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DOE OSTI2025

Asymptotic gauge symmetry and UV extension of the nonperturbative coupling in holographic QCD

We extend our recent analytic study of the strong coupling 𝛼 eff in the nonperturbative and near-perturbative regimes [Phys. Rev. Lett. 133, 181901 (2024)] by imposing rigorous renormalization-group constraints from asymptotically free gauge theories at 𝑄 2 → ∞. The asymptotic boundary conditions modify the scaling properties of 𝛼eff at large values of the momentum transfer 𝑄 2 and lead to a scale-dependent confinement strength 𝜅⁡(𝑄 2 ). This requires that both 𝜅⁡(𝑄 2 ) and 𝛼 eff⁡ (𝑄 2 , 𝜅⁡(𝑄 2 )) remain holomorphic in the complex 𝑄 2 plane, except at the physical cuts associated with the heavy-quark thresholds and the singularity flow trajectory studied in our previous Letter. For color SU(3), a precise connection is found between the scaling exponent of 𝜅⁡(𝑄 2 ) in the ultraviolet, the value of the infrared fixed point of the strong coupling, and the number of flavors in agreement with observations. The nonperturbative analytic model gives an accurate description of the strong coupling across all scales, up to the highest available data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Effects of final state interactions on Landau singularities

In certain kinematic and particle mass configurations, triangle singularities may lead to line-shapes which mimic the effects of resonances. This well-known effect is scrutinized here in the presence of final-state rescattering. The goal is achieved first by utilizing general arguments provided by Landau equations, and second by applying a modern scattering formalism with explicit two- and three-body unitarity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Dijet Acoplanarity in CUJET3 as a Probe of the Nonperturbative Color Structure of QCD Perfect Fluids

Using the CUJET3=DGLV+VISHNU jet-medium interaction framework, we show that dijet azimuthal acoplanarity in high energy A + A collisions is sensitive to possible non-perturbative enhancement of the jet transport coefficient, $\hat{q}$(T,E), in the QCD crossover temperature T ~ 150–300 MeV range. With jet-medium couplings constrained by global RHIC& LHC χ 2 fits to nuclear modification data on R AA (p T > 20) GeV, we compare predictions of the medium induced dijet transverse momentum squared, $Q_s^2~\langle \hat{q}L\rangle~ΔΦ^2E^2$, in two models of the temperature, T, and jet energy E dependence of the jet medium transport coefficient, $\hat{q}$(T,E)). In one model, wQGP, the chromo degrees of freedom (dof) are approximated by a perturbative dielectric gas of quark and gluons dof. In the second model, sQGMP, we consider a nonperturbative partially confined semi-Quark-Gluon-Monopole-Plasma with emergent color magnetic dof constrained by lattice QCD data. Unlike the slow variation of the scaled jet transport coefficient, $\hat{q}_{wQGP}/T^3$, the sQGMP model $\hat{q}_{sQGMP}/T^3$ features a sharp maximum in the QCD confinement crossover T range. We show that the dijet path averaged medium induced azimuthal acoplanarity, Δφ 2 , in sQGMP is robustly ~ 2 times larger than in perturbative wQGP. even though the radiative energy loss in both models is very similar as needed to fit the same R AA data. Future A+A dijet acoplanarity measurements constrained together with single jet R AA and ν n measurements therefore appears to be a promising strategy to search for possible signatures of critical opalescence like phenomena in the QCD confinement temperature range.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Nonperturbatively renormalized nucleon gluon momentum fraction in the continuum limit of N f = 2 + 1 + 1 lattice QCD

We present the nonperturbatively renormalized nucleon gluon momentum fraction using ensembles with 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by the MILC Collaboration. The calculation is done using clover fermions for the valence action with three pion masses, 220, 310, and 690 MeV, and three lattice spacings, 0.09, 0.12, and 0.15 fm. The renormalization is done using RI/MOM nonperturbative renormalization and using cluster-decomposition error reduction (CDER) to enhance the signal-to-noise ratio of the renormalization constant. We find the CDER technique is particularly important to improve the signal at the finer lattice ensembles where the lattice volume is larger. We extrapolate the gluon momentum fraction to the continuum-physical limit and obtain $\langle{x}\rangle$ g = 0.502⁢(53) stat+NPR ⁢(50) mixing in the $\overline{MS}$ scheme at 2 GeV, where first error includes the statistical error and uncertainties in nonperturbative renormalization, while the latter systematic error accounts for ignoring quark mixing. Our gluon momentum fraction is consistent with other recent lattice-QCD results at physical pion mass.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Renormalons in the energy-energy correlator

