Differential Elliptic Flow Research Articles

Effect of the Temperature-Dependent Shear Viscosity on Rapidity Differential Elliptic Flow in Relativistic Heavy Ion Collisions

Effect of the Temperature-Dependent Shear Viscosity on Rapidity Differential Elliptic Flow in Relativistic Heavy Ion Collisions

Multimessenger heavy-ion collision physics

This work studies the production of direct photons in relativistic nuclear collisions, along with the production of hadrons. Radiation from the very first instants to the final moments of the evolution is included. The hybrid model used here describes all stages of relativistic heavy-ion collisions. Chronologically, those are an initial state reflecting the collision of nuclei described within the Color Glass Condensate effective theory; a pre-equilibrium phase based on non-equilibrium linear response; relativistic viscous hydrodynamics, and a hadronic afterburner. The effect of the pre-equilibrium phase on both photonic and hadronic observables is highlighted for the first time. The potential of photon observables -- spectrum, differential elliptic and triangular flow -- to reveal the chemical equilibration time is studied. Finally, we consider "small collision systems", including proton+nucleus collisions and collisions of light nuclei, as probed by hadronic and electromagnetic observables. We demonstrate how photon production can signal the formation of quark-gluon plasma in such small systems.

Quantifying the Effect of Initial Fluctuations on Isospin-Sensitive Observables from Heavy-Ion Collisions at Intermediate Energies

Initial fluctuation is one of the ingredients that washes fingerprints of the nuclear symmetry energy on observables in heavy-ion collisions. By artificially using the same initial nuclei in all collision events, the effect of the initial fluctuation on isospin-sensitive observables, e.g., the yield ratio of free neutrons with respect to protons Nn/Np, 3H/3He yield ratio, the yield ratio between charged pions π−/π+, and the elliptic flow ratio or difference between free neutrons and protons v2n/v2p (v2n-v2p), are studied within the ultrarelativistic quantum molecular dynamics (UrQMD) model. In practice, Au + Au collisions with impact parameter b = 5 fm and beam energy Elab = 400 MeV/nucleon are calculated. It is found that the effect of the initialization on the yields of free protons and neutrons is small, while for the yield of pions, the directed and elliptic flows are found to be apparently influenced by the choice of initialization because of the strong memory effects. Regarding the isospin-sensitive observables, the effect of the initialization on Nn/Np and 3H/3He is negligible, while π−/π+ and v2n/v2p (v2n-v2p) display a distinct difference among different initializations. The fingerprints of symmetry energy on π−/π+ and v2n/v2p can be either enhanced or reduced when different initializations are utilized.

Comparative analysis of nucleonic flows for isospin degree of freedom

We performed a detailed investigation on the role of neutron-proton asymmetry on collective flows viz directed flow (transverse flow), elliptic flow, differential transverse flow, and differential elliptic flow for central collisions of 132Sn+124Sn and 56Ca+132Sn at 100 MeV/nucleon. The role of nuclear symmetry energy (and its density dependence) and isospin dependence of binary collisions cross-sections is examined on various types of nucleonic flows. Our findings reveal that transverse flow in mass symmetric collisions is best suited to explore isospin effects via nuclear symmetry energy at energies close to Fermi energies, however, isospin effects at high energies could be probed via elliptic and differential elliptic flows. A confrontation of our theoretical calculations with available measurements on the energy of disappearance of transverse flow favored the stiff behavior of nuclear symmetry energy at supra-saturation densities.

