent factorization (ITMD), which, for a general two-to-two massless scattering can be proved within the color glass condensate (CGC) theory for transverse momenta of particles greater than the saturation scale, we provide predictions for isolated forward photon and jet production in proton-proton and proton-nucleus collisions within the planned ALICE FoCal detector acceptance. We study azimuthal correlations, p_T spectra, as well as normalized ratios of proton-proton cross sections for different energies. The only TMD distribution needed for that process is the “dipole” TMD gluon distribution, which in our computations is based on HERA data and undergoes momentum space BK evolution equation with DGLAP corrections and Sudakov resummation. We conclude, that the process provides an excellent probe of the dipole TMD gluon distribution in saturation regime.

Characterizing the initial conditions of heavy-ion collisions at the LHC with mean transverse momentum and anisotropic flow correlations

The study of the initial conditions of relativistic heavy-ion collisions and the subsequent development of hot and dense nuclear matter at the LHC is fundamental for the understanding of the strong nuclear force. The traditional approach of comparing observables with hydrodynamical models based on different initial conditions typically fails to isolate the effects of the initial conditions due to the sensitivity of the observables to the collective behaviour of the expanding system. Correlations of the mean transverse momentum [p T] and the anisotropic flow Fourier coefficients v n have been shown to serve as a unique probe of the initial conditions of the heavy-ion collisions with little to no bias from final state effects.In this talk, correlations between [p T] and v 2 or v 3 are presented as a function of centrality in Pb−Pb and Xe−Xe collisions at TeV and TeV, respectively, measured with ALICE. Additionally, measurements of the higher-order correlation between [p T], v 2, and v 3 is measured for the first time. All of these measurements are compared with hydrodynamical models using IP-Glasma or TRENTo initial conditions. The former is based on Color Glass Condensate effective theory with gluon saturation and the latter is a parameterized model with nucleons as the relevant degrees of freedom. The data is best described by models using IP-Glasma initial conditions, whereas the TRENTo based models fail to describe the data regardless of the parametrization.

Back-to-back inclusive dijets in DIS at small x: gluon Weizsäcker-Williams distribution at NLO

In [1], we performed the first complete computation of the back-to-back inclusive dijet cross-section in Deeply Inelastic Scattering (DIS) at small xBj to next-to-leading order (NLO) in the Color Glass Condensate effective field theory (CGC EFT). We demonstrate here that for dijets with relative transverse momentum P⊥ and transverse momentum imbalance q⊥, to leading power in q⊥/P⊥, the cross-section for longitudinally polarized photons can be fully factorized into the product of a perturbative impact factor and the non-perturbative Weizsäcker-Williams (WW) transverse momentum dependent (TMD) gluon distribution to NLO accuracy. The impact factor can further be expressed as the product of a universal soft factor which resums Sudakov double and single logs in P⊥/q⊥ and a coefficient function given by a remarkably compact analytic expression. We show that in the CGC EFT the WW TMD satisfies a kinematically constrained JIMWLK renormalization group evolution in rapidity. This factorization formula is valid to all orders in Qs/q⊥ for q⊥, Qs ≪ P⊥, where Qs is the semi-hard saturation scale that grows with rapidity.

Multiscale Imaging of Nuclear Deformation at the Electron-Ion Collider.

We show within the color glass condensate framework that exclusive vector meson production at high energy is very sensitive to the geometric deformation of the target nucleus at multiple length scales. We show that different multipole deformation parameters affect different regions of transverse momentum transfer. These results have two important consequences: (1)Deformations of nuclear targets need to be taken into account when making predictions for and interpreting certain observables at the EIC. (2)Differential diffractive vector meson production has the potential to become a powerful tool, enabling the most direct measurements of nuclear structure at different length scales, ranging from large scale nuclear deformation at low transverse momentum transfer to fluctuations on nucleon- and subnucleon-size scales at higher transverse momentum transfer.

