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We developed a deep learning feed-forward network for estimating elliptic flow ($v_2$) coefficients in heavy-ion collisions from RHIC to LHC energies. The success of our model is mainly the estimation of $v_2$ from final state particle kinematic information and learning the centrality and the transverse momentum ($p_{\rm T}$) dependence of $v_2$ in wide $p_{\rm T}$ regime. The deep learning model is trained with AMPT-generated Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV minimum bias events. We present $v_2$ estimates for $\pi^{\pm}$, $\rm K^{\pm}$, and $\rm p+\bar{p}$ in heavy-ion collisions at various LHC energies. These results are compared with the available experimental data wherever possible., Comment: 4 pages, 2 figures

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 quasi-thermalized 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., Comment: 11 pages and 4 captioned figures. Submitted for publication

The present investigation reports the design and development of an advanced material with a high figure of merit (FoM) for beampipe applications in particle accelerators by bringing synergy between computational and experimental approaches. Machine learning algorithms have been used to predict the phase(s), low density, and high radiation length of the designed Al-Ti-V alloys. Al-Ti-V alloys with various compositions for single-phase and dual-phase mixtures, liquidus temperature, and density values are obtained using the Latin hypercube sampling method in TC Python Thermo-Calc software. The obtained dataset is utilized to train the machine-learning algorithms. Classification algorithms such as XGBoost and regression models such as Linear Regression and Random Forest regressor have been used to compute the number of phases, radiation length, and density respectively. The XGBoost algorithms show an accuracy of $98\%$, the Linear regression model shows an accuracy of $94\%$, and the Random Forest regressor model is accurate up to $99\%$. The developed Al-Ti-V alloys exhibit high radiation length as well as a good combination of high elastic modulus and toughness due to the synergistic effect of the presence of hard $Al_3Ti$ phase along with a minor volume fraction of FCC $(Al)_{ss}$ solid solution phase mixture. The comparison of our alloys, alloy-1 ($Al_{75.2}Ti_{22.8}V_{2}$) and alloy-2 ($Al_{89}Ti_{10}V_{1}$) shows an increase in the radiation length by seven-times and a decrease in the density by two to three times as compared to stainless steel 304, the preferred material for constructing beampipes in low-energy particle accelerators. Further, we experimentally verify the elastic modulus of the alloy-1 and compute the FoM equal to 0.416, which is better than other existing materials for beampipes in low-energy experiments., Comment: 9 pages and 4 captioned figures. Submitted for publication

In relativistic heavy-ion collisions, the formation of a deconfined and thermalized state of partons, known as quark-gluon plasma, leads to enhanced production of strange hadrons in contrast to proton-proton (pp) 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 pp collisions at the LHC energies. Alternatively, event shape observables, such as charged particle multiplicity, 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 pp 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 pp 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 similar quantitative enhancement as seen for the analysis based on the number of multi-parton interactions., Comment: 14 pages and 12 captioned figures. Submitted for publication

Nuclei having $4n$ number of nucleons are theorized to possess clusters of $\alpha$ particles ($^4$He nucleus). The Oxygen nucleus ($^{16}$O) is a doubly magic nucleus, where the presence of an $\alpha$-clustered nuclear structure grants additional nuclear stability. In this study, we exploit the anisotropic flow coefficients to discern the effects of an $\alpha$-clustered nuclear geometry w.r.t. a Woods-Saxon nuclear distribution in O--O collisions at $\sqrt{s_{\rm NN}}=7$ 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 ($v_{2}$) and triangular flow ($v_{3}$), as a function of collision centrality. 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 $\alpha$-clustered nuclear distribution gives rise to an enhanced value of $v_{2}$ and $v_3$ towards the highest multiplicity classes. Consequently, a rise in $v_3/v_2$ is also observed for the (0-10)\% centrality class. Further, for $\alpha$-clustered O--O collisions, fluctuations of $v_{2}$ are larger for the most central collisions, which decrease towards the mid-central collisions. In contrast, for a Woods-Saxon $^{16}$O nucleus, $v_{2}$ fluctuations show an opposite behavior with centrality. This study, when confronted with experimental data may reveal the importance of nuclear density profile on the discussed observables., Comment: 13 pages and 10 captioned figures, submitted for publication