Modified equilibrium distributions for Cooper-Frye particlization

We introduce a positive definite single-particle distribution that is suitable for describing the transition from a macroscopic hydrodynamic to a microscopic kinetic description during the late stages of heavy-ion collisions in the presence of moderately large viscous corrections. The modified equilibrium distribution function can be constructed with hydrodynamic input from either relativistic viscous fluid dynamics or anisotropic fluid dynamics. We test the modified equilibrium distribution's hydrodynamic output for a stationary hadron resonance gas subject to either shear stress, bulk pressure, or baryon diffusion current at a given freeze-out temperature and baryon chemical potential. While it does not reproduce all components of the net baryon current and energy-momentum tensor exactly, it significantly improves upon the customary linearized approximations for the non-equilibrium correction $\delta f_n$ which typically lead to unphysical negative distribution functions at large particle momenta. A comparison of particle spectra and $p_T$-differential elliptic flow coefficients from the Cooper-Frye formula computed with the modified equilibrium distribution and with linearized $\delta f_n$ corrections is presented, for two different (2+1)-dimensional hypersurfaces corresponding to central and non-central Pb+Pb collisions at the Large Hadron Collider (LHC).

Number of constituent quark scaling of elliptic flows in high multiplicity p-Pb collisions at [formula omitted

We briefly summarize our recent study on the number of constituent quark (NCQ) scaling of hadron elliptic flows in high multiplicity p-Pb collisions at sNN=5.02TeV. With the inclusion of hadron production via the quark coalescence model at intermediate pT, the viscous hydrodynamics at low pT, and jet fragmentation at high pT, our Hydro – Coal – Frag model provides a nice description of the pT-spectra and differential elliptic flow ν2(pT) of pions, kaons and protons over the pT range from 0 to 6 GeV. Our results demonstrate that including the quark coalescence is essential for reproducing the observed approximate NCQ scaling of hadron ν2 at intermediate pT in experiments, indicating strongly the existence of partonic degrees of freedom and the formation of quark-gluon plasma in high multiplicityp-Pb collisions at the LHC.

Elliptic flow splitting between protons and antiprotons from hadronic potentials

The difference in elliptic flow between protons and antiprotons, produced in [Formula: see text] collisions at center-of-mass energies [Formula: see text], is studied within a modified version of the ultra-relativistic quantum molecular dynamics (UrQMD) model. Two different model scenarios are compared: the cascade mode and the mean field mode which includes potential interactions for both formed and pre-formed hadrons. The model results for the elliptic flow of protons and the relative elliptic flow difference between protons and antiprotons obtained from the mean field mode agree with the available experimental data, while the elliptic flow difference is near zero for the cascade mode. Our results show that the elliptic flow splitting, observed for particles and antiparticles, can be explained by the inclusion of proper hadronic interactions. In addition, the difference in elliptic flow between protons and antiprotons depends on the centrality and the rapidity window. With smaller centrality and/or rapidity acceptance, the observed elliptic flow splitting is more sensitive to the beam energy, indicating a strong net baryon density dependence of the effect. We propose to confirm this splitting at the upcoming experiments from Beam Energy Scan (BES) Phase-II at Relativistic Heavy Ion Collider (RHIC), the Compressed Baryonic Matter (CBM) at Facility for Antiproton and Ion Research (FAIR), High Intensity heavy ion Accelerator Facility (HIAF) and Nuclotron-based Ion Collider fAcility (NICA).

Probing the Partonic Degrees of Freedom in High-Multiplicity p-Pb collisions at sqrt[s_{NN}]=5.02 TeV.

We investigate the role of partonic degrees of freedom in high-multiplicity p-Pb collisions at sqrt[s_{NN}]=5.02 TeV carried out at the Large Hadron Collider (LHC) by studying the production and collective flow of identified hadrons at intermediate p_{T} via the coalescence of soft partons from the viscous hydrodynamics (VISH2+1) and hard partons from the energy loss model, linear Boltzmann transport (LBT). We find that combining these intermediate p_{T} hadrons with the low p_{T} hadrons from the hydrodynamically expanding fluid and high p_{T} hadrons from the fragmentation of quenched jets, the resulting hydro-dynamics-coalescence-fragmentation model provides a nice description of measured p_{T} spectra and differential elliptic flow v_{2}(p_{T}) of pions, kaons, and protons over the p_{T} range from 0 to 6GeV. We further demonstrate the necessity of including the quark coalescence contribution to reproduce the experimentally observed approximate number of constituent quark scaling of hadron v_{2} at intermediate p_{T}. Our results thus indicate the importance of partonic degrees of freedom and also hint at the possible formation of quark-gluon plasma in high-multiplicity p-Pb collisions at the LHC.

