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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Advances for QCD and the standard model: color-confining light-front holography and the principle of maximum conformality

Here, I review how the application of superconformal quantum mechanics and light-front holography leads to new insights into the physics of color confinement, the spectroscopy and dynamics of hadrons, as well as surprising supersymmetric relations between the masses of mesons, baryons, and tetraquarks. Spontaneous chiral symmetry breaking is automatically fulfilled by supersymmetric Light-Front QCD. The light-front holographic approach (HLFQCD) also predicts the behavior of the QCD running coupling and other observables from the nonperturbative color-confining domain to the perturbative domain. One can determine the QCD running coupling to high precision from the data of just a single experiment over the entire perturbative regime by using the Principle of Maximum Conformality (PMC). The PMC, which generalizes the conventional Gell-Mann-Low method for scale-setting in perturbative QED to non-Abelian QCD, provides a rigorous method for achieving unambiguous scheme-independent, fixed-order Standard Model predictions, consistent with the principles of the renormalization group. I also briefly review a novel feature of hadronic physics predicted by QCD: intrinsic heavy quarks.

Brodsky, Stanley J. [SLAC National Accelerator Lab↗
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

String-based model with Hagedorn temperature of 𝑇 𝐻 ∼ 300 MeV describes the spectrum of mesons and glueballs

We consider the thermodynamics of a color-confined phase of quantum chromodynamics (QCD) and pure gauge theory within a string-inspired corresponding to a physical spatial dimension, 𝑑 = 3. We show that the physical mass spectrum of massive mesons—in both the strange and nonstrange sectors separately—is reasonably well described and extended by the exponential mass spectrum of open strings, 𝜌⁡(𝑚), characterized by a unique Hagedorn temperature 𝑇 𝐻 = $\sqrt3⁢𝜎/2⁢𝜋$, expressed by the string tension 𝜎. This 𝑇 𝐻 is the value appropriate for 𝑑 = 3 spatial dimensions and is of the order of 𝑇 𝐻 ∼ 300 MeV for typical values of the string tension. It is much larger than the values of 𝑇 𝐻 which have been phenomenologically extracted so far to describe the meson spectrum. Glueball states in pure gauge theory, modeled by closed strings, exhibit a similarly large Hagedorn temperature, highlighting a universal feature of the exponential spectrum. We further analyze the thermodynamic properties of the equation of state at finite temperature and demonstrate that, in the confined phase, the string models agree with lattice QCD results. This lends further support to the recent interpretation of the QCD phase diagram that incorporates strings as relevant degrees of freedom.

Phase transitions↗
DOE OSTI2025

Enhancing charge ratio sensitivity to hadronization effects via jet selections on resolved SoftDrop splitting

The study of quantum chromodynamics (QCD) at ultrarelativistic energies can be performed in a controlled environment through lepton-hadron deep inelastic scatterings. In such collisions, the high-energy partonic emissions that follow from the ejected hard partons are accurately described by perturbative QCD. However, the lower energy scales at which quarks and gluons experience color confinement, i.e., hadronization mechanism, fall outside the validity regions for perturbative calculations, requiring phenomenological models tuned to data to describe it. As such, hadronization physics cannot be currently derived from first principles alone. Monte Carlo event generators are useful tools to describe these processes as they simulate both the perturbative and the nonperturbative interactions, with model-dependent energy scales that control parton dynamics. This work employs jets—experimental reconstructions of final-state particles likely to have a common partonic origin—to inspect this transition further. Although originally proposed to circumvent hadronization effects, we show that jets can be utilized as probes of nonperturbative phenomena via their substructure. The charge correlation ratio was recently shown to be sensitive to hadronization effects. Our work further improves this sensitivity to nonperturbative scales by introducing a new selection based on the relative placement of the within the clustering tree, defined as the unclustering that resolves the jet’s leading charged particles. Published by the American Physical Society 2025

