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DOE OSTI2020

Test Results of the First Two Full-Length Quadrupole Magnets for the LHC Hi Lumi Upgrade

The future high luminosity (Hi-Lumi) upgrade of the Large Hadron Collider (LHC) at CERN will include eight (plus two spares) 8.4 m-long cryostatted cold masses which will be components of the triplets for two LHC insertion regions. Each cold mass will consist of two 4.2 m long Nb 3 Sn high gradient quadrupole magnets, designated MQXFA, with aperture 150 mm and operating gradient 132.6 T/m, for a total of twenty magnets. Before assembling and testing the final cold masses at Fermilab, the twenty component quadrupoles will be tested first at the ver-tical superconducting magnet test facility of the Superconducting Magnet Division at Brookhaven National Laboratory (BNL), in superfluid He at 1.9 K and to 18.0 kA, to meet LHC operational requirements. The first two full-length prototype quadrupole magnets, MQXFAP1 and MQXFAP2, have been tested at BNL. This paper reports on the quench test and training results of these magnets, and also the retest of the first prototype, rebuilt and designated as MQXFAP1b. We note the test results of these magnets will be important for validating the MQXFA design.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Collins function for pion-in-jet production in polarized pp collisions: a test of universality and factorization

We present an updated study of the Collins azimuthal asymmetries for pion-in-jet production in polarized pp collisions. To this aim, we employ a recent extraction of the transversity and Collins fragmentation functions from semi-inclusive deep inelastic scattering and e + e - annihilation into hadron pairs processes, obtained within a simplified transverse momentum dependent (TMD) approach at leading order in the strong coupling constant α s . In the present case we adopt a collinear configuration for the initial state, keeping transverse momentum effects only in the fragmentation mechanism. Our theoretical estimates, when compared against 200 GeV and 510 GeV data from the STAR Collaboration, show a generally good agreement for the distributions in the transverse momentum of the jet, the pion longitudinal momentum fraction and its transverse momentum with respect to the jet direction. While not being a proof, due the assumptions and limitations behind the entire approach, these findings corroborate the hypothesis of TMD factorization for such processes as well as of the universality of the Collins function and, once again, of a reduced impact of the proper TMD evolution on azimuthal asymmetries. We will also present predictions based on an extraction of the Collins and transversity distributions where information from data on single spin asymmetry for inclusive pion production in p ↑ p collisions is included through a Bayesian reweighting procedure.

Azimuthal asymmetries↗
DOE OSTI2022

Na 22 activation level measurements of fused silica rods in the LHC target absorber for neutrals compared to simulations

The Target Absorbers for Neutrals (TANs) are located in a high intensity radiation environment inside the tunnel of the Large Hadron Collider (LHC). TANs are positioned about 140 m downstream from the beam interaction points. Seven 40-cm long fused silica rods with different dopant specifications were irradiated in the TAN by the Beam RAte of Neutrals (BRAN) detector group during p + p data taking from 2016 to 2018 at the LHC. The peak dose delivered to the fused silica rods was 18 MGy. We report measurements of the 22 Na activation of the fused silica rods carried out at the University of Illinois at Urbana-Champaign and Argonne National Laboratory. At the end of the irradiation campaign, the maximum 22 Na activity observed was A = 21 kBq/cm 3 corresponding to a density, ρ = 2.5 x 10 12 /cm 3 , of 22 Na nuclei. FLUKA Monte Carlo simulations have been performed by the CERN FLUKA team to estimate 22 Na activities for the irradiated BRAN rod samples. The simulations reproduce the 22 Na activity profile measured along the rods, with a 35% underestimation of the experimental measurement results.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Hadronic Vacuum Polarization for the Muon 𝑔 − 2 from Lattice QCD: Long-Distance and Full Light-Quark Connected Contribution

We present results for the dominant light-quark connected contribution to the long-distance window of the hadronic vacuum polarization (HVP) contribution to the muon 𝑔 − 2 from lattice quantum chromodynamics. Specifically, with a new determination of the lattice scale on MILC’s physical-mass HISQ ensembles, using the Ω− baryon mass, we obtain a result of 𝑎$^{𝑙⁢𝑙,LD}_{𝜇}$⁡(conn) = 400.2⁢(2.3) stat ⁢(3.7) syst ⁢[4.3] total × 10 −10 . Summing this result with our recent determinations of the light-quark connected contributions to the short- and intermediate-distance windows, we obtain a subpercent precision determination of the light-quark-connected contribution to HVP of 𝑎$^{𝑙⁢𝑙}_{𝜇}$⁡(conn) = 655.2⁢(2.3) stat ⁢(3.9) syst ⁢[4.5]total×10 −10 . Finally, as a consistency check, we verify that an independent analysis of the full contribution is in agreement with the sum of individual windows. We discuss our future plans for improvements of our HVP calculations to meet the target precision of the Fermilab 𝑔 − 2 experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Investigation of low-energy particle remnants in high-energy collisions at the LHC with a skipper-CCD detector

