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.

China

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

We develop the theoretical framework for semi-inclusive deep-inelastic scattering on a polarized spin-1 target and apply it to scattering on the polarized deuteron with spectator nucleon tagging. In Part I (this article) we present the general form of the semi-inclusive cross section and polarization observables for the spin-1 target. A relativistically covariant formulation in terms of four-vectors and invariant polarization parameters is employed. The target polarization is described by a spin density matrix with vector and tensor polarization. The spin and azimuthal angle dependence of the semi-inclusive cross section is derived and parametrized in terms of invariant structure functions. To validate the result, the structure functions are expressed as photon-target helicity amplitudes with known symmetry properties. The expressions presented here are kinematic (no assumptions about particle production dynamics) and valid in all regions of the deep-inelastic final state (current and target fragmentation regions). In Part II (following article), we consider deep-inelastic scattering on the polarized deuteron with spectator nucleon tagging as a special case of target fragmentation. The semi-inclusive structure functions are computed by separating nuclear and hadronic structure, and the polarization observables are explored as functions of the tagged nucleon momentum.

United States

W. Cosyn

C. Weiss

Semi-inclusive deep-inelastic scattering on a polarized spin-1 target. I. Cross section and spin observables

We develop the theoretical framework for semi-inclusive deep-inelastic scattering on a polarized spin-1 target and apply it to scattering on the polarized deuteron with spectator nucleon tagging. In Part I (previous article), we present the general form of the semi-inclusive cross section and polarization observables for the spin-1 target. In Part II (this article), we consider deep-inelastic scattering on the polarized deuteron with spectator nucleon tagging as a special case of target fragmentation. Methods of light-front quantization are employed to separate nuclear and hadronic structure in the high-energy process and achieve a composite description. The light-front wave function of the polarized deuteron is obtained from a rotationally covariant three-dimensional wave function in the center-of-mass frame of the proton-neutron system. The tagged structure functions are computed in the impulse approximation. The momentum and spin distribution of the active nucleon are controlled by the deuteron polarization and the detected spectator momentum (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>D</mi><mo>/</mo><mi>S</mi></mrow></math> wave ratio). The cross section and spin asymmetries are evaluated for general deuteron polarization (vector and tensor, longitudinal and transverse) as functions of the spectator momentum. Tensor-polarized spin asymmetries of order unity are achieved for spectator momenta of approximately 300 MeV, which select configurations with a large <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math> wave. Sum rules for the tagged spin structure functions are derived. The results can be used for simulations of spectator tagging in future polarized fixed-target experiments (Jefferson Lab) or at the Electron-Ion Collider.

Semi-inclusive deep-inelastic scattering on a polarized spin-1 target. II. Deuteron and spectator nucleon tagging

The thermal modification of the exclusive decay <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>K</mi><mn>1</mn><mo>+</mo></msubsup><mrow><mo>(</mo><mn>1270</mn><mo>)</mo></mrow><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup></mrow></math> in a hot hadronic medium is studied. The decay amplitude is constructed from effective hadronic interactions dominated by the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ρ</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>K</mi><mo>*</mo></msup></math>-pole contributions, thereby enabling a Dalitz-level analysis of the three-body decay in the medium. Thermal effects associated with partial chiral-symmetry restoration are incorporated through a phenomenological interpolation toward vector–axial-vector degeneracy near the chiral crossover. As the temperature increases, the reduction of the parent <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>K</mi><mn>1</mn></msub></math> mass strongly compresses the available three-body phase space, leading to substantial deformation of the Dalitz distribution and invariant-mass spectra, as well as to a pronounced suppression of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi mathvariant="normal">Γ</mi><mrow><msub><mi>K</mi><mn>1</mn></msub><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup></mrow></msub><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></math>. As a further step toward future transport-based phenomenological comparisons, Normalized shape observables are introduced to quantify the thermal evolution of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>K</mi><mo>*</mo></msup></math>-dominated <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>π</mi><mi>K</mi></mrow></math> region, the upper-edge weight of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>π</mi><mi>π</mi></mrow></math> spectrum, and the compactification of the Dalitz population. The dominant effect identified in the present framework is therefore kinematic: thermal phase-space reduction in the strange axial-vector channel. These results suggest that the exclusive <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>K</mi><mn>1</mn></msub><mrow><mo>(</mo><mn>1270</mn><mo>)</mo></mrow></mrow></math> channel may provide a useful qualitative probe of in-medium strange axial-vector dynamics near the pseudocritical region.