Long-range multi-particle correlations in heavy-ion collisions have shown conclusive evidence of the hydrodynamic behavior of strongly interacting matter, and are associated with the final-state azimuthal momentum anisotropy. In small collision systems, azimuthal anisotropy can be influenced by the hadronization mechanism and residual jet-like correlations. Thus, one of the motives of the planned p--O and O--O collisions at the LHC and RHIC is to understand the origin of small system collectivity. As the anisotropic flow coefficients ($v_n$) are sensitive to the initial-state effects including nuclear shape, deformation, and charge density profiles, studies involving $^{12}$C and $^{16}$O nuclei are transpiring due to the presence of exotic $\alpha$ ($^{4}$He) clusters in such nuclei. In this study, for the first time, we investigate the effects of nuclear $\alpha$--clusters on the azimuthal anisotropy of the final-state hadrons in p--C and p--O collisions at $\sqrt{s_{\rm NN}}= 9.9$ TeV within a multi-phase transport model framework. We report the transverse momentum ($p_{\rm T}$) and pseudorapidity ($\eta$) spectra, participant eccentricity ($\epsilon_2$) and triangularity ($\epsilon_3$), and estimate the elliptic flow ($v_2$) and triangular flow ($v_3$) of the final-state hadrons using the two-particle cumulant method. These results are compared with a model-independent Sum of Gaussians (SOG) type nuclear density profile for $^{12}$C and $^{16}$O nuclei., Comment: 16 pages and 10 captioned figures. Submitted for publication

Relativistic heavy-ion collisions produce quark-gluon plasma (QGP), which is locally thermalized. QGP with higher thermal conductivity advances towards global thermalization. Being made of electrically charged particles (quarks), QGP exhibits interesting thermoelectric phenomena during its evolution, resulting in the induction of an electric field in the medium. For the first time, we estimate the induced electric field in the QGP due to thermoelectric effect. This can be seen even in the QGP produced in the head-on collisions. The Seebeck coefficient is essential in determining the induced field. However, spectator current can produce a magnetic field in peripheral heavy-ion collisions. This breaks the isotropy of the thermoelectric coefficient matrix and introduces magneto-Seebeck and Nernst coefficients that contribute to the induced electric field in peripheral collisions. We have taken care of the temperature evolution of QGP with different hydrodynamic cooling rates to calculate the transport coefficients. The induced electric field is estimated with the cooling rate obtained from Gubser hydrodynamic flow. We estimated the space-time profile of the induced field and found that it is zero at the center and increases as we go away from the center. At the early time of evolution, the electric field can reach a maximum value of $eE \approx 1~m_\pi^2$, and the strength decreases in time. Moreover, we estimated the transport coefficients in the presence of the external time-varying magnetic field. The effect of the intensity and decay parameter of the magnetic field on the induced electric field is also explored., Comment: 38 pages and 9 figures. Submitted for publication

The global and local polarization measurements of $\Lambda$ ($\bar{\Lambda}$) hyperons by STAR and ALICE Collaborations open up an immense interest in investigating the polarization dynamics in heavy-ion collisions. Recent studies suggest the transverse component of the vorticity field is responsible for the global spin polarization, while the longitudinal component of the vorticity field accounts for the local polarization. The local polarization of $\Lambda$-hyperons arises due to the anisotropic flows in the transverse plane, indicating a quadrupole pattern of the longitudinal vorticity along the beam direction. The present study focuses on the local (longitudinal) polarization of $\Lambda$ and $\bar{\Lambda}$ in Au$+$Au and Pb$+$Pb collisions at $\sqrt{s_{NN}}$ = 200 GeV and 5.02 TeV, respectively. Further, we explore the centrality and transverse momentum ($p_{\rm T}$) dependence of longitudinal polarization using hydrodynamic and transport models. All these models predict a maximum longitudinal polarization in mid-central collisions around 30-50 \% centrality at $p_{\rm T} \approx$ 2.0 - 3.0 GeV/c. These findings on longitudinal polarization advocate the existence of a thermal medium in non-central heavy-ion collisions. Our findings are in agreement with corresponding experimental data at the RHIC and LHC energies., Comment: 9 pages and two captioned figures. Submitted for publication

n 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, $D^{0}$ meson ($c\Bar{u}$), can originate from two separate sources. The prompt $D^{0}$ 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 $D^{0}$ meson signal from its background. The ML models are trained using the invariant mass through its hadronic decay channel, i.e., $D^{0}\rightarrow\pi^{+} K^{-}$, pseudoproper time, pseudoproper decay length, and distance of closest approach of $D^{0}$ meson, using PYTHIA8 simulated $pp$ collisions at $\sqrt{s}=13~\rm{TeV}$. 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 $D^{0}$ yield, the self-normalized yield of prompt and nonprompt $D^{0}$ and explore the charmonium, $J/\psi$ to open-charm, $D^{0}$ yield ratio as a function of transverse momenta and normalized multiplicity. The observables studied in this manuscript are well predicted by all the ML models compared to the simulation., Comment: Same as the published version in Phys. Rev. D

The recent observation of global polarization of $\Lambda$ ($\bar{\Lambda}$) hyperons and 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 polarization, 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 (eB), baryonic chemical potential ($\mu_{B}$), and medium anisotropy ($\xi$), vorticity, etc., certainly affects the particle polarization. In this work, we explore the global hyperon 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 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 polarization in comparison with the magnetic field and baryon chemical potential., Comment: 13 pages and 8-captioned figures. Submitted for publication

