The early stage of a heavy-ion collision is marked by rapid entropy production and the transition from a gluon saturated initial condition to a plasma of quarks and gluons that evolves hydrodynamically. However, during the early times of the hydrodynamic evolution, the chemical composition of the QCD medium is still largely unknown. We present a study of quark chemical equilibration in the (Q)GP using a novel model of viscous hydrodynamic evolution in partial chemical equilibrium. Motivated by the success of gluon saturated initial condition models, we initialize the QCD medium as a completely gluon dominated state. Local quark production during the hydrodynamic phase is then simulated through the evolution of time-dependent fugacities for each independent quark flavor, with the timescales set as free parameters to compare different rates of equilibration. We present the results of complete heavy-ion collision simulations using this partial chemical equilibrium model, and show the effects on hadronic and electromagnetic observables. In particular, we show that the development of flow is sensitive to the equilibration timescale, providing an empirical way to probe the chemical equilibration of the QCD medium.

United States

Andrew Gordeev

Steffen A. Bass

Berndt Müller

Jean-François Paquet

Quark flavor equilibration of the quark-gluon plasma

Using the Monte Carlo <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>HYDJET</mi><mo>+</mo><mo>+</mo></mrow></math> model, we investigate the transverse momentum (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>) spectra of heavy-flavor hadrons, namely <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup><mo>,</mo><mo> </mo><msup><mover><mi>D</mi><mo>¯</mo></mover><mn>0</mn></msup><mo>,</mo><mo> </mo><msup><mi>D</mi><mo>+</mo></msup><mo>,</mo><mo> </mo><msup><mi>D</mi><mo>−</mo></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math>, along with the nuclear modification factors of <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"><msup><mi>D</mi><mo>±</mo></msup></math> in Au <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo></math> Au 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>200</mn></mrow></math> GeV RHIC energy across various centrality bins. This work extends the earlier study by relaxing the assumption of identical chemical and thermal freezeout and by exploring the effect of a higher chemical freezeout temperature relative to thermal freezeout. The study also explores the centrality and mass dependence of the charm enhancement factor (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>γ</mi><mi>c</mi></msub></math>). Furthermore, we investigate medium-induced energy loss, particle-antiparticle asymmetry, and the role of fragmentation in the hadronization process. The <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>HYDJET</mi><mo>+</mo><mo>+</mo></mrow></math> model, with its default parameters, is unable to reproduce heavy hadron yields due to their early thermal freezeout and initial state production of heavy quarks. Therefore, a systematic tuning of model parameters is performed to improve the overall agreement with experimental data. Additionally, to assess the performance of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>HYDJET</mi><mo>+</mo><mo>+</mo></mrow></math> model relative to other theoretical approaches, its results are compared with the TAMU, SUBATECH, Torino, and Duke models, for which corresponding simulation data are available. This study shows a decreasing trend in <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>γ</mi><mi>c</mi></msub></math> from central to peripheral collisions. Moreover, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>γ</mi><mi>c</mi></msub></math> increases with increasing charm-hadron mass. The model approximately reproduces the experimental data of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math> spectra at low and intermediate <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>. However, it overestimates the data at high <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>, indicating a need for improvements in modeling the energy loss of heavy quarks. The 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 <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub></math>) for <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup></math> mesons exhibit significant suppression at high <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>. At low <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub><mo>,</mo><mo> </mo><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub></math> results show deviations from the data, reflecting limitations in the model where coalescence becomes important. The antiparticle-to-particle ratios are consistent with experimental data, whereas mixed-particle ratios are underestimated, revealing the model's limitation in estimating the baryon-to-meson enhancement.

India

Sunidhi Saxena

Rajiv Gupta

Gauri Devi

Ajay Kumar

Heavy hadron production in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Au</mi><mo>+</mo><mi>Au</mi></math> collisions at a center-of-mass energy of <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>200</mn></mrow></math> GeV

We propose a new method to investigate the existence and location of the conjectured high-temperature critical point of strongly interacting matter via contours of constant entropy density. By approximating these lines as a power series in the baryon chemical potential <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>μ</mi><mi>B</mi></msub></math>, one can extrapolate them from first-principle results at zero net-baryon density, and use them to locate the quantum chromodynamics (QCD) critical point, including the associated first-order and spinodal lines. As a proof of principle, we employ currently available continuum-extrapolated lattice data from the Wuppertal-Budapest collaboration to find a critical point at a temperature and a baryon chemical potential of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>T</mi><mi>c</mi></msub><mo>=</mo><mn>114.3</mn><mo>±</mo><mn>6.9</mn></mrow></math> MeV and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>μ</mi><mrow><mi>B</mi><mo>,</mo><mi>c</mi></mrow></msub><mo>=</mo><mn>602.1</mn><mo>±</mo><mn>62.1</mn></mrow></math> MeV, respectively, at expansion order <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="script">O</mi><mo>(</mo><msubsup><mi>μ</mi><mi>B</mi><mn>2</mn></msubsup><mo>)</mo></mrow></math>. We advocate for a more precise determination of the required expansion coefficients via lattice QCD simulations as a means of pinpointing the location of the critical endpoint in the phase diagram of strongly interacting matter.

