Gluon Saturation Research Articles

Energy independent scaling of the ridge and final state description of high multiplicity p+p collisions at s=7 and 13 TeV

An energy independent scaling of the near-side ridge yield at a given multiplicity has been observed by the ATLAS and the CMS collaborations in p+p collisions at s = 7 and 13 TeV. Such a striking feature of the data can be successfully explained by approaches based on initial state momentum space correlation generated due to gluon saturation. In this paper, we try to examine if such a scaling is also an inherent feature of the approaches that employ strong final state interaction in p+p collisions. We find that hydrodynamical modeling of p+p collisions using EPOS 3 shows a violation of such scaling. The current study can, therefore, provide important new insights on the origin of long range azimuthal correlations in high multiplicity p+p collisions at the LHC energies.

Prompt inclusive production of J/ψ , ψ′ and χc mesons at the LHC in forward directions within the NRQCD kt -factorization approach: Search for the onset of gluon saturation

We discuss prompt production of $J/\ensuremath{\psi}$ mesons in proton-proton collisions at the LHC within the NRQCD ${k}_{t}$-factorization approach using Kimber-Martin-Ryskin (KMR) unintegrated gluon distributions (UGDF). We include both direct color-singlet production ($gg\ensuremath{\rightarrow}J/\ensuremath{\psi}g$) as well as a feed down from ${\ensuremath{\chi}}_{c}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\gamma}$ and ${\ensuremath{\psi}}^{\ensuremath{'}}\ensuremath{\rightarrow}J/\ensuremath{\psi}X$ decays. The production of the decaying mesons (${\ensuremath{\chi}}_{c}$ or ${\ensuremath{\psi}}^{\ensuremath{'}}$) is also calculated within the NRQCD ${k}_{t}$-factorization approach. The corresponding matrix elements for $gg\ensuremath{\rightarrow}J/\ensuremath{\psi}\text{ }\text{ }\mathrm{g}$, $gg\ensuremath{\rightarrow}{\ensuremath{\psi}}^{\ensuremath{'}}g$ and $gg\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c}$ include parameters of the nonrelativistic space wave functions of the quarkonia at $r=0$, which are taken from potential models in the literature. We get the ratio of the corresponding cross section ratio for ${\ensuremath{\chi}}_{c}(2)$-to-${\ensuremath{\chi}}_{c}(1)$ at midrapidities much closer to experimental data than obtained in a recent analysis. Differential distributions in rapidity and transverse momentum of $J/\ensuremath{\psi}$ and ${\ensuremath{\psi}}^{\ensuremath{'}}$ are calculated and compared with experimental data of the ALICE and LHCb Collaborations. We discuss a possible onset of gluon saturation effects in the production of $J/\ensuremath{\psi}$ and ${\ensuremath{\chi}}_{c}$ mesons at forward/backward rapidities. We show that it is necessary to modify the standard KMR UGDF to describe ALICE and LHCb data. A mixed UGDF scenario was proposed. Then, we can describe the experimental data for $J/\ensuremath{\psi}$ production within model uncertainties with a color-singlet component only. Therefore, our theoretical results leave only relatively small room for the color-octet contributions. We discuss relations to other models in the literature. The results for the so-called hybrid model are compared to the results of the original ${k}_{t}$-factorization approach.

Diffusion of charm and beauty in the Glasma

Relativistic nuclear collisions offer a unique way to study strong interactions at very high energy. The collision process can be described within the gluon saturation framework as the interaction of two colored glasses, and because of this interaction strong longitudinal gluon fields, namely the Glasma, are produced immediately after the collision. Besides, heavy quarks are also produced in the very early stage and because of their large mass and small concentration, their motion does not affect the evolution of the Glasma, thus behaving as ideal probes of the Glasma itself. We study the evolution of the heavy quarks in the Glasma allegedly produced in high energy p-Pb collisions by solving consistently the equations of motion of the quarks in the evolving Glasma fields. We find that this motion can be understood in terms of diffusion in momentum space, similarly to the random motion of a heavy probe in a hot thermalized medium. We show how the diffusion of heavy probes affects the nuclear modification factor of D and B mesons in p-Pb collisions.