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 ($\Gamma_{D}$) 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., Comment: 11 pages and 4 captioned figures, same as the published version in EPJC

Strong transient magnetic fields are generated in non-central relativistic heavy-ion collisions. These fields induce anisotropy within the strongly interacting medium that, in principle, can affect the thermodynamic properties of the medium. We use the Polyakov loop extended Nambu Jona-Lasinio model to study the quark matter subjected to an external magnetic field at vanishing baryon chemical potential ($\mu_{B}$). We have estimated the degree of anisotropy in the speed of sound and isothermal compressibility within the magnetized quark matter as a function of temperature ($T$) and magnetic field ($eB$). This study helps us to understand the extent of directionality generated in the initial stages of non-central collisions while giving us useful information about the system., Comment: Same as the published version in Phys. Rev. D

Recent observations of quark-gluon plasma (QGP) like signatures in high multiplicity proton-proton (pp) collisions, have compelled the heavy-ion physics community to re-examine the pp collisions for proper baseline studies. Event-shape-based studies in pp collisions have succeeded to a certain extent in identifying rare events mimicking such heavy-ion-like behaviour. In this manuscript, we incorporate PYTHIA8 to study radial flow-like signatures in pp collisions at $\sqrt{s} = 13$ TeV as a function of transverse spherocity and pseudo-rapidity. The pseudo-rapidity dependence would help understand the scientific community for future upgrades. At the same time, the transverse spherocity will serve its purpose of identifying soft-QCD-dominated events in small collision systems. We present the mean transverse momentum, particle ratios, and kinetic freezeout parameters as a function of transverse spherocity and pseudo-rapidity in pp collisions at $\sqrt{s}$ = 13 TeV using PYTHIA8. We observe that the isotropic events show enhanced radial-flow effects and jetty events show the absence of radial-flow-like effects. For the first time, we show the transverse spherocity and pseudorapidity dependence of partonic modification factor in pp collisions, which clearly shows that by choosing transverse spherocity one can directly probe the radial-flow-like effects in pp collisions at the LHC., Comment: 12 pages and 13 captioned figures. Submitted for publication

The production mechanisms of charmonium states in both hadronic and heavy-ion collisions hold great significance for investigating the hot and dense QCD matter. Studying charmonium polarization in ultra-relativistic collisions can also provide insights into the underlying production mechanisms. With this motivation, we explore the $J/\psi$ and $\psi$(2S) polarization in proton+proton collisions at $\sqrt{s}$ = 7, 8, and 13 TeV using a pQCD-inspired Monte-Carlo event generator called PYTHIA8. This work considers reconstructed quarkonia through their dimuons decay channel in the ALICE forward rapidity acceptance range of $2.5 < y_{\mu \mu} < 4$. Further, we calculate the polarization parameters $\lambda_{\theta}$, $\lambda_{\phi}$, $\lambda_{\theta \phi}$ from the polar and azimuthal angular distributions of the dimuons in helicity and Collins-Soper frames. This study presents a comprehensive measurement of the polarization parameters as a function of transverse momentum, charged-particle multiplicity, and rapidity at the LHC energies. Our findings of charmonium polarization are in qualitative agreement with the corresponding experimental data., Comment: Same as the published version in Phys. Rev. C

An estimate of the proton number cumulants in the hadronic matter is presented considering a van der Waals-type interaction between the constituent particles. We argue that the attractive and repulsive parameters in the VDW hadron resonance gas (VDWHRG) model change as functions of baryochemical potential ($\mu_{B}$) and temperature ($T$). This, in turn, affects the estimation of thermodynamic properties and, consequently, the conserved charge fluctuations. We employ a simple parametrization to bring in the center-of-mass energy ($\sqrt{s_{\rm NN}}$) dependence on temperature and baryochemical potential and then estimate the proton number cumulants with the modified approach. The modified van der Waals hadron resonance gas model (MVDWHRG) explains the existing experimental data very well., Comment: 9-pages and 6-captioned figures, Submitted for publication

The present work focuses on Oxygen-Oxygen (O-O) collisions, which are planned at the CERN Large Hadron Collider. Oxygen, being a doubly magic number nucleus, has some very unique features. This study attempts to probe the exotic state of QCD matter in O-O collisions. Additionally, the role of different nuclear density profiles in governing the final state dynamics in ultra-relativistic nuclear collisions is also explored. Using a multi-phase transport model, we obtain the nuclear modification factor ($\textit R_{\textit {AA}}$) for all charged hadrons and identified particles for O-O collisions at $\sqrt{s_{\rm{NN}}}$ = 7 TeV. Furthermore, we investigate the behavior of $\textit R_{\textit {AA}}$ as a function of transverse momentum ($\textit{p}_{\rm{T}}$) for three centralities (most central, mid-central, and peripheral) considering both $\alpha$-cluster and Woods-Saxon nuclear density profiles. We also extend this work to study the rapidity dependence of $\textit R_{\textit {AA}}$ for all charged hadrons. To better understand our findings of O-O collisions, the results are confronted with the available data of $\textit R_{\textit {AA}}$ for Pb-Pb collisions. The present study sheds light on particle production mechanisms, emphasizing factors influencing particle yield from pre-collision to post-collision stages in the context of O-O collisions., Comment: Same as the published version in Phys. Rev. C