Apolinário, Liliana (ORCID:0000000335009681)↗
DOE OSTI2024

Coulomb confinement in the Hamiltonian limit

The Gribov-Zwanziger scenario attributes the phenomenon of confinement to the instantaneous interaction term in the QCD Hamiltonian in the Coulomb gauge. For a static quark-antiquark pair, it leads to a potential energy that increases linearly with the distance between them. Lattice studies of the SU(2) Yang-Mills theory determined the corresponding (Coulomb) string tension for sources in the fundamental representation, 𝜎 𝐶 , to be about 3 times larger than the Wilson loop string tension, 𝜎 𝐹 . It is far above the Zwanziger variational bound, 𝜎 𝐶 ≥ 𝜎 𝐹 . We argue that the value often reported in the literature is artificially inflated. We examine the lattice definition of the instantaneous potential, find the source of the string tension’s enhancement, and perform its improved determination in SU(2) lattice gauge theory. We report our conservative estimate for the value of the Coulomb string tension as 𝜎 𝐶 /𝜎 𝐹 = 2.0 ± 0.4 and discuss its phenomenological implications.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Gauge invariance and color charge fluctuations

The nature of confinement is connected with color charge. Unfortunately, the color charge densities in QCD, the Noether charge densities associated with the global color invariance, are not invariant under local color rotations. This implies that the expectation values of the net color charge in any region of any physical state in QCD—states that satisfy the color Gauss law—are automatically zero for all components of color. In this Letter, it is shown that the expectation value of the square of the net color charge in a region—a measure of the color charge fluctuations—is necessarily nonzero when evaluated in physical states and the result, while depending on the scheme and scale by which the theory is regulated, is gauge invariant. This holds despite the formal lack of gauge invariance of the operator. Moreover, there is a particular combination of the color charge fluctuations for the vacuum and for a system describable by a nontrivial density matrix that is independent that has a well-defined continuum limit.

color confinement↗
DOE OSTI2025

Phases of Theories with ℤ 𝑁 1-Form Symmetry, and the Roles of Center Vortices and Magnetic Monopoles

We analyze the phases of theories having a microscopic ℤ 𝑁 1-form symmetry, starting with a topological BF theory and deforming it so that only the microscopic symmetry is preserved. These theories have a well-defined notion of confinement, prototypical examples being pure SU⁡(𝑁) and ℤ 𝑁 gauge theories in the continuum and on the lattice. Our analysis shows that the generic phases are in 𝑑 = 2, only the confined phase; in 𝑑 = 3, both the confined phase and the topological BF phase; and in 𝑑 = 4, the confined phase, the topological BF phase, and a Coulomb phase. We construct a ℤ𝑁 lattice gauge theory with a deformation that, surprisingly, produces up to (𝑁−1) photons. We give an interpretation of these findings in terms of the behaviors of two competing drivers of confinement—magnetic monopoles and center vortices—and conclude that proliferation of center vortices is necessary but insufficient for confinement, while proliferation of magnetic monopoles is both necessary and sufficient.

Color confinement↗
DOE OSTI2025

Bayesian optimization of PYTHIA 8 tunes

A new tune (set of model parameters) is found for the six most important parameters of the PYTHIA 8 final state parton shower and hadronization model using Bayesian optimization. The tune fits the Large Electron-Positron collider (LEPI) data from ALEPH better than the default tune in PYTHIA 8. To the best of our knowledge, we present the most comprehensive application of Bayesian optimization to the tuning of a parton shower and hadronization model using the LEPI data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Spatial String Tension and Its Effects on Screening Correlators in a Thermal QCD Plasma

