We apply a constituent quark equal-velocity combination (EVC) model to study the elliptic flow (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math>) and triangular flow (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>3</mn></msub></math>) of light-flavor and single-charmed hadrons in Pb+Pb 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></mrow></math> 2.76 and 5.02 TeV. <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></math> of hadrons in the EVC model can be expressed as a linear superposition of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></math> of quarks at the same velocity as that of the hadrons. We find that available experimental data for <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>3</mn></msub></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>,</mo><mo> </mo><mi mathvariant="normal">Λ</mi><mo>,</mo><mo> </mo><mi mathvariant="normal">Ξ</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Ω</mi></math> as a function of transverse momentum (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>) can be consistently explained by the EVC formula using the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> of up/down quarks and the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> of strange quarks. In comparison with <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> data of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi></math> 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><mspace width="0.16em"></mspace><mn>2.76</mn></mrow></math> TeV, which can be naturally explained by the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> of strange quarks, explanation of the data of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi></math> mesons 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><mspace width="0.16em"></mspace><mn>5.02</mn></mrow></math> TeV requires an additional contribution of two-kaon coalescence, which indicates approximately 20% influence of final-state hadronic rescattering on <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi></math> 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><mspace width="0.16em"></mspace><mn>5.02</mn></mrow></math> TeV. Using <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>3</mn></msub></math> of light-flavor quarks obtained in studying light-flavor hadrons and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>3</mn></msub></math> of charm quarks determined from <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup></math> meson data, we apply the EVC model to predict the anisotropic flows of <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>D</mi><mrow><mi>s</mi></mrow><mo>+</mo></msubsup><mo>,</mo><mo> </mo><msubsup><mi mathvariant="normal">Λ</mi><mrow><mi>c</mi></mrow><mo>+</mo></msubsup><mo>,</mo><mo> </mo><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi></mrow><mn>0</mn></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi mathvariant="normal">Ω</mi><mrow><mi>c</mi></mrow><mn>0</mn></msubsup></math> and compare them with the available experimental data. The preliminary data for <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup><mo>,</mo><mo> </mo><msubsup><mi>D</mi><mrow><mi>s</mi></mrow><mo>+</mo></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi mathvariant="normal">Λ</mi><mrow><mi>c</mi></mrow><mo>+</mo></msubsup></math> 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></mrow></math> 5.36 TeV are found to be naturally described by the EVC model.

China

Yan-ting Feng

Rui-qin Wang

Feng-lan Shao

Jun Song

Anisotropic flows of light-flavor and charmed hadrons in Pb+Pb collisions at energies available at the CERN Large Hadron Collider

We compare the longitudinal deposition of various conserved quantities in the initial condition models of a string based (SMASH) and a saturation based (McDipper) approach. SMASH has been shown to work reasonably well at lower collision energies as an initial condition for the SMASH-vHLLE hybrid approach, while McDipper, based on the color-glass-condensate, works well in the regime of perturbative quantum chromodynamics. The two models are capable of providing longitudinally resolved initial conditions, which is essential for three-dimensional hydrodynamical simulations. The goal of this study is to interface the different regions of applicability of the two models, to investigate the initial state dynamics in the intermediate energy regime. We analyze the deposition of transverse energy, charge and baryon number across a large range of collision energies (62.4 GeV to 5.02 TeV) and find that, while they are good agreement at lower energies, their energy and baryon deposition differs substantially at higher center of mass energies.

Germany

Lucas Constantin

Spain

Oscar Garcia-Montero

Niklas Götz

Hannah Elfner

3D initial-state dynamics across scales: A comparative study of saturation and string-based descriptions

We investigate the exclusive semileptonic decays of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Λ</mi><mo>→</mo><mi>p</mi><msup><mi>ℓ</mi><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo>¯</mo></mover><mi>ℓ</mi></msub><mspace width="4pt"></mspace><mrow><mo>(</mo><mi>ℓ</mi><mo>=</mo><mi>e</mi><mo>,</mo><mi>μ</mi><mo>)</mo></mrow></mrow></math> within the standard model using the light-front quark model. The transition form factor behaviors of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Λ</mi><mo>→</mo><mi>p</mi></mrow></math> are obtained from the effective treatment of nonvalence contributions in addition to the valence ones in the Drell-Yan-West frame due to the Bethe-Salpeter formalism. Based on these form factors, we obtain that the branching ratios of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Λ</mi><mo>→</mo><mi>p</mi><msup><mi>e</mi><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo>¯</mo></mover><mi>e</mi></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><msup><mi>μ</mi><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo>¯</mo></mover><mi>μ</mi></msub></mrow></math>, including nonvalence contributions, are around <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>8.32</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1.31</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math>, which are consistent with the latest measurements from the BESIII Collaboration, respectively. Our results indicate that nonvalence contributions can play a non-negligible role in the semileptonic baryon decays within the light-front framework.