Predictions on three-particle azimuthal correlations in proton--proton collisions

The ridge signal, which is long-ranged in rapidity, in the di-hadron correlations in high-multiplicity p-p and p-A collisions opened up a whole new research area in high-energy QCD. Although the ridge had been observed in A-A collisions and interpreted as a result of the radial flow of quark-gluon plasma, it had not appeared until recently in the data of small collision systems such as p-p and p-A, nor had it been predicted theoretically or seen in the event generators. There are two competing approaches that attempt to explain the systematics of the di-hadron ridge signal; hydrodynamics and gluon saturation physics (color glass condensate/glasma). In this work, we present predictions for the transverse momentum and rapidity dependence of the three-particle correlation function within the gluon saturation physics. Tri-hadron correlations can be measured, and the data can possibly rule out one of the two alternative approaches.

High‐energy scattering in quantum chromodynamics at small Bjorken x

After a brief introduction to perturbative quantum chromodynamics (pQCD), we consider particle production in the high‐energy limit of QCD. We motivate the need for a novel dynamical effect, namely gluon saturation, to slow down the sharp rise of perturbative cross‐sections at small Bjorken x in order not to violate the Froissart bound. Gluon saturation dynamics in QCD can be efficiently studied using an effective action approach. The two main effects included are high gluon density effects, which lead to multiple scatterings, and the energy dependence of observables, which is included via the small x evolution equations. We discuss the signatures of and prospects for observing gluon saturation in high‐energy processes.

Cumulant expansion in gluon saturation and five- and six-gluon azimuthal correlations

Correlations between the momenta of the final state hadrons measured in proton or nucleus collisions contain information that sheds light on the initial conditions and evolutionary dynamics of the collision system. These correlation measurements have revealed the long-range rapidity correlations in p-p and p-Pb systems, and they have also made it possible to extract the elliptic flow coefficient from hadron correlation measurements. In this work, we calculate five- and six-gluon correlation functions in the framework of saturation physics by using superdiagrams. We also derive the cumulant expansion of the gluon correlators that is valid in the gluon saturation limit. We show that the cumulant expansion of the gluon correlators that is used for counting the number of diagrams to be calculated does not follow the standard cumulant expansion. We also explain how these findings can be used in obtaining experimentally relevant observables such as flow coefficients calculated from correlations as well as ratios of the correlation functions of different orders.

Low-x Physics in pA Collisions and at the EIC

In this proceeding, I review what we have learned, and what we will be able to learn, about low-x physics from proton-nucleus (pA) collisions at RHIC and the LHC, and how this complements future Electron-Ion Collider (EIC) measurements. EIC not only will provide us essential and complementary information about the gluon saturation to the knowledge that we have learned from pA collisions at RHIC and the LHC, it will also allow us to visualize the internal structure of protons and nuclei in a multi-dimensional fashion with unprecedented precision.

Systematic Study of Highly Asymmetric Systems Using π0, h± and ϕ Production at PHENIX

The observation of long range correlations in highly asymmetric systems, as in p+Pband d+Aucollisions, suggests a creation of a medium with collective behavior. Furthermore, hints of gluon saturation effects have been observed at forward rapidities in d+Aucollisions at RHIC. Single particle production has proven to be a valuable tool to probe the quark-gluon plasma in heavy-ion collisions as it is sensitive to energy loss, modifications of the nuclear wave function, and the dynamics of the projectile wave function. In order to systematically study these highly asymmetric collisions, RHIC provided beams for p+Al, p+Au, d+Auand 3He+Aucollisions. We present the new measurements of π0 at mid-rapidity (|η|<0.35) in p+Auand 3He+Aucollisions at sNN=200 GeV; and the charged hadron and ϕ production in forward (1.2<η<2.4) and backward (−2.2<η<−1.2) rapidities in p+Al, p+Auand 3He+Aucollisions at sNN=200 GeV.