Studies related to $\rm{J}/\psi$ meson, a bound state of charm and anti-charm quarks ($c\bar{c}$), in heavy-ion collisions, provide genuine testing grounds for the theory of strong interaction, quantum chromodynamics (QCD). To better understand the underlying production mechanism, cold nuclear matter effects, and influence from the quark-gluon plasma, baseline measurements are also performed in proton-proton ($pp$) and proton-nucleus ($p$--A) collisions. The inclusive $\rm{J}/\psi$ measurement has contributions from both prompt and non-prompt productions. The prompt $\rm{J}/\psi$ is produced directly from the hadronic interactions or via feed-down from directly produced higher charmonium states, whereas non-prompt $\rm{J}/\psi$ comes from the decay of beauty hadrons. In experiments, $\rm{J}/\psi$ is reconstructed through its electromagnetic decays to lepton pairs, in either $e^{+}+e^{-}$ or $\mu^{+}+\mu^{-}$ decay channels. In this work, for the first time, machine learning techniques are implemented to separate the prompt and non-prompt dimuon pairs from the background to obtain a better identification of the $\rm{J}/\psi$ signal for different production modes. The study has been performed in $pp$ collisions at $\sqrt{s} = 7$ and 13 TeV simulated using PYTHIA8. Machine learning models such as XGBoost and LightGBM are explored. The models could achieve up to 99\% prediction accuracy. The transverse momentum ($p_{\rm T}$) and rapidity ($y$) differential measurements of inclusive, prompt, and non-prompt $\rm{J}/\psi$, its multiplicity dependence, and the $p_{\rm T}$ dependence of fraction of non-prompt $\rm{J}/\psi$ ($f_{\rm B}$) are shown. These results are compared to experimental findings wherever possible., Comment: Same as the published version in Phys. Rev. D

With the advent of unprecedented collision energy at the Large Hadron Collider, CERN, Geneva, a new domain of particle production and possible formation of Quark-Gluon Plasma (QGP) in high-multiplicity proton-proton collisions and the collisions of light nuclei has been a much-discussed topic recently. In this review, I discuss some of the recent observations leading to such a possibility, associated challenges, and some predictions for the upcoming light-nuclei collisions at the LHC., Comment: DAE-HEP Symposium, 2022 Proceedings of the mini-review. To be published in Springer Nature Proceedings

The effect of the temperature evolution of QGP on its thermal conductivity and elliptic flow is investigated here in the presence of a time-varying magnetic field. Thermal conductivity plays a vital role in the cooling rate of the medium or its temperature evolution. The magnetic field produced during the early stages of (non-central) heavy-ion collisions decays with time, where electrical conductivity plays a significant role. As the medium expands, the electrical and thermal properties change, reflecting the effect in various observables. In this study, we have calculated the thermal conductivity of the QGP medium, incorporating the effects of temperature and magnetic field evolution. We discovered that conductivity significantly depends on the cooling rate, and its value increases due to temperature evolution. Furthermore, the influence of these evolutions on the elliptic flow coefficient is measured, and elliptic flow decreases due to the evolution. We also extend our study for the case of Gubser flow, where, along with the longitudinal Bjorken expansion, the radially transverse expansion is also present., Comment: Same as the published version in Phys. Rev D

Heavy quarks are excellent probes to understand the hot and dense medium formed in ultra-relativistic collisions. In a hadronic medium, studying the transport properties, e.g. the drag ($\gamma$), momentum diffusion ($B_{0}$), and spatial diffusion ($D_{s}$) coefficients of open charmed hadrons can provide useful information about the medium. Moreover, the fluctuations of charmed hadrons can help us to locate the onset of their deconfinement. In this work, we incorporate attractive and repulsive interactions in the well-established van der Waals hadron resonance gas model (VDWHRG) and study the diffusion and fluctuations of charmed hadrons. This study helps us understand the importance of interactions in the system, which affect both the diffusion and fluctuations of charmed hadrons., Comment: Same as the published version in Phys. Rev. D

