Based on the kinetic theory with relaxation time approximation, we investigate the bulk viscosity <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>ζ</mi><mo>)</mo></math> and its ratio to shear viscosity <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>(</mo><mi>ζ</mi><mo>/</mo><mi>η</mi><mo>)</mo></mrow></math> of quark matter at finite temperature and chemical potential with the in-medium particle masses derived in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> flavor Polyakov-loop improved Nambu–Jona-Lasinio model. We explore the behaviors of specific bulk viscosity <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>(</mo><mi>ζ</mi><mo>/</mo><mi>s</mi><mo>)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>η</mi></mrow></math> across different QCD phase transitions, including the Mott phase transition, the chiral crossover, and the first-order transition with the associated metastable phase. The calculation shows that both <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>s</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>η</mi></mrow></math> are extremely small at high temperatures, approaching the nature of a conformal theory. Larger <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>s</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>η</mi></mrow></math> are derived near the chiral phase transition at finite temperature. Along the chiral crossover line, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>s</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>η</mi></mrow></math> generally increase with decreasing temperature, though <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>η</mi></mrow></math> exhibits a slight decline near the critical end point. On the boundary of the first-order transition, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>s</mi></mrow></math> shows a nonmonotonic variation with temperature. Furthermore, an additional peak structure emerges beyond the chiral phase boundary for both <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>s</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>η</mi></mrow></math>, with magnitudes even exceeding those near the chiral crossover of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>u</mi><mo>,</mo><mi>d</mi></mrow></math> quarks. Our analysis indicates this peak originates from the chiral crossover transformation of strange quark.

Chong-long Xie

Guo-yun Shao

Ming-zheng-xuan Wu

Wei-bo He

Bulk viscosity of quark matter across the QCD phase transitions

Recent theoretical analyses show that spin current can be induced by the baryon chemical potential gradient <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>∇</mi><msub><mi>μ</mi><mi>B</mi></msub></mrow></math> which becomes sizable in the fireballs created in heavy-ion collisions (HIC) at a beam energy of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="script">O</mi><mo>(</mo><mn>10</mn><mo>)</mo></mrow></math> GeV. This spin transport phenomenon can be considered as the cousin effect of the spin-Hall effect (SHE) in condensed matter systems with <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>∇</mi><msub><mi>μ</mi><mi>B</mi></msub></mrow></math> playing the role of the analogous electric field. In this letter, we study this important mechanism, which we call “baryonic SHE” or <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>∇</mi><msub><mi>μ</mi><mi>B</mi></msub></mrow></math>-induced polarization (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>∇</mi><msub><mi>μ</mi><mi>B</mi></msub></mrow></math>-IP), for differential spin polarization generation that has not been systematically explored before. We predict the signature of the baryonic SHE in HIC using a <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>)</mo><mi mathvariant="normal">D</mi></mrow></math> viscous hydrodynamic model MUSIC with a multiphase transport initial condition. We propose to use the second Fourier coefficients of the net spin polarization of Λ hyperon as sensitive probes for the baryonic SHE. Those baryonic SHE observables show a qualitative difference in sign and beam energy dependence for the situations with and without the baryonic SHE. Future experimental observation of these distinct qualitative features would provide strong evidence for the existence of this “baryonic SHE” in the hot and dense quantum chromodynamics matter.

Baochi Fu

Long-Gang Pang

Huichao Song

Yi Yin

Signatures of a baryonic spin-Hall effect in dense QCD matter

The contrast between the as-yet unmeasurable energy-loss effects in proton-nucleus collisions and the striking magnitude of the so-called high-momentum flow coefficients challenges our understanding of jet quenching mechanisms in large nucleus-nucleus collisions when applied to smaller systems. Intermediate-sized, light ion collisions will offer key insight into the system-size dependence of the interplay between jet energy loss and jet flow effects. To make quantitative predictions, we extend a semianalytic jet quenching framework by coupling it to state-of-the-art event-by-event hydrodynamics and, for the first time, incorporate pre-equilibrium energy loss via the hydrodynamic attractor. A Bayesian analysis shows that an early-time onset of energy loss is compatible with BNL Relativistic Heavy Ion Collider and CERN Large Hadron Collider measurements of jet suppression and jet elliptic flow in large systems, as well as hadron suppression, with the exception of hadron elliptic flow. Using these constraints, we predict both hadron and jet quenching observables in oxygen-oxygen collisions, finding sizable energy loss that exceeds the no-quenching baseline.

