Coherent hard exclusive reactions on light nuclei provide access to their quark and gluon structure and enable three-dimensional tomography of these complex systems. We study deeply virtual Compton scattering on a helium-4 target, including both kinematic twist-3 and twist-4 corrections, as well as next-to-leading-order corrections to the twist-2 amplitude in the strong coupling <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>α</mi><mi>s</mi></msub></math>. We show that these contributions are crucial for achieving a precise description of the data and, as a result, obtain the first tomographic image of the helium-4 nucleus at the quark-gluon level.

United States

France

V. Martínez-Fernández

B. Pire

Poland

P. Sznajder

J. Wagner

Coherent deeply virtual Compton scattering on <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi>He</mi><mprescripts></mprescripts><none></none><mn>4</mn></mmultiscripts></math> beyond leading power

We present a new formulation for the mean-field propagation part of relativistic quantum molecular dynamics, simulating an <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math>-body system of interacting Gaussian wave packets via Lorentz scalar and vector potentials. Covariant equations of motion are derived based on the principle of least action with a weak form of mass-shell conditions and time-fixation constraints defined with respect to a chosen foliation. However, as is common with traditional relativistic quantum molecular dynamics, the dynamics exhibits a residual dependence on the chosen foliation, which is unavoidable because a finite number of interacting degrees of freedom is not strictly compatible with relativity. Nevertheless, we show that this dependence remains small for physically reasonable choices of the foliation in practical applications. By introducing a new approximation method to the spatial integral in the equations of motion, these covariant equations of motion can be solved with a computational cost comparable to that of conventional noncovariant quantum molecular dynamics. Furthermore, the new equations of motion accurately estimate the density-dependent potential, as demonstrated through comparison of the forces with the numerical integration. We apply them to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math>-body systems interacting via the Skyrme-type potentials or the relativistic mean field to simulate heavy-ion collisions. Our results show that the derived equations of motion provide a robust approximation to the dynamics of the full numerical integrations.

Japan

Yasushi Nara

Asanosuke Jinno

Koichi Murase

Covariant formulation of relativistic quantum molecular dynamics for a system of interacting wave packets

The simultaneous observation of strong sequential bottomonium suppression and small azimuthal anisotropy constrains the time scale and geometry of quarkonium dissociation in relativistic heavy-ion collisions. This work investigates an early-time contribution in which strong pre-equilibrium color fields generate an effective proper-acceleration scale and an associated causal length. The maximal acceleration is fixed through the phenomenological anchoring assumption <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>T</mi><mi>U</mi><mo movablelimits="true" form="prefix">max</mo></msubsup><mo>≃</mo><msub><mi>T</mi><mi>c</mi></msub></mrow></math>, without identifying the kinematic Unruh scale with an equilibrium temperature. The survival probability is described by an event-averaged one-scale exponential ansatz. With no state-by-state adjustment, the resulting horizon component gives a quantitatively reasonable description of the LHC centrality dependence. For the directly measured <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Υ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo></mrow></math>-to-<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Υ</mi><mo>(</mo><mn>1</mn><mi>S</mi><mo>)</mo></mrow></math> double ratio, the fixed horizon term supplies a substantial part of the relative suppression, while the data require an additional state-dependent late-stage factor. A minimal one-parameter effective quark-gluon plasma (QGP) attenuation gives a quantitative multistage description. At RHIC, the absolute <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub></math> central values lie below the isolated horizon component, while the relative <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>2</mn><mi>S</mi></mrow></math>-to-<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn><mi>S</mi></mrow></math> suppression remains compatible with the predicted state-size hierarchy within present uncertainties. Because the proposed early factor is local and scalar, it gives the exact leading-order null contribution <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>v</mi><mn>2</mn><mi>H</mi></msubsup><mo>=</mo><mn>0</mn></mrow></math> within this construction, consistent with current CMS measurements.

Taiwan

Yi Yang

Causal-horizon scaling of quarkonium suppression in strong QCD fields

Equations of a boost-invariant and cylindrically symmetric perfect hydrodynamics are solved numerically for initial conditions inspired by the wounded nucleon model. The energy-momentum and spin tensors are used in the form that describes a relativistic massive gas governed by Boltzmann statistics. In contrast to one-dimensional boost-invariant expansion, we find a coupling between the azimuthal and longitudinal components of the electric and magnetic components of the spin polarization tensor. This feature is similar to that found earlier for the Gubser symmetry; however, our treatment allows for a more general form of initial conditions and expansion geometry. Defining the freeze-out hypersurface by the constant temperature condition, we evaluate the Pauli-Lubański four-vector and find that for the assumed geometry the only nonzero total polarization may be induced by the longitudinal component of the magnetic part of the spin polarization tensor, coupled with the azimuthal electric component. The obtained results may serve as a reference point for more realistic models of hydrodynamic expansion.