We study the behavior of a hadronic matter in the presence of an external magnetic field within the van der Waals hadron resonance gas model, considering both attractive and repulsive interactions among the hadrons. Various thermodynamic quantities like pressure ($P$), energy density ($\varepsilon$), magnetization ($\mathcal{M}$), entropy density ($s$), squared speed of sound ($c_{\rm s}^{2}$), and specific-heat capacity at constant volume ($c_{v}$) are calculated as functions of temperature ($T$) and static finite magnetic field ($eB$). We also consider the effect of baryochemical potential ($\mu_{B}$) on the above-mentioned thermodynamic observables in the presence of a magnetic field. Further, we estimate the magnetic susceptibility ($\chi_{\rm M}^{2}$), relative permeability ($\mu_{\rm r}$), and electrical susceptibility ($\chi_{\rm Q}^{2}$) which can help us to understand the system better. Through this model, we quantify a liquid-gas phase transition in the T-eB-$\mu_B$ phase space., Comment: Same as the published version in Phys. Rev. D

To understand the true origin of flowlike signatures and applicability of hydrodynamics in small collision systems, effects of soft QCD dynamics, the sensitivity of jetlike correlations, and nonequilibrium effects, efforts are being made to perform \textit{p}-O and O-O collisions at the LHC and RHIC energies. It is equally interesting to look into the possible signatures of an $\alpha$-clustered nuclear geometry in $^{16}$O-$^{16}$O collisions by studying the initial-state effects on the final-state observables. In this work, within a multiphase transport model, we implement an $\alpha$-cluster tetrahedral density profile in the oxygen nucleus along with the default Woods-Saxon density profile. We study the eccentricity ($\epsilon_2$), triangularity ($\epsilon_3$), normalized symmetric cumulants [NSC(2,3)], elliptic flow ($v_2$), and triangular flow ($v_3$) in $^{16}$O-$^{16}$O collisions at $\sqrt{s_{\rm NN}} = 7~$TeV. The constituent quark number scaling of the elliptic flow is also reported. For the most central collisions, enhanced effects in $\langle \epsilon_3 \rangle/ \langle \epsilon_2 \rangle$ and $\langle v_3 \rangle/ \langle v_2 \rangle$ with a negative value of NSC(2,3), and an away-side broadening in the two-particle azimuthal correlation function [$C(\Delta \phi)$] of the identified particles are observed in the presence of an $\alpha$-clustered geometry., Comment: Same as the published version in Phys. Rev. D

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 ($\varepsilon$), entropy density ($s$), trace anomaly ($(\varepsilon - 3P)/T^{4}$), specific heat ($c_{\rm v}$) and squared speed of sound ($c_{\rm s}^{2}$) 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 $T$ -- $\omega$ phase space., Comment: 11 pages and 6 captioned figures. Same as the published version in EPJC

Signatures of the formation of a strongly interacting thermalized matter of partons have been observed in nucleus-nucleus, proton-nucleus, and high-multiplicity proton-proton collisions at LHC energies. Strangeness enhancement in such ultra-relativistic heavy-ion collisions is considered to be a consequence of this thermalized phase, known as quark-gluon plasma (QGP). Simultaneously, proper modeling of hadronic energy fraction in interactions of ultra-high energy cosmic rays (UHECR) has been proposed as a solution for the muon puzzle, an unexpected excess of muons in air showers. These interactions have center-of-mass collision energies of the order of energies attained at the LHC or even higher, indicating that the possibility of a thermalized partonic state cannot be overlooked in UHECR-air interactions. This work investigates the hadronic energy fraction and strangeness enhancement to explore QGP-like phenomena in UHECR-air interactions using various high-energy hadronic models. A core-corona system with a thermalized core undergoing statistical hadronization is considered through the EPOS LHC model. In contrast, PYTHIA 8, QGSJET II-04, and SYBILL 2.3d consider string fragmentation without thermalization. We have found that EPOS LHC gives a better description of strangeness enhancement as compared to other models. We conclude that adequately treating all the relevant effects and further retuning the models is necessary to explain the observed effects., Comment: Same as the published version

We have estimated the electrical and thermal conductivity of a hadron resonance gas for a time-varying magnetic field, which is also compared with constant and zero magnetic field cases. Considering the exponential decay of electromagnetic fields with time, a kinetic theory framework can provide the microscopic expression of electrical and thermal conductivity in terms of relaxation and decay times. In the absence of the magnetic field, only a single time scale appears, and in the finite magnetic field case, their expressions carry two-time scales, relaxation time and cyclotron time period. Estimating the conductivities for HRG matter in three cases -- zero, constant, and time-varying magnetic fields, we have studied the validity of the Wiedemann-Franz law. We noticed that at a high-temperature domain, the ratio saturates at a particular value, which may be considered as Lorenz number of the hadron resonance gas. With respect to the saturation values, the deviation of the Wiedemann-Franz law has been quantified at the low-temperature domain. For the first time, the present work sketches this quantitative deviation of the Wiedemann-Franz law for hadron resonance gas at a constant and a time-varying magnetic field., Comment: Same as the published version in Phys. Rev. D

