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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Quantum Scaling in Energy Correlators beyond the Confinement Transition

We study the QCD scaling behavior of the small-angle energy-energy correlator (EEC), focusing on the transition between its perturbative preconfinement and nonperturbative postconfinement regimes. Applying the light-ray operator product expansion (OPE), we develop a formalism that describes the scaling of the EEC with the input energy 𝑄 in the transition and the postconfinement region, where the latter quantum scaling is determined by the 𝐽 = 5 DGLAP anomalous dimension. A key result of our Letter is a novel connection between the light-ray OPE and the dihadron fragmentation function (DFF), where we show that the nonperturbative OPE coefficients correspond to moments of the DFF. This finding establishes a new paradigm for studying hadronization. Our theoretical predictions are validated against Monte Carlo simulations for both 𝑒 + ⁢𝑒 − and 𝑝⁢𝑝 collisions, showing excellent agreement. The potential role of the quantum scaling in the precision determination of 𝛼 𝑠 is also discussed.

Chang, Cyuan-Han [University of Chicago, IL (Unite↗
DOE OSTI2026

Factorization and Resummation for the Near-Side Energy-Energy Correlators

By utilizing the dihadron fragmentation formalism, we extend the previous factorization of near-side energy-energy correlators (EECs) in the collinear limit and derive an all order resummation in the Fourier transform 𝑏 𝑇 -space. A perfect matching is obtained when we compare to the fixed-order results. We further demonstrate the resummation effects for the EECs in 𝑒 + ⁢𝑒 − annihilation and show that they will significantly improve the theoretical predictions at small angles.

Guo, Yuxun [University of California, Berkeley, CA↗
DOE OSTI2024

Imaging the wakes of jets with energy-energy-energy correlators

As the partons in a high energy jet propagate through the droplet of quark-gluon plasma (QGP) produced in a heavy-ion collision they lose energy to, kick, and are kicked by the medium. The resulting modifications to the parton shower encode information about the microscopic nature of QGP. A direct consequence, however, is that the momentum and energy lost by the parton shower are gained by the medium and, since QGP is a strongly coupled liquid, this means that the jet excites a wake in the droplet of QGP. After freezeout, this wake becomes soft hadrons with net momentum in the jet direction meaning that what an experimentalist later reconstructs as a jet includes hadrons originating from both the modified parton shower and its wake. This has made it challenging to find experimental observables that provide an unambiguous view of the dynamical response of a droplet of QGP to a jet shooting through it. Recent years have seen significant substantial advances in the theoretical and experimental understanding of the substructure of jets, in particular, using correlation functions, $\langle$ ($\vec{n}$ 1 )•••$\mathcal{E}$($\vec{n}$ k ) $\rangle$, of the energy flux operator in proton-proton collisions and, recently, in heavy-ion collisions. So far, such studies have focused primarily on the two-point correlator, which allows for the identification of the angular scale of the underlying dynamics. Higher-point correlators hold the promise of mapping out the dynamics themselves. In this paper we perform the first study of the shape-dependent three-point energy-energy-energy correlator in heavy-ion collisions. Using the Hybrid Model to simulate the interactions of high energy jets with the QGP medium, we show that the three-point correlator presents us with a striking new opportunity. We find that hadrons originating from wakes are the dominant contribution to the three-point correlator in the kinematic regime in which the three points are well-separated in angle, forming a roughly equilateral triangle. This equilateral region of the correlator is far from the region populated by collinear vacuum emissions, making it a canvas on which jet wakes are laid out, where experimentalists can map their shapes. Our work provides a key step towards the systematic use of energy correlators to image and unravel the dynamical response of a droplet of QGP that has been probed by a passing jet, and motivates numerous experimental and theoretical studies.

Jets and Jet Substructure↗
DOE OSTI2026

Collins-type fragmentation energy correlator in semi-inclusive deep inelastic lepton-hadron scattering

We initiate a systematic study of fragmentation energy correlators (FECs), which generalize traditional fragmentation functions and encode non-perturbative information about transverse dynamics in parton fragmentation processes. We define boost-invariant, non-perturbative FECs and derive a corresponding collinear factorization formula. A spin decomposition of the FECs is carried out, analogous to that of transverse-momentum-dependent fragmentation functions. In this work we focus particularly on the Collins-type quark FEC, which is sensitive to chiral symmetry breaking and characterizes the azimuthal asymmetry in the fragmentation of a transversely polarized quark. We perform a next-to-leading-order calculation of the corresponding hard coefficient in semi-inclusive deep-inelastic scattering for the quark non-singlet component, thereby validating the consistency of our theoretical framework.