The energy-energy correlator (EEC) is an observable of wide interest for collider physics and Standard Model measurements, due to both its simple theoretical description in terms of the energy-momentum tensor and its novel features for experimental studies. Significant progress has been made in both applications and higher-order perturbative predictions for the EEC. Here, we analyze the nature of the asymptotic perturbative series for the EEC by determining its analytic form in Borel space under the bubble-sum approximation. This result provides information on the leading and subleading nonperturbative power corrections through renormalon poles. We improve the perturbative convergence of the $\overline{MS}$ series for the EEC by removing its leading renormalon using an MSR scheme, which is independent of the bubble-sum approximation. Using the leading MSR scheme power correction determined by fits to thrust, we find good agreement with EEC OPAL data already at O(α$^{2}_{s}$).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Measuring spin correlation between quarks during QCD confinement

The vacuum is now understood to have a rich and complex structure, characterized by fluctuating energy fields and a condensate of virtual quark–antiquark pairs. The spontaneous breaking of the approximate chiral symmetry, signalled by the nonvanishing quark condensate $\langle$$q\bar{q}$$\rangle$, is dynamically generated through topologically nontrivial gauge configurations such as instantons. The precise mechanism linking the chiral symmetry breaking to the mass generation associated with quark confinement remains a profound open question in quantum chromodynamics (QCD)—the fundamental theory of strong interaction. High-energy proton–proton collisions could liberate virtual quark–antiquark pairs from the vacuum that subsequently undergo confinement to form hadrons, whose properties could serve as probes into QCD confinement and the quark condensate. Here we report evidence of spin correlations in $Λ\bar{Λ}$ hyperon pairs inherited from spin-correlated strange quark–antiquark virtual pairs. Measurements by the STAR experiment at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory reveal a relative polarization signal of (18 ± 4)% that links the virtual spin-correlated quark pairs from the QCD vacuum to their final-state hadron counterparts. Crucially, this correlation vanishes when the hyperon pairs are widely separated in angle, consistent with the decoherence of the quantum system. Our findings provide a new experimental model for exploring the dynamics and interplay of quark confinement and entanglement.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Insights into the emergence of mass from studies of pion and kaon structure

There are two mass generating mechanisms in the standard model of particle physics (SM). One is related to the Higgs boson and fairly well understood. The other is embedded in quantum chromodynamics (QCD), the SM’s strong interaction piece; and although responsible for emergence of the roughly 1 GeV mass scale that characterises the proton and hence all observable matter, the source and impacts of this emergent hadronic mass (EHM) remain puzzling. As bound states seeded by a valence-quark and -antiquark, pseudoscalar mesons present a simpler problem in quantum field theory than that associated with the nucleon. Consequently, there is a large array of robust predictions for pion and kaon properties whose empirical validation will provide a clear window onto many effects of both mass generating mechanisms and the constructive interference between them. This has now become significant because new-era experimental facilities, in operation, construction, or planning, are capable of conducting such tests and thereby contributing greatly to resolving the puzzles of EHM. These aspects of experiment, phenomenology, and theory, along with contemporary successes and challenges, are reviewed herein. In addition to providing an overview of the experimental status, we focus on recent progress made using continuum Schwinger function methods and lattice-regularised QCD. Further, advances made using other theoretical tools are also sketched. Our primary goal is to highlight the potential gains that can accrue from a coherent effort aimed at finally reaching an understanding of the character and structure of Nature’s Nambu–Goldstone modes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

QCD Running Coupling in the Nonperturbative and Near-Perturbative Regimes

We use analytic continuation to extend the gauge-gravity duality nonperturbative description of the strong force coupling into the transition, near-perturbative, regime where perturbative effects become important. By excluding the unphysical region in coupling space from the flow of singularities in the complex plane, we derive a specific relation between the scales relevant at large and short distances; this relation is uniquely fixed by requiring maximal analyticity. The unified effective coupling model gives an accurate description of the data in the nonperturbative and the near-perturbative regions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