Daniel Pablos

Adam Takacs

Bayesian constraints on pre-equilibrium jet quenching and predictions for oxygen collisions

The chiral magnetic effect (CME) in relativistic heavy-ion collisions originates from a chirality imbalance among quarks within metastable QCD vacuum domains and may be linked to charge-parity violation, which is believed to play a crucial role in the matter-antimatter asymmetry of the universe. Over the past two decades, extensive experimental efforts at the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider have been devoted to the search for evidence of the CME. Recent advances have greatly improved our understanding of background contributions that can mimic CME-like signals. In particular, analyses utilizing techniques designed to suppress flow-related backgrounds indicate that the CME signal at the RHIC, if present, is small. To further investigate potential background sources, particularly those associated with strong electromagnetic fields, we estimate the contribution from coherent photon-nuclear interactions. These interactions are driven by intense electromagnetic fields produced in ultrarelativistic heavy-ion collisions, with cross sections that scale with the field strength. Notably, the polarization of the incident photons is aligned with the electric field, which is oriented along the impact parameter direction and perpendicular to the magnetic field. Consequently, such processes can generate charge-dependent correlations that mimic key features of the CME signal, yet originate from different physics mechanisms and are distinct from flow-induced backgrounds. In this study, we quantitatively assess the influence of these coherent photon-nuclear interactions on the precision measurement of the CME, aiming to improve the separation of the genuine CME signal from these background contributions.

Jing Gu

Jinhui Chen

Jie Zhao

Isolation of photon-nuclear interaction backgrounds in the search for the chiral magnetic effect in relativistic heavy-ion collisions

We investigate the inclusive <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> production in proton-proton <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>(</mo><mi>p</mi><mi>p</mi><mo>)</mo></mrow></math> collisions at center-of-mass energies <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>5.02</mn></mrow></math>, 7, and 13 TeV using the parton and hadron cascade model PACIAE 4.0. This model extends PYTHIA 8.3 by incorporating partonic and hadronic rescatterings before and after hadronization, respectively. Compared to our earlier study [K.-F. Ye et al., <a href="http://dx.doi.org/10.1103/PhysRevC.109.035201">Phys. Rev. C 109, 035201 (2024)</a>], which considered only the color-singlet processes, the present work includes both the color-singlet and color-octet contributions within the nonrelativistic QCD (NRQCD) framework. In addition to the NRQCD, we also consider the contributions from the cluster collapse and weak decays of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> hadrons. We find that the simulated inclusive <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> transverse momentum differential cross sections agree well with the experimental data at both the middle and forward rapidities. We provide a quantitative analysis of the relative contributions for different production mechanisms and their energy and rapidity dependence in the inclusive <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> production. Furthermore, we offer a quantification of the relative contributions of the various components and their energy and rapidity dependence in the NRQCD channels, including the direct production via the hard scattering and the feed-down from the decays of heavier charmonium states such as <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ψ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></math>. Finally, we examine the effects of partonic and hadronic rescatterings and offer the quantitative estimate of their impact on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> production. These results are entirely new and represent a significant step forward in understanding the mechanisms of the inclusive <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> production in high-energy <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions.

Jin-Peng Zhang

Guan-Yu Wang

Wen-Chao Zhang

Bo Feng

An-Ke Lei

Zhi-Lei She

Hua Zheng

Dai-Mei Zhou

Yu-Liang Yan

Ben-Hao Sa

Inclusive <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> productions in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><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>5.02</mn><mo>,</mo><mo> </mo><mn>7</mn><mo>,</mo><mo> </mo><mtext>and</mtext><mo> </mo><mn>13</mn><mo> </mo><mi>TeV</mi></mrow></math> with the parton and hadron cascade model PACIAE

The GlueX experiment at Jefferson Lab has observed <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></mrow></math> and, for the first time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Λ</mi><mover><mi mathvariant="normal">Λ</mi><mo>¯</mo></mover></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mover><mi mathvariant="normal">Λ</mi><mo>¯</mo></mover></mrow></math> photoproduction from a proton target at photon energies up to 11.6 GeV. The angular distributions are forward peaked for all produced pairs, consistent with Regge-like <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>-channel exchange. Asymmetric wide-angle antibaryon distributions show the presence of additional processes. In a phenomenological model, we find consistency with a double-<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>-channel exchange process where antibaryons are created only at the middle vertex. The model matches all observed distributions with a small number of free parameters. In the hyperon channels, we observe a clear distinction between photoproduction of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Λ</mi><mover><mi mathvariant="normal">Λ</mi><mo>¯</mo></mover></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mover><mi mathvariant="normal">Λ</mi><mo>¯</mo></mover></mrow></math> systems but general similarity to the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></mrow></math> system. We report both total cross sections and cross sections differential with respect to momentum transfer and the invariant masses of the created particle pairs. No narrow resonant structures were found in these reaction channels. The suppression of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>s</mi><mover><mi>s</mi><mo>¯</mo></mover></mrow></math> quark pairs relative to <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>d</mi><mover><mi>d</mi><mo>¯</mo></mover></mrow></math> quark pairs is similar to what has been seen in other reactions.