Deep Inelastic Scattering or Small-x Physics↗
DOE OSTI2024

Three-point energy correlators in hadronic Higgs boson decays

We present the analytic calculation of the leading-order three-point energy correlator (EEEC) in hadronic Higgs decays, including both the gluon-initiated channel H → g g + X and quark-initiated channel H → q q ¯ + X . The phase-space integration is evaluated directly using Mandelstam variables s i j = ( p i + p j ) 2 , and the appearing square roots can be rationalized by either conformal ratios or celestial coordinate variables. Throughout the calculation, we observe the same transcendental function space as in N = 4 super–Yang-Mills theory and e + e − → hadrons . Different infrared limits are also explored using the full analytic result, offering the fixed-order data for EEEC factorization and resummation. Given its nontrivial shape dependence, the EEEC presents an excellent opportunity to explore the dynamics of gluon jets originating from the H → g g decay channel at future lepton colliders. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2025

Measurement of Two-Point Energy Correlators within Jets in 𝑝 + 𝑝 Collisions at $\sqrt{𝑠}$ = 200 GeV

Hard-scattered partons ejected from high-energy proton-proton collisions undergo parton shower and hadronization, resulting in collimated collections of particles that are clustered into jets. A substructure observable that highlights the transition between the perturbative and nonperturbative regimes of jet evolution in terms of the angle between two particles is the two-point energy correlator (EEC). In this Letter, the first measurement of the EEC at RHIC is presented, using data taken from 200 GeV 𝑝 + 𝑝 collisions by the STAR experiment. The EEC is measured both for all the pairs of particles in jets and separately for pairs with like and opposite electric charges. These measurements demonstrate that the transition between perturbative and nonperturbative effects occurs within an angular region that is consistent with expectations of a universal hadronization regime that scales with jet momentum for a given initiator flavor. Additionally, a deviation from Monte Carlo predictions at small angles in the charge-selected sample could result from mechanics of hadronization not fully captured by current models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

The transverse energy-energy correlator at next-to-next-to-next-to-leading logarithm

Abstract We present an operator based factorization formula for the transverse energy-energy correlator in the back-to-back (dijet) region, and uncover its remarkable perturbative simplicity and relation to transverse momentum dynamics. This simplicity enables us to achieve next-to-next-to-next-to leading logarithmic (N 3 LL) accuracy for a hadron collider dijet event shape for the first time. Our factorization formula applies toW/Z/γ+ jet, and dijet production, providing a natural generalization of transverse momentum observables to one- and two-jet final states. This provides a laboratory for precision studies of QCD and transverse momentum dynamics at hadron colliders, as well as an opportunity for understanding factorization and its violation in a perturbatively well controlled setting.

Physics↗
DOE OSTI2024

Collinear limit of the four-point energy correlator in N = 4 supersymmetric Yang-Mills theory

We present a compact formula, expressed in terms of classical polylogarithms up to weight three, for the leading order four-point energy correlator in maximally supersymmetric Yang-Mills theory, in the limit where the four detectors are collinear. This formula is derived by combining a simplified, manifestly dual conformal invariant form of the 1 → 4 splitting function obtained from the square of the tree-level five-particle form factor of stress-tensor multiplet operators, with a novel integration-by-parts algorithm operating directly on Feynman parameter integrals. Our results provide valuable data for exploring the structure of physical observables in perturbation theory, and for calculations of jet substructure observables in quantum chromodynamics. Published by the American Physical Society 2024

Chicherin, Dmitry (ORCID:000000028985084X)↗
DOE OSTI2025

Long range energy-energy correlator at the LHC

We study the forward-backward azimuthal angular correlations of hadrons in association with multiparticle production in the central rapidity region in proton-proton collisions at the LHC. We apply the nucleon energy-energy correlator framework, where the spinning gluon distribution introduces a nontrivial cos⁡(2⁢𝜙) asymmetries. We will demonstrate that the fundamental helicity structure of quantym chromodynamics (QCD) amplitudes predicts a unique power counting rule: cos⁡(2⁢𝜙) asymmetry starts at 𝒪⁡(𝛼$^{2}_{s}$) order for dijet, 𝒪⁡(𝛼 𝑠 ) for three jet and 𝒪⁡(1) for four (and more) jet productions. Our results will help us to understand the longstanding puzzle of nearside ridge behavior observed in high multiplicity events of 𝑝⁢𝑝 collisions at the LHC.

Quantum chromodynamics↗
DOE OSTI2025

Thermal modifications of mesons and energy-energy correlators from real-time simulations of a 𝑈⁡(1) lattice gauge theory

We investigate thermal properties of a 𝑈⁡(1) lattice gauge theory in 1 + 1 dimensions through real-time simulations. We extract the spectral functions directly coupling to the pseudoscalar and scalar mesons, demonstrating the thermal modifications of these states with increasing temperatures. Introducing the notion of energy-flow operators, we quantify the temporal buildup of correlations in the energy flows across the lattice. We demonstrate that energy-energy correlators fail to factorize to products of energy flows, both in the vacuum and at nonzero temperature, indicating the presence of nontrivial correlations in the quantum states. Our results constitute a first real-time ab initio study of bound-state thermal broadening and finite temperature energy-flow correlations in a gauge theory, providing a benchmark for future studies of hadronic matter under extreme conditions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Correlating energy density induced residual stress, porosity, and mechanical property variations in directed energy deposition using neutron diffraction and imaging techniques