Chong-Chung Lih

Chao-Qiang Geng

Semileptonic decays of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Λ</mi><mo>→</mo><mi>p</mi><msup><mi>ℓ</mi><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo>¯</mo></mover><mi>ℓ</mi></msub></mrow></math> in light-front dynamics

The neutron-skin thickness in neutron-rich nuclei has traditionally been measured using low-energy hadronic and electronic scatterings at hadronic level. In this paper, we propose an alternative probe to the neutron-skin thickness through deep-inelastic scattering in high-energy electron-ion collisions, leveraging the intrinsic correlation between final-state jet charge distribution and initial-state partonic distributions in nucleons. Specifically, we demonstrate the sensitivity of jet charge distribution to the neutron skin-thickness and density profile in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mo>+</mo><mi>Pb</mi></mrow></math> collisions with varying centralities as determined using Glauber model, and in isobar collisions of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mo>+</mo><mi>Ru</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mo>+</mo><mi>Zr</mi></mrow></math>. We predict a strong suppression of positive jet charge distribution and an enhancement for negative jet charge distribution in peripheral electron-ion collisions, revealing the neutron-skin effect. Premised on the effective determination of centrality, this proposal can also be extended to photon and Z-boson tagged jet charge distribution in proton-nucleus collisions at the Large Hadron Collider, providing another similar access to neutron-skin structure.

Shan-Liang Zhang

Enke Wang

Xin-Nian Wang

Hongxi Xing

Probing the neutron skin thickness through jet charge in deep-inelastic scattering

It is well known that nonrelativistic or semirelativistic constituent quark models can describe a large number of the meson and baryon properties with surprising accuracy. In this work, we study the Killingbeck potential using the WKB approximation in the constituent quark model. The implicit approximate solutions for the energy eigenvalues, together with analytical expressions for the root-mean-square radii and the probability densities at the origin, of the Schrödinger equation are obtained by using appropriate quantization conditions. Finally, we discuss applications to double-heavy-meson spectroscopy within the Killingbeck potential.

Cheng-Qun Pang

Lhamo Chosto

Ya-Rong Wang

Zhi-Bin Gao

Hao Chen

Yu-Long Kang

Wei Li

WKB approximation under a Killingbeck potential and its application to double-heavy-meson spectroscopy

The observed fluid behavior of the matter produced in heavy ion and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions implies that the strings stretched between the constituents of the projectile and target should have a hard core giving rise to a repulsion between them. It is shown that in these collisions there are two critical string densities, one corresponding to the well-studied percolation of strings and another to the percolation of the hard core of the strings. These two critical densities are related to two critical temperatures, one <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>T</mi><mspace width="4pt"></mspace><mo>≈</mo><mspace width="4pt"></mspace><mn>160</mn></mrow></math> MeV would correspond to the restoration of chiral symmetry and partial deconfinement and a second transition <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>T</mi><mspace width="4pt"></mspace><mo>≈</mo><mspace width="4pt"></mspace><mn>220</mn></mrow></math> MeV form the fluid behavior of quantum chromodynamics matter strongly interacting to a quasi free gas of quarks and gluons. This argument is supported by the recently published results on the sudden increase in the degrees of freedom above the deconfinement temperature in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>A</mi><mtext>−</mtext><mi>A</mi></mrow></math> collisions [Mishra et al., <a href="http://dx.doi.org/10.1016/j.nuclphysa.2024.122865">Nucl. Phys. A 1046, 122865 (2024)</a>].