Hitansh Shah

Brazil

Mauricio Hippert

Jorge Noronha

Claudia Ratti

Volodymyr Vovchenko

Locating the QCD critical point through contours of constant entropy density

The evolution of nuclear excitation in electron-gold (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mspace width="0.16em"></mspace><mo>+</mo><mspace width="0.16em"></mspace><mi>Au</mi></mrow></math>) collisions at the forthcoming Electron-Ion Collider (EIC) is investigated using the beagle event generator. The EIC's collider kinematics and detector-motivated rapidity selections enable a clear separation, in the laboratory frame, of the dominant reaction stages: hard scattering, intranuclear cascade (INC), and nuclear deexcitation. A systematic study of the event-by-event mean transverse momentum fluctuation observable <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>κ</mi></math> reveals strong sensitivity to the intranuclear-cascade formation time and to nuclear geometry, with only weak dependence on the electron-beam energy. These findings indicate that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>κ</mi></math> can serve as an exploratory diagnostic for disentangling the cascade and deexcitation stages of nuclear excitation at the EIC. The pronounced sensitivity observed within the beagle framework underscores the model dependence of the present results while at the same time motivating systematic cross-model investigations to establish the broader applicability of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>κ</mi></math>. The results yield stage-resolved, testable predictions for early EIC measurements.

Niseem Magdy

Tracing the evolution of nuclear excitation at the future Electron-Ion Collider

A generalization of the phenomenological blast-wave-Tsallis-power model, recently proposed by the author for the hadrons' transverse momentum (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mtext>T</mtext></msub></math>) spectra measured at the CERN Large Hadron Collider (LHC), is developed to also describe the hadrons' <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mtext>T</mtext></msub></math>-differential elliptic flow coefficients <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> in identical nuclei collisions of different centralities. The model describes well the available data on <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mtext>T</mtext></msub></math> spectra and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> for any <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mtext>T</mtext></msub></math> of various particles, from pions to charmonia, 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 and in Xe-Xe 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> 5.44 TeV. Also, predictions for OO 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> 5.36 TeV are given. While the model is mainly targeting the energies available at the LHC, it also works at much lower energies available at the BNL Relativistic Heavy Ion Collider.

JINR

Smbat Grigoryan

Blast-wave-Tsallis-power model for <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math> spectra and elliptic flow <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> of hadrons in collisions of identical nuclei at energies available at the CERN Large Hadron Collider

This study presents a systematic investigation of the transverse-momentum differential radial flow fluctuations observable <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>v</mi><mn>0</mn></msub><mrow><mo>(</mo><msub><mi>p</mi><mi>T</mi></msub><mo>)</mo></mrow></mrow></math> in relativistic heavy-ion collisions at top Relativistic Heavy Ion Collider (<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>200</mn></mrow></math> GeV) and Large Hadron Collider (<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> and 5.02 TeV) energies. Using a multistage hydrodynamic model, this study assesses the sensitivity of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>v</mi><mn>0</mn></msub><mrow><mo>(</mo><msub><mi>p</mi><mi>T</mi></msub><mo>)</mo></mrow></mrow></math> to a wide range of physical effects, including bulk and shear viscosities, off-equilibrium corrections at particlization, the presence of a hadronic afterburner, and the nucleon size in the initial conditions. By employing complementary rescaling strategies, this study demonstrates how different physical effects leave distinct imprints on the shape of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>v</mi><mn>0</mn></msub><mrow><mo>(</mo><msub><mi>p</mi><mi>T</mi></msub><mo>)</mo></mrow></mrow></math>. A combined double-rescaling of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>v</mi><mn>0</mn></msub><mrow><mo>(</mo><msub><mi>p</mi><mi>T</mi></msub><mo>)</mo></mrow><mo>/</mo><msub><mi>v</mi><mn>0</mn></msub></mrow></math> versus <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>p</mi><mi>T</mi></msub><mo>/</mo><mrow><mo>〈</mo><msub><mi>p</mi><mi>T</mi></msub><mo>〉</mo></mrow></mrow></math> reveals a universality across a wide range of energies and model assumptions in the low-<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math> regime, a robust signature of collective behavior. This allows us to disentangle the universal dynamics of the bulk medium from model-specific features that emerge at higher <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>. These results establish <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>v</mi><mn>0</mn></msub><mrow><mo>(</mo><msub><mi>p</mi><mi>T</mi></msub><mo>)</mo></mrow></mrow></math> as a powerful and complementary observable for constraining quark-gluon plasma transport properties and initial-state granularity, offering a unique probe of the created QCD medium.

