Gluon Saturation Research Articles

Spatial imaging of polarized deuterons at the Electron-Ion Collider

We study diffractive vector meson production at small-x in the collision of electrons and polarized deuterons e+d↑. We consider the polarization dependence of the nuclear wave function of the deuteron, which results in an azimuthal angular dependence of the produced vector meson when the deuteron is transversely polarized. The Fourier coefficients extracted from the azimuthal angular dependence of the vector meson differential cross-section exhibit notable differences between longitudinally and transversely polarized deuterons. The angular dependence of the extracted effective deuteron radius provides direct insight into the structure of the polarized deuteron wave function. Furthermore, we observe slightly increased gluon saturation effects when the deuteron is longitudinally polarized compared to the transversely polarized case. The small-x observables studied in this work will be accessible at the future Electron-Ion Collider.

Beam test of n-type Silicon pad array detector at PS CERN

This work reports the test of an n-type silicon pad array detector at the CERN PS in the context of the future Forward Calorimeter (FoCal) detector. FoCal is a proposed upgrade in the ALICE detector operating within the pseudorapidity range of 3.2 < η < 5.8. It aims to measure direct photons, neutral hadrons, vector mesons, and jets for the study of gluon saturation effects in the unexplored region of low momentum fraction x (∼ 10-5–10-6). The prototype is a 8×9 n-type Si pad array detector with each pad occupying one cm2 area, fabricated on a 6-in, 325 ± 10 μm thick, and high-resistivity (∼ 7 kΩ cm) Si wafer, which is readout using the HGCROCv2 chip. The detector is tested using pion beams of energy 10 GeV and electron beams of energy 1–5 GeV. The measurements of the Minimum Ionizing Particle (MIP) response of pions and the shower profiles of electrons are reported.

Event generator for jet tomography in electron-ion collisions

We develop the first event generator, the electron-heavy-ion-jet-interaction-generator (eHIJING), for the jet tomography study of electron-ion collisions. In this generator, energetic jet partons produced from the initial hard scattering undergo multiple collisions with the nuclear target. The collision rate is proportional to the transverse-momentum-dependent (TMD) gluon density in the nucleus, which is given by a simple model inspired by the physics of gluon saturation. Medium-modified QCD splitting functions within the higher-twist (HT) and generalized higher-twist (GHT) frameworks are utilized to simulate parton showering in the nuclear medium that takes into account the non-Abelian Landau-Pomeranchuck-Midgal interference effect. Employing eHIJING, we revisit hadron production in semi-inclusive deep inelastic scattering (SIDIS) as measured by EMC, HERMES, and recent CLAS experiments. eHIJING with both GT and GHT frameworks gives reasonably good descriptions of these experimental data. Predictions for experiments at the future electron-ion colliders are also provided. It is demonstrated that future measurements of the transverse momentum broadening of single hadron spectra can be used to map out the two-dimensional kinematic (Q2, xB) dependence of the jet transport coefficient q^ in cold nuclear matter. Published by the American Physical Society 2024

Quasiclassical Gluon Fields and Low's Soft Theorem at Small Momentum-Fraction x.

In the high-energy limit, soft gluons can be approximately described by quasiclassical gluon fields. It is well known that the gluon field is a pure gauge field on the transverse plane at eikonal order. We derived the complete next-to-eikonal order solutions of the classical Yang-Mills equations for soft gluons in the dense nuclear regime. Utilizing these solutions, it is shown that Low's soft theorem at small x can be obtained by considering off-diagonal matrix elements of quasiclassical chromoelectric field between single-gluon states in the dilute regime. We further propose on extending Low's soft theorem at small x to incorporate the effects of gluon saturation in the dense regime.

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.

Classical information entropy of parton distribution functions and an application in searching gluon saturation

Classical information entropy of parton distribution functions and an application in searching gluon saturation

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

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

Incoherent J/ψ production at large |t| identifies the onset of saturation at the LHC

We predict that the onset of gluon saturation can be uniquely identified using incoherent J/ψ production in Pb–Pb collisions at currently accessible energies of the LHC. The diffractive incoherent photo-production of a J/ψ vector meson off a hadron provides information on the partonic structure of the hadron. Within the Good-Walker approach it specifically measures the variance over possible target configurations of the hadronic colour field. For this process then, gluon saturation sets in when the cross section reaches a maximum, as a function of the centre-of-mass energy of the photon-hadron system (W), and then decreases. We benchmark the energy-dependent hot-spot model against data from HERA and the LHC and demonstrate a good description of the available data. We show that the study of the energy dependence of the incoherent production of J/ψ allows us to pinpoint the onset of saturation effects by selecting the region of Mandelstam-t around 1 GeV2 where the contribution of hot spots is dominant. We predict the onset of saturation in a Pb target to occur for W around a few hundred GeV. This can be measured with current data in ultra-peripheral Pb–Pb collisions at the LHC.