QCD Constraints on Isospin-Dense Matter and the Nuclear Equation of State

Understanding the behavior of dense hadronic matter is a central goal in nuclear physics as it governs the nature and dynamics of astrophysical objects such as supernovae and neutron stars. Because of the nonperturbative nature of quantum chromodynamics (QCD), little is known rigorously about hadronic matter in these extreme conditions. Here, lattice QCD calculations are used to compute thermodynamic quantities and the equation of state of QCD over a wide range of isospin chemical potentials with controlled systematic uncertainties. Agreement is seen with chiral perturbation theory when the chemical potential is small. Comparison to perturbative QCD at large chemical potential allows for an estimate of the gap in the superconducting phase, and this quantity is seen to agree with perturbative determinations. Since the partition function for an isospin chemical potential μ I bounds the partition function for a baryon chemical potential μ B = 3 μ I / 2 , these calculations also provide rigorous nonperturbative QCD bounds on the symmetric nuclear matter equation of state over a wide range of baryon densities for the first time. Published by the American Physical Society 2025

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

QCD evolution of entanglement entropy

Entanglement entropy has emerged as a novel tool for probing nonperturbative quantum chromodynamics (QCD) phenomena, such as color confinement in protons. While recent studies have demonstrated its significant capability in describing hadron production in deep inelastic scatterings, the QCD evolution of entanglement entropy remains unexplored. Here, in this work, we investigate the differential rapidity-dependent entanglement entropy within the proton and its connection to final-state hadrons, aiming to elucidate its QCD evolution. Our analysis reveals a strong agreement between the rapidity dependence of von Neumann entropy, obtained from QCD evolution equations, and the corresponding experimental data on hadron entropy. These findings provide compelling evidence for the emergence of a maximally entangled state, offering new insights into the nonperturbative structure of protons.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Nonperturbative and perturbative dynamics of a light QCD axion: Dark matter and the strong 𝐶⁢𝑃 problem

Considerable theoretical efforts have gone into expanding the reach of the quantum chromodynamics (QCD) axion beyond its canonical mass–decay-constant relation. The 𝑍 𝒩 QCD axion model reduces the QCD axion mass naturally, by invoking a discrete 𝑍 𝒩 symmetry through which the axion field is coupled to 𝒩 copies of the Standard Model. Before the QCD phase transition at temperature 𝑇 QCD , the 𝑍 𝒩 potential has a minimum at misalignment angle 𝜃 = 𝜋. At 𝑇 QCD , 𝜃 = 𝜋 becomes a maximum; the axion potential becomes exponentially suppressed and develops 𝒩 minima—only one of which actually solves the strong 𝐶⁢𝑃 problem. Before 𝑇 QCD , 𝜃 relaxes toward 𝜋. After 𝑇 QCD , the axion field starts from around the hilltop and may have sufficient kinetic energy to overcome the newly suppressed potential barriers. Such a field evolution leads to nonperturbative effects via the self-interactions near the hilltop, which can cause the exponential growth of fluctuations and backreaction on the coherent motion. This behavior can influence the relic density of the field and the minimum in which it settles. We conduct the first lattice simulations of the 𝑍 𝒩 QCD axion using 𝒞osmoℒattice to accurately calculate dark matter abundances and find nonperturbative dynamics reduce the abundance by up to a factor of two. We furthermore find that the probability of solving the strong 𝐶⁢𝑃 problem tends to diverge considerably from the naïve expectation of 1/𝒩.

Axions↗
DOE OSTI2021

Large-momentum effective theory

Since the parton model was introduced by Feynman more than 50 years ago, much has been learned about the partonic structure of the proton through a large body of high-energy experimental data and dedicated global fits. However, limited progress has been made in calculating partonic observables such as the parton distribution function (PDFs) from the fundamental theory of strong interactions, quantum chromodynamics (QCD). Recently some advocated for a formalism, large-momentum effective theory (LaMET), through which one can extract parton physics from the properties of the proton traveling at a moderate boost factor such as γ ~ 2 – 5 . The key observation behind this approach is that Lorentz symmetry allows the standard formalism of partons in terms of light-front operators to be replaced by an equivalent one with large-momentum states and time-independent operators of a universality class. With LaMET, the PDFs, generalized PDFs or generalized parton distributions, transverse-momentum-dependent PDFs, and light-front wave functions can all be extracted in principle from lattice simulations of QCD (or other nonperturbative methods) through standard effective field theory matching and running. Future lattice QCD calculations with exascale computational facilities could help one to understand the experimental data related to the hadronic structure, including those from the upcoming electron-ion colliders dedicated to exploring the partonic landscape of the proton. In this work, the progress made in the past few years in the development of the LaMET formalism and its applications is reviewed, with an emphasis on a demonstration of its effectiveness from initial lattice QCD simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Transverse Momentum Distributions from Lattice QCD without Wilson Lines

