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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

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 sensitive to the geometric deformation of the target nucleus at multiple length scales. Studying e+U collisions and varying the deformation of the uranium target, we demonstrate that larger deformations result in enhanced incoherent vector meson production cross sections. Further, different multipole deformation parameters affect different regions of transverse momentum transfer. Employing JIMWLK evolution to study the Bjorken-x dependence of our results, we find that the ratio of incoherent to coherent cross sections decreases with decreasing x, largely independently of the quadrupole deformation of the target. Comparing results for the same process using 20 Ne targets with 16 O targets, we find that differences in deformation are clearly visible in the incoherent cross section. These findings show that certain observables at the Electron-Ion Collider are very sensitive to nuclear structure. Consequently, deformations need to be taken into account when interpreting experimental results. More importantly, this also means that |t|-differential diffractive vector meson production could become a powerful tool, enabling the most direct measurements of nuclear structure at different length scales, ranging from nuclear deformation at low |t| to nucleon and subnucleon-size scales at higher |t|.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

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. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Jet Definition and Transverse-Momentum–Dependent Factorization in Semi-inclusive Deep-Inelastic Scattering

Using the color dipole picture of deep inelastic scattering (DIS) and the color glass condensate effective theory, we study semi-inclusive jet production in DIS at small x in the limit where the photon virtuality Q 2 is much larger than the transverse momentum squared P$^{2}_{⊥}$ of the produced jet. In this limit, the cross section is dominated by aligned jet configurations, that is, quark–antiquark pairs in which one of the fermions—the would-be struck quark in the Breit frame—carries most of the longitudinal momentum of the virtual photon. We show that physically meaningful jet definitions in DIS are such that the effective axis of the jet sourced by the struck quark is controlled by its virtuality rather than by its transverse momentum. For such jet definitions, we show that the next-to-leading order cross section admits factorization in terms of the (sea) quark transverse momentum dependent distribution, which in turn satisfies a universal Dokshitzer-Gribov-Lipatov-Altarelli-Parisi and Sudakov evolution.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

SIDIS at small 𝑥 at next-to-leading order: Transverse photon

We calculate the next-to-leading order corrections to single inclusive hadron production in deep inelastic scattering at small 𝑥 using the color glass condensate formalism, for the case when the exchanged photon is transversely polarized. We show all UV and soft divergences cancel while collinear and rapidity divergences result in scale evolution of quark-hadron fragmentation function and small-x evolution of dipole amplitudes, respectively.

quantum chromodynamics↗
DOE OSTI2026

Evidence of Spin-Interference Effects in Exclusive 𝐽/𝜓 → 𝑒 + ⁢𝑒 − Photoproduction in Ultraperipheral Heavy-Ion Collisions

Here, we report the first evidence of spin interference in exclusive 𝐽/𝜓 → 𝑒 + ⁢𝑒 − photoproduction in ultraperipheral heavy-ion collisions at STAR at $\sqrt{𝑠_{𝑁⁢𝑁}}$ = 200 GeV. In Au + Au collisions, a negative cos⁡(2⁢𝜙) modulation is found for 𝑝 𝑇 < 120 MeV/𝑐 with a significance of 3.2⁢𝜎, while the isobar data (Ru + Ru, Zr + Zr) show a consistent negative modulation with a significance of 1.9⁢𝜎, opposite in sign to that in 𝜌 0 → 𝜋 + ⁢𝜋 − photoproduction. This establishes for the first time that the interference sign is controlled by the spin structure of the final-state daughters, resolving the ambiguity present in the all-boson 𝜌 0 channel. The compact 𝐽/𝜓 probes gluon distributions at perturbative scales, resulting in a weaker modulation and providing stringent constraints on color glass condensate calculations. These findings demonstrate that spin-dependent interference in heavy vector mesons provides a new, experimentally accessible handle on gluon structure beyond traditional cross-section measurements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Angular correlations in pA collisions from CGC: multiplicity and mean transverse momentum dependence of $$v_2$$

Abstract Within the dense-dilute Color Glass Condensate approach, and using the Golec–Biernat–Wuesthoff model for the dipole scattering amplitude, we calculate $$v_2^2$$ v 2 2 as well as the correlations between $$v_2^2$$ v 2 2 and both the total multiplicity and the mean transverse momentum of produced particles. We find that the correlations are generally very small consistent with the observations. We note an interesting sharp change in the value of $$v^2_2$$ v 2 2 as well as of its correlations as a function of the width of the transverse momentum bin. This crossover is associated with the change from Bose enhancement dominance of the correlation for narrow bin to HBT dominated correlations for larger bin width.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

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.

Li, Ming↗
DOE OSTI2021

Proceedings of RIKEN BNL Research Center Workshop: Small-x Physics in the EIC Era [Slides]