We deployed the Mobile Skipper Testing Apparatus ∼33 m away from the Compact Muon Solenoid collision point, the first skipper-CCD detector probing low-energy particles produced in high-energy collisions at the Large Hadron Collider. In this work, we search for beam-related events using data collected in 2024 during beam-on and beam-off periods. The dataset corresponds to integrated luminosities of 113.3 fb −1 and 1.54 nb −1 for the proton-proton and Pb-Pb collision periods, respectively. We report observed event rates in a model-independent framework across two ionization regions: ≤ 20⁢𝑒 − and > 20⁢𝑒 − . For the low-energy region, we perform a likelihood analysis to test the null hypothesis of no beam-correlated signal. We found no significant correlation during proton-proton and Pb-Pb collisions. For the high-energy region, we present the energy spectra for both collision periods and compare event rates for images with and without luminosity. We observe a slight increase in the event rate following the Pb-Pb collisions, coinciding with a rise in the single-electron rate, which will be investigated in future work. Using the low-energy proton-proton results, we place 95% confidence level constraints on the mass-millicharge parameter space of millicharged particles. Overall, the results in this work demonstrate the viability of skipper-CCD technology to explore new physics at high-energy colliders and motivate future searches with more massive detectors.

Cervantes-Vergara, Brenda A. [Fermi National Accel↗
DOE OSTI2019

Cryogenic RF tests of US LARP DQW SPS-series cavities

Crab cavities are one of the several components included in the luminosity upgrade of the Large Hadron Collider (HL-LHC). For nominal operation, the cavities have to provide a nominal deflecting kick of 3.4 MV per cavity in Continuous Wave operation at 2 K. The requirement for an unjacketed cavity – bare cavity equipped with Higher-Order Mode (HOM) filters and field antenna – is to reach at least a deflecting voltage of 4.1 MV (20% margin) with the heat load to the 2 K bath below 10 W. Cryogenic RF tests confirmed the required performances in bare cavities, with several cavities exceeding the required voltage by more than 50%. However, the first tests of a Double-Quarter Wave (DQW) cavity with one out of three HOM filters did not reach the required voltage. The present paper describes the studies and tests conducted to understand the limiting factor in the operation of a DQW cavity with HOM filters in the most up-to-date prototypes produced in the US and based on the DQW SPS-series design. The recipe to meet the performance specification for a bare DQW cavity with HOM filters and exceed the voltage requirement by more than 35% is discussed.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Resonant and random excitations on the proton beam in the Large Hadron Collider for active halo control with pulsed hollow electron lenses

We present the results of numerical simulations and experimental studies about the effects of resonant and random excitations on proton losses, emittances, and beam distributions in the Large Hadron Collider (LHC). In addition to shedding light on complex nonlinear effects, these studies are applied to the design of hollow electron lenses (HEL) for active beam halo control. In the High-Luminosity Large Hadron Collider (HL-LHC), a considerable amount of energy will be stored in the beam tails. To control and clean the beam halo, the installation of two hollow electron lenses, one per beam, is being considered. In standard electron-lens operation, a proton bunch sees the same electron current at every revolution. Pulsed electron beam operation (i.e., different currents for different turns) is also considered, because it can widen the range of achievable halo removal rates. For an axially symmetric electron beam, only protons in the halo are excited. If a residual field is present at the location of the beam core, these particles are exposed to time-dependent transverse kicks and to noise. We discuss the numerical simulations and the experiments conducted in 2016 and 2017 at injection energy in the LHC. The excitation patterns were generated by the transverse feedback and damping system, which acted as a flexible source of dipole kicks. Proton beam losses, emittances, and transverse distributions were recorded as a function of excitation patterns and strengths. The resonant excitations induced rich dynamical effects and nontrivial changes of the beam distributions, which, to our knowledge, have not previously been observed and studied in this detail. We conclude with a discussion of the tolerable and achievable residual fields and proposals for further studies.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Gold-gold luminosity increase in RHIC for a beam energy scan with colliding beam energies extending below the nominal injection energy