Investigation of Particle Antiparticle Elliptic Flow Difference at STAR Experiment

The azimuthal anisotropy in particle emission in the transverse plane, known as anisotropic flow, is used to study the properties of strongly interacting hot and dense medium created in heavy-ion collisions. Anisotropic flow coefficients are the key observables which reflect the viscous hydrodynamic response to the initial spatial anisotropy, produced in the early stages of the collision. In previous studies performed by the Solenoidal Tracker At RHIC (STAR) collaboration at the Relativistic Heavy Ion Collider (RHIC) the increase of the elliptic flow ($${{{v}}_{2}}$$) difference between particles and antiparticles at the lower collision energies has been observed. In these proceedings we present the measurement of the two-particle elliptic and triangular flow correlations for identified particles performed by the STAR experiment. Our measurements are compared with the EPOS model simulations as well.

Effects of impact parameter filters on observables in heavy-ion collisions at INDRA energies

The collision centrality (or the impact parameter b) in heavy-ion experiments is inferred from final state observables, however, usually b is an input to theoretical calculations. The effects of different methods used for the centrality selection (i.e. total charged multiplicity Mch, total transverse kinetic energy of light charged particles , and the ratio of transverse-to-longitudinal kinetic energy ERAT) on the nuclear stopping and the collective flow are studied in Xe+Sn collisions at INDRA energies (/nucleon). The study is conducted within the framework of the ultra-relativistic quantum molecular dynamics (UrQMD) model. It is found that the nuclear stopping power RE obtained from events binning with ERAT is larger than the experimental data as well as the results obtained using Mch and . At Ebeam = 50 MeV/nucleon, the elliptic flow from events selected with different methods spreads widely, especially for more central collisions. The elliptic flow from events sorted by ERAT is weakly dependent on the collision centrality. The difference in elliptic flow at mid-rapidity among different centrality filters steadily decreases with increasing beam energy and impact parameter. At 150 MeV/nucleon, the differences in directed and elliptic flows arising from different centrality filters vanish.

Complications in the interpretation of the charge-asymmetry-dependent π flow for the chiral magnetic wave

The charge asymmetry ($A_{\rm ch}$) dependence of the $\pi^{-}$ and $\pi^{+}$ elliptic flow difference, $\Delta v_{2}(A_{\rm ch})$, has been regarded as a sensitive observable for the possible chiral magnetic wave (CMW) in relativistic heavy ion collisions. In this work, we first demonstrate that, due to non-flow backgrounds, the flow measurements by the Q-cumulant method using all charged particles as reference introduce a trivial linear term to $\Delta v_{2}(A_{\rm ch})$. The trivial slope can be negative in the triangle flow difference $\Delta v_{3}(A_{\rm ch})$ if the non-flow is dominated by back-to-back pairs. After eliminating the trivial term, we find that the non-flow between like-sign pairs gives rise to an additional positive slope to $\Delta v_{2}(A_{\rm ch})$ because of the larger dilution effect to $\pi^{+}$ ($\pi^{-}$) at positive (negative) $A_{\rm ch}$. We further find that the competition between different $\pi$ sources can introduce another non-trivial linear-$A_{\rm ch}$ term due to their different multiplicity fluctuations and anisotropic flows. We then study the effect of neutral cluster (resonance) decays as a mechanism for local charge conservation on the slope parameter of $\Delta v_{2}(A_{\rm ch})$. We find that the slope parameter is sensitive to the kinematics of those neutral clusters. Light resonances give positive slopes while heavy resonances give negative slopes. Local charge conservation from continuum cluster mass distribution can give a positive slope parameter comparable to experimental data. Our studies indicate that many non-CMW physics mechanisms can give rise to a $A_{\rm ch}$-dependent $\Delta v_{2}(A_{\rm ch})$ and the interpretation of $\Delta v_{2}(A_{\rm ch})$ in terms of the CMW is delicate.

