In ultrarelativistic collisions of nuclei at the Large Hadron Collider, the created QCD environment rapidly changes, leading to a nonadiabatic evolution of the quantum states involved. Considering this, we first examine the preequilibrium state of QCD matter and its effect on the initially produced charmonium using a temperature-independent Hamiltonian. As the QCD matter reaches local thermal equilibrium, this Hamiltonian transforms to its finite temperature counterpart. To model the preequilibrium stage, we use the bottom-up thermalization approach to determine the effective temperature of the QCD matter, followed by a Gubser-type expansion for the thermalized medium. Additionally, we consider collisional damping, gluonic dissociation, and regeneration mechanisms, which specifically modify the charmonium yield in the thermalized medium. Mainly, the gluonic dissociation and collisional damping cause a reduction in the yield conversely, regeneration through gluonic deexcitation enhances the yield of charmonium. Further, we explore the combined effects of these mechanisms on the collective yield of charmonium states with transverse momentum (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>p</mi><mi mathvariant="normal">T</mi></msub></math>) and event multiplicity in the proton-proton collisions at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>. Based on our findings, we contend that the combined effects of these mechanisms can serve as a robust probe for determining the possible existence of a thermalized QCD medium in such a small collision system.

India

Captain R. Singh

Partha Bagchi

Raghunath Sahoo

Jan-e Alam

Exploring QGP-like phenomena with charmonia in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mo>+</mo><mi>p</mi></math> collisions at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>

The recent observation of global spin polarization of $$\Lambda $$ ( $$\bar{\Lambda }$$ ) hyperons and the spin alignment of $$\phi $$ and $$K^{*0}$$ vector mesons create remarkable interest in investigating the particle polarization in the relativistic fluid produced in heavy-ion collisions at GeV/TeV energies. Among other sources of spin polarization phenomena, the Debye mass of a medium plays a crucial role in particle polarization. Any modification brought to the effective mass due to the temperature, strong magnetic field ($\textit{eB}$), baryonic chemical potential ( $$\mu _{B}$$ ), medium anisotropy ( $$\xi $$ ), and vorticity, etc., certainly affects the particle spin polarization. In this work, we explore the global hyperon spin polarization and the spin alignment of vector mesons corresponding to the strong magnetic field, baryonic chemical potential, and medium anisotropy. We find that the degree of spin polarization is flavor-dependent for hyperons. Meanwhile, vector meson spin alignment depends on the hadronization mechanisms of initially polarized quarks and anti-quarks. Medium anisotropy significantly changes the degree of spin polarization compared to the magnetic field and baryon chemical potential.

Bhagyarathi Sahoo

Captain Singh

Impact of strong magnetic field, baryon chemical potential, and medium anisotropy on polarization and spin alignment of hadrons

The hot and dense hadronic medium formed during the heavy-ion collisions at the Relativistic Heavy Ion Collider and Large Hadron Collider energies can show thermoelectric effects in the presence of temperature gradients and nonzero baryon chemical potential. In this article, we study the thermoelectric coefficients of an interacting hot and dense hadron gas using the relativistic Boltzmann transport equation under the relaxation time approximation. We discuss the thermoelectric properties within different frameworks of hadron resonance gas models. In the presence of an external magnetic field, the thermoelectric coefficients become anisotropic, which leads to Hall-like thermoelectric coefficients, namely Nernst coefficients, along with the magneto-Seebeck coefficients. For the first time, we also estimate the Thomson coefficient of the medium, which comes into the picture due to the temperature dependence of the Seebeck coefficient of the medium. In the context of studying the thermoelectric generator performance, we calculate the values of the thermoelectric figure of merit of the medium.

Kamaljeet Singh

Kshitish Kumar Pradhan

Dushmanta Sahu

Thermoelectric effects of an interacting hadron gas in the presence of an external magnetic field

In relativistic heavy-ion collisions, the formation of a deconfined and thermalized state of partons, known as quark-gluon plasma (QGP), leads to enhanced production of strange hadrons in contrast to proton-proton (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math>) collisions, which are taken as baseline. This observation is known as strangeness enhancement in heavy-ion collisions and is considered one of the important signatures that can signify the formation of QGP. However, in addition to strangeness enhancement, recent measurements hint at observing several heavy-ion-like features in high multiplicity <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions at energies available at the CERN Large Hadron Collider. Alternatively, event shape observables, such as transverse spherocity, transverse sphericity, charged particle flattenicity, and relative transverse activity classifiers, can fundamentally separate hard interaction-dominated jetty events from soft isotropic events. These features of event shape observables can probe the observed heavy-ion-like features in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions with significantly reduced selection bias and can bring all collision systems on equal footing. In this article, we present an extensive summary of the strange particle ratios to pions as a function of different event classifiers using the PYTHIA 8 model with color reconnection and rope hadronization mechanisms to understand the microscopic origin of strangeness enhancement in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions and also prescribe the applicability of these event classifiers in the context of strangeness enhancement. Charged-particle flattenicity is found to be most suited for the study of strangeness enhancement, and it shows a quantitative enhancement similar to that seen for the analysis based on the number of multiparton interactions.