South Korea

Seung-il Nam

Thermal modification of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>K</mi><mn>1</mn></msub><mrow><mo>(</mo><mn>1270</mn><mo>)</mo></mrow><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup></mrow></math> in a hot hadronic medium

In the extended Linear-<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math> Model (eLSM), the chiral phase structure of meson states, including pseudoscalars (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>J</mi><mrow><mi>p</mi><mi>c</mi></mrow></msup><mo>=</mo><msup><mn>0</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></mrow></math>), scalars (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>J</mi><mrow><mi>p</mi><mi>c</mi></mrow></msup><mo>=</mo><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></mrow></math>), vectors (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>J</mi><mrow><mi>p</mi><mi>c</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></mrow></math>), and axial vectors (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>J</mi><mrow><mi>p</mi><mi>c</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></mrow></math>), is investigated with the mean-field approximation. A systematic comparison between SU(3) and SU(4) configurations is provided. It has been found that the estimations of meson masses derived from SU(4) eLSM are more congruent with experimental values than those derived from SU(3) eLSM. Consequently, we conclude that an increase in quark degrees of freedom significantly enhances the accuracy of meson mass simulations. We investigate the effect of temperature on the masses of various meson states calculated in the SU(3) and SU(4) eLSM. After establishing all the fitting parameters, the temperature dependence of meson masses shows that although various meson states exhibit unique patterns in their mass changes with temperature, they all seem to share a similar range of dissolution temperatures. This means that the critical temperature that marks the phase transition from hadrons to quarks appears to vary slightly depending on the meson states. In this regard, we find that the quarkonium states, formed by a quark and its antiquark, are largely unaffected by variations in the temperature.

JINR

A. Friesen

Yu. Kalinovsky

Saudi Arabia

S.O. Allehabi

Egypt

N.M. Rfeek

A.A. Alshehri

A. Tawfik

Temperature dependence of the masses of various meson states: A comparative study in the SU(3) and SU(4) extended linear-<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math> models

Using the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>HYDJET</mi><mrow><mo>+</mo><mo>+</mo></mrow></mrow></math> model, we study the production of multistrange particles <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>ϕ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Ω</mi><mo>)</mo></math> 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></mrow></math> 11.5, 19.6, 27, 39, and 200 GeV as functions of transverse momentum and centrality. The model calculations employ earlier freeze-out hypersurfaces for multistrange particle production and are compared with STAR experimental data. Results indicate that the ++ model demonstrates a better agreement with experimental data for multistrange particles at higher energies, particularly in relation to early thermal freeze-out. Meanwhile, the default version performs more accurately for lighter, nonstrange particles at the same energy scales. We also analyze identified particle and mixed particle ratios, providing insights into strangeness enhancement. The results provide additional constraints on parton energy loss models, contributing to a more precise determination of the transport properties of hot and dense QCD matter.

India

Gauri Devi

Satya Ranjan Nayak

B.K. Singh

Particle production 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>11.5</mn><mo>−</mo><mn>200</mn><mspace width="0.16em"></mspace><mi>GeV</mi></mrow></math> using the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>HYDJET</mi><mrow><mo>+</mo><mo>+</mo></mrow></mrow></math> framework

The global spin polarization of hyperons in heavy-ion collisions have been investigated by including spin-correlation effects among their constituent quarks. The available data on global spin polarizations of hyperons and spin alignments of vector mesons provide constraints on phase-space functions of the spin polarization and correlation. These constraints can lead to inequalities under some approximations, which might provide possible clues for the presence of quark spin correlation inside hyperons at lower collision energies.