The strongly interacting transient state of quark-gluon plasma (QGP) medium created in ultra-relativistic collisions survives for a duration of a few fm/c. The spacetime evolution of QGP crucially depends on the equation of state (EoS), vorticity, viscosity, and external magnetic field. In the present study, we obtain the lifetime of a vortical QGP fluid within the ambit of relativistic second-order viscous hydrodynamics. We observe that the coupling of vorticity and viscosity significantly increases the lifetime of vortical QGP. The inclusion of a static magnetic field, vorticity, and viscosity makes the evolution slower. However, the static magnetic field slightly decreases the QGP lifetime by accelerating the evolution process for a non-rotating medium. We also report the rate of change of vorticity in the QGP, which will be helpful in studying the behavior of the medium in detail., Comment: Same as the EPJC published version

Recent developments on a deep learning feed-forward network for estimating elliptic flow ($v_2$) coefficients in heavy-ion collisions have shown us the prediction power of this technique. The success of the model is mainly the estimation of $v_2$ from final state particle kinematic information and learning the centrality and the transverse momentum ($p_{\rm T}$) dependence of $v_2$. The deep learning model is trained with Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV minimum bias events simulated with a multiphase transport model (AMPT). We extend this work to estimate $v_2$ for light-flavor identified particles such as $\pi^{\pm}$, $\rm K^{\pm}$, and $\rm p+\bar{p}$ in heavy-ion collisions at RHIC and LHC energies. The number of constituent quark (NCQ) scaling is also shown. The evolution of $p_{\rm T}$-crossing point of $v_2(p_{\rm T})$, depicting a change in meson-baryon elliptic flow at intermediate-$p_{\rm T}$, is studied for various collision systems and energies. The model is further evaluated by training it for different $p_{\rm T}$ regions. These results are compared with the available experimental data wherever possible., Comment: Same as the published version

The charged-particle transverse momentum spectra ($p_{\rm T}$-spectra) measured by the ALICE collaboration for $pp$ collisions at $\sqrt {s} =$ 7 and 13 TeV have been studied using a thermodynamically consistent form of Tsallis non-extensive statistics. The Tsallis distribution function is fitted to the $p_{\rm T}$-spectra and the results are analyzed as a function of final state charged-particle multiplicity for various light flavor and strange particles, such as $\pi^{\pm}, K^{\pm}, p+\bar{p}, \phi, \Lambda+\bar{\Lambda}, \Xi+\bar{\Xi}, \Omega+\bar{\Omega}$. At the LHC energies, particles and antiparticles are produced in equal numbers. However, the equality of particle and antiparticle yields at the kinetic freeze-out may imply that they have the same but opposite chemical potential which is not necessarily zero. We use an alternative procedure that makes use of parameter redundancy, by introducing a finite chemical potential at the kinetic freeze-out stage. This article emphasizes the importance of the chemical potential of the system produced in $pp$ collisions at the LHC energies using the Tsallis distribution function which brings the system to a single freeze-out scenario., Comment: Same as the published version in EPJA

Pion condensation in an ultra-relativistic collision is an open puzzle yet to be verified experimentally. However, it is not trivial to have a conclusive result of pion condensation due to various experimental constraints. Nevertheless, numerous theoretical approaches can help in understanding the high-temperature Bose-Einstein condensation (BEC) in a better way. This work uses the shear ($\eta$) and bulk viscosity ($\zeta$) phenomena for a hot and dense pion gas to investigate the effect of possible Bose-Einstein condensation in such an environment. This study considers the relaxation time approximation under the Boltzmann transport equation to estimate $\eta$ and $\zeta$. Further, it explores the significance of the temperature and chemical potential on the number of particles in the condensate and viscosities. We find a substantial change in the viscosity when the pion gas is under BEC. In addition, we also study the speed of sound ($c_{\rm s}$) for the pion gas under BEC., Comment: 9 pages and 5 captioned figures. Submitted for publication

The hadronic phase and its dynamics in relativistic heavy-ion collisions are topics of immense discussion. The hadronic phase contains various massive hadrons with an abundance of the lightest hadron, i.e., $\pi$-mesons. In this work, we consider that pions are in the thermal equilibrium in the hadronic phase and use second-order massive viscous hydrodynamics to obtain its expansion to the boundary of the kinetic freeze-out. We achieve the kinetic freeze-out boundary with the Knudsen number ($Kn$) limit: $Kn>1$. When this condition is met, hydrodynamics expansion breaks down, and the mean free path becomes sufficiently large in comparison with the system size so that the particle yields get preserved. Further, we investigate the effect of the massive fluid on the resonance particle yields, including re-scattering and regeneration, along with their natural decay width. These resonances can play an important role in determining the characteristics of the hadronic phase as they have sufficiently small lifetimes, which may be comparable to the hadronic phase lifetime. In the current study, we predict the hadronic phase lifetime, which is further used to determine the $K^*(892)^0/K$, $\phi(1020)/K$, and $\rho(770)^0/\pi$ ratios at the kinetic freeze-out. We obtain these ratios as a function of charged particle multiplicity and transverse momentum and compare our findings with experimental data. Our results qualitatively agree with the experimental data indicating the possible hydrodynamical evolution of the hadronic phase., Comment: 11 pages and 6 figures. Submitted for publication