The Beam Energy Scan phase II (BES-II), performed in the Relativistic Heavy Ion Collider (RHIC) from 2019 to 2021, explored the phase transition between quark-gluon plasma and hadronic gas. BES-II exceeded the goal of a fourfold increase in the average luminosity over that achieved during Beam Energy Scan phase I (BES-I), at five gold beam energies: 9.8, 7.3, 5.75, 4.59, and 3.85 GeV / nucleon. This was accomplished by addressing several beam dynamics effects, including intrabeam scattering, beam-beam, space charge, beam instability, and field errors induced by superconducting magnet persistent currents. Some of these effects are especially detrimental at low energies. BES-II achievements are presented, and the measures taken to improve RHIC performance are described. These measures span the whole RHIC complex, including ion beam sources, injectors, beam lifetime improvements in RHIC, and operation with the world’s first bunched beam Low Energy RHIC electron Cooler (LEReC).

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

First JSNS 2 measurement of the electron neutrino flux using the 12 C⁡(𝜈 𝑒 ,𝑒 − )⁢ 12 N g.s. reaction

JSNS2 (J-PARC Sterile Neutrino Search at J-PARC Spallation Neutron Source) is an experiment searching for sterile neutrinos through the observation of ν¯μ→ν¯e appearance oscillations, using neutrinos produced by muon decay-at-rest. A key aspect of the experiment involves accurately understanding the neutrino flux and the quantities of pions and muons, which are progenitors of (anti)neutrinos, given that their production rates have yet to be measured. We present the first electron-neutrino flux measurement using C12(νe,e−)12Ng.s. reaction in JSNS2, yielding a flux of (6.7±1.6(stat)±1.7(syst))×10−9 cm−2 proton−1 at the JSNS2 detector location, located at 24 meters distance from the mercury target. This flux measurement is consistent with predictions from simulations based on hadron models.

Particle decays↗
DOE OSTI2025

Search for decays of the Higgs boson into scalar particles decaying into four or six 𝑏 quarks using 𝑝⁢𝑝 collisions at $\sqrt{𝑠}$ = 13 TeV with the ATLAS detector

A search for exotic decays of the Higgs boson 𝐻 into new scalar or pseudoscalar particles that subsequently decay into 𝑏-quarks is presented. The search considers 𝑍⁢𝐻 production with several decay scenarios for the Higgs boson; first to a pair of identical scalars, 𝐻 → 2⁢𝑎 → 4⁢𝑏, second to a pair of scalars with different masses (𝑚 𝑎⁢1 < 𝑚 𝑎⁢2 ), either directly, 𝐻 → 𝑎 1 ⁢𝑎 2 → 4⁢𝑏, or via a longer decay chain, 𝐻 → 𝑎 1 ⁢𝑎 2 → 3⁢𝑎 1 → 6⁢𝑏. The analysis uses proton-proton collision data at $\sqrt{𝑠}$ = 13 TeV collected with the ATLAS detector at the Large Hadron Collider, corresponding to an integrated luminosity of 140 fb −1 . No significant excess above the Standard Model prediction is observed. The search sets upper limits at 95% confidence level on the ratio of the Higgs boson production cross section to the SM prediction times the branching ratio of Higgs bosons decaying into 4⁢𝑏 or 6⁢𝑏, between 4% and 25% for 𝜎⁡(𝑍⁢𝐻)/𝜎 SM ⁡(𝑍⁢𝐻) × ℬ⁡(𝐻→ 2⁢𝑎→ 4⁢𝑏), between 24% and 38% for 𝜎⁡(𝑍⁢𝐻)/𝜎 SM ⁡(𝑍⁢𝐻) × ℬ⁡(𝐻 → 𝑎 1 ⁢𝑎 2 → 4⁢𝑏), and between 10% and 20% for 𝜎⁡(𝑍⁢𝐻)/𝜎 SM ⁡(𝑍⁢𝐻) × ℬ⁡(𝐻→𝑎 1⁢ 𝑎 2 → 3⁢𝑎 1 → 6⁢𝑏), depending on the masses of the scalar particles.

extensions of Higgs sector↗
DOE OSTI2025

Project FELICIA - A probe to survey the RHIC magnet beampipe diameter for EIC beam screen insertion