We calculate the spatial Wilson line correlator for 2 +1 flavor QCD using highly improved staggered quark discretization for fermions and in quenched QCD for a wide range of temperatures, from the chiral crossover temperature 𝑇 pc ≃ 156 MeV or the deconfinement temperature ≃300 MeV, respectively, up to 2 GeV. Extracting the spatial string tension for different lattice cutoffs and by performing a continuum extrapolation of this observable, we show that the soft (magnetic) gluons interact nonperturbatively even at temperatures ≳1 GeV. We provide incriminating evidences to demonstrate that dimensionally reduced effective theories can describe these soft quark and gluon quasi-particles for both quenched and 2 +1 flavor QCD, at temperatures 𝑇 ≳ 5⁢𝑇 pc . We also show for the first time the imprints of the nonperturbative pseudopotential in the properties of mesonic screening masses for temperatures ranging from 0.8 to 164 GeV in the quark-gluon plasma.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Suppression of neutral-pion production in deep-inelastic scattering off nuclei with the CLAS detector

We present the first threefold differential measurement for neutral-pion multiplicity ratios produced in semi-inclusive deep-inelastic electron scattering on carbon, iron, and lead nuclei normalized to deuterium from CLAS at Jefferson Lab. We found that the neutral-pion multiplicity ratio is maximally suppressed for the leading hadrons (energy fraction 𝑧 → 1), suppression varying from 25% in carbon up to 75% in lead. An enhancement of the multiplicity ratio at low 𝑧 and high 𝑝$^2_𝑇$ is observed, suggesting an interconnection between these two variables. This behavior is qualitatively similar to the previous twofold differential measurement of charged pions by the HERMES Collaboration and, recently, by CLAS Collaboration. The largest enhancement was observed at high 𝑝$^2_𝑇$ for heavier nuclei, namely, iron and lead, while the smallest enhancement was observed for the lightest nucleus, carbon. This behavior suggests a competition between partonic multiple scattering, which causes enhancement, and hadronic inelastic scattering, which causes suppression.

color confinement↗
DOE OSTI2025

Lanczos Algorithm, the Transfer Matrix, and the Signal-to-Noise Problem

This Letter introduces a method for determining the energy spectrum of lattice quantum chromodynamics by applying the Lanczos algorithm to the transfer matrix and using a bootstrap generalization of the Cullum-Willoughby method to filter out spurious eigenvalues. Proof-of-principle analyses of the simple harmonic oscillator and the lattice quantum chromodynamics proton mass demonstrate that this method provides faster ground-state convergence than the “effective mass,” which is related to the power-iteration algorithm. Lanczos provides more accurate energy estimates than multistate fits to correlation functions with small imaginary times while achieving comparable statistical precision. Two-sided error bounds are computed for Lanczos results and guarantee that excited-state effects cannot shift Lanczos results far outside their statistical uncertainties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Perturbative stability of non-Abelian electric field solutions

We consider SU(2) gauge theory with a scalar field in the fundamental representation. The model is known to contain electric field solutions sourced by the scalar field that are distinct from embedded Maxwell electric fields. We examine the perturbative stability of the solution and identify a region of parameter space where the solution is stable. In the regime where the scalar field has a negative mass squared, the solution has two branches, and we identify an instability in one of the branches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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

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 OSTI2026

String-Breaking Dynamics in Quantum Adiabatic and Diabatic Processes

Confinement prohibits isolation of color charges, e.g., quarks, in nature via a process called string breaking : the separation of two charges results in an increase in the energy of a color flux, visualized as a string, connecting those charges. Eventually, creating additional charges is energetically favored, hence breaking the string. Such a phenomenon can be probed in simpler models, including quantum spin chains, enabling enhanced understanding of string-breaking dynamics. A challenging task is to understand how string breaking occurs as time elapses, in an out-of-equilibrium setting. This work establishes the phenomenology of dynamical string breaking induced by a gradual increase of string tension over time. It, thus, goes beyond instantaneous quench processes and enables tracking the real-time evolution of strings in a more controlled setting. We focus on domain-wall confinement in a family of quantum Ising chains. Our results indicate that, for sufficiently short strings and slow evolution, string breaking can be described by the transition dynamics of a two-state quantum system akin to a Landau-Zener process. For longer strings, a more intricate spatiotemporal pattern emerges: the string breaks by forming a superposition of bubbles (domains of flipped spins of varying sizes), which involve highly excited states. We finally demonstrate that string breaking driven only by quantum fluctuations can be realized in the presence of sufficiently long-ranged interactions. This work holds immediate relevance for studying string breaking in quantum-simulation experiments.