Suraj Prasad

CERN

Sushanta Tripathy

Neelkamal Mallick

Probing strangeness with event topology classifiers in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions at energies available at the CERN Large Hadron Collider with the rope hadronization mechanism in PYTHIA

We study the diffusion properties of an interacting hadron gas and evaluate the diffusion coefficient matrix for the baryon, strange, electric, and charm quantum numbers. For the first time, this study sheds light on the charm current and estimates the diffusion matrix coefficient for the charmed states by treating them as a part of the quasithermalized medium. We explore the diffusion matrix coefficient as a function of temperature and center-of-mass energy. A van der Waals–like interaction is assumed between the hadrons, including attractive and repulsive interactions. The calculation of diffusion coefficients is based on relaxation time approximation to the Boltzmann transport equation. A good agreement with available model calculations is observed in the hadronic limit. To conclude the study, we discuss, with a detailed explanation, that charm fluctuation is expected to be a better tool for probing the QCD critical point.

Kangkan Goswami

Jayanta Dey

Can charm fluctuation be a better probe to study the QCD critical point?

Relativistic heavy-ion collisions produce quark-gluon plasma (QGP), which is locally thermalized. Due to electrically charged particles (quarks), QGP exhibits interesting thermoelectric phenomena during its evolution, resulting in an electromagnetic (EM) field in the medium. In this study, for the first time, we estimate the induced electric field in QGP due to the thermoelectric effect. This phenomenon can induce an EM field even in QGP produced by the head-on heavy-ion collision. In peripheral heavy-ion collisions, the presence of a spectator current generates a transient magnetic field at the early stage, which disrupts the isotropy of the induced electric field. For the numerical estimation, we use a quasiparticle-based model that incorporates the lattice quantum chromodynamics equation of state for QGP. The induced electric field is estimated with cooling rates derived from Gubser hydrodynamic flow. Thermoelectric coefficients such as Seebeck, magneto-Seebeck, and Nernst coefficients play a crucial role in determining the induced field. Additionally, we account for the temperature evolution of QGP using different hydrodynamic cooling rates to calculate the transport coefficients. We also estimate the transport coefficients and the induced electric field in the presence of an external time-varying magnetic field, including the quantum effect of Landau quantization, and explore the effects of the intensity and decay parameter of the magnetic field on the induced electric field. Our findings reveal that the space-time profile of the induced electric field is zero at the center and increases as we go away from the center. During the early stages of evolution, the electric field can reach a maximum value of <math><mi>e</mi><mi>E</mi><mo>≈</mo><mn>1</mn><msubsup><mi>m</mi><mi>π</mi><mn>2</mn></msubsup></math>, decreasing in strength over time.

Electric field induction in quark-gluon plasma due to thermoelectric effects

Nuclei having 4n number of nucleons are theorized to possess clusters of α particles ($^{4}$He nucleus). The Oxygen nucleus ($^{16}$O) is a doubly magic nucleus, where the presence of an α-clustered nuclear structure grants additional nuclear stability. In this study, we exploit the anisotropic flow coefficients to discern the effects of an α-clustered nuclear geometry with respect to a Woods-Saxon nuclear distribution in O–O collisions at <math><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>NN</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>7</mn></math> TeV using a hybrid of IP-Glasma + MUSIC + iSS + UrQMD models. In addition, we use the multi-particle cumulants method to measure anisotropic flow coefficients, such as elliptic flow (<math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math>) and triangular flow (<math><msub><mrow><mi>v</mi></mrow><mrow><mn>3</mn></mrow></msub></math>), as a function of multiplicity class. Anisotropic flow fluctuations, which are expected to be larger in small collision systems, are also studied for the first time in O–O collisions. It is found that an α-clustered nuclear distribution gives rise to an enhanced value of <math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math> and <math><msub><mrow><mi>v</mi></mrow><mrow><mn>3</mn></mrow></msub></math> for the low-multiplicity events. Consequently, a rise in <math><msub><mrow><mi>v</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>/</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math> is also observed for the 0–10% multiplicity class. Further, for α-clustered O–O collisions, fluctuations of <math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math> are larger for the highest multiplicity events, which decrease as the final-state multiplicity decreases. In contrast, for a Woods-Saxon $^{16}$O nucleus, <math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math> fluctuations show an opposite behavior with decreasing multiplicity. When confronted with experimental data, this study may reveal the importance of the nuclear density profile on the discussed observables and provide physics validation for the hybrid model discussed in this work.

