Elliptic Flow Coefficient Research Articles

Two-gluon one-photon vertex in a magnetic field and its explicit one-loop approximation in the intermediate field strength regime

We find the general structure for the two-gluon one-photon vertex in the presence of a constant magnetic field. We show that, when accounting for the symmetries satisfied by the strong and electromagnetic interactions under parity, charge conjugation and gluon interchange, and for gluons and photons on mass-shell, there exist only three possible tensor structures that span the vertex. These correspond to external products of the polarization vectors for each of the particles in the vertex. We also explicitly compute the one-loop approximation to this vertex in the intermediate field strength regime, which is the most appropriate one to describe possible effects of the presence of a magnetic field to enhance photon emission during preequilibrium in peripheral relativistic heavy-ion collisions. We show that the most favored direction for the photon to propagate is in the plane transverse to the field, which is consistent with a positive contribution to ν2 and may help to understand the larger than expected elliptic flow coefficient measured in this kind of reaction. Published by the American Physical Society 2024

Small systems and the single-hit approximation in the AMY parton cascade Alpaca

Understanding how momentum anisotropies arise in small collision systems is important for a quantitative understanding of collectivity in terms of QCD dynamics in small and large collision systems. In this letter we present results for small collision systems from the newly developed parton cascade Alpaca, which faithfully encodes the AMY effective kinetic theory. Alpaca reproduces quantitatively previously known results from a calculation in the single-hit approximation for small values of the coupling. We discuss in detail how such a comparison is to be carried out. Particularly at larger coupling a generic difference between the two approaches becomes apparent, namely that in parton cascades particles interact over a finite distance while in direct integrations of the Boltzmann equation the interactions are local. This leads to quantitative differences in the extracted values for the elliptic flow coefficient. These discrepancies appear in situations where the mean free path is not large compared to the interaction time and the applicability of kinetic theory is thus questionable.

Quenching and flow of charm and bottom quarks via semi-leptonic decay of D and B mesons in Pb+Pb collisions at the LHC* *Supported in part by the National Natural Science Foundation of China (12225503, 11935007, 11890710, 11890711, 12175122, 2021-867). W.-J. X. is supported in part by China Postdoctoral Science Foundation (2023M742099). Some of the calculations were performed in the Nuclear

Heavy flavor particles provide important probes of the microscopic structure and thermodynamic properties of the quark-gluon plasma (QGP) produced in high-energy nucleus-nucleus collisions. We studied the energy loss and flow of charm and bottom quarks inside the QGP via the nuclear modification factor ( ) and elliptic flow coefficient ( ) of their decayed leptons in heavy-ion collisions at the LHC. The dynamical evolution of the QGP was performed using the CLVisc (3+1)-dimensional viscous hydrodynamics model; the evolution of heavy quarks inside the QGP was simulated with our improved Langevin model that considers both collisional and radiative energy loss of heavy quarks; the hadronization of heavy quarks was simulated via our hybrid coalescence-fragmentation model; and the semi-leptonic decay of D and B mesons was simulated via PYTHIA. Using the same spatial diffusion coefficient for charm and bottom quarks, we obtained smaller and larger of charm decayed leptons than bottom decayed leptons, indicating stronger energy loss of charm quarks than bottom quarks inside the QGP within our current model setup.

Pseudorapidity dependence of anisotropic flow and its decorrelations using long-range multiparticle correlations in Pb–Pb and Xe–Xe collisions

The pseudorapidity dependence of elliptic (v2), triangular (v3), and quadrangular (v4) flow coefficients of charged particles measured in Pb–Pb collisions at a centre-of-mass energy per nucleon pair of sNN=5.02TeV and in Xe–Xe collisions at sNN=5.44TeV with ALICE at the LHC are presented. The measurements are performed in the pseudorapidity range −3.5<η<5 for various centrality intervals using two- and multi-particle cumulants with the subevent method. The flow probability density function (p.d.f.) is studied with the ratio of flow coefficient v2 calculated with four- and two-particle cumulant, and suggests that the variance of flow p.d.f. is independent of pseudorapidity. The decorrelation of the flow vector in the longitudinal direction is probed using two-particle correlations. The results measured with respect to different reference regions in pseudorapidity exhibit differences, argued to be a result of saturating decorrelation effect above a certain pseudorapidity separation, in contrast to previous publications which assign this observation to non-flow effects. The results are compared to 3+1 dimensional hydrodynamic and the AMPT transport model calculations. Neither of the models is able to simultaneously describe the pseudorapidity dependence of measurements of anisotropic flow and its fluctuations. The results presented in this work highlight shortcomings in our current understanding of initial conditions and subsequent system expansion in the longitudinal direction. Therefore, they provide input for its improvement.

