Color Glass Condensate Framework Research Articles

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

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

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.

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.

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.

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.

Forward inclusive jet productions in pA collisions

Motivated by recent experimental LHC measurements on the forward inclusive jet productions and based on our previous calculations on forward hadron productions, we calculate a single inclusive jet cross section in $pA$ collisions at forward rapidity within the color glass condensate framework up to the next-to-leading order. Moreover, with the application of a jet algorithm and proper subtraction of the rapidity and collinear divergences, we further demonstrate that the resulting next-to-leading-order hard coefficients are finite. In addition, in order to deal with the large logarithms that can potentially spoil the convergence of the perturbative expansion and improve the reliability of the numerical predictions, we introduce the collinear jet function and the threshold jet function and resum these large logarithms hidden in the hard coefficients.

CGC for ultra-peripheral Pb+Pb collisions at the Large Hadron Collider: a more realistic calculation

We provide the first calculation of two-gluon production at mid-rapidity in ultra-peripheral collisions in the Color Glass Condensate framework. To estimate systematic uncertainty associated with poor understanding of the wave function of the nearly real photon, we consider two diametrically different models: the dilute quark-antiquark dipole approximation and a vector meson, in which color charge density is approximated by McLerran-Venugopalan model. In the experimentally relevant range, the target nucleus can be faithfully approximated by a highly saturated state. This simplification enables us to perform efficient numerical simulations and extract the two-gluon correlation functions and the associated azimuthal harmonics.

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 proton and hot spot sizes as well as the structure of the probe at medium $t$ and again by color fluctuations at large $t$. While the $t$-dependence of the cross section is well reproduced in our model, the relative normalization between the coherent and the incoherent cross sections points to the need for additional fluctuations in the proton.

Complete calculation of exclusive heavy vector meson production at next-to-leading order in the dipole picture

Exclusive production of transversely polarized heavy vector mesons in deep inelastic scattering at high energy is calculated at next-to-leading order accuracy in the Color Glass Condensate framework. In addition to the first QCD correction proportional to the strong coupling constant αs, we systematically also include the first relativistic correction proportional to the heavy quark velocity squared v2. When combined with our previously published results for longitudinal vector meson production at next-to-leading order accuracy, these results make phenomenological calculations of heavy vector meson production possible at the order mathcal{O} (αsv0, {alpha}_{mathrm{s}}^0 v2). When applied to J/ψ and Υ production at HERA and at the LHC, a good agreement between the next-to-leading order calculations and experimental data is found. Additionally, we demonstrate that vector meson production can provide additional constraints compared to structure function analyses when the nonperturbative initial condition for the Balitsky-Kovchegov evolution equation is extracted.

Bayesian inference of the fluctuating proton shape

Using Bayesian inference, we determine probabilistic constraints on the parameters describing the fluctuating structure of protons at high energy. We employ the color glass condensate framework supplemented with a model for the spatial structure of the proton, along with experimental data from the ZEUS and H1 Collaborations on coherent and incoherent diffractive J/ψ production in e+p collisions at HERA. This data is found to constrain most model parameters well. This work sets the stage for future global analyses, including experimental data from e+p, p+p, and p+A collisions, to constrain the fluctuating structure of nucleons along with properties of the final state.

Gluon saturation in proton and its contribution to single inclusive soft gluon production in high energy proton-nucleus collisions

The leading order single inclusive soft gluon production in high energy proton-nucleus (pA) collisions has been studied by various approaches for more than two decades. The first correction due to the gluon saturation in proton was analytically attempted recently through a diagrammatic approach in which only partial results were obtained. An important feature of the first saturation correction is that it includes both initial state and final state interactions. In this paper, we present the complete result derived from the Color Glass Condensate framework. Our approach is to analytically solve the classical Yang-Mills equations in the dilute-dense regime and then use the Lehmann-Symanzik-Zimmermann (LSZ) reduction formula to obtain gluon production from classical gluon fields.

Single inclusive jet production in pA collisions at NLO in the small-x regime

We present the first complete next-to-leading-order (NLO) prediction with full jet algorithm implementation for the single inclusive jet production in pA collisions at forward rapidities within the color glass condensate (CGC) effective theory. Our prediction is fully differential over the final state physical kinematics, which allows the implementation of any infra-red safe observable including the jet clustering procedure. The NLO calculation is organized with the aid of the observable originated power counting proposed in [1] which gives rise to the novel soft contributions in the CGC factorization. We achieve the fully-differential calculation by constructing suitable subtraction terms to handle the singularities in the real corrections. The subtraction contributions can be exactly integrated analytically. We present the NLO cross section with the jets constructed using the anti-kT algorithm. The NLO calculation demonstrates explicitly the validity of the CGC factorization in jet production. Furthermore, as a byproduct of the subtraction method, we also derive the fully analytic cross section for the forward jet production in the small-R limit. We show that in the small-R approximation, the forward jet cross section can be factorized into a semi-hard cross section that produces a parton and the semi-inclusive jet functions (siJFs). We argue that this feature holds for generic jet production and jet substructure observables in the CGC framework. Last, we show numerical analyses of the derived formula to validate our calculations. We justify when the small-R approximation is appropriate. Like forward hadron production, the obtained NLO result also exhibits the negativity of the cross section in the large jet transverse regime, which signals the need for the threshold resummation. A sketch of the threshold resummation in the CGC framework is presented based on the multiple emission picture and it is found to agree with the approach using the rapidity renormalization group equation developed in [2].

