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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 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↗
DOE OSTI2025

Background-field Method and QCD Factorization

One method for deriving a factorization for QCD processes is to use successive integration over fields in the functional integral. In this approach, we separate the fields into two categories: dynamical fields with momenta above a relevant cutoff, and background fields with momenta below the cutoff. The dynamical fields are then integrated out in the background of the low-momentum background fields. This strategy works well at tree level, allowing us to quickly derive QCD factorization formulas at leading order. However, to extend the approach to higher loops, it is necessary to rigorously define the functional integral over dynamical fields in an arbitrary background field. This framework was carefully developed for the calculation of the effective action in a background field at the two-loop level in the classic paper by Abbott «The Background Field Method Beyond One Loop», Nucl. Phys. B 185 , 189 (1981). Building on this work, I specify the renormalized background-field Lagrangian and define the notion of the quantum average of an operator in a background field, consistent with the “separation of scales” scheme mentioned earlier. As examples, I discuss the evolution of the twist-2 gluon light-ray operator and the one-loop gluon propagator in a background field near the light cone.

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

Inching toward the QCD axions with axion magnetic resonance in helioscopes

Utilizing a helical magnet profile to enhance axion-photon conversion showed great promise in laboratory searches for high axion masses. We extend the mechanism, known as the axion-magnetic resonance (AMR), from laser experiments to axion helioscopes and demonstrate its potential in covering QCD axion parameter space. Specifically, we apply AMR to the CAST experiment legacy, make projections for the upcoming IAXO experiment, and assess its implications for both axion-like particles and QCD axions. We observe considerable improvement in the experiment’s sensitivity reach in all cases.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

More about the lattice Hamiltonian for Adjoint QCD 2

In our earlier work [1], we introduced a lattice Hamiltonian for Adjoint QCD 2 using staggered Majorana fermions. We found the gauge invariant space of states explicitly for the gauge group SU(2) and used them for numerical calculations of observables, such as the spectrum and the expectation value of the fermion bilinear. In this paper, we carry out a more in-depth study of our lattice model, extending it to any compact and simply-connected gauge group G. We show how to find the gauge invariant space of states and use it to study various observables. We also use the lattice model to calculate the mixed ’t Hooft anomalies of Adjoint QCD 2 for arbitrary G. We show that the matrix elements of the lattice Hamiltonian can be expressed in terms of the Wigner 6j-symbols of G. For G = SU(3), we perform exact diagonalization for lattices of up to six sites and study the low-lying spectrum, the fermion bilinear condensate, and the string tension. We also show how to write the lattice strong coupling expansion for ground state energies and operator expectation values in terms of the Wigner 6j-symbols. For SU(3) we carry this out explicitly and find good agreement with the exact diagonalizations, and for SU(4) we give expansions that can be compared with future numerical studies.

confinement↗
DOE OSTI2024

Gluon to $\textrm{q}\overline{\textrm{q}}$ antenna in anisotropic QCD matter: spin-polarized and azimuthal jet observables

We study the production of a quark-antiquark antenna in the presence of a dense and anisotropic QCD medium. We assume the antenna to originate from an unpolarized gluon state, and consider both massless and massive final states. The medium anisotropy is captured by allowing the jet quenching coefficient to take different magnitudes in orthogonal directions with respect to the jet axis. We find that the final particle distribution is sensitive to the medium anisotropy, and more importantly, that this effect couples directly to the helicity/spin of the final states. We propose to look into these effects by performing a Fourier decomposition of the particle distribution inside the jet. In our medium model, we find that the spin independent terms contribute to the even harmonics of the cosine series. The helicity/spin dependence enters only through the sine Fourier series. We further explore the spin dependence by examining the degree of polarization of the final states in different directions. Our results indicate that the anisotropies present in the QCD matter produced in heavy ion collisions can be probed by studying azimuthal and spin observables inside jets.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Fantômas unconfined: global QCD fits with Bézier parameterizations

Fantômas is a C++ toolkit for exploring the parametrization dependence of parton distribution functions (PDFs) and other correlator functions in quantum chromodynamics (QCD). Fantômas facilitates the generation of adaptable polynomial parametrizations for PDFs, called metamorphs, to find best-fit PDF solutions and quantify the epistemic uncertainty associated with the parametrizations during their fitting. The method employs Bézier curves as universal approximators for a variety of PDF shapes. Integrated into the xFitter framework for the global QCD analysis, Fantômas provides a foundation for general models of PDFs, while reducing the computational time compared to the approaches utilizing traditional polynomial parametrizations as well as providing an interpretable alternative to neural-network-based models. This paper outlines the structure and practical usage of the Fantômas toolkit, including its inputs, outputs, and implementation within xFitter. It also provides a practical example of using Fantômas for uncertainty quantification as well as the combination of PDF fits into a single ensemble.