Accessing the gluon Wigner distribution in ultraperipheral pA collisions

We propose to constrain the gluon Wigner distribution in the nucleon by studying the exclusive diffractive dijet production process in ultraperipheral proton-nucleus collisions (UPCs) at RHIC and the LHC. Compared to the previous proposal in Ref. [Y. Hatta, B. W. Xiao, and F. Yuan, Phys. Rev. Lett. 116, 202301 (2016).] to study the same observable in lepton-nucleon scattering, the use of UPCs has a few advantages: not only is the cross section larger, but the extraction of the Wigner distribution from the data also becomes simpler, including its elliptic angular dependence. We compute the corresponding cross section and evaluate the coefficients using models which include the gluon saturation effects. A potential for the measurements of the Wigner distribution at current and future experimental facilities is also discussed.

Investigating the impact of the gluon saturation effects on the momentum transfer distributions for the exclusive vector meson photoproduction in hadronic collisions

The exclusive vector meson production cross section is one of the most promising observables to probe the high energy regime of the QCD dynamics. In particular, the squared momentum transfer (t) distributions are an important source of information about the spatial distribution of the gluons in the hadron and about fluctuations of the color fields. In this paper we complement previous studies on exclusive vector meson photoproduction in hadronic collisions presenting a comprehensive analysis of the t-spectrum measured in exclusive ρ, ϕ and J/Ψ photoproduction in pp and PbPb collisions at the LHC. We compute the differential cross sections taking into account gluon saturation effects and compare the predictions with those obtained in the linear regime of the QCD dynamics. Our results show that gluon saturation suppresses the magnitude of the cross sections and shifts the position of the dips towards smaller values of t.

Multi-Reggeon exchanges at high pt from gluon saturation

We show that the JIMWLK equation for rapidity evolution of 2 n Wilson lines at high pt reduces to the BJKP equation for the rapidity evolution of t-channel exchange of 2 n Reggeized gluons.

Energy dependence of dissociative J/ψ photoproduction as a signature of gluon saturation at the LHC

We have developed a model in which the quantum fluctuations of the proton structure are characterised by hot spots, whose number grows with decreasing Bjorken-$x$. Our model reproduces the $F_2(x,Q^2)$ data from HERA at the relevant scale, as well as the exclusive and dissociative $\mathrm{J/}\psi$ photoproduction data from H1 and ALICE. Our model predicts that for $W_{\gamma\mathrm{p}} \approx 500$ GeV, the dissociative $\mathrm{J/}\psi$ cross section reaches a maximum and then decreases steeply with energy, which is in qualitatively good agreement to a recent observation that the dissociative $\mathrm{J/}\psi$ background in the exclusive $\mathrm{J/}\psi$ sample measured in photoproduction by ALICE decreases as energy increases. Our prediction provides a clear signature for gluon saturation at LHC energies.

Single spin asymmetry in forward pA collisions. II. Fragmentation contribution

We compute the twist-three fragmentation contribution to the transverse single spin asymmetry (SSA) in light hadron production $p^\uparrow p\to hX$ and $p^\uparrow A\to hX$ including the gluon saturation effect in the unpolarized nucleon/nucleus. Together with the results in our previous paper, this completes the full evaluation of the SSA in this process in the "hybrid" formalism. We argue that the dependence of SSAs on the atomic mass number in the forward region can elucidate the relative importance of the soft gluon pole contribution from the twist-three quark-gluon-quark correlation in the polarized nucleon and the twist-three fragmentation contribution from the final state hadron.

Probing gluon saturation with next-to-leading order photon production at central rapidities in proton-nucleus collisions

We compute the cross section for photons emitted from sea quarks in proton-nucleus collisions at collider energies. The computation is performed within the dilute-dense kinematics of the Color Glass Condensate (CGC) effective field theory. Albeit the result obtained is formally at next-to-leading order in the CGC power counting, it provides the dominant contribution for central rapidities. We observe that the inclusive photon cross section is proportional to all-twist Wilson line correlators in the nucleus. These correlators also appear in quark-pair production; unlike the latter, photon production is insensitive to hadronization uncertainties and therefore more sensitive to multi-parton correlations in the gluon saturation regime of QCD. We demonstrate that k⊥ and collinear factorized expressions for inclusive photon production are obtained as leading twist approximations to our result. In particular, the collinearly factorized expression is directly sensitive to the nuclear gluon distribution at small x. Other results of interest include the realization of the Low-Burnett-Kroll soft photon theorem in the CGC framework and a comparative study of how the photon amplitude is obtained in Lorenz and light-cone gauges.

