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DOE OSTI2025

Investigating the universality of five-point QCD scattering amplitudes at high energy

We investigate 2 → 3 QCD scattering amplitudes in multi-Regge kinematics, i.e. where the final partons are strongly ordered in rapidity. In this regime amplitudes exhibit intriguing factorisation properties which can be understood in terms of effective degrees of freedom called reggeons. Working within the Balitsky/JIMWLK framework, we predict these amplitudes for the first time to next-to-next-to-leading logarithmic order, and compare against the limit of QCD scattering amplitudes in full colour and kinematics. We find that the latter can be described in terms of universal objects, and that the apparent non-universality arising at NNLL comes from well-defined and under-control contributions that we can predict. Thanks to this observation, we extract for the first time the universal vertex that controls the emission of the central-rapidity gluon, both in QCD and $\mathcal{N}$ = 4 super Yang-Mills.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

QCD material parameters at zero and non-zero chemical potential from the lattice

Using an eighth-order Taylor expansion in baryon-chemical potential, we recently obtained the (2+1) flavor QCD equation of state (EoS) at non zero conserved charge chemical potentials from the lattice. We focused on strangeness-neutral, isospin-symmetric QCD matter, which closely resembles the situation encountered in heavy-ion collision experiments. Using this EoS, we present here results on various QCD material parameters; in particular we compute the specific heat, speed of sound, and compressibility along appropriate lines of constant physics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Warm inflation with a heavy QCD axion

We propose the first model of warm inflation in which the particle production emerges directly from coupling the inflaton to Standard Model particles. Warm inflation, an early epoch of sustained accelerated expansion at finite temperature, is a compelling alternative to cold inflation, with distinct predictions for inflationary observables such as the amplitude of fluctuations, the spectral tilt, the tensor-to-scalar ratio, and non-gaussianities. In our model a heavy QCD axion acts as the warm inflaton whose coupling to Standard Model gluons sources the thermal bath during warm inflation. Axion-like couplings to non-Abelian gauge bosons have been considered before as a successful microphysical theory with emerging thermal friction that can maintain finite temperature during inflation via sphaleron heating. However, the presence of light fermions charged under the non-Abelian group suppresses particle production, hindering a realization of warm inflation by coupling to QCD. We point out that the Standard Model quarks can be heavy during warm inflation if the Higgs field resides in a high-energy second minimum which restores efficient sphaleron heating. A subsequent large reheating temperature is required to allow the Higgs field to relax to its electroweak minimum. Exploring a scenario in which hybrid warm inflation provides the large reheating temperature, we show that future collider and beam dump experiments have discovery potential for a heavy QCD axion taking the role of the warm inflaton.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

b ¯ b ¯ u d and b ¯ b ¯ u s tetraquarks from lattice QCD using symmetric correlation matrices with both local and scattering interpolating operators

We study the b ¯ b ¯ u d tetraquark with quantum numbers I ( J P ) = 0 ( 1 + ) as well as the b ¯ b ¯ u s tetraquark with quantum numbers J P = 1 + using lattice QCD. We improve on existing work by including both local and scattering interpolating operators on both sides of the correlation functions and use symmetric correlation matrices. This allows not only a reliable determination of the energies of QCD-stable tetraquark ground states, but also of low-lying excited states, which are meson-meson scattering states. The latter is particularly important for future finite-volume scattering analyses. Here, we perform chiral and continuum extrapolations of just the ground-state energies, for which finite-volume effects are expected to be small. Our resulting tetraquark binding energies, − 100 ± 10 − 51 + 36 MeV for b ¯ b ¯ u d and − 30 ± 3 − 31 + 11 MeV for b ¯ b ¯ u s , are consistent with other recent lattice-QCD predictions. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2024