Rare fluctuations of S-matrix in target rapidity representation in the color glass condensate framework

Rare fluctuations of S-matrix in target rapidity representation in the color glass condensate framework

Isolated photon-hadron production in high energy pp and pA collisions at RHIC and LHC

We compute the isolated photon production in association with a charged hadron at mid rapidity in $pp$ and $pA$ based on the Color Glass Condensate (CGC) framework of high energy QCD where, for the first time, we incorporate the Sudakov effect of soft gluon emissions. Our results are based on the leading order $q g \to q \gamma$ channel in the CGC framework and confronted with the recent data from RHIC and LHC concerning the angular distributions and out-of-plane transverse momentum distributions. We find that, while the CGC computation alone results in too narrow distributions, with the help of the Sudakov effect, we can get a satisfactory description of the data. With this as a benchmark, we provide predictions for the magnitude of the nuclear effect brought by the phenomena of gluon saturation in the CGC.

Accessing subnuclear fluctuations and saturation with multiplicity dependent J/ψ production in p+p and p+Pb collisions

We study the production of J/ψ vector mesons as a function of charged hadron multiplicity in p+p and p+Pb collisions at LHC energies. We employ the color glass condensate framework, using running coupling Balitsky-Kovchegov evolved dipole amplitudes, to compute gluon and cc¯-pair production. We use fragmentation functions to obtain charged hadrons, and explore two different hadronization schemes for the J/ψ: non-relativistic quantum chromodynamics and the improved color evaporation model. In our framework, event-by-event multiplicity fluctuations of both hadrons and J/ψ are driven by geometric and saturation scale normalization fluctuations. Studying the correlation between J/ψ and hadron multiplicity, we show that the characteristic difference between forward and backward rapidity in p+Pb collisions is a result of different degrees of saturation probed at different rapidities. We demonstrate that experimental data on heavy-flavor production as a function of event activity provide stringent constraints on the fluctuating proton structure.

Perturbative structure of two- and four-point functions of color charge in a non-Gaussian small-x action

We compute the perturbative expansion of the two- and four-point functions of color charges in the Color Glass Condensate framework considering the quartic correction to the McLerran–Venugopalan (MV) model of Gaussian color charge fluctuations. Expressions for these correlators in the perturbative expansion for small and large non-Gaussian color charge fluctuations are derived for arbitrary orders in perturbation theory. We explicitly show that the perturbative series does not converge at higher orders as expected. We apply the Borel–Padé resummation method to our problem to construct a convergent series. It is shown that the fully non-perturbative solution can be described by the Borel–Padé approximants constructed from the first few terms of the perturbative series for small non-Gaussian fluctuations.

Suppressions of dijet azimuthal correlations in the future EIC

Quark-antiquark pair (or dijet) production at the electron-ion collider (EIC) has been argued to be one of most important processes that allowing to access the Weizs\"acker-Williams (WW) gluon distributions at small $x$ limit. Within the framework of Color Glass Condensate (CGC) effective field theory (EFT), we calculated the dijet cross sections and the azimuthal correlations by including the Sudakov resummations, numerical results shown that the back-to-back correlations are significantly suppressed when the Sudakov resummations are taken into account. In addition, by using the solutions of running-coupling Balitsky-Kovchegov (rcBK) equation, the unpolarized and linearly polarized WW gluon distributions both in coordinate and momentum space are presented.

Gluonic hot spot initial conditions in heavy-ion collisions

The initial conditions in heavy-ion collisions are calculated in many different frameworks. The importance of nucleon position fluctuations within the nucleus and sub-nucleon structure has been established when modeling initial conditions for input to hydrodynamic calculations. However, there remain outstanding puzzles regarding these initial conditions, including the measurement of the near equivalence of the elliptical $v_{2}$ and triangular $v_{3}$ flow coefficients in ultra-central 0-1% Pb+Pb collisions at the LHC. Recently a calculation termed MAGMA incorporating gluonic hot spots via two-point correlators in the Color Glass Condensate framework, and no nucleons, provided a simultaneous match to these flow coefficients measured by the ATLAS experiment, including in ultra-central 0-1% collisions. Our calculations reveal that the MAGMA initial conditions do not describe the experimental data when run through full hydrodynamic SONIC simulations or when the hot spots from one nucleus resolve hot spots from the other nucleus, as predicted in the Color Glass Condensate framework. We also explore alternative initial condition calculations and discuss their implications.