Zbigniew Drogosz

Wojciech Florkowski

Jakub Witkowski

Boost-invariant and cylindrically symmetric perfect spin hydrodynamics

We study fluctuations and correlations of conserved charges in QCD using a string-based description of the hadronic mass spectrum. Mesons and baryons are modeled as open relativistic strings with quark-antiquark and quark-diquark endpoints, respectively, leading to an exponential Hagedorn growth of states with a limiting temperature fixed by the string tension. We find that continuous Hagedorn spectra constrained by experimentally established hadrons underestimate net-baryon number fluctuations obtained in lattice QCD (LQCD) calculations. By extracting the Hagedorn string spectrum directly from lattice QCD through a fit to the second-order net-baryon number susceptibility, we obtain a consistent description of a broad set of fluctuations of conserved charges from LQCD with the Hagedorn temperature <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>T</mi><mi>H</mi></msub><mo>≃</mo><mn>323</mn><mspace width="0.16em"></mspace><mi>MeV</mi></mrow></math>, without introducing additional free parameters. Our results provide thermodynamic evidence in support of a string quark-diquark picture of baryons in the confined phase of QCD.

Michał Marczenko

Krzysztof Redlich

Evidence for quark-diquark structure of baryons from fluctuations of conserved charges

Jet substructure studies at the CERN Large Hadron Collider have been used to constrain parton distribution functions, test perturbative quantum chromodynamics, measure the strong-coupling constant, and probe the properties of the quark-gluon plasma. We extend these studies to lower collision energies at the BNL Relativistic Heavy Ion Collider (RHIC) and present a feasibility and strategy study for the sPHENIX experiment. In this work, we perform a <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal" mathsize="small">PYTHIA8</mi></math> based Monte Carlo study of jet substructure in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mo>+</mo><mi>p</mi></mrow></math> collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>200</mn></mrow></math> GeV with selection criteria adapted for a realistic measurement at sPHENIX. We consider jet substructure observables such as jet angularities and the primary Lund plane projection. In particular, we quantify the discriminating power of jet angularities for quark/gluon and light versus heavy flavor jets, and demonstrate how these observables can serve as experimentally accessible proxies for flavor separation at RHIC. We further show that the primary Lund plane exhibits a characteristic suppression pattern consistent with the dead cone effect for heavy quarks, and outline a concrete measurement strategy at sPHENIX based on a combination of heavy-flavor jet tagging and differential substructure observables.

Zhuoheng Yang

Finland

Oleh Fedkevych

Roli Esha

Simulation-based study of jet substructure of light- and heavy-flavor jets in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mo>+</mo><mi>p</mi></mrow></math> collisions at 200 GeV

We investigate the elliptic-flow splitting between prompt <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> mesons within a heavy-quark transport framework with sequential hadronization, in which <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> forms at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1.2</mn><mspace width="0.16em"></mspace><msub><mi>T</mi><mi>c</mi></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>c</mi></msub></math>. We present model calculations for the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>-differential <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> and predictions for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo>/</mo><msup><mi>D</mi><mn>0</mn></msup></mrow></math> yield ratio in O-O <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>0</mn><mo>–</mo><mspace width="0.16em"></mspace><mn>20</mn><mo>%</mo></mrow></math> collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>5.36</mn></mrow></math> TeV, where preliminary ALICE data are available. The sequential scenario reproduces the observed <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>v</mi><mn>2</mn></msub><mrow><mo>(</mo><msup><mi>D</mi><mn>0</mn></msup><mo>)</mo></mrow><mo>&gt;</mo><msub><mi>v</mi><mn>2</mn></msub><mrow><mo>(</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo>)</mo></mrow></mrow></math> ordering and predicts an enhanced <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo>/</mo><msup><mi>D</mi><mn>0</mn></msup></mrow></math> ratio at low <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>, whereas a simultaneous baseline yields the opposite ordering. Decomposing the hadronic splitting into its partonic components, we show that the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> ordering is driven by the late-stage flow accumulated by <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup></math>-parent charm quarks during the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1.2</mn><mspace width="0.16em"></mspace><msub><mi>T</mi><mi>c</mi></msub><mo>→</mo><msub><mi>T</mi><mi>c</mi></msub></mrow></math> interval, with hadronic rescattering essential to preserve the signal in small systems. A systematic scan across nine collision configurations spanning O-O and Pb-Pb centralities reveals a universal linear scaling between the hadronic splitting and the partonic flow increment accumulated during this window. This establishes the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>D</mi><mn>0</mn></msup><mo>–</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></mrow></math> flow splitting as a hadronization chronometer of the QGP at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>5.36</mn></mrow></math> TeV.