F. Afzal

M. Albrecht

M. Amaryan

S. Arrigo

V. Arroyave

A. Asaturyan

A. Austregesilo

Z. Baldwin

F. Barbosa

J. Barlow

E. Barriga

R. Barsotti

D. Barton

V. Baturin

V.V. Berdnikov

A. Berger

W. Boeglin

M. Boer

W.J. Briscoe

T. Britton

R. Brunner

S. Cao

C. Chen

E. Chudakov

G. Chung

P.L. Cole

O. Cortes

V. Crede

M.M. Dalton

D. Darulis

A. Deur

L. Dietrich

S. Dobbs

A. Dolgolenko

M. Dugger

R. Dzhygadlo

D. Ebersole

M. Edo

H. Egiyan

P. Eugenio

A. Fabrizi

C. Fanelli

S. Fang

M. Fritsch

S. Furletov

L. Gan

H. Gao

A. Gardner

A. Gasparian

D.I. Glazier

C. Gleason

B. Grube

J. Guo

J. Hernandez

K. Hernandez

N. Herrmann

N.D. Hoffman

D. Hornidge

G.M. Huber

P. Hurck

W. Imoehl

D.G. Ireland

M.M. Ito

I. Jaegle

N.S. Jarvis

T. Jeske

M. Jing

R.T. Jones

V. Kakoyan

G. Kalicy

X. Kang

V. Khachatryan

C. Kourkoumelis

A. LaDuke

I. Larin

D. Lawrence

D.I. Lersch

H. Li

B. Liu

K. Livingston

L. Lorenti

V. Lyubovitskij

H. Marukyan

V. Matveev

M. McCaughan

M. McCracken

C.A. Meyer

R. Miskimen

R.E. Mitchell

P. Moran

L. Ng

E. Nissen

S. Orešić

A.I. Ostrovidov

Z. Papandreou

L. Pentchev

K.J. Peters

L. Puthiya Veetil

S. Rakshit

J. Reinhold

Baryon–antibaryon photoproduction cross sections off the proton

Jet suppression in high-energy heavy-ion collisions results from jet energy loss and transverse-momentum broadening during jet propagation through the quark-gluon plasma (QGP). The jet cone size (<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math>) dependence of this suppression offers crucial insights into the energy loss mechanisms and QGP transport properties. In our study, we implement a comprehensive approach within the perturbative QCD parton model that incorporates both elastic and inelastic energy loss mechanisms. For elastic processes the contribution from recoiling thermal partons reduces the net in-cone energy loss for a given jet radius. For inelastic processes, we account for the angular distribution of radiated gluons, the thermalization of soft gluons, and transverse-momentum broadening. Using this framework, we calculate the jet nuclear modification factors (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub></math>) and their double ratios <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub><mrow><mo>(</mo><mi>R</mi><mo>=</mo><mn>0.2</mn><mo>–</mo><mn>1.0</mn><mo>)</mo></mrow><mo>/</mo><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub><mrow><mo>(</mo><mi>R</mi><mo>=</mo><mn>0.2</mn><mo>)</mo></mrow></mrow></math>, and systematically compare with ALICE, ATLAS, and CMS data in 0–10% and 30–50% <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Pb</mi><mo>+</mo><mi>Pb</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>5.02</mn><mspace width="0.28em"></mspace><mi>TeV</mi></mrow></math>. Numerical results show that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub></math> increases with the cone size <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> because the in-cone energy loss decreases at larger radii. Specifically, as the radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> grows, the probability for elastically scattered partons to escape the jet cone and the likelihood for radiated gluons to fall outside the cone both decrease, resulting in a net reduction of energy loss. The <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub></math> double ratios are approximately unity for small radii (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>R</mi><mo>=</mo><mn>0.4</mn></mrow></math> relative to <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>R</mi><mo>=</mo><mn>0.2</mn></mrow></math>) and at high <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>p</mi><mi mathvariant="normal">T</mi></msub><mo>≳</mo><mn>200</mn><mspace width="0.28em"></mspace><mi>GeV</mi><mo>/</mo><mi>c</mi></mrow></math>, in agreement with the data within uncertainties.