Dirac spectral density in N f = 2 + 1 QCD at T = 230 MeV

We compute the renormalized Dirac spectral density in N f = 2 + 1 QCD at physical quark masses, temperature T = 230 MeV , and system size L s = 3.4 fm . To that end, we perform a pointwise continuum limit of the staggered density in lattice QCD with staggered quarks. We find, for the first time, that a clear infrared structure (IR peak) emerges in the density of the Dirac operator describing dynamical quarks. We also provide numerical evidence that a component of this peak, which becomes dominant in the thermodynamic limit, is due to a nontrivial accumulation of near-zero modes. Features of this structure are consistent with those previously attributed to the recently proposed IR phase of thermal QCD. Our results (i) provide the only complete first-principles evidence that these IR features exist and are physical, (ii) improve the upper bound for IR phase transition temperature T IR so that the new window is 200 < T IR < 230 MeV , and (iii) are consistent with the nonrestoration of anomalous U A ( 1 ) symmetry (chiral limit) below T = 230 MeV . Published by the American Physical Society 2024

Alexandru, Andrei (ORCID:0000000345471554)↗
DOE OSTI2024

The ALICE experiment: a journey through QCD

The ALICE experiment was proposed in 1993, to study strongly-interacting matter at extreme energy densities and temperatures. This proposal entailed a comprehensive investigation of nuclear collisions at the LHC. Its physics programme initially focused on the determination of the properties of the quark–gluon plasma (QGP), a deconfined state of quarks and gluons, created in such collisions. The ALICE physics programme has been extended to cover a broader ensemble of observables related to Quantum Chromodynamics (QCD), the theory of strong interactions. The experiment has studied Pb–Pb, Xe–Xe, p–Pb and pp collisions in the multi-TeV centre of mass energy range, during the Run 1–2 data-taking periods at the LHC (2009–2018). The aim of this review is to summarise the key ALICE physics results in this endeavor, and to discuss their implications on the current understanding of the macroscopic and microscopic properties of strongly-interacting matter at the highest temperatures reached in the laboratory. It will review the latest findings on the properties of the QGP created by heavy-ion collisions at LHC energies, and describe the surprising QGP-like effects in pp and p–Pb collisions. Measurements of few-body QCD interactions, and their impact in unraveling the structure of hadrons and hadronic interactions, will be discussed. ALICE results relevant for physics topics outside the realm of QCD will also be touched upon. Finally, prospects for future measurements with the ALICE detector in the context of its planned upgrades will also be briefly described.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Candidate phases for SU(2) adjoint QCD$_4$ with two flavors from $\mathcal{N}=2$ supersymmetric Yang-Mills theory

We study four-dimensional adjoint QCD with gauge group SU(2) and two Weyl fermion flavors, which has an SU(2) R chiral symmetry. The infrared behavior of this theory is not firmly established. We explore candidate infrared phases by embedding adjoint QCD into N = 2 supersymmetric Yang-Mills theory deformed by a supersymmetry-breaking scalar mass M that preserves all global symmetries and 't Hooft anomalies. This includes 't Hooft anomalies that are only visible when the theory is placed on manifolds that do not admit a spin structure. The consistency of this procedure is guaranteed by a nonabelian spin-charge relation involving the SU(2) R symmetry that is familiar from topologically twisted N = 2 theories. Since every vacuum on the Coulomb branch of the N = 2 theory necessarily matches all 't Hooft anomalies, we can generate candidate phases for adjoint QCD by deforming the theories in these vacua while preserving all symmetries and 't Hooft anomalies. One such deformation is the supersymmetry-breaking scalar mass M itself, which can be reliably analyzed when M is small. In this regime it gives rise to an exotic Coulomb phase without chiral symmetry breaking. By contrast, the theory near the monopole and dyon points can be deformed to realize a candidate phase with monopole-induced confinement and chiral symmetry breaking. The low-energy theory consists of two copies of a CP 1 sigma model, which we analyze in detail. Certain topological couplings that are likely to be present in this CP 1 model turn the confining solitonic string of the model into a topological insulator. We also examine the behavior of various candidate phases under fermion mass deformations. We speculate on the possible large-M behavior of the deformed N = 2 theory and conjecture that the CP 1 phase eventually becomes dominant.