The Electron Ion Collider (EIC) Hadron Storage Ring (HSR) will reuse many of the existing superconducting (SC) magnets of the RHIC storage rings. To comply with the beamline vacuum requirements in more demanding operational scenarios, the beampipe of the RHIC SC magnets will be equipped with low surface impedance, low secondary electron yield (SEY) beam screens. The installation of these beam screens will be done with the SC magnets as installed today, thus making it a critical operation for a timely EIC installation. The beam screen inner dimensions must be maximized to retain enough aperture to the beam. On the other hand, keeping enough clearance between the screen and the beampipe is critical to ensure a smooth beam screen installation. A survey probe was designed and built to measure the inner diameter of several RHIC SC magnets in-situ and provide critical data for the beam screen design optimization. This paper reports on the design of the probe and the results from the survey campaign.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Measurement of Charged Current Inclusive $\bar{V}_\mu$ Interactions and 2p2h Contribution Using the NOvA Near Detector

More precise measurements of the scattering of antineutrinos on nuclei in the few GeV region of incident energy, $E_{\nu}$, can reveal new aspects of $v/\bar{v}$ interactions and of nuclear structure, while providing information crucial to continued progress by neutrino oscillation experiments. This Thesis reports an investigation of charged current $\bar{v}_\mu$ interactions in the predominantly hydrocarbon medium of the NOvA Near Detector. The data are obtained with the detector exposed to a narrow-band $\bar{v}$ µ beam with spectral peak at E ν = 2.0 GeV, for a total accumulated exposure of 12.5×10$^{20}$ protons-on-target. The analysis expresses results in terms of three-momentum transfer,|$\vec{q}$| and available hadronic energy, $E$ avail . These variables approximate (q 0 , |$\vec{q}$|), the variables used in theoretical treatments of lepton scattering on multi-nucleon systems such as in 2-particle-2-hole (2p2h) processes. This Thesis delivers two core measurements: Firstly, the double-dierential cross section $d^2σ/d|\vec{q} |dE_{avail}$ for inclusive CC $\bar{v}_\mu$ interactions in the NOvA detector medium is obtained. The cross section has a roughly gaussian shape in its projection onto |$\vec{q}$|, while being largely concentrated at values of $E$ avail below 100 MeV. The single diferential cross sections dσ/d|$\vec{q}$| and dσ/dE avail are also obtained, and are compared to predictions based on the GENIE v3.0.6 neutrino generator augmented with four different implementations of 2p2h reactions. Secondly, the contribution of 2p2h reactions to the CC inclusive scattering sample is determined. Its presence is characterized in terms of double-differential and single-differential cross sections. The latter 2p2h distributions are compared to predictions from two experimental data-tune models and from two theory-based models, namely the SuSAv2 model and the Valencia model. Both of the theoretical models underpredict the measured cross-section strength and predict a shape for dσ/d|$\vec{q}$| that is flatter than the measured shape. Thus, this Thesis provides new information about CC antineutrino-nucleus scattering in the vicinity of Eν ~ 2 GeV, and it highlights improvements that are needed in theoretical treatments of 2p2h reactions.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Physics Division Strategic Plan Fiscal Years 2020-2024