Lipei Du

Characterizing radial flow fluctuations in relativistic heavy-ion collisions at top RHIC and LHC energies

Predictions of charm-correlation functions and, more specifically, balance functions are presented in proton-proton (pp) collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mtext>NN</mtext></msub></msqrt><mo>=</mo><mn>13</mn><mspace width="0.28em"></mspace><mtext>TeV</mtext></mrow></math> based on the Pythia 8.3 event generator. Correlations are computed for identical and cross-species charmed hadrons in both minimum bias and high-<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>p</mi><mi mathvariant="normal">T</mi></msub><mspace width="0.28em"></mspace></mrow></math> biased collisions. We study the strength of correlations as a function of the number of balanced flavors and investigate the impact of variations of Pythia parameters controlling the Lund string fragmentation on the shape and strength of the correlation functions. The feasibility of measurements of the charm-balance function presented is discussed in the context of the future LHC experiments.

Oveis Sheibani

Claude Pruneau

Victor Gonzalez

Sumit Basu

Romania

Alexandru Florin Dobrin

Yash Patley

Basanta Nandi

Sadhana Dash

Probing partonic evolution and hadronization via balance functions and correlations of charmed hadrons

Background: Phenomenological relativistic models of strongly interacting systems have proved to be useful for modeling few-nucleon and few-quark systems at the few-GeV scale. They have the advantage that relativistic invariance is exact; however, satisfying cluster properties requires a complicated construction which has never been used in applications. In addition, there is no straightforward connection to local field theories. Purpose: To explore an alternative approach for constructing relativistic quantum mechanical models that addresses these two deficiencies. This work examines the general structure of the dynamical input to these models. Method: Relativistic models that address these two deficiencies can be formulated using reflection positive Euclidean kernels. Relaxing the locality requirement of the axioms of Euclidean field theories leads to a weaker form of reflection positivity. Constraints imposed by the spectral condition and cluster properties are used to determine the structure of a class of kernels satisfying this weaker form of reflection positivity. Results: The resulting kernels lead to a representation of the quantum mechanical Hilbert space in terms of Euclidean variables that has a positive norm, a set of self-adjoint Poincaré generators with a Hamiltonian satisfying cluster properties and a spectral condition. Relativistic dynamical calculations can be performed directly in the Euclidean representation without analytic continuation. Schwinger functions of a local field theory also satisfy the weakened form of reflection positivity, which provides the desired connection with local field theories. Conclusion: This work provides the structure of a large class of reflection positive kernels that can be used to test this Euclidean formulation of relativistic quantum mechanics. What is still missing is a dynamical principle that generates model kernels with the desired properties.

Gohin Shaikh Samad

W.N. Polyzou

Reflection positivity in Euclidean formulations of relativistic quantum mechanics of particles

This study investigates the color-charge dependence of parton energy loss in the quark-gluon plasma (QGP) medium and the associated relative modifications of quark and gluon jet fractions compared to vacuum, using jet axis decorrelation observables. Recent CMS jet axis decorrelation measurements in <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>PbPb</mtext></math> collisions at 5.02 TeV are interpreted using Pythia simulations with varied quark/gluon jet compositions and emulated color-charge dependent energy loss. A template-fit procedure is employed to estimate the limits on gluon jet fractions in the published CMS data and average shift in jet momentum due to quenching for quark- and gluon-initiated jets traversing the QGP. The extracted gluon jet fractions and the estimated quark and gluon energy losses based on this study of jet axis decorrelations are found to be consistent with other model calculations based on inclusive observables. This work illustrates the use of jet substructure measurements for providing constraints on the color-charge dependence of parton energy loss and offers valuable insights for jet quenching models.

Raghunath Pradhan

Olga Evdokimov

Constraining color-charge effects of partonic energy loss with jet-axis-based inclusive jet substructure measurement

We discuss the general behavior of the scattering amplitude with channel couplings near the two-body threshold. It is known that the Flatté amplitude, which is often used in the analysis of experimental data involving exotic hadrons, has some constraint in the near-threshold energy region. While the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>M</mi></mrow></math>-matrix gives the general expression of the scattering amplitude, it is not smoothly connected to the Flatté amplitude, due to the property of the determinant of the amplitude in channel space. In this paper, based on the effective field theory, we propose new parametrization of the scattering amplitude which gives the general expression near the threshold and has a well-defined limit reproducing the Flatté amplitude. We show that the nonresonant background contribution exists in the general amplitude even in the first order in the momentum. Finally, we quantitatively evaluate the cross sections by changing the strength of the background contribution. We find that the interference with the background term may induce a dip structure of the cross section near the threshold, in addition to the peak and threshold cusp structures.

Japan

Katsuyoshi Sone

Tetsuo Hyodo

General amplitude of near-threshold hadron scattering for exotic hadrons