Ising model↗
NASA NTRS1986

UGC 8508 - A dwarf galaxy associated with the M 101 group

Two-color CCD photometry of UGC 8508 has resolved the system into stars. The color-magnitude diagram shows blue and red supergiants, the apparent magnitudes of the brightest stars indicate that UGC 8508 lies within 2 Mpc of the adopted 6 Mpc distance of the M 101 group. The galaxy contains a significant color gradient; star formation is confined to the central 1.5 scale lengths (0.8 kpc). UGC 8508 has a central surface brightness intermediate between bursting and quiescent dwarf irregular galaxies.

Mould, J. R.↗
DOE OSTI2025

Dark baryon black holes

We explore a novel mechanism for dark matter production through the formation of light black holes from the collapse of dark baryons in confining SU(N) gauge theories in the large- N limit. While glueballs and mesons cannot form black holes under physically reasonable conditions, we prove that for appropriate ranges of the confinement scale, quark masses, number of colors N , and dark sector temperature, dark baryons can produce Planck-scale black hole relics in the early Universe. Assuming the relics are stable, the abundance of both the dark baryon black hole population directly arising at confinement and that frozen in from dark glueball and meson pair annihilation are exponentially suppressed in N , leading to an upper limit N ≲ 100 and of a few hundred Planck units in mass for models where the black hole relics are the entirety of the dark matter. We present a detailed numerical study of the parameter space where this scenario is realized. Published by the American Physical Society 2025

Profumo, Stefano (ORCID:0000000291597556)↗
DOE OSTI2025

New state of matter between the hadronic phase and the quark-gluon plasma?

Lattice-quantum chromodynamics (QCD) simulations and theoretical arguments hint at the existence of an intermediate phase of strongly interacting matter between a confined hadron gas and a deconfined quark-gluon plasma (QGP). We qualitatively and semiquantitatively explore and differentiate the phase structures in the temperature window from the QCD pseudocritical temperature 𝑇 c ≃ 160 MeV to the pure gluonic deconfinement temperature 𝑇 d ≃ 285 MeV. We propose a three-regime picture using a hadron resonance gas description augmented with the exponential spectrum of strings, corresponding to highly excited mesons and glueballs, based on the analysis of a large number 𝑁 c of colors. We estimate the entropy density from our model to confirm that the lattice-QCD data are bracketed with three regimes, i.e., a hadron gas, a QGP, and a new phase for 𝑇 c ≲ 𝑇 ≲ 𝑇 d . In this new phase, which we name a spaghetti of quarks with glueballs (SQGBs), thermal degrees of freedom of quarks are liberated, yet gluons remain confined in glueballs. Since the Hagedorn temperature 𝑇 H ∼ 285 MeV is universal in the meson and the glueball sectors, in the infinite-𝑁 c limit, the phase diagram in the plane of the baryon chemical potential and the temperature is reduced to one with the confined and deconfined phases and quarkyonic matter at high density. At large but finite 𝑁 c , an SQGB window may open between these phases. We point out that the SQGB has interesting similarities with quarkyonic matter and that this matter in the large-𝑁 c limit is confined as measured by the interaction between heavy quarks, but behaves in other respects like a quasifree gas of quarks. As a result of the extrapolation to 𝑁 c = 3, we present a revised phase diagram with the SQGB phase bounded by thermal crossovers. Finally, we give a quantitative analysis of chiral-symmetry restoration in the SQGB phase.

Color confinement↗