Córdova, Clay↗
DOE OSTI2026

Exploring the QCD Phase Diagram

Exploring the QCD phase diagram through relativistic heavy-ion collisions is a primary goal of modern nuclear physics. This contribution focuses on fluctuations and correlations of conserved charges — specifically net-baryon and net-charge cumulants — as sensitive probes of the phase structure and the QCD critical point. We discuss recent theoretical and experimental advancements, highlighting constraints from lattice QCD and new results from the RHIC Beam Energy Scan program. Key challenges in theory-to-experiment comparisons at high baryon density are discussed, alongside the systematic requirements for meaningful physical interpretation. Finally, we identify open issues and outline the discovery potential of future low-energy experiments, such as CBM, in resolving the high-density regime of the phase diagram.

Koch, V. [Lawrence Berkeley National Laboratory (L↗
DOE OSTI2026

Renormalon subtracted nonrelativistic QCD for heavy hadron systems

We present a renormalon-subtracted formulation of potential nonrelativistic QCD (pNRQCD) for precision spectroscopy of heavy hadron systems, combining variational and Green's function Monte Carlo (VMC/GFMC) methods with NNLO static two- and three-body potentials. Minimal renormalon subtraction (MRS) systematically sums leading factorially growing terms, thereby stabilizing perturbative convergence and reducing renormalization-scale dependence. We tune charm and bottom quark masses to spin-averaged $1S$ quarkonium states and predict $Ω_{ccc}$, $Ω_{ccb}$, $Ω_{cbb}$, and $Ω_{bbb}$ baryon masses, as well as QCD-stable baryons containing top quarks. NNLO MRS results undershoot lattice QCD by 125--175~MeV, with fractional differences decreasing as $\sim 1/m_Q$, consistent with neglected $\mathcal{O}(1/m_Q)$ corrections. Applying these methods to unequal-mass fully-heavy tetraquarks, we determine the critical heavy-to-light mass ratio for binding and compute binding energies across the mass-ratio landscape.

Assi, Benoît [Cincinnati U.; Fermilab]↗
DOE OSTI2025

Lattice QCD constraints on the critical point from an improved precision equation of state

In this paper we employ lattice simulations to search for the critical point of QCD. We search for the onset of a first-order QCD transition on the phase diagram by following contours of constant entropy density from imaginary to real chemical potentials under conditions of strangeness neutrality. We scan the phase diagram and investigate whether these contours meet to determine the probability that the critical point is located in a certain region on the 𝑇−𝜇 𝐵 plane. To achieve this we introduce a new, continuum extrapolated equation of state at zero density with improved precision using lattices with 𝑁 𝜏 =8, 10, 12, 16 time slices, and supplement it with new data at imaginary chemical potential. The current precision allows us to exclude, at the 2⁢𝜎 level, the existence of a critical point at 𝜇 𝐵 <450 MeV.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

A unified neural-network framework for nucleon imaging from numerical simulations of QCD

Parton distributions encode the momentum-space structure and, in their generalizations, the spatial tomography of quarks and gluons inside hadrons, the building blocks of visible matter. We present a unified neural-network approach that learns these distributions directly from matrix elements calculated via numerical simulations of quantum chromodynamics (QCD) on the lattice by fitting two complementary inputs simultaneously: data matched to physical quantities via known momentum-space and coordinate-space formalisms. Utilizing data from both methods stabilizes the extraction and mitigates biases that can arise when either is used alone. We validate the method on controlled mock data and apply it to lattice-QCD matrix elements to extract parton distribution functions (PDFs). We show benefits of such an approach for determining the physical quantities. We further extend the framework to zero-skewness generalized parton distributions and demonstrate nucleon tomography within the same neural-network parameterization. Our results provide an adaptable and systematically improvable approach for extracting partonic distributions from Euclidean correlators. It can incorporate polarization, additional channels, and future experimental constraints from current and future facilities, such as the Electron-Ion Collider.