The vision of the Physics Division (PHY) at Argonne National Laboratory is to continue enhancing its role as a world-leading institution in basic nuclear physics research and its applications. Key to this vision is for PHY to continue to safely and effectively operate and evolve the capabilities of the Argonne Tandem Linac Accelerator System (ATLAS) facility to best serve its users. ATLAS is the Department of Energy (DOE) accelerator facility for low-energy nuclear physics research. The research carried out by PHY covers many themes in contemporary science but can be distilled into five areas of focus. These themes are interconnected, with continuously evolving synergies between the various groups and facilities in PHY and the broader Laboratory. This five-year strategic plan serves to illustrate our current capabilities and new directions related to these five areas of focus (ATLAS also develops an independent strategic plan): Accelerator research and design. The goal of this theme is to design, fabricate, test, and implement novel accelerator systems, with a focus on high-intensity ion and electron systems. These R&D activities have led to enhancements in the ATLAS accelerator system. Among others, the division’s accelerator systems are in use or planned for use at Fermilab, the Advanced Photon Source, and in a broad variety of applications at the Facility for Rare Isotope Beams (FRIB). Atom trapping and fundamental symmetries. The goal of this theme is to explore and exploit the uses of advanced laser cooling and trapping techniques to manipulate atoms. There are three main areas of focus. First is in the application of the atom trap trace analysis (ATTA) technique for age determination of groundwater and ice by using radio-krypton dating. The next two trapping-based programs involve tests of fundamental symmetries in nature: the cooling and trapping of radium-225 with the aim of determining limits on an observation of its electric dipole moment and precision measurements of the beta decay properties of helium-6 to set limits on the tensor coupling constant. This is complemented by measurements of similar properties in lithium-8 and boron-8. Nuclear astrophysics. The goal of this theme is to enhance our understanding of how elements are created in the universe via explosive nucleosynthesis and how stars evolve. To meet the challenges of this theme, many of the capabilities of ATLAS are being enhanced, including the development of new beams through a new in-flight separator (RAISOR) and the anticipated neutron-generator upgrade of the Californium Rare Isotope Breeder Upgrade facility (nuCARIBU). These are coupled to state-of-the-art instruments such as the Canadian Penning Trap, Helical Orbit Spectrometer, Gammasphere, GRETINA, Multi-Sampling Ionization Chamber, the Fragment Mass Analyzer, and Argonne Gas-filled Fragment Analyzer, and a new low-background experimental area for decay studies. Nuclear structure. The goal of this theme is to understand the structure of nuclei, both stable and radioactive, in terms of single-particle properties, their shapes, and the dynamics governing reactions between them. These include questions such as what are the limits of nuclear stability and what are the properties of super heavy nuclei. As with the nuclear astrophysics theme, the capabilities of ATLAS, guided by the ATLAS user community, are continuously being enhanced to this end. The Division has strategic initiatives to play a leading role in the development of instrumentation and research programs at the FRIB. Quantum chromodynamics (QCD) and hadron physics. The goal of this theme is to lead major research programs focused on revealing the quark and gluon structure of protons, neutrons, nuclei, and short-lived mesons and baryons. These involve major programs at Jefferson Lab, Fermilab, and smaller facilities. They are complemented by theoretical endeavors centered on the question of how hadrons and their properties emerge from QCD. Out of these activities arise strategic initiatives to play a major role in the forthcoming Electron-Ion Collider (EIC).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Search for electroweak production of vector-like leptons in $\tau$-lepton and b-jet final states in pp collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector

A search for pair-production of vector-like leptons is presented, considering their decays into a third-generation Standard Model (SM) quark and a vector leptoquark ( U 1 ) as predicted by an ultraviolet-complete extension of the SM, referred to as the ‘4321’ model. Given the assumed decay of U 1 into third-generation SM fermions, the final state can contain multiple τ-leptons and b-quarks. This search is based on a dataset of pp collisions at $\sqrt{s}=13$ TeV recorded with the ATLAS detector during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of up to $140~\textrm{fb}^{-1}$. No significant excess above the SM background prediction is observed, and 95% confidence level limits on the cross-section times branching ratio are derived as a function of the vector-like lepton mass. A lower observed (expected) limit of 910 GeV (970 GeV) is set on the vector-like lepton mass. Additionally, the results are interpreted for a supersymmetric model with an R-parity violating coupling to the third-generation quarks and leptons. Lower observed (expected) limits are obtained on the higgsino mass at 880 GeV (940 GeV) and on the wino mass at 1170 GeV (1170 GeV).

Aad, G. [CPPM, Aix-Marseille Université, CNRS/IN2P↗
DOE OSTI2025

Search for new physics in final states with semivisible jets or anomalous signatures using the ATLAS detector

A search is presented for hadronic signatures of beyond the Standard Model (BSM) physics, with an emphasis on signatures of a strongly coupled hidden dark sector accessed via resonant production of a 𝑍′ mediator. The ATLAS experiment dataset collected at the Large Hadron Collider from 2015 to 2018 is used, consisting of proton-proton collisions at $\sqrt{𝑠}$ = 13 TeV and corresponding to an integrated luminosity of 140 fb −1 . The 𝑍′ mediator is considered to decay to two dark quarks, which each hadronize and decay to showers containing both dark and Standard Model particles, producing a topology of interacting and noninteracting particles within a jet known as “semivisible.” Machine learning methods are used to select these dark showers and reject the dominant background of mismeasured multijet events, including an anomaly detection approach to preserve broad sensitivity to a variety of BSM topologies. A resonance search is performed by fitting the transverse mass spectrum based on a functional form background estimation. No significant excess over the expected background is observed. Results are presented as limits on the production cross section of semivisible jet signals, parametrized by the fraction of invisible particles in the decay and the 𝑍′ mass, and by quantifying the significance of any generic Gaussian-shaped mass peak in the anomaly region.