Hungary

Gergely Gábor Barnaföldi

Anisotropic flow fluctuation as a possible signature of clustered nuclear geometry in O–O collisions at the Large Hadron Collider

Studying the thermodynamics of the systems produced in ultra-relativistic heavy-ion collisions is crucial in understanding the QCD phase diagram. Recently, a new avenue has opened regarding the implications of large initial angular momentum and subsequent vorticity in the medium evolution in high-energy collisions. This adds a new type of chemical potential into the partonic and hadronic systems, called the rotational chemical potential. We study the thermodynamics of an interacting hadronic matter under rotation, formed in an ultra-relativistic collision. We introduce attractive and repulsive interactions through the van der Waals equation of state. Thermodynamic properties like the pressure (P), energy density ( $$\varepsilon $$ <math> <mi>ε</mi> </math> ), entropy density (s), trace anomaly ( $$(\varepsilon - 3P)/T^{4}$$ <math> <mrow> <mrow> <mo>(</mo> <mi>ε</mi> <mo>-</mo> <mn>3</mn> <mi>P</mi> <mo>)</mo> </mrow> <mo>/</mo> <msup> <mi>T</mi> <mn>4</mn> </msup> </mrow> </math> ), specific heat ( $$c_\textrm{v}$$ <math> <msub> <mi>c</mi> <mtext>v</mtext> </msub> </math> ) and squared speed of sound ( $$c_\textrm{s}^{2}$$ <math> <msubsup> <mi>c</mi> <mtext>s</mtext> <mn>2</mn> </msubsup> </math> ) are studied as functions of temperature (T) for zero and finite rotation chemical potential. The conserved charge fluctuations, which can be quantified by their respective susceptibilities, are also studied. The rotational (spin) density corresponding to the rotational chemical potential is explored. In addition, we explore the possible liquid–gas phase transition in the hadron gas with van der Waals interaction in the T – $$\omega $$ <math> <mi>ω</mi> </math> phase space.

Kshitish Pradhan

Thermodynamics of a rotating hadron resonance gas with van der Waals interaction

Quarkonium production in ultra-relativistic collisions plays a crucial role in probing the existence of hot QCD matter. This study explores quarkonia states dissociation and regeneration in the hot QCD medium while considering momentum anisotropy. The net quarkonia decay width ( $$\Gamma _{D}$$ <math> <msub> <mi>Γ</mi> <mi>D</mi> </msub> </math> ) arises from two essential processes: collisional damping and gluonic dissociation. The quarkonia regeneration includes the transition from octet to singlet states within the anisotropic medium. Our study utilizes a medium-modified potential that incorporates anisotropy via particle distribution functions. This modified potential gives rise to collisional damping for quarkonia due to the surrounding medium, as well as the transition of quarkonia from singlet to octet states due to interactions with gluons. Furthermore, we employ the detailed balance approach to investigate the regeneration of quarkonia within this medium. Our comprehensive analysis spans various temperature settings, transverse momentum values, and anisotropic strengths. Notably, we find that, in addition to medium temperatures and heavy quark transverse momentum, anisotropy significantly influences the dissociation and regeneration of various quarkonia states.

Mohammad Jamal

Impact of medium anisotropy on quarkonium dissociation and regeneration

In proton-proton and heavy-ion collisions, the study of charm hadrons plays a pivotal role in understanding the QCD medium and provides an undisputed testing ground for the theory of strong interaction, as they are mostly produced in the early stages of collisions via hard partonic interactions. The lightest open charm, <math><msup><mi>D</mi><mn>0</mn></msup></math> meson (<math><mrow><mi>c</mi><mover><mrow><mi>u</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math>), can originate from two separate sources. The prompt <math><msup><mi>D</mi><mn>0</mn></msup></math> originates from either direct charm production or the decay of excited open charm states, while the nonprompt stems from the decay of beauty hadrons. In this paper, using different machine learning (ML) algorithms such as XGBoost, CatBoost, and Random Forest, an attempt has been made to segregate the prompt and nonprompt production modes of the <math><msup><mi>D</mi><mn>0</mn></msup></math> meson signal from its background. The ML models are trained using the invariant mass through its hadronic decay channel, i.e., <math><msup><mi>D</mi><mn>0</mn></msup><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>, pseudoproper time, pseudoproper decay length, and distance of closest approach of <math><msup><mi>D</mi><mn>0</mn></msup></math> meson, using pythia8 simulated <math><mi>p</mi><mi>p</mi></math> collisions at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>. The ML models used in this analysis are found to retain the pseudorapidity, transverse momentum, and collision energy dependence. In addition, we report the ratio of nonprompt to prompt <math><msup><mi>D</mi><mn>0</mn></msup></math> yield, the self-normalized yield of prompt and nonprompt <math><msup><mi>D</mi><mn>0</mn></msup></math>, and explore the charmonium, <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> to open charm, <math><msup><mi>D</mi><mn>0</mn></msup></math> yield ratio as a function of transverse momenta and normalized multiplicity. The observables studied in this paper are well predicted by all the ML models compared to the simulation.