Hadronic Spectroscopy↗
DOE OSTI2024

The 1 → 3 massive splitting functions from QCD factorization and SCET

Splitting functions are universal functions describing the collinear dynamics of gauge theories, and as such are crucial ingredients for a wide variety of calculations in perturbative QCD. We present analytic results for the triple collinear splitting functions in QCD with a single massive parton. We derive the splitting functions using two distinct methods; first by expanding the squared matrix elements in the collinear limit, and secondly by using soft-collinear effective theory with massive quarks. We find agreement between these two approaches, providing a strong check of our results. Additionally, we also check all iterated and soft limits of our results, finding agreement with predictions from factorization. Our results provide an important ingredient for higher order perturbative calculations involving massive partons, and for the description of the collinear dynamics of heavy flavor jets.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Decoding the proton’s gluonic density with lattice QCD-informed machine learning

We present a first machine learning-based decoding of the gluonic structure of the proton from lattice QCD using a variational autoencoder inverse mapper (VAIM). Harnessing the power of generative AI, we predict the parton distribution function (PDF) of the gluon given information on the reduced pseudo-Ioffe-time distributions (RpITDs) as calculated from an ensemble with lattice spacing a ≈ 0.09 fm and a pion mass of M π ≈ 310 MeV. The resulting gluon PDF is consistent with phenomenological global fits within uncertainties, particularly in the intermediate-to-high-x region where lattice data are most constraining. A subsequent correlation analysis confirms that the VAIM learns a meaningful latent representation, highlighting the potential of generative AI to bridge lattice QCD and phenomenological extractions within a unified analysis framework.

Gluon parton distribution function↗
DOE OSTI2025

Global QCD analysis of spin PDFs in the proton with high-𝑥 and lattice constraints

We perform a comprehensive global QCD analysis of spin-dependent parton distribution functions (PDFs), combining all available data on inclusive and semi-inclusive deep-inelastic scattering (DIS), as well as inclusive weak boson and jet production in polarized 𝑝⁢𝑝 collisions, simultaneously extracting spin-averaged PDFs and fragmentation functions. Including recent Jefferson Lab DIS data at high 𝑥, together with subleading power corrections to the leading-twist framework, allows us to verify the stability of the PDFs for 𝑊 2 ≥ 4 GeV 2 and quantify the uncertainties on the spin structure functions more reliably. We explore the use of new lattice QCD data on gluonic pseudo-Ioffe time distributions, which, together with jet production and high-𝑥 DIS data, improve the constraints on the polarized gluon PDF. The expanded kinematic reach afforded by the data into the high-𝑥 region allows us to refine the bounds on higher-twist contributions to the spin structure functions, and test the validity of the Bjorken sum rule.

Perturbative QCD↗
DOE OSTI2026

Locating the QCD critical point through contours of constant entropy density

We propose a new method to investigate the existence and location of the conjectured high-temperature critical point of strongly interacting matter via contours of constant entropy density. By approximating these lines as a power series in the baryon chemical potential 𝜇 𝐵 , one can extrapolate them from first-principle results at zero net-baryon density, and use them to locate the quantum chromodynamics (QCD) critical point, including the associated first-order and spinodal lines. As a proof of principle, we employ currently available continuum-extrapolated lattice data from the Wuppertal-Budapest collaboration to find a critical point at a temperature and a baryon chemical potential of 𝑇 𝑐 = 114.3 ± 6.9 MeV and 𝜇 𝐵,𝑐 = 602.1 ± 62.1 MeV, respectively, at expansion order 𝒪⁡(𝜇$^{2}_{𝐵}$). We advocate for a more precise determination of the required expansion coefficients via lattice QCD simulations as a means of pinpointing the location of the critical endpoint in the phase diagram of strongly interacting matter.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Binding energy of the 𝑇 𝑏⁢𝑏 tetraquark from lattice QCD with relativistic and nonrelativistic heavy-quark actions