The discovery and characterization of hot and dense QCD matter, known as Quark Gluon Plasma (QGP), remains the most international collaborative effort and synergy between theorists and experimentalists in modern nuclear physics to date. The experimentalists around the world not only collect an unprecedented amount of data in heavy-ion collisions, at Relativistic Heavy Ion Collider (RHIC), at Brookhaven National Laboratory (BNL) in New York, USA, and the Large Hadron Collider (LHC), at CERN in Geneva, Switzerland but also analyze these data to unravel the mystery of this new phase of matter that filled a few microseconds old universe, just after the Big Bang. In the meantime, advancements in theoretical works and computing capability extend our wisdom about the hot-dense QCD matter and its dynamics through mathematical equations. The exchange of ideas between experimentalists and theoreticians is crucial for the progress of our knowledge. The motivation of this first conference named "HOT QCD Matter 2022" is to bring the community together to have a discourse on this topic. In this article, there are 36 sections discussing various topics in the field of relativistic heavy-ion collisions and related phenomena that cover a snapshot of the current experimental observations and theoretical progress. This article begins with the theoretical overview of relativistic spin-hydrodynamics in the presence of the external magnetic field, followed by the Lattice QCD results on heavy quarks in QGP, and finally, it ends with an overview of experiment results., Comment: Compilation of the contributions (148 pages) as presented in the `Hot QCD Matter 2022 conference', held from May 12 to 14, 2022, jointly organized by IIT Goa & Goa University, Goa, India

Recently, with the upgradation of LHC, it is realized that study of heavy-flavored hadrons, namely $\Lambda_{c}^{+}$ and $\rm{D}^{0}$ in hadronic collisions, could reveal the possibility of thermalization of charm quarks. With this motivation, we study the production dynamics of these hadrons in proton+proton collisions at $\sqrt{s}$ = 13 TeV by exploiting their dependence on charged-particle multiplicity, transverse momentum, and pseudorapidity using a pQCD-inspired model called PYTHIA8. With the help of the established PYTHIA8 tunes to mimic the behavior of thermalization, we investigated the variation of effective temperature and degree of non-extensivity using thermodynamically consistent non-extensive Tsallis statistics. We further attempted to establish a connection between the initial state and final state by estimating the correlation between the number of multi-partonic interactions ($\rm{n}_{MPI}$) with the Knudsen number., Comment: 13 pages and 8 figures. Submitted for publication

Anisotropic flow is accredited to have effects from the initial state geometry and fluctuations in the nuclear overlap region. The elliptic flow ($v_2$) and triangular flow ($v_3$) coefficients of the final state particles are expected to have influenced by eccentricity ($\varepsilon_2$) and triangularity ($\varepsilon_3$) of the participants, respectively. In this work, we study $v_2$, $v_3$, $\varepsilon_2$, $\varepsilon_3$ and the correlations among them with respect to event topology in the framework of a multi-phase transport model (AMPT). We use transverse spherocity and reduced flow vector as event shape classifiers in this study. Transverse spherocity has the unique ability to separate events based on geometrical shapes, i.e., jetty and isotropic, which pertain to pQCD and non-pQCD domains of particle production in high-energy physics, respectively. We use the two-particle correlation method to study different anisotropic flow coefficients. We confront transverse spherocity with a more widely used event shape classifier -- reduced flow vector ($q_n$) and they are found to have significant (anti-)correlations among them. We observe significant spherocity dependence on $v_2$, $v_3$ and $\varepsilon_2$. This work also addresses transverse momentum dependent crossing points between $v_2$ and $v_3$, which varies for different centrality and spherocity percentiles., Comment: Same as the published version in Phys. Rev. D

We study the drag and diffusion coefficients of the charm quark in the deconfined matter produced in the ultra-relativistic collisions by taking the Color String Percolation Model (CSPM) approach. CSPM, being a QCD-inspired model, can give us essential information about the hot and dense system produced in ultra-relativistic collisions. With the information on initial percolation temperature and percolation density, we estimate the relaxation time ($\tau_{c}$), drag coefficient ($\gamma$), transverse momentum diffusion coefficient ($B_{0}$), and spatial diffusion coefficient ($D_{s}$) of charm quark inside a deconfined medium. Finally, we compare the obtained results with lattice QCD and with various other theoretical models. A good agreement can be observed between the results obtained from CSPM and lattice QCD., Comment: 7 pages and 5 figures