Heavy-flavor transport and hadronization in pp collisions

Recent experimental results on the Λc+/D0 ratio in proton-proton (pp) collisions have revealed a significant enhancement compared to expectations based on universal fragmentation fractions/functions across different colliding systems, from e+e− to pp. This unexpected enhancement has sparked speculation about the potential effects of a deconfined medium impacting hadronization, previously considered exclusive to heavy-ion collisions. In this study, we propose a novel approach that assumes the formation of a small, deconfined, and expanding fireball even in pp collisions, where charm quarks can undergo rescattering and hadronization. We make use of the same in-medium hadronization mechanism developed for heavy-ion collisions, which involves local color-neutralization through recombination of charm quarks with nearby opposite color charges from the background fireball. Our model incorporates the presence of diquark excitations in the hot medium, which promotes the formation of charmed baryons. Moreover, the recombination process, involving closely aligned partons from the same fluid cell, effectively transfers the collective flow of the system to the final charmed hadrons. We show that this framework can qualitatively reproduce the observed experimental findings in heavy-flavor particle-yield ratios, pT-spectra and elliptic-flow coefficients. Our results provide new, complementary supporting evidence that the collective phenomena observed in small systems naturally have the same origin as those observed in heavy-ion collisions. Published by the American Physical Society 2024

Heavy-flavor transport and hadronization in a small fireball

We study heavy-flavor hadron production in high-energy pp collisions, assuming the formation of a small, deconfined and expanding fireball where charm quarks can undergo rescattering and hadronization. We adopt the same in-medium hadronization mechanism developed for heavy-ion collisions, which involves Local Color-Neutralization (LCN) through recombination of charm quarks with nearby opposite color charges from the background fireball. Diquark excitations in the hot medium favor the formation of charmed baryons. The recombination process, involving closely aligned partons from the same fluid cell, effectively transfers the collective flow of the system to the final charmed hadrons. This framework can qualitatively reproduce the observed experimental findings in heavy-flavor particle-yield ratios, pT -spectra and ellipticflow coefficients. Our results provide new, complementary support to the idea that the collective phenomena observed in small systems have the same origin as those observed in heavy-ion collisions.

Looking for QGP signatures in ultraperipheral PbPb collisions

Ultraperipheral collisions of relativistic heavy ion beams lead to a diverse set of photon-nucleus (photonuclear) interactions. The measurements of particles and their interaction produced in photonuclear reactions can shed light on the QCD dynamics of these novel, extremely asymmetric colliding systems, with energies between those available at RHIC and the LHC. Previous studies by ATLAS indicate significant elliptic and triangular flow coefficients in these events [1]. Thus, it is imperative to check these events for other potential QGP signatures including radial flow, strangeness enhancement, and enhanced baryon/meson production. This proceeding presents the measurement of charged hadron yields in photonuclear collisions using 5.02 TeV Pb+Pb data collected in 2018 by ATLAS, with a dedicated photo-nuclear event trigger. The charged hadron yields are presented as a function of pseudorapidity and transverse momentum in different categories of event multiplicity. The results are compared with 5.02 TeV p+Pb data collected in 2016 by ATLAS, at the same event multiplicities. The results are also compared with calculations from DPMJET and hydrodynamic-based models. These comparisons enable detailed characterizations of photonuclear collision properties, including the photon energy distribution, and whether small QGP droplets may be formed.