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.

Forward hadron productions in proton-proton collisions in small-xformalism

Employing the so-called hybrid formalism, we calculate the cross section of inclusive hadron production in proton-proton collisions at forward rapidity in small-$x$ formalism at one-loop order. For the case of hadron production at forward rapidity, we can uses collinear parton distributions for projectile proton and $k_\perp$ dependent gluon distribution for target proton. We show that collinear divergences associated with initial and final state parton radiations are renormalized into parton distributions and fragmentation functions in terms of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equation, respectively. Furthermore, rapidity divergence can be absorbed into the wave function of target proton which gives rise to the well-known Balitsky-Fadin-Kuraev-Lipatov equation. These divergences are completely separated from the short distance partonic hard parts, which is now finite at the next-to-leading order accuracy. The result presented in this paper can be reckoned as a baseline calculation without any non-linear QCD effects in small-$x$ formalism. As a consistency check, we compare our results with the previous calculation for non-linear proton-nucleus collisions in the small-$x$ formalism and find complete agreement in the dilute and large $N_c$ limit. In phenomenology, the direct comparison of the above two separate calculations can reveal the role and strength of the non-linear dynamics in high energy QCD, and thus help us reliably study the onset of gluon saturation when genuine non-linear interactions become important.

Wigner, Husimi, and generalized transverse momentum dependent distributions in the color glass condensate

We study the phase space distributions of gluons inside a nucleon/nucleus in the small-$x$ regime including the gluon saturation effect. This can be done by using the relation between the gluon Wigner distribution and the dipole S-matrix at small-$x$, the latter satisfies the Balitsky-Kovchegov (BK) equation. By efficiently solving the BK equation with impact parameter dependence, we compute the Wigner, Husimi and generalized TMD (GTMD) distributions in the saturation regime. We also investigate the elliptic angular dependence of these distributions which has been recently shown to be measurable in DIS experiments.

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

The production of forward J/ψ 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.

Flow Harmonics vn in pPb and PbPb Collisions

Previous CMS measurements have demonstrated the collective nature of multiparticle correlations in high-multiplicity pPb collisions at the LHC. This collectivity is consistent with a hydrodynamic flow origin. However, it can also be interpreted in terms of initial state effects arising from gluon saturation. The pseudorapidity dependence of the azimuthal Fourier coefficients (vn) is expected to be sensitive to the underlying mechanism with, in the hydrodynamic picture, the longer lifetime of the fireball on the Pb-going side expected to lead to a larger flow signal than found on the p-going side. To investigate the detailed properties of the observed collectivity, differential vn values in transverse momentum (pT) and pseudorapidity (η) are presented over the full range of the CMS tracker detector (−2.4<η<2.4) for pPb collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV. Results based on multiparticle analyses involving four or more particles are shown. An event plane analysis is presented where the influence of recently demonstrated event-plane decorrelation is considered. Comparisons are made with peripheral PbPb collisions measured at similar mid-rapidity particle multiplicities. The results will be discussed in the context of current models of the longitudinal dependence of the multiparticle correlations.

Gluon Saturation and EIC

The fundamental structure of nucleons and nuclear matter is described by the properties and dynamics of quarks and gluons in quantum chromodynamics. Electron-nucleon collisions are a powerful method to study this structure. As one increases the energy of the collisions, the interaction process probes regions of progressively higher gluon density. This density must eventually saturate. An high-energy polarized Electron-Ion Collider (EIC) has been proposed to observe and study the saturated gluon density regime. Selected measurements will be discussed, following a brief introduction.