Dihadron production in DIS at NLO: the real corrections

By using the formalism of the light-cone wave function along with the colour glass condensate effective theory, we consider next-to-leading order (NLO) corrections to the production of a pair of hadrons in electron-proton, or electron-nucleus, collisions at small Bjorken x. To the order of interest, the process involves the fluctuation of a virtual photon into a quark-antiquark pair, followed by the emission of a gluon from either the quark, or the antiquark. For the case of a virtual photon with transverse polarization, we compute the real NLO corrections, where the emitted gluon is present in the final state. We first compute the tree-level cross-section for the production of the quark-antiquark-gluon system and then deduce the real NLO corrections to dihadron production by integrating out the kinematics of the gluon. We verify in detail that, in the limit where the gluon is soft, our calculation reproduces the (real piece of the) B-JIMWLK evolution of the leading-order cross-section for quark-antiquark production. Similarly, in the limit where the gluon is collinear with its emitter, we recover the real terms in the DGLAP evolution of the fragmentation function. The virtual NLO corrections to dihadron production will be presented by one of us in a subsequent publication.

Measurements of J/ψ Production vs. Event Multiplicity in Forward Rapidity in p + p Collisions in the PHENIX Experiment

J/ψ, a charmonium bound state made of a charm and an anti-charm quark, was discovered in the 1970s and confirmed the quark model. Because the mass of charm quarks is significantly above the quantum chromodynamics (QCD) scale ΛQCD, charmonia are considered excellent probes to test perturbative quantum chromodynamics (pQCD) calculations. In recent decades, they have been studied extensively at different high-energy colliders. However, their production mechanisms, which involve multiple scales, are still not very well understood. Recently, in high-multiplicity p+p collisions at RHIC and at the LHC, a significant enhancement of J/ψ production yield has been observed, which suggests a strong contribution of multi-parton interaction (MPI). This is different from the traditional pQCD picture, where charm quark pairs are produced from a single hard scattering between partons in p+p collisions. In this work, we will report the J/ψ normalized production yield as a function of normalized charged particle multiplicity over a board range of rapidity and event multiplicity in the J/ψ→μ+μ− channel with PHENIX Run 15 p+p data at s=200 GeV. The results are compared with PYTHIA 8 simulations with the MPI option turned on and off. Finally, the outlooks of J/ψ in p+Au and Au+p collisions, along with color glass condensate (CGC) predictions and the multiplicity-dependent ψ(2S)/J/ψ ratio in p+p data, will be briefly discussed.

Structure of the Medium Formed in Heavy Ion Collisions

We investigate the structure of the medium formed in heavy ion collisions using three different models: the Color String Percolation Model (CSPM), the Core–Shell-Color String Percolation Model (CSCSPM), and the Color Glass Condensate (CGC) framework. We analyze the radial distribution function of the transverse representation of color flux tubes in each model to determine the medium’s structure. Our results indicate that the CSPM behaves as an ideal gas, while the CSCSPM exhibits a structural phase transition from a gas-like to a liquid-like structure. Additionally, our analysis of the CGC framework suggests that it produces systems that behave like non-ideal gases for AuAu central collisions at RHIC energies and liquid-like structures for PbPb central collisions at LHC energies.

Incoherent diffractive dijet production in electron DIS off nuclei at high energy

We study incoherent diffractive dijet production in electron-nucleus deep inelastic scattering at small ${x}_{\mathrm{Bj}}$ within the color glass condensate. We follow the general approach of [1] but we focus on the correlation limit, that is, when the momentum transfer ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\perp}}$ and the gluon saturation momentum ${Q}_{s}$ of the nucleus are much smaller than the individual jet momentum ${P}_{\ensuremath{\perp}}$. We arrive at analytic expressions for the dijet cross section, which can be written as a sum of four terms which exhibit factorization: each such term is a product between a hard factor, which includes the decay of the virtual photon to the $q\overline{q}$ pair, and a semihard one which involves the dipole-nucleus scattering amplitude. We further calculate the azimuthal anisotropies $⟨\mathrm{cos}2\ensuremath{\phi}⟩$ and $⟨\mathrm{cos}4\ensuremath{\phi}⟩$. They are of the same order in the hard momentum ${P}_{\ensuremath{\perp}}$, but the $⟨\mathrm{cos}4\ensuremath{\phi}⟩$ is logarithmically suppressed due to its dependence on the semihard factor. Finally, in order to extend the validity of our result towards the perturbative domain, we calculate the first higher kinematic twist, i.e., the correction of relative order ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\perp}}^{2}/{P}_{\ensuremath{\perp}}^{2}$.