Probing parton propagation in heavy-ion collisions with ALICE heavy-flavour measurements

Heavy quarks (charm and beauty) are valuable probes for investigating the properties of the quark–gluon plasma (QGP) formed in ultra-relativistic heavy-ion collisions, as they are mainly produced through hard-scattering processes prior to the formation of the QGP, and their number is conserved during the subsequent QGP evolution. Measurements of the nuclear modification factor RAA of charm and beauty hadrons allow us to characterise the in-medium energy loss of heavy quarks while traversing the QGP. Information on their diffusion and degree of participation in the collective motion of the medium can be obtained by measuring the elliptic-flow coefficient v2 of heavy-flavour particles. Complementary insights into heavy-quark fragmentation and energy redistribution can be obtained by measuring angular correlations involving heavy-flavour particles. In this contribution, the recently published results on the non-prompt v2 coefficient of D0 mesons are presented, comparing them with those of other particle species in Pb–Pb collisions at √SNN = 5.02 TeV. Additionally, we report the recent findings on the RAA of prompt D mesons and Λc+ baryons in Pb–Pb collisions at the same energy. Furthermore, we discuss the new Pb–Pb results on angular correlations between heavy-flavour decay electrons and charged particles in the same collision system.

Probing the chiral magnetic wave with charge-dependent flow measurements in Pb-Pb collisions at the LHC

The Chiral Magnetic Wave (CMW) phenomenon is essential to provide insights into the strong interaction in QCD, the properties of the quark-gluon plasma, and the topological characteristics of the early universe, offering a deeper understanding of fundamental physics in high-energy collisions. Measurements of the charge-dependent anisotropic flow coefficients are studied in Pb-Pb collisions at center-of-mass energy per nucleon-nucleon collision sNN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s_{\ extrm{NN}}} $$\\end{document} = 5.02 TeV to probe the CMW. In particular, the slope of the normalized difference in elliptic (v2) and triangular (v3) flow coefficients of positively and negatively charged particles as a function of their event-wise normalized number difference, is reported for inclusive and identified particles. The slope r3Norm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {r}_3^{\ extrm{Norm}} $$\\end{document} is found to be larger than zero and to have a magnitude similar to r2Norm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {r}_2^{\ extrm{Norm}} $$\\end{document}, thus pointing to a large background contribution for these measurements. Furthermore, r2Norm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {r}_2^{\ extrm{Norm}} $$\\end{document} can be described by a blast wave model calculation that incorporates local charge conservation. In addition, using the event shape engineering technique yields a fraction of CMW (fCMW) contribution to this measurement which is compatible with zero. This measurement provides the very first upper limit for fCMW, and in the 10–60% centrality interval it is found to be 26% (38%) at 95% (99.7%) confidence level.

Deep learning predicted elliptic flow of identified particles in heavy-ion collisions at the RHIC and LHC energies

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.

Effects of the QCD critical point on the spectra and flow coefficients of hadrons

The space-time evolution of the hot and dense fireball of quarks and gluons produced in ultrarelativistic heavy-ion collisions at nonzero baryonic chemical potential and temperature has been studied by using relativistic dissipative hydrodynamics. For this purpose, a numerical code has been developed to solve the relativistic viscous causal hydrodynamics in ($3+1$) dimensions with the inclusion of QCD critical point ($CP$) through the equation of state and scaling behavior of transport coefficients. We compute the transverse momentum spectra, directed and elliptic flow coefficients of pions and protons to comprehend the effect of $CP$ on these observables. It is found that the integration over the entire space-time history of the fireball largely obliterates the effects of $CP$ on the spectra and flow coefficients for the event averaged initial conditions considered here.

Probing initial geometrical anisotropy and final azimuthal anisotropy in heavy-ion collisions at Large Hadron Collider energies through event-shape engineering

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 (${ϵ}_{2}$) and triangularity (${ϵ}_{3}$) of the participants, respectively. In this work, we study ${v}_{2}$, ${v}_{3}$, ${ϵ}_{2}$, ${ϵ}_{3}$, and the correlations among them with respect to event topology in the framework of a multiphase 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 ${ϵ}_{2}$. This work also addresses transverse momentum dependent crossing points between ${v}_{2}$ and ${v}_{3}$, which varies for different centrality and spherocity percentiles.

Production of in heavy ion collisions* *Supported by Guangdong Major Project of Basic and Applied Basic Research (2020B0301030008), the National Natural Science Foundation of China (12105107) and Science and Technology Program of Guangzhou (2019050001)

The yields of with its two possible configurations, i.e., the hadronic molecular state and tetraquark state, for Pb-Pb collisions at is studied. A volume effect is found from the centrality distribution of , which could help to distinguish the inner structure of . We also show the rapidity and the transverse momentum distributions of production as well as its elliptic flow coefficient as a function of the transverse momentum.