The transverse-momentum-dependent distributions (TMDs), which are defined by gauge-invariant 3D parton correlators with staple-shaped lightlike Wilson lines, can be calculated from quark and gluon correlators fixed in the Coulomb gauge on a Euclidean lattice. These quantities can be expressed gauge invariantly as the correlators of Coulomb-gauge-dressed fields, which reduce to the standard TMD correlators under principal-value prescription in the infinite boost limit. In the framework of large-momentum effective theory, a quasi-TMD defined from such correlators in a large-momentum hadron state can be matched to the TMD via a factorization formula, whose exact form is derived using soft collinear effective theory and verified at one-loop order. Compared to the currently used gauge-invariant correlators, this new method can substantially improve statistical precision and simplify renormalization for the time-reversal-even TMDs, which will greatly enhance the predicative power of lattice QCD in the nonperturbative region.

Effective field theory↗
DOE OSTI2025

Role of the chiral anomaly in polarized deeply inelastic scattering. III. Wess-Zumino-Witten contributions and chiral Ward identities for finite quark mass

We extend our prior results on the worldline computation of the axial vector-vector-vector (AVV) triangle anomaly in polarized deeply inelastic scattering (DIS) to the finite mass case by computing in addition the pseudoscalar-vector-vector (PVV) triangle graph. For the well-studied QED case, we show explicitly how the off-forward AVV pole exactly cancels an identical PVV pole. We then demonstrate the dramatic difference in QCD due to the chiral condensate, which qualitatively modifies anomalous Ward identities. As in the massless case, the anomaly pole in QCD is canceled by the dynamics of a primordial isosinglet pseudoscalar η ¯ -meson, whose Wess-Zumino-Witten coupling to the topological charge density shifts the pole to the physical η ′ mass, with the finite quark mass contribution differing by O ( 10 % ) from the Witten-Veneziano formula. We obtain a compact analytic expression for the finite mass corrections to Shore and Veneziano’s result that the proton’s net quark helicity Δ Σ ∝ χ QCD ′ | m = 0 ( 0 ) , the forward slope of the topological susceptibility in the chiral limit, and show they are of the order of a few percentages. Our prior prediction that the polarized DIS structure function g 1 is quenched by sphaleronlike topological transitions at small x is unaffected by quark mass effects. Our results illustrate how worldline computations of anomalous processes, in synergy with lattice computations and nonet chiral perturbation theory, can uncover novel nonperturbative features of QCD at the Electron-Ion Collider. Published by the American Physical Society 2025

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Accessing the gluon momentum fraction of nucleons through the gradient flow

We calculate the gluon momentum fraction of the nucleon using lattice QCD, with a nonperturbative renormalization technique based on the gradient flow. The gluon momentum fraction is determined on a single Wilson-clover ensemble using 𝑁 𝑓 =2 +1 flavors with pion mass 358 MeV and lattice spacing 0.094 fm. We employ the variational method to reduce excited-state contamination and apply the distillation framework to ensure a large operator basis. To reduce systematic uncertainties, we apply Bayesian model averaging to all fit procedures. We apply matching coefficients to the flow-time dependent lattice results to recover the gluon momentum fraction in the $\overline{MS}$-scheme at 2 GeV. Our final result is ⟨𝑥⟩ 𝑔 ⁢(𝜇 =2 GeV) =0.482⁢(35), where we quote only statistical uncertainties.

Lattice QCD↗
DOE OSTI2022

Explainable machine learning of the underlying physics of high-energy particle collisions

We present an implementation of an explainable and physics-aware machine learning model capable of inferring the underlying physics of high-energy particle collisions using the information encoded in the energy-momentum four-vectors of the final state particles. We demonstrate the proof-of-concept of our White Box AI approach using a Generative Adversarial Network (GAN) which learns from a DGLAP-based parton shower Monte Carlo event generator. The constrained generator network architecture mimics the structure of a parton shower exhibiting similarities with Recurrent Neural Networks (RNNs). We show, for the first time, that our approach leads to a network that is able to learn not only the final distribution of particles, but also the underlying parton branching mechanism, i.e. the Altarelli-Parisi splitting function, the ordering variable of the shower, and the scaling behavior. While the current work is focused on perturbative physics of the parton shower, we foresee a broad range of applications of our framework to areas that are currently difficult to address from first principles in QCD. Examples include nonperturbative and collective effects, factorization breaking and the modification of the parton shower in heavy-ion, and electron-nucleus collisions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