A few-degree calorimeter for the future electron-ion collider

Measuring the region 0.1<Q2<1.0 GeV2 is essential to support searches for gluon saturation at the future Electron-Ion Collider. Recent studies have revealed that covering this region at the highest beam energies is not feasible with current detector designs, resulting in the so-called Q2 gap. In this work, we present a design for the Few-Degree Calorimeter (FDC), which addresses this issue. The FDC uses SiPM-on-tile technology with tungsten absorber and covers the range of −4.6<η<−3.6. It offers fine transverse and longitudinal granularity, along with excellent time resolution, enabling standalone electron tagging. Our design represents the first concrete solution to bridge the Q2 gap at the EIC.

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.

Forward dijet production at the LHC within an impact parameter dependent TMD approach

We investigate possible signatures of gluon saturation using forward p + A → j + j + X di-jet production processes at the Large Hadron Collider. In the forward rapidity region, this is a highly asymmetric process where partons with large longitudinal momentum fraction x in the dilute projectile are used as a probe to resolve the small x partonic content of the dense target. Such dilute-dense processes can be described in the factorization framework of Improved Transverse Momentum Distributions (ITMDs). We present a new model for ITMDs where we explicitly introduce the impact parameter (b) dependence in the ITMDs, to properly account for the nuclear enhancement of gluon saturation effects, and discuss the phenomenological consequences for p − Pb, p − Xe and p − O collisions at the LHC. While the case of p − p and e − p collisions is used to fix the model parameters, we find that, on average, the nuclear enhancement of the saturation scale is noticeably weaker than expected from naive scaling with a simple dependence on the atomic number. Since our model explicitly accounts for event-by-event fluctuations of the nuclear geometry, it can also be applied to study forward central correlations in p − A collisions.

Investigating the partonic entanglement entropy at low Bjorken‐x within Gluon saturation approach

AbstractIn this work, the entanglement entropy is examined within the context of deep inelastic scattering in collisions. The calculation is based on a formalism where the partonic state at small‐ is maximally entangled, consisting of a large number of micro‐states occurring with equal probabilities. Analytical expressions for the number of gluons, , are considered, derived from gluon saturation models for dipole‐target amplitudes within the framework of the Quantum Chromodynamics (QCD) color dipole picture. A comparison of the entanglement entropy with thermodynamic entropy measured in and collisions at high energies is done.

First global study of super dense gluonic matter with UPCs by ALICE

ALICE was the first experimental collaboration observing a moderate nuclear suppression down to low Bjorken-x in lead nuclei using coherent J/ψ photoproduction. In this contribution, we present new results extending the studies of the photonuclear cross section by covering the Bjorken-x interval of 1.1 · 10−5 &lt; x &lt; 3.3 · 10−2, corresponding to the photon-nuclear energies 17 &lt; WγPb,n &lt; 920 GeV. This is achieved by using multiple methods to extract the energy dependence, including new results on the forward neutron emission accompanying the coherent photoproduction process. These new results, combined with ALICE measurements of J/ψ off a proton target, probe the gluonic structure of the lead nuclei at the lowest Bjorken-x possible with any current experiment, challenging both gluon saturation and shadowing models to describe the data.

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.

ALICE Forward Calorimeter (FoCal): Physics program and performance

This contribution outlines the physics program and performance of the Forward Calorimeter (FoCal), which is a planned new detector subsystem for the ALICE experiment in Run 4. The forward pseudorapidity coverage of 3.2 &lt; η &lt; 5.8 allows to study the gluon density in hadronic matter down to x ∼ 10−6 and enables the search for gluon saturation at the LHC.

Theoretical developments on the initial state in relativistic particle collisions

We discuss recent progress towards developing accurate initial state descriptions for heavy ion collisions focusing on weak coupling based approaches, that enable one to constrain the high-energy structure of nuclei from deep inelastic scattering or proton-nucleus collisions. We review recent developments to determine the event-by-event fluctuating nuclear geometry, to describe gluon saturation phenomena at next-to-leading order accuracy, and to include longitudinal dynamics to the initial state descriptions.

Probing gluon saturation via diffractive jets in ultra-peripheral nucleus-nucleus collisions

We argue that semi-inclusive photo-production of a pair of hard jets via coherent diffraction in nucleus-nucleus ultra-peripheral collisions at high energy is a golden channel to study gluon saturation. The dominant contribution is the diffractive production of three jets in an asymmetric configuration. Two of the jets are hard and propagate at nearly central pseudo-rapidities. The third jet is semi-hard, with transverse momentum comparable to the nuclear saturation momentum, and is well separated in pseudo-rapidity from the hard dijets. The emission of the semi-hard jet allows for strong scattering, thus avoiding the “higher-twist” suppression of the exclusive dijet production due to colour transparency. We compute the trijet cross-section using the diffractive TMD factorisation which emerges from the CGC effective theory at high energy. The cross-section is controlled by gluon saturation, which leaves its imprints on the structure of the final state, notably on the rapidity distribution.

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.