Effects of weak magnetic field and finite chemical potential on the transport of charge and heat in hot QCD matter

We have studied the effects of weak magnetic field and finite chemical potential on the transport of charge and heat in hot QCD matter by estimating their respective response functions, viz. the electrical conductivity ( $$\sigma _{\textrm{el}}$$ ), the Hall conductivity ( $$\sigma _{\textrm{H}}$$ ), the thermal conductivity ( $$\kappa _0$$ ) and the Hall-type thermal conductivity ( $$\kappa _1$$ ). The expressions of charge and heat transport coefficients are obtained by solving the relativistic Boltzmann transport equation in the relaxation time approximation at weak magnetic field and finite chemical potential. The interactions among partons are incorporated through their thermal masses. We have observed that $$\sigma _{{\textrm{el}}}$$ and $$\kappa _0$$ decrease and $$\sigma _{{\textrm{H}}}$$ and $$\kappa _1$$ increase with the magnetic field in the weak magnetic field regime. On the other hand, the presence of a finite chemical potential increases these transport coefficients. The effects of weak magnetic field and finite chemical potential on aforesaid transport coefficients are found to be more conspicuous at low temperatures, whereas at high temperatures, they have only a mild dependence on magnetic field and chemical potential. We have found that the presence of finite chemical potential further extends the lifetime of the magnetic field. Furthermore, we have explored the effects of weak magnetic field and finite chemical potential on the Knudsen number, the elliptic flow coefficient and the Wiedemann–Franz law.

Perturbative and non-perturbative interactions between heavy quarks and quark-gluon plasma within a unified approach

While perturbative QCD is sufficient for understanding the color, mass and energy dependences of parton energy loss and jet quenching at large transverse momentum in heavy-ion collisions, a simultaneous description of heavy flavor nuclear modification factor RAA and elliptic flow coefficient v2 at low and intermediate pT still remains a challenge due to the effects from non-perturbative interactions. In this work, we extend the linear Boltzmann transport model by implementing a generalized Cornell-type potential that incorporates both short-range Yukawa interaction and long-range color confining interaction between heavy quarks and the QGP medium. Combining our new approach for heavy-quark-QGP interaction with a (3+1)-dimensional hydrodynamic model CLVisc for the QGP evolution and a hybrid fragmentation-coalescence model for heavy quark hadronization, we obtain a satisfactory description of heavy meson RAA and v2 from low to intermediate to high pT observed at both RHIC and the LHC. By model-data-comparison, we obtain for the first time the in-medium heavy quark potential from open heavy flavor measurements; the result is in agreement with the lattice QCD calculation. Our study indicates that while jet quenching at high pT is dominated by perturbative QCD interactions, non-perturbative interactions are indispensible for understanding heavy flavor quenching and flow at low and intermediate pT.

Interactions between heavy quarks and tilted QGP fireballs in 200 A GeV Au+Au collisions* *Supported by the National Natural Science Foundation of China (11935007, 12175122, 2021-867), Guangdong Major Project of Basic and Applied Basic Research (2020B0301030008), Natural Science Foundation of Hubei Province (2021CFB272), Education Department of Hubei Province of China with Young Talents Project (Q20212703), Open Foundation of Key Laboratory

Heavy quark observables are applied to probe the initial energy density distribution with violation of longitudinal boost invariance produced in relativistic heavy-ion collisions. Using an improved Langevin model coupled to a (3+1)-dimensional viscous hydrodynamic model, we study the nuclear modification factor () and directed flow () and elliptic flow () coefficients of heavy mesons and their decayed electrons at an RHIC energy. We find that the counter-clockwise tilt of nuclear matter in the reaction plane results in a positive (negative) heavy flavor in the backward (forward) rapidity region, whose magnitude increases with the heavy quark transverse momentum. The difference in the heavy flavor between different angular regions is also proposed as a complementary tool to characterize the asymmetry of the medium profile. Our model results are consistent with currently available data at the RHIC and provide predictions that can be tested by future measurements.