In a directed energy deposition (DED) process, the energy density deposited into the materials drives the structure and properties. The energy density is influenced by several printing parameters, such as laser power, hatch spacing, scanning speed, etc. In this study, 316L stainless steels samples were fabricated with varying hatch spacing aiming to induce variations in sample microstructure and properties. A combination of techniques including engineering neutron diffraction, neutron computed tomography, and tensile testing, were employed to correlate the structure and macroscopic properties. Porosity was predominantly observed at the bottom of the deposited materials and was effectively reduced by decreased hatch spacing. Correlatively, compressive residual stress was observed at the bottom of the specimens, while internal stress is largely determined by the hatch spacing. The residual stress in general decreases as the hatch spacing decreases. The maximum ultimate tensile strength (UTS) was found to increase from 517.4 to 528.6 MPa with a strain increased from 0.847 to 0.897 as the hatch spacing decreased from 0.45 to 0.42 mm. However, further increase in energy density by reducing the hatch spacing resulted in a significant decrease in UTS (as low as 452 MPa). This work provides new insights from bulk non-destructive techniques into correlating energy density induced residual stress, porosity, and mechanical property variations in directed energy deposition.

316L stainless steel↗
DOE OSTI2025

Ab initio calculations of the carbon and oxygen isotopes: Energies, correlations, and superfluid pairing

We perform ab initio nuclear lattice calculations of the neutron-rich carbon and oxygen isotopes using high-fidelity chiral interactions. We find good agreement with the observed binding energies and compute correlations associated with each two-nucleon interaction channel. For the isospin T = 1 channels, we show that the dependence on T z provides a measure of the correlations among the extra neutrons in the neutron-rich nuclei. For the spin-singlet S-wave channel, we observe that any paired neutron interacts with the nuclear core as well as its neutron pair partner, while any unpaired neutron interacts primarily with only the nuclear core. For the other partial waves, the correlations among the extra neutrons grow more slowly and smoothly with the number of neutrons. These general patterns are observed in both the carbon and oxygen isotopes and may be universal features that appear in many neutron-rich nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Observable optimization for precision theory: machine learning energy correlators

The practice of collider physics typically involves the marginalization of multi-dimensional collider data to uni-dimensional observables relevant for some physics task. In many cases, such as classification or anomaly detection, the observable can be arbitrarily complicated, such as the output of a neural network. However, for precision measurements, the observable must correspond to something computable systematically beyond the level of current simulation tools. In this work, we demonstrate that precision-theory-compatible observable space exploration can be systematized by using neural simulation-based inference techniques from machine learning. We illustrate this approach by exploring the space of marginalizations of the energy 3-point correlator to optimize sensitivity to the top quark mass. We first learn the energy-weighted probability density from simulation, then search in the space of marginalizations for an optimal triangle shape. Although simulations and machine learning are used in the process of observable optimization, the output is an observable definition which can be then computed to high precision and compared directly to data without any memory of the computations which produced it. We find that the optimal marginalization is isosceles triangles on the sphere with a side ratio approximately $1 : 1 : \sqrt{2}$ (i.e. right triangles) within the set of marginalizations we consider.

Jets and Jet Substructure↗
DOE OSTI2025

Static Subspace Approximation for Random Phase Approximation Correlation Energies: Applications to Materials for Catalysis and Electrochemistry

Modeling complex materials using high-fidelity, ab initio methods at low cost is a fundamental goal for quantum chemical software packages. The GW approximation and random phase approximation (RPA) provide a unified description of both electronic structure and total energies using the same physics in a many-body perturbative approach that can be more accurate than generalized-gradient density functional theory (DFT) methods. However, GW/RPA implementations have historically been limited to either specific materials classes or application toward small chemical systems. Here, the static subspace approximation allows for reduced cost full-frequency GW/RPA calculations and has previously been benchmarked thoroughly for GW calculations. Here, we describe our approach to including partial occupations of electronic orbitals in full-frequency GW and RPA calculations for the study of electrocatalysts. We benchmarked RPA total energy calculations using the subspace approximation across a diverse test suite of materials for a variety of computational parameters. The benchmarking quantifies the impact of different extrapolation procedures for representing the static polarizability at infinite screened cutoff, and shows that using screened cutoffs above 20-25 Ryd result in diminishing accuracy returns for predicting RPA total energies. Additionally, for moderately sized electrocatalytic models, 2-3 times fewer computational resources are used to compute RPA total energies by representing the static polarizability with 20-30% of the static subspace basis, with an error of approximately 0.01 eV or better in RPA adsorption energy calculations. Finally, we show that for these electrochemical models RPA can shift DFT adsorption energy shifts by up to 0.5 eV and that GW can frequently shift DFT eigenvalues of surface and adsorbate states by approximately 0.5-1 eV.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