China

Hui Du

Xiao-Wei Hao

Wei Dai

Germany

Jiaxing Zhao

Ben-Wei Zhang

Enke Wang

System-size dependence of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>D</mi><mn>0</mn></msup><mtext>−</mtext><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></mrow></math> flow splitting from early <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> formation at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>5.36</mn></mrow></math> TeV

In this study, we calculate the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>γ</mi><mi>Z</mi></mrow></math>-exchange contribution to elastic <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mi>p</mi></mrow></math> scattering at large momentum transfer within perturbative quantum chromodynamics (pQCD). We present analytical expressions for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>γ</mi><mi>Z</mi></mrow></math>-exchange contributions to the amplitudes. We also estimate the asymptotic behaviors of the amplitude contributions and of the physical quantity <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mtext>PV</mtext></msub></math> at high momentum transfer. These asymptotic behaviors determine the subtraction order in the dispersion relations (DRs) satisfied by the amplitudes. At high <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>Q</mi><mn>2</mn></msup></math> beyond the forward limit, our pQCD analysis shows that this subtraction order is fixed by the high-<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ν</mi></math> behavior of the amplitude coefficients <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>c</mi><mi>i</mi><mrow><mi>γ</mi><mi>Z</mi><mo>,</mo><mtext>PV</mtext></mrow></msubsup></math>, and that <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>c</mi><mrow><mn>3</mn><mo>,</mo><mi>A</mi></mrow><mrow><mi>γ</mi><mi>Z</mi><mo>,</mo><mtext>PV</mtext></mrow></msubsup></math> requires a once-subtracted DR. Within the present pQCD framework and the adopted proton distribution amplitudes, these high-energy results also provide nontrivial constraints on low-energy DR assumptions.

Qian-Qian Guo

Hui-Yun Cao

Hai-Qing Zhou

<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>γ</mi><mi>Z</mi></mrow></math>-exchange contribution in elastic <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mi>p</mi></mrow></math> scattering by perturbative QCD

Heavy-ion collisions produce final states with thousands to tens of thousands of particles, making their simulation among the most computationally intensive tasks in high-energy nuclear physics. We present a fast, high-fidelity generative model for heavy-ion events based on a score-driven diffusion process and the point-edge transformer architecture within the OmniLearn framework. A two-stage training strategy is performed: Stage 1 trains on lower-multiplicity O-O collisions, allowing the model to learn a stable event-and-particles representation; this is followed in Stage 2 by fine tuning on challenging high-multiplicity Pb-Pb collisions. We benchmark the generator with a broad set of closure checks, including agreement of event- and particle-level observables in one and two dimensions, flow consistency reconstructed from the generated particles, end-to-end jet finding with FastJet including key jet and substructure observables, and a classifier-based application to quantify the sample fidelity. The results are promising, showing that a compact generative model can produce realistic, high-multiplicity heavy-ion events, at a level that makes local-scale generation for heavy-ion collisions at high energies a practical goal.

Rita Sadek

Vinicius Mikuni

Mateusz Płoskoń

Diffusion-based point-cloud generation of heavy-ion events

We systematically investigate the scaling properties of the transverse momentum spectra for pions, kaons, and protons in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Au</mi><mo>+</mo><mi>Au</mi></mrow></math> collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>7.7</mn></mrow></math>, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV, as well as in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">U</mi><mo>+</mo><mi mathvariant="normal">U</mi></mrow></math> collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>193</mn><mspace width="0.16em"></mspace><mi>GeV</mi></mrow></math>, across different centrality classes, using experimental data from the collaborations at the Relativistic Heavy Ion Collider (RHIC). Universal scaling emerges when the particle transverse momentum spectra are scaled by global physical quantities, i.e., the average total particle multiplicity and mean transverse momentum, confirming recent scaling findings from the data at the Large Hadron Collider (LHC) by the ExTrEMe Collaboration. The scaling behavior breaks down in the high <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi mathvariant="normal">T</mi></msub></math> region and in peripheral collisions. We provide a natural explanation for these observations in the framework of a blast-wave-type model built upon the Cooper-Frye formula. Furthermore, we demonstrate the equivalence between the scaling found by the ExTrEMe Collaboration and the Hwa-Yang scaling, which was proposed two decades ago.

Xi-Yao Guo

Hua Zheng

Wen-Chao Zhang

Li-Lin Zhu

Xing-Quan Liu

Zhi-Guang Tan

Dai-Mei Zhou

Ben-Hao Sa

Deciphering the universal scaling of particle transverse momentum spectra in heavy-ion collisions