Qing-Fei Han

Man Xie

Han-Zhong Zhang

Jet cone size dependence of single inclusive jet suppression due to jet quenching in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Pb</mi><mo>+</mo><mi>Pb</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>5.02</mn><mspace width="0.28em"></mspace><mi>TeV</mi></mrow></math>

The <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>T</mi></mrow></math> matrix of the heavy quark-antiquark (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Q</mi><mover accent="true"><mi>Q</mi><mo>¯</mo></mover><mspace width="0.28em"></mspace></mrow></math>) pair interacting through a screened Cornell potential in the quark-gluon plasma is computed without employing the partial-wave expansion. This is compared with the results obtained using the conventional method of partial-wave expansion. Through a comprehensive survey over a range of screening mass and center-of-mass (c.m.) energy, which, when combined, determine the orbital angular momentum involved in the scattering, it is demonstrated that a substantial number of partial-wave terms are necessary to precisely match the full scattering amplitude directly obtained from the method without partial-wave expansion. For moderate screening masses (corresponding to one to two times the crossover transition temperature) and c.m. energy, the number of partial waves required for satisfactory matching turns out as large as 10–20, substantially larger than what one would expect based on simply measuring the magnitudes of the first few partial-wave amplitudes. This highlights the efficacy and advantage of the new method in directly obtaining the full scattering amplitude needed for further computation of physical observables, which is illustrated by comparing the calculations of heavy quark-antiquark scattering cross section and heavy quark drag coefficient between the two methods. We also employ the new method to calculate the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>T</mi></mrow></math> matrix at c.m. energies below the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Q</mi><mover accent="true"><mi>Q</mi><mo>¯</mo></mover><mspace width="0.28em"></mspace></mrow></math>mass threshold, and demonstrate the presence of bound states of different orbital quantum numbers simultaneously in a single energy scan.

Anurag Tiwari

Min He

In-medium heavy quark-antiquark <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> matrix without partial-wave expansion

I present a calculation of the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><msub><mi>σ</mi><mi>r</mi></msub><msub><mi>F</mi><mn>2</mn></msub></mfrac><mrow><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math> in a momentum-space approach using the Block-Durand-Ha parametrization of the proton structure function <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>F</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math>. The results are compared with the H1 data and extended to high inelasticity. I also examine the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><msub><mi>σ</mi><mi>r</mi></msub><msub><mi>F</mi><mn>2</mn></msub></mfrac><mrow><mo>(</mo><mfrac><msup><mi>Q</mi><mn>2</mn></msup><mi>s</mi></mfrac><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math> obtained at a fixed <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>s</mi></msqrt></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>Q</mi><mn>2</mn></msup></math> to the minimum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>Q</mi><mn>2</mn></msup><mo>/</mo><mi>s</mi></mrow></math>, comparing them with both the HERA data and the color dipole model bounds. These results and comparisons with HERA data demonstrate that the suggested method for the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>σ</mi><mi>r</mi></msub><msub><mi>F</mi><mn>2</mn></msub></mfrac></math> can be applied in analyses of the CERN Large Hadron Collider and Future Circular Collider projects. The effect of adding a simple higher twist term of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>F</mi><mn>2</mn></msub><mo>*</mo><msub><mi>H</mi><mn>2</mn></msub><mo>/</mo><msup><mi>Q</mi><mn>2</mn></msup></mrow></math> to the description of the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><msub><mi>σ</mi><mi>r</mi></msub><msub><mi>F</mi><mn>2</mn></msub></mfrac><mrow><mo>(</mo><mfrac><msup><mi>Q</mi><mn>2</mn></msup><mi>s</mi></mfrac><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math> at low-<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> and low-<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>Q</mi><mn>2</mn></msup></math> values for comparison with the color dipole bounds and the HERA data is investigated.

G.R. Boroun

Investigation of the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><msub><mi>σ</mi><mi>r</mi></msub><msub><mi>F</mi><mn>2</mn></msub></mfrac><mrow><mo>(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>/</mo><mi>s</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math> in the momentum-space approach

While hybrid approaches of relativistic <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>hydrodynamics</mi><mo>+</mo><mi>transport</mi></mrow></math> have been well established for the dynamical description of heavy-ion collisions at high beam energies, moving to lower beam energies is challenging. In this work, we propose dynamic initial conditions for the viscous hydrodynamic evolution in heavy-ion collisions at low to intermediate beam energies. They are comprised of core hadrons based on the local energy density during the preequilibrium hadronic evolution. The smash-vhlle hybrid approach is then applied to lower beam energies, achieving good agreement with measured bulk observables between <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>3</mn></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>9.1</mn><mspace width="4pt"></mspace><mi>GeV</mi></mrow></math>, thus providing theoretical guidance for the Beam Energy Scan performed by the STAR Collaboration at RHIC and the future Compressed Baryonic Matter experiment at GSI.

Renan Góes-Hirayama

Joscha Egger

Zuzana Paulínyová

Iurii Karpenko

Hannah Elfner

Pushing the hybrid approach to low beam energies with dynamic initial conditions from hadronic transport