In this work, a hadron resonance gas under van der Waals (VDW) interactions has been studied. Both attractive and repulsive interactions between the meson-meson and (anti)baryon-(anti)baryon have been taken into consideration. Various transport properties such as electrical conductivity ($\sigma_{\rm el}$) and thermal conductivity ($\kappa_{\rm th}$) have been estimated by solving the Boltzmann transport equation under the relaxation time approximation. The effect of baryochemical potential ($\mu_{\rm B}$) and temperature is also explicitly explored for the mentioned observables. Comparisons have been made with the results obtained from other existing theoretical models. We observe the violation of Wiedemann-Franz law in a hadron resonance gas at a high-temperature regime. The corresponding diffusivities have also been estimated, which can help us to understand the system in a better way., Comment: Same as the published version in Phys. Rev. C

Machine Learning (ML) techniques have been employed for the high energy physics (HEP) community since the early 80s to deal with a broad spectrum of problems. This work explores the prospects of using Deep Learning techniques to estimate elliptic flow ($v_2$) in heavy-ion collisions at the RHIC and LHC energies. A novel method is developed to process the input observables from particle kinematic information. The proposed DNN model is trained with Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV minimum bias events simulated with AMPT model. The predictions from the ML technique are compared to both simulation and experiment. The Deep Learning model seems to preserve the centrality and energy dependence of $v_2$ for the LHC and RHIC energies. The DNN model is also quite successful in predicting the $p_{\rm T}$ dependence of $v_2$. When subjected to event simulation with additional noise, the proposed DNN model still keeps the robustness and prediction accuracy intact up to a reasonable extent., Comment: Same as the published version in Phys. Rev. D

We have estimated the dimensionless parameters such as Reynolds number ($Re$), Knudsen number ($Kn$) and Mach number ($Ma$) for a multi-hadron system by using the excluded volume hadron resonance gas (EVHRG) model along with Hagedorn mass spectrum to include higher resonances in the system. The size dependence of these parameters indicate that the system formed in proton+proton collisions may achieve thermal equilibrium making it unsuitable as a benchmark to analyze the properties of the system produced in heavy ion collisions at similar energies. While the magnitude of $Kn$ can be used to study the degree of thermalization and applicability of inviscid hydrodynamics, the variations of $Re$ and $Ma$ with temperature ($T$) and baryonic chemical potential ($\mu_B$) assist to understand the change in the nature of the flow in the system. Indeed the nature of flow changes from laminar to turbulent as $Re$ increases and the system is characterized as incompressible for low $Ma (<<1)$ and compressible for larger $Ma$. $Ma$ can also be used to understand whether the flow is subsonic or supersonic., Comment: Same as the published version

Our universe was born about 13.8 billion years ago from an extremely hot and dense singular point, in a process known as the Big Bang. The hot and dense matter which dominated the system within a few microseconds of its birth was in the form of a soup of elementary quarks and gluons, known as the quark-gluon plasma (QGP). Signatures compatible with the formation of the QGP matter have experimentally been observed in heavy-ion (such as Au or Pb) collisions at ultra-relativistic energies. Recently, experimental data of proton-proton (pp) collisions at the CERN Large Hadron Collider (LHC) have also shown signals resembling those of the QGP formation, which made these studies quite stimulating as to how the collision of small systems features in producing the early universe signals. In this article, we report on some of the compelling experimental results and give an account of the present understanding. We review the pp physics program at the LHC and discuss future prospects in the context of exploring the nature of the primordial matter in the early universe., Comment: 7 pages and 7 figures, written for general multi-disciplinary readers, Published version in Current Science

In the framework of a multi-source thermal model at the partonic-level, we have analyzed transverse momentum spectra of hadrons measured by the ALICE Collaboration in proton-proton ($pp$ or $p$-$p$) collisions at the center-of-mass energy of $\sqrt{s}=7$ and 13 TeV, proton-lead ($p$-Pb) collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV, and lead-lead (Pb-Pb) collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV. For meson(baryon), the contributions of two(three) constituent quarks are considered, in which each quark contributes to hadron transverse momentum to obey the revised phenomenological Tsallis transverse momentum distribution for the Maxwell-Boltzmann particles (the TP-like function in short) with isotropic random azimuthal angle. Three main parameters, namely, the revised index $a_0$, effective temperature $T$, and entropy-related index $n$ are obtained, which show the same tendency for small and large systems with respect to the centrality (or multiplicity) of events, rest mass of hadrons, and constituent mass of quarks., Comment: Please see the published version in the journal Symmetry following the reference and DOI