Italy

Lucia Oliva

Qun Wang

Germany

Xin-Nian Wang

Quark spin correlation inside hyperons

As an extended and more complete version of the primary QCD nucleation model presented in [<a href="http://dx.doi.org/10.1103/PhysRevC.95.024907">Phys. Rev. C 95, 024907 (2017)</a>], the new model introduces explicitly the transition balance and formulates it in both macroscopic and microscopic descriptions. The microscopic description of the transition balance in QCD nucleation is implemented in a kinetic parton cascade model and tested for a first-order phase transition from gluons to pions in a one-dimensional expansion with Bjorken boost invariance.

Tianzhe Zhou

Qiuze Sun

Jin Hu

Carsten Greiner

Zhe Xu

Transition balance in QCD nucleation

We present the yield, average transverse momentum, and collective flow calculations of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup></math> resonances 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>19.6</mn></mrow></math>, 14.5, and 7.7 GeV using the AMPT model. It is found that, due to hadronic rescattering, the decay daughters of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup></math> interact with other particles in the medium, causing the yield of reconstructable <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup></math> to be significantly suppressed, especially at low transverse momentum. The model results are compared with recent experimental data from Phase-II of the Beam Energy Scan (BES-II) program at the Relativistic Heavy-Ion Collider. The string-melting version of the AMPT model successfully reproduces the measured <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><mo>/</mo><mi>K</mi></mrow></math> ratios at all three analyzed collision energies. Interestingly, AMPT calculations that exclude the hadronic phase nevertheless provide a reasonable description of the data, thereby challenging the conventional interpretation that hadronic rescattering is the primary mechanism responsible for suppressing the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><mo>/</mo><mi>K</mi></mrow></math> ratio in central heavy-ion collisions. In addition, we find that the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><mo>/</mo><mi>K</mi></mrow></math> ratio appears to be largely insensitive to the lifetime of the hadronic phase, whereas the average transverse momentum, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>〈</mo><msub><mi>p</mi><mi>T</mi></msub><mo>〉</mo></mrow></math>, of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup></math> shows a strong dependence, increasing significantly as the lifetime of the hadronic phase becomes longer. We further show that the directed flow <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><msub><mi>v</mi><mn>1</mn></msub><mo>)</mo></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup></math> mesons is strongly influenced by hadronic rescattering, whereas the elliptic flow <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><msub><mi>v</mi><mn>2</mn></msub><mo>)</mo></math> exhibits only weak sensitivity to hadronic effects. These results establish <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup></math> directed flow as a sensitive probe of the late-stage hadronic medium in heavy-ion collisions. These model calculations therefore provide valuable insight into the underlying physics governing the observed experimental results at RHIC.

Pranjal Barik

Kadambini Menduli

Aswini Kumar Sahoo

Md. Nasim

<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup></math> meson production using a multiphase transport model at RHIC BES energies

The production of <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> baryons 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></mrow></math> TeV is investigated within the quark recombination framework, including the energy loss of light and charm quarks inside the hot and dense medium. The model simultaneously describes the transverse momentum (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>) spectra of <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> baryons, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>/</mo><msup><mi>D</mi><mn>0</mn></msup></mrow></math> yield ratio, which is attributed to the dominance of the quark recombination mechanism in the quark-gluon plasma), and the second harmonic coefficient of <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> baryons with emphasis on the effects of minijets on the azimuthal anisotropy. Furthermore, we extend the theoretical calculation to <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>2.76</mn></mrow></math> TeV and make predictions for <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> baryons and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>/</mo><msup><mi>D</mi><mn>0</mn></msup></mrow></math> yield ratio. The simultaneous description of the yield, baryon-to-meson ratio, and azimuthal anisotropy further validates that the recombination model is an effective hadronization mechanism in heavy-ion collisions.

Jing-Zong Zhang

Lilin Zhu

Hadronization of <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi mathvariant="normal">Λ</mi><mrow><mi>c</mi></mrow><mo>+</mo></msubsup></math> baryons from a recombination model in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Pb</mi><mo>+</mo><mi>Pb</mi></mrow></math> collisions at energies available at the CERN Large Hadron Collider