Understanding the high energy limit of hadronic and nuclear collisions is at the forefront of nuclear and particle physics. When boosted to ultrahigh energies, all hadrons and nuclei eventually transform into a universal form of matter called the Color Glass Condensate (CGC). The CGC is characterized by the high density (saturation) of small-x gluons which leads to distinct experimental signatures. Tantalizing hints of the CGC have been observed at HERA, RHIC and the LHC, but the prospects for the discovery of the CGC are more promising at future experiments such as the Electron-Ion Collider (EIC) at BNL Indeed, according to the National Science Academy report published in 2019, one of the three major goals of the EIC is to address the nature of the gluon saturation. (The other two are the mass and spin structure of the nucleons.) With this in mind, the small-x community is gearing up to meet the challenges of the EIC era. Over the past several years, there has been impressive progress in the next-to-leading order (NLO) calculations in the CGC framework of various observables such as single hadron production in proton-nucleus collisions, inclusive and exclusive dijet and trijet production in Deep Inelastic Scattering (DIS), jet-plus-photon production in DIS, etc. We expect that NLO calculations will be the standard tool to confront future experimental data at the EIC. Another emerging trend of the community is the interplay between small-x physics and spin physics. The RHIC result for the gluon helicity ΔG has underscored the necessity to understand the longitudinal spin structure of the proton at small-x. There have been theoretical indications that a significant fraction of spin and orbital angular momentum is stored in the small-x region. As for the transversely polarized proton, a surprising new connection between the gluon Sivers function at small-x and the QCD Odderon has been pointed out and its implications at the EIC has been discussed. In view of these developments, we think it is timely to organize a dedicated workshop on small-x physics to summarize the present status of the field and to discuss future directions. A major focus of this workshop will be to identify outstanding problems that could significantly benefit from collaborative efforts amongst scientists working on formal, phenomenological, and computational aspects of small-x physics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Probing gluon saturation and nuclear structure in photon-nucleus collisions

We calculate exclusive vector meson photoproduction within the Color Glass Condensate framework in high-energy photon-nucleus scattering probed experimentally in ultra peripheral heavy ion collisions at RHIC and at the LHC. When the free parameters are constrained by the γ + p data from HERA, we predict significant nuclear suppression for both the coherent and incoherent photoproduction cross section in the TeV range. Our results indicate that the LHC data prefers even stronger saturation effects at the highest collision energies. Furthermore, we demonstrate how the linear polarization of photons in ulra peripheral collisions generates azimuthal modulations in the decay products of the exclusively produced vector meson. We show how these measurements can probe details of the nuclear geometry, specifically the deformed structure of the uranium nuclei.

Mäntysaari, Heikki [University of Jyväskylä (Finla↗
DOE OSTI2025

QCD–Gravity Double Copy in Regge Asymptotics: From \(2\rightarrow n\) Amplitudes to Radiation in Shockwave Collisions

This paper discusses multi-particle production in QCD and in gravity at ultrarelativistic energies, their double-copy relations, and strong parallels in emergent shockwave dynamics. Dispersive techniques are applied to derive the BFKL equation for multi-gluon production in Regge asymptotics. Identical methods apply in gravity and are captured by a gravitational Lipatov equation. The building blocks in both cases are Lipatov vertices and reggeized propagators satisfying double-copy relations; in gravity, Weinberg’s soft theorem is recovered as a limit of the Lipatov framework. BFKL evolution in QCD generates wee parton states of maximal occupancy characterized by an emergent semi-hard saturation scale. Renormalization group equations in the Color Glass Condensate (CGC) EFT describe wee parton correlations and their rapidity evolution. A shockwave picture of deeply inelastic scattering and hadron–hadron collisions follows, with multi-particle production described by Cutkosky’s rules in strong time-dependent fields. Gluon radiation in the CGC EFT has a double copy in gravitational shockwave collisions, with a similar correspondence applicable between gluon and graviton shockwave propagators. Possible extensions of this semi-classical double copy are outlined for computing multi-particle production in gravitational shockwave collisions, self-force and tidal contributions, and classical and quantum noise in the focusing of geodesics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Bayesian Inference of the Fluctuating Proton Shape in DIS and Hadronic Collisions

We determine the likelihood distribution for the model parameters describing the event-by-event fluctuating proton geometry at small $x$ by performing a Bayesian analysis within the Color Glass Condensate framework. The exclusive J/ψ production data from HERA is found to constrain the model parameters well, and we demonstrate that complementary constraints can be obtained from simulations of Pb+Pb collisions at the LHC.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Collectivity in Ultra-peripheral Heavy-ion and \(e+A\) Collisions

We review recent theoretical progress in describing collective effects in photon+nucleus collisions. The approaches considered range from the color glass condensate, where correlations are encoded in the initial state, to hydrodynamic frameworks, where a strong final-state response to the initial geometry of the collision is the key ingredient to generate momentum-space correlations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Pre-equilibrium evolution of conserved charges with initial conditions in the ICCING Monte Carlo event generator

Heavy-ion collisions can be well described through relativistic viscous hydrodynamics, but questions still remain when hydrodynamics is applicable because the initial state may begin very far from equilibrium. Thus, a pre-equilibrium evolution phase is used to bridge the gap between the initial state and hydrodynamics. KøMPøST is one such pre-equilibrium model that propagates the energy-momentum tensor by decomposing it into the background and fluctuations around that background, whose evolution is captured by Green's functions. We extend this formalism to include conserved charges and calculate the corresponding nonequilibrium Green's functions in the relaxation-time approximation. The ICCING algorithm initializes conserved charges in the initial state by sampling $g$ → $q$$\overline{q}$ splitting probabilities and is, thus, perfectly positioned to implement Green's functions for charge propagation. As a result, we show that this method alters the initial-state charge geometries and is applicable in central to mid-central collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Initializing BSQ with Open-Source ICCING

While it is well known that there is a significant amount of conserved charges in the initial state of nuclear collisions, the production of these due to gluon splitting has yet to be thoroughly investigated. The ICCING (Initial Conserved Charges in Nuclear Geometry) algorithm reconstructs these quark distributions, providing conserved strange, baryon, and electric charges, by sampling a given model for the g → qq¯ splitting function over the initial energy density, which is valid at top collider energies, even when µB = 0. The ICCING algorithm includes fluctuations in the gluon longitudinal momenta, a structure that supports the implementation of dynamical processes, and the c++ version is now open-source. A full analysis of parameter choices on the model has been done to quantify the effect these have on the underlying physics. We find there is a sustained difference across the different charges that indicates sensitivity to hot spot geometry.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