particle dark matter↗
DOE OSTI2025

Search for events with one displaced vertex from long-lived neutral particles decaying into hadronic jets in the ATLAS muon spectrometer in 𝑝⁢𝑝 collisions at $\sqrt{𝑠}$ = 13 TeV

A search for events with one displaced vertex from long-lived particles using data collected by the ATLAS detector at the Large Hadron Collider is presented, using 140 fb −1 of proton-proton collision data at $\sqrt{𝑠}$ =13 TeV recorded in 2015–2018. The search employs techniques for reconstructing vertices of long-lived particles decaying into hadronic jets in the muon spectrometer displaced between 3 m and 14 m from the primary interaction vertex. The observed number of events is consistent with the expected background and limits for several benchmark signals are determined. A scalar-portal model and a Higgs-boson-portal baryogenesis model are considered. A dedicated analysis channel is employed to target Z-boson associated long-lived particle production, including an axionlike particle and a dark photon model. For the Higgs boson model, branching fractions above 1% are excluded at 95% confidence level for long-lived particle proper decay lengths ranging from 5 cm to 40 m. For the photophobic axionlike particle model considered, this search produces the strongest limits to date for proper decay lengths greater than 𝒪⁡(10) cm.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

First Measurement of the |𝑡| Dependence of Incoherent 𝐽/𝜓 Photonuclear Production

The first measurement of the cross section for incoherent photonuclear production of J/ψ vector mesons as a function of the Mandelstam |t| variable is presented. The measurement was carried out with the ALICE detector at midrapidity, |y|<0.8, using ultraperipheral collisions of Pb nuclei at a center-of-mass energy per nucleon pair of $\sqrt{s_{NN}}$ = 5.02 TeV. This rapidity interval corresponds to a Bjorken-x range (0.3–1.4)×10 -3 . Cross sections are given in five |t| intervals in the range 0.04 < |t |< 1 GeV 2 and compared to the predictions by different models. Models that ignore quantum fluctuations of the gluon density in the colliding hadron predict a |t| dependence of the cross section much steeper than in data. The inclusion of such fluctuations in the same models provides a better description of the data.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Entanglement, trace anomaly, and confinement in QCD

We formulate confinement in quantum chromodynamics (QCD) as an entropic surface phenomenon. Quark and gluon quantum information is localized on a transverse, entangling two-sphere of radius 𝑅 𝐸⁢𝐸 ; at this radius the QCD vacuum—partitioned by a hadron into interior and exterior regions—reaches its maximal entanglement entropy. Lattice-QCD determinations of the scalar (trace) gravitational form factors fix both 𝑅 𝐸⁢𝐸 and the transverse trace-anomaly density 𝜌 ℎ ⁡(𝑅 𝐸⁢𝐸 ), yielding a parameter-free slope 𝑐 ℎ = 8⁢𝜋 2 ⁢𝑅𝑆$^2_{𝐸⁢𝐸}$𝜌 ℎ ⁡(𝑅 𝐸⁢𝐸 ) and a mechanical entropy 𝑆 𝐸⁢𝐸 ⁡(𝑦) = 𝑐 ℎ ⁢𝑦 that grows linearly with rapidity 𝑦. The entropy gradient ∂ 𝑅 𝑆 𝐸⁢𝐸 changes sign at 𝑅 𝐸⁢𝐸 : it pushes colored degrees of freedom outward for 𝑟 <𝑅 𝐸⁢𝐸 and pulls them inward for 𝑟 >𝑅 𝐸⁢𝐸 , thereby localizing them on the codimension-2 entangling two-sphere Σ ⊥ = 𝑆$^2_{𝑅_{𝐸⁢𝐸}}$ (which, in the infinite-momentum frame (IMF), projects onto the transverse plane)—the “information wall.” This provides a high-energy (large-𝑦) entropic confinement diagnostic that complements—rather than replaces—Wilson’s area-law criterion, which probes long-distance dynamics near the rest frame (𝑦 → 0). Imposing unitarity on an entropic ansatz for the amplitude yields 𝜎⁡(𝑠) ∝ 𝑦 𝛿 . World data favor 𝛿 = 2 for elastic 𝑝⁡𝑝⁡($𝑝\bar{⁡𝑝}$) scattering and heavy-quark photoproduction, whereas 𝜙 photoproduction favors a softer 𝛿 = 0.387. All extracted cross sections remain well below the Froissart-Martin bound. These results provide a confinement criterion quantified directly from nonperturbative QCD inputs, unifying the trace anomaly, entanglement entropy, and high-energy scattering within a single quantitative framework.

Color confinement↗