C. Pajares

United States

R.P. Scharenberg

B.K. Srivastava

Existence of a second phase transition in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>A</mi><mtext>−</mtext><mi>A</mi></mrow></math> collisions at energies available at the CERN Large Hadron Collider: A physical interpretation

We consider nonequilibrium evolution of non-Gaussian fluctuations in a hydrodynamic system undergoing a boost-invariant expansion described by Bjorken flow. We derive the evolution equations for two- and three-point velocity correlators using the effective field-theory framework and present analytical solutions for them. We show that the average Landau frame is better suited for studying non-Gaussian fluctuations of velocity when relativistic effects are important. In the Bjorken background, the average Landau frame corresponds to the density frame. We demonstrate that the three-point correlators depend nonlinearly on the nonequilibrium dynamics of the two-point functions and exhibit nontrivial effects such as memory. The importance of these effects in the context of the search for the QCD critical point via fluctuations is discussed.

Gökçe Başar

Shuo Song

Non-Gaussian hydrodynamic fluctuations in an expanding relativistic fluid

The energy-energy correlator (EEC) inside jets is a sensitive observable for studying jet modification in the quark-gluon plasma. However, its interpretation in heavy-ion collisions remains challenging, requiring a consistent understanding of jet evolution across multiple dynamical scales together with a proper treatment of the background subtraction. In this work, we employ an updated CoLBT-hydro framework in which a medium scale <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>Q</mi><mi>M</mi></msub><mo>=</mo><mn>2.0</mn></mrow></math> GeV is introduced to separate the vacuum and in-medium stages of the parton shower, enabling a more self-consistent treatment of jet evolution. Using a theoretical background subtraction within the model, the resulting simulation reproduces the recent CMS measurement of the in-jet EEC and, through a decomposition of the different contributions, highlights the impact of medium modification on the observable. To further validate the experimental procedure, we also implement the CMS mixed-event background-subtraction method directly in the simulation and find that the results are consistent with those obtained with the theoretical background subtraction. Using <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>-ranked jets in each event, we further investigate the dependence of medium modification on the in-medium path length, reflected in the different EECs of leading and subleading jets. Finally, we explore the dependence of the leading-jet EEC on the dijet rapidity gap as a signal of the jet-induced diffusion wake.

Zhong Yang

Raghav Kunnawalkam Elayavalli

Energy-energy correlators inside single inclusive jets in heavy-ion collisions with the CoLBT-hydro model

<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>t</mi></msub></math>-differential quantity <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>v</mi><mn>2</mn></msub><mrow><mo>(</mo><msub><mi>p</mi><mi>t</mi></msub><mo>)</mo></mrow></mrow></math> is meant to measure elliptic flow manifested by a dense QCD medium formed in high-energy nucleus-nucleus collisions. Elliptic flow may be referred to more neutrally as a cylindrical quadrupole component of the transverse motion of particle sources within a collision. As defined, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>v</mi><mn>2</mn></msub><mrow><mo>(</mo><msub><mi>p</mi><mi>t</mi></msub><mo>)</mo></mrow></mrow></math> relies on an implicit assumption that almost all produced particles emerge from a single source. This article describes a detailed study of the algebraic structure of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>v</mi><mn>2</mn></msub><mrow><mo>(</mo><msub><mi>p</mi><mi>t</mi></msub><mo>)</mo></mrow></mrow></math>. A procedure is developed to derive a common monopole boost (“radial flow”) value and quadrupole <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>t</mi></msub></math> spectra for several hadron species. The method is applied to <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>v</mi><mn>2</mn></msub><mrow><mo>(</mo><msub><mi>p</mi><mi>t</mi></msub><mo>)</mo></mrow></mrow></math> data for four hadron species from 2.76-TeV Pb-Pb collisions. According to available <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>v</mi><mn>2</mn></msub><mrow><mo>(</mo><msub><mi>p</mi><mi>t</mi></msub><mo>)</mo></mrow></mrow></math> data the assumption of a single dominant particle source within <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>A</mi></mrow><mtext>−</mtext><mrow><mi>A</mi></mrow></math> collisions is unjustified. Combined with a previous study of quadrupole amplitude variation for 200-GeV <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mtext>−</mtext><mi>p</mi></mrow></math> collisions these results demonstrate that quadrupole structure is related to a novel QCD process separate from projectile-nucleon dissociation and jet production. Given quadrupole evolution it is unlikely that a hydrodynamic description is relevant to that process.

Thomas A. Trainor

Quadrupole spectra derived from 2.76-TeV Pb-Pb identified-hadron <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>v</mi><mn>2</mn></msub><mrow><mo>(</mo><msub><mi>p</mi><mi>t</mi></msub><mo>)</mo></mrow></mrow></math> data

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.

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