Bézier curves↗
DOE OSTI2025

Overview of high-density QCD studies with the CMS experiment at the LHC

We review key measurements performed by CMS in the context of its heavy ion physics program, using event samples collected in 2010-2018 with several collision systems and energies. These studies provide detailed macroscopic and microscopic probes of the quark-gluon plasma (QGP) created at the LHC energies, a medium characterized by the highest temperature and smallest baryon-chemical potential ever reached in the laboratory. Numerous observables related to high-density quantum chromodynamics (QCD) were studied, leading to some of the most impactful and qualitatively novel results in the 40-year history of the field. Using a dedicated high-multiplicity trigger in the first pp run, CMS discovered that small collision systems can exhibit signs of collectivity, a generic phenomenon with significant implications and presently understood to affect essentially all soft physics processes. This observation opened new paths to understand how fluidity and plasma properties emerge in QCD matter as a function of system size. Measurements of jet quenching have reached a completely new level of detail by directly assessing, for the first time, the medium modification of parton showers, as opposed to simply observing leading hadrons or di-hadrons. The first fully reconstructed beauty hadron and heavy-flavor jet nuclear modifications were also measured. The large size of the event samples, the precision of the measurements, and the extension of the probed kinematical phase space, allowed many other hard probes of the QGP medium to be explored in detail, leading to multiple groundbreaking findings. In particular, the seminal measurements of bottomonium suppression patterns answer fundamental questions that have been actively pursued, both theoretically and experimentally, by the community since the mid-1980s. We conclude by outlining the opportunities offered by the continuation of this physics program at the LHC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Electroweak, QCD and flavour physics studies with ATLAS data from Run 2 of the LHC

A of precision measurements sensitive to electroweak, QCD and quark-flavour effects performed by the ATLAS Collaboration at the Large Hadron Collider is reported. The measurements are predominantly performed on proton–proton ( p p ) collision data recorded at a centre-of-mass energy of 13 TeV taken from 2015 to 2018, with an integrated luminosity of up to 140 fb−1, with some results based on p p and Pb+Pb data recorded at lower nucleon centre-of-mass energies. The results cover a wide range of topics, from strong production of particles at low energies and the spectroscopy of hadrons to perturbative QCD with hadronic jets and electroweak and strong production of single and multiple vector bosons. They provide precise measurements of fundamental constants and stringent tests of the Standard Model with unprecedented precision and in energy ranges never explored before. They are also used to explore the proton structure and to perform model-independent searches for new physics.

Source record↗
DOE OSTI2025

Cascading from $\mathscr{N}$ = 2 supersymmetric Yang–Mills theory to confinement and chiral symmetry breaking in adjoint QCD

We argue that adjoint QCD in 3 + 1 dimensions, with any SU(N) gauge group and two Weyl fermion flavors (i.e. one adjoint Dirac fermion), confines and spontaneously breaks its chiral symmetries via the condensation of a fermion bilinear. We flow to this theory from pure $\mathscr{N}$ = 2 SUSY Yang–Mills theory with the same gauge group, by giving a SUSY-breaking mass M to the scalars in the $\mathscr{N}$ = 2 vector multiplet. This flow can be analyzed rigorously at small M, where it leads to a deconfined vacuum at the origin of the $\mathscr{N}$ = 2 Coulomb branch. The analysis can be extended to all M using an Abelian dual description that arises from the N multi-monopole points of the $\mathscr{N}$ = 2 theory. At each such point, there are N −1 hypermultiplet Higgs fields h$^{i=1,2}_m$, which are SU(2) R doublets. We provide a detailed study of the phase diagram as a function of M, by analyzing the semi-classical phases of the dual using a combination of analytic and numerical techniques. The result is a cascade of first-order phase transitions, along which the Higgs fields h i m successively turn on, and which interpolates between the Coulomb branch at small M, where all h$^{i}_m$ = 0, and a maximal Higgs branch, where all h$^{i}_m$ ≠ 0, at sufficiently large M. We show that this maximal Higgs branch precisely matches the confining and chiral symmetry breaking phase of two-flavor adjoint QCD, including its broken and unbroken symmetries, its massless spectrum, and the expected large-N scaling of various observables. The spontaneous breaking pattern SU(2) R → U(1) R , consistent with the Vafa–Witten theorem, is ensured by an intricate alignment mechanism for the h$^{i}_m$ in the dual, and leads to a CP 1 sigma model of increasing radius along the cascade.

D’Hoker, Eric [Univ. of California, Los Angeles, C↗