We present a new determination of the $b\bar{b}$𝑢⁢𝑑 (𝐽 𝑃 = 1 + , 𝐼 = 0) tetraquark binding energy using lattice quantum chromodynamics (QCD) with domain-wall light quarks and a nonperturbatively tuned three-parameter anisotropic-clover “relativistic” action for the 𝑏 quarks. We also perform a direct comparison with a reanalysis of data generated in prior work using a lattice-nonrelativistic QCD (NRQCD) action for the 𝑏 quarks and otherwise identical parameters. Using the new data with relativistic 𝑏 quarks from seven different ensembles with multiple lattice spacings and pion masses, we perform combined chiral and continuum extrapolations and obtain (𝑚 𝑇 𝑏⁢𝑏 −𝑚 𝐵 −𝑚 𝐵* ) RHQ =(−76 ±23) MeV. For the NRQCD data from five ensembles, we perform chiral-only extrapolations and obtain (𝑚 𝑇 𝑏⁢𝑏 −𝑚 𝐵 −𝑚 𝐵* ) NRQCD = (−74 ±17 ±10) MeV. The lower magnitude of the results obtained here, compared to the original analysis in [Phys. Rev. D 100, 014503 (2019)], is due to the use of the symmetric parts of the correlation matrices with local four-quark operators only.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Transverse-momentum-dependent pion structures from lattice QCD: Collins-Soper kernel, soft factor, TMDWF, and TMDPDF

We present the first lattice quantum chromodynamics (QCD) calculation of the pion valence-quark transverse-momentum-dependent parton distribution function (TMDPDF) within the framework of large-momentum effective theory (LaMET). Using correlators fixed in the Coulomb gauge (CG), we computed the quasi-TMD beam function for a pion with a mass of 300 MeV, a fine lattice spacing of 𝑎 =0.06 fm, and multiple large momenta up to 3 GeV. The intrinsic soft functions in the CG approach are extracted from form factors with large momentum transfer, and as a byproduct, we also obtain the corresponding Collins-Soper (CS) kernel. Our determinations of both the soft function and the CS kernel agree with perturbation theory at small transverse separations (𝑏 ⊥ ) between the quarks. At larger 𝑏 ⊥ , the CS kernel remains consistent with recent results obtained using both CG and gauge-invariant TMD correlators in the literature. By combining next-to-leading logarithmic factorization of the quasi-TMD beam function and the soft function, we obtain an 𝑥-dependent pion valence-quark TMDPDF for transverse separations 𝑏 ⊥ ≳1 fm. Interestingly, we find that the 𝑏 ⊥ dependence of the phenomenological parametrizations of TMDPDF for moderate values of 𝑥 are in reasonable agreement with our QCD determinations. In addition, we present results for the transverse-momentum-dependent wave function for a heavier pion with 670 MeV mass.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

From chiral effective field theory to perturbative QCD: A Bayesian model mixing approach to symmetric nuclear matter

Constraining the equation of state (EOS) of strongly interacting, dense matter is the focus of intense experimental, observational, and theoretical effort. Chiral effective field theory (𝜒⁢EFT ) can describe the EOS between the typical densities of nuclei and those in the outer cores of neutron stars, while perturbative QCD (pQCD) can be applied to properties of deconfined quark matter, both with quantified theoretical uncertainties. However, describing the full range of densities in between with a single EOS that has well-quantified uncertainties is a challenging problem. Bayesian multimodel inference from 𝜒⁢EFT and pQCD can help bridge the gap between the two theories. In this work, we introduce a correlated Bayesian model mixing framework that uses a Gaussian process (GP) to assimilate different information into a single QCD EOS for symmetric nuclear matter. The present implementation uses a stationary GP to infer this mixed EOS solely from the EOSs of 𝜒⁢EFT and pQCD while accounting for the truncation errors of each theory. The GP is trained on the pressure as a function of number density in the low- and high-density regions where 𝜒⁢EFT and pQCD are, respectively, valid. We impose priors on the GP kernel hyperparameters to suppress unphysical correlations between these regimes. This, together with the assumption of stationarity, results in smooth 𝜒⁢EFT-to-pQCD curves for both the pressure and the speed of sound. We show that using uncorrelated mixing requires uncontrolled extrapolation of at least one of 𝜒⁢EFT or pQCD into regions where the perturbative series breaks down and leads to an acausal EOS. Here, we also discuss extensions of this framework to nonstationary and less differentiable GP kernels, its future application to neutron-star matter, and the incorporation of additional constraints from nuclear theory, experiment, and multimessenger astronomy.

Bayesian methods↗