Isospin splitting of pion elliptic flow in relativistic heavy-ion collisions

Based on the framework of an extended multiphase transport model with mean-field potentials in both the partonic phase and the hadronic phase, we explain the elliptic flow difference between π+ and π− in the beam-energy scan program at the relativistic heavy-ion collider by incorporating the vector-isovector potential for quarks and antiquarks with different flavors or isospins. It is found that the isospin splitting of pion elliptic flow favors a strong vector-isovector interaction, and thus serves as a probe of the quark matter equation of state as well as the QCD phase structure at finite baryon and isospin chemical potentials.

Elliptic flow of hadrons in Au + Au collisions at and 39 GeV from a multi-phase transport model based on a dynamical quark coalescence mechanism

We present a study of the transverse momentum (pT) spectra and the differential elliptic flow (v2) in a multi-phase transport model based on a dynamical quark coalescence model for Au + Au collisions at and 39 GeV. We have compared our results with the experimental data. The v2 of is found to be sensitive to the size parameter for mesons in the model. Our study indicates that the elliptic flow splitting between p and at lower energies may be partly due to quark coalescence in phase space.

Hydrodynamic collectivity in proton–proton collisions at 13 TeV

In this paper, we investigate the hydrodynamic collectivity in proton–proton (p–p) collisions at 13 TeV, using iEBE-VISHNU hybrid model with HIJING initial conditions. With properly tuned parameters, our model simulations can remarkably describe all the measured 2-particle correlations, including integrated and differential elliptic flow coefficients for all charged and identified hadrons (KS0, Λ). However, our model calculations show positive 4-particle cumulant c2{4} in high multiplicity pp collisions, and can not reproduce the negative c2{4} measured in experiment. Further investigations on the HIJING initial conditions show that the fluctuations of the second order anisotropy coefficient ε2 increases with the increase of its mean value, which leads to a similar trend of the flow fluctuations. For a simultaneous description of the 2- and 4- particle cumulants within the hydrodynamic framework, it is required to have significant improvements on initial condition for pp collisions, which is still lacking of knowledge at the moment.

Chiral magnetic effect in the anomalous transport model

We report our recent study of the effect of the magnetic field on the elliptic flows of quarks and antiquarks in relativistic heavy ion collisions using the anomalous transport model. We have found that the magnetic field can lead to a charge quadrupole moment in the transverse plane of a heavy ion collisions if the magnetic field lasts sufficiently long and the charge asymmetry of produced matter is nonzero. As the matter expands, the charge quadrupole moment leads to a splitting between the elliptic flows of quarks and antiquarks. However, the elliptic flow difference increases with the charge asymmetry, which is expected from the chiral magnetic wave formed in the quark-gluon plasma, only if the Lorentz force is neglected and the quark-antiquark scattering is dominated by the chirality changing channel.

Erratum to: Influence of the time-step on the production of free nucleons and pions from heavy-ion collisions around 1 GeV/nucleon

By considering different values of the time-step for the potential updates in the ultra-relativistic quantum molecular dynamics (UrQMD) model, we examine its influence on observables, such as the yield and collective flow of nucleons and pions from heavyion collisions around 1 GeV/nucleon. It is found that these observables are affected to some extent by the choice of the time-step, and the impact of the time-step on the pion-related observables is more visible than that on the nucleon-related ones. However, its effect on the π −/π + yield ratio and elliptic flow difference between neutrons and protons, which have been taken as sensitive observables for probing the density-dependent nuclear symmetry energy at high densities, is fairly weak.