Elliptic flow of charged particles at midrapidity relative to the spectator plane in Pb–Pb and Xe–Xe collisions

Measurements of the elliptic flow coefficient relative to the collision plane defined by the spectator neutrons v2{ΨSP} in collisions of Pb ions at center-of-mass energy per nucleon–nucleon pair sNN=2.76 TeV and Xe ions at sNN=5.44 TeV are reported. The results are presented for charged particles produced at midrapidity as a function of centrality and transverse momentum for the 5–70% and 0.2–6 GeV/c ranges, respectively. The ratio between v2{ΨSP} and the elliptic flow coefficient relative to the participant plane v2{4}, estimated using four-particle correlations, deviates by up to 20% from unity depending on centrality. This observation differs strongly from the magnitude of the corresponding eccentricity ratios predicted by the TRENTo and the elliptic power models of initial state fluctuations that are tuned to describe the participant plane anisotropies. The differences can be interpreted as a decorrelation of the neutron spectator plane and the reaction plane because of fragmentation of the remnants from the colliding nuclei, which points to an incompleteness of current models describing the initial state fluctuations. A significant transverse momentum dependence of the ratio v2{ΨSP}/v2{4} is observed in all but the most central collisions, which may help to understand whether momentum anisotropies at low and intermediate transverse momentum have a common origin in initial state fluctuations. The ratios of v2{ΨSP} and v2{4} to the corresponding initial state eccentricities for Xe–Xe and Pb–Pb collisions at similar initial entropy density show a difference of (7.0±0.9)% with an additional variation of +1.8% when including RHIC data in the TRENTo parameter extraction. These observations provide new experimental constraints for viscous effects in the hydrodynamic modeling of the expanding quark–gluon plasma produced in heavy-ion collisions at the LHC.

Physical characteristics of glasma from the earliest stage of relativistic heavy ion collisions

We present analytic results that describe the gluon field, or glasma, at very early times after a collision of relativistic heavy ions at proper time $\tau=0$. We use a Colour Glass Condensate approach, and perform an expansion in $\tau$. The full details of our method are described in our previous paper [1]. In this paper we present an analysis of various physical quantities that can be obtained from the energy-momentum tensor. We show that the expansion to order $\tau^6$ can be trusted to about $\tau=0.05$ fm. For times small enough that the expansion converges, the transverse and longitudinal pressures move towards their equilibrium values of one third of the energy density. The Fourier coefficients of the azimuthal flow are larger than expected, which contradicts the usual assumption that anisotropy is mostly generated during the hydrodynamic evolution of the plasma. We find a significant correlation between the elliptic flow coefficient and the eccentricity, which indicates that the spatial asymmetry introduced by the initial geometry is effectively transmitted to the azimuthal distribution of the gluon momentum field, even at very early times. This result is interesting because correlations of this kind are characteristic of the onset of hydrodynamic behaviour. We show that the angular momentum of the glasma is orders of magnitude smaller than the angular momentum of the initial system of ions colliding with non-zero impact parameter. This indicates that most of the angular momentum carried by the valence quarks is not transmitted to the glasma, and contradicts the picture of a rapidly rotating initial glasma state that has been proposed by several authors, but agrees with the current lack of experimental evidence for a significant polarization effect of the hyperons and vector mesons produced in heavy ion collisions at the highest accessible energies.

Estimating elliptic flow coefficient in heavy ion collisions using deep learning

Machine learning techniques have been employed for the high energy physics 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 deep neural network (DNN) model is trained with Pb-Pb collisions at $\sqrt{{s}_{\mathrm{NN}}}=5.02\text{ }\text{ }\mathrm{TeV}$ minimum bias events simulated with a multiphase transport model. The predictions from the machine learning 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 ${p}_{\mathrm{T}}$ 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.

Event topology and constituent-quark scaling of elliptic flow in heavy-ion collisions at the Large Hadron Collider using a multiphase transport model

Transverse spherocity is an event shape observable, which separates the events based on their geometrical shapes. In this work, we use transverse spherocity to study the identified light flavor production in heavy-ion collisions using A Multi-Phase Transport (AMPT) model. We obtain the elliptic flow coefficients for pions, kaons and protons in Pb+Pb collisions at sqrt{s_mathrm{{NN}}} = 5.02 TeV as a function of transverse spherocity and collision centrality. Also, we study the number of constituent-quark (NCQ) scaling of elliptic flow which interprets the dominance of the quark degrees of freedom at the early stages of the collision. We observe a clear dependence of the elliptic flow for identified particles on transverse spherocity. It is found that the NCQ-scaling is strongly violated in events with low transverse spherocity compared to transverse spherocity-integrated events, confirming the fragmentation-based hadronization mechanism for high-momentum partons involved in the dynamics of jetty-like events.