Effects of the high-momentum tail of nucleon momentum distribution on the isospin-sensitive observables

Based on the Isospin-dependent transport model Boltzmann-Uehling-Uhlenbeck (IBUU), effects of the high momentum tail (HMT) of nucleon momentum distribution in colliding nuclei on some isospin-sensitive observables are studied in the semi-central $^{197}\rm {Au}+^{197}\rm {Au}$ reactions at incident beam energy of 400 MeV/nucleon. It is found that the nucleon transverse flow, the difference of neutron and proton transverse flows, the nucleon elliptic flow and free neutron to proton ratio are all less sensitive to the HMT, while the isospin-sensitive nucleon elliptic flow difference is clearly affected by the HMT. Except at very high kinetic energies, the kinetic energy distributions of $\pi^{-}$, $\pi^{+}$ and charged pion ratio $\pi^{-}/\pi^{+}$ are all sensitive to the HMT.

Influence of the time-step on the production of free nucleons and pions from heavy-ion collisions around 1 GeV/nucleon

By considering different values of the time-step for the potential updates in the ultra-relativistic quantum molecular dynamics (UrQMD) model, we examine its influence on observables, such as the yield and collective flow of nucleons and pions from heavyion collisions around 1 GeV/nucleon. It is found that these observables are affected to some extent by the choice of the time-step, and the impact of the time-step on the pion-related observables is more visible than that on the nucleon-related ones. However, its effect on the π−/π+ yield ratio and elliptic flow difference between neutrons and protons, which have been taken as sensitive observables for probing the density-dependent nuclear symmetry energy at high densities, is fairly weak.

Anomalous transport model study of chiral magnetic effects in heavy ion collisions

Using an anomalous transport model for massless quarks and antiquarks, we study the effect of a magnetic field on the elliptic flows of quarks and antiquarks in relativistic heavy ion collisions. With initial conditions from a blast wave model and assuming that the strong magnetic field produced in non-central heavy ion collisions can last for a sufficiently long time, we obtain an appreciable electric quadrupole moment in the transverse plane of a heavy ion collision. The electric quadrupole moment subsequently leads to a splitting between the elliptic flows of quarks and antiquarks. The slope of the charge asymmetry dependence of the elliptic flow difference between positively and negatively charged particles is positive, which is expected from the chiral magnetic wave formed in the produced QGP and observed in experiments at the BNL Relativistic Heavy Ion Collider, only if the Lorentz force acting on the charged particles is neglected and the quark-antiquark scattering is assumed to be dominated by the chirality changing channel.

Influence of differential elastic nucleon-nucleon cross section on stopping and collective flow in heavy-ion collisions at intermediate energies

By considering three different Nucleon-Nucleon (NN) elastic differential cross sections: the Cugnon \emph{et al.} parameterized differential cross section [Nucl. Instrum. Methods Phys. Res., Sect. \textbf{B111}, 215 (1996)], and the differential cross section derived from the collision term of the self-consistent relativistic Boltzmann-Uehling-Uhlenbeck equation proposed by Mao \emph{et al.} [Z.\ Phys.\ A {\bf 347}, 173 (1994)], as well as the isotropic differential cross section, within the newly updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model, the influence of the differential elastic NN cross section on various observables (e.g., nuclear stopping, both the rapidity and transverse-velocity dependence of the directed and elliptic flows) in Au+Au collisions at beam energies 150, 250, 400, and 800 MeV$/$nucleon is investigated. By comparing calculations with those three differential cross sections, it is found that the nuclear stopping power, the directed and elliptic flows are affected to some extent by the differential cross sections, and the impact of differential cross section on those observables becomes more visible as the beam energy increases. The effect on the elliptic flow difference $v_{2}^{n}$-$v_{2}^{H}$ and ratio $v_{2}^{n}$/$v_{2}^{H}$ of neutrons versus hydrogen isotopes ($Z=1$), which have been used as sensitive observables for probing nuclear symmetry energy at high densities, is weak.