Non-central Collisions Research Articles

Off-centre binary collision of droplets: A numerical investigation

The paper presents results from a numerical investigation of the non-central binary collision of two equal size droplets in a gaseous phase. The flow field is two phase and three dimensional; the investigation is based on the finite volume numerical solution of the Navier–Stokes equations, coupled with the Volume of Fluid Method (VOF), expressing the unified flow field of the two phases, liquid and gas. A recently developed adaptive local grid refinement technique is used, in order to increase the accuracy of the solution particularly in the region of the liquid–gas interface. The reliability of the solution procedure is tested by comparing predictions with available experimental data. The numerical results predict the collision process of the two colliding droplets (permanent coalescence or separation) and in the case of separation the formation and the size of the satellite droplets. The time evolution of the geometrical characteristics of the ligament, for various Weber numbers and impact parameters, is calculated and details are shown of the velocity and pressure fields particularly at the ligament pinch off location not hitherto available. Gas bubbles due to collision are trapped within the liquid phase as it has also been observed in experiments and their volume is calculated.

Can a strong magnetic background modify the nature of the chiral transition in QCD?

The presence of a strong magnetic background can modify the nature and the dynamics of the chiral phase transition at finite temperature: for high enough magnetic fields, comparable to the ones expected to be created in noncentral high-energy heavy ion collisions at RHIC and the LHC, the original crossover is turned into a first-order transition. We illustrate this effect within the linear sigma model with quarks to one loop in the MS ¯ scheme for N f = 2 .

CP Violation in the Linear Sigma Model

Motivated by the possibility of the formation of CP-odd domains in heavy ion collisions, we investigate the effects of CP violation on the chiral transition within the linear sigma model with two flavors of quarks. We also study how the CP-odd system is affected by the presence of a strong magnetic field, that is presumably generated in a non-central heavy ion collision. We find that both ingredients play an important role, influencing drastically the nature of the phase transition and the critical temperature.

Single photons from relativistic collisions of lead nuclei at energies available at the CERN Super Proton Synchrotron (SPS): A reanalysis

We present a reanalysis of single photon production from a relativistic collision of lead nuclei at CERN SPS measured by the WA98 experiment. The refinements include use of isospin and shadowing corrected NLO pQCD treatment for prompt photon production using an optimized scale for factorization, renormalization, and fragmentation and use of hydrodynamics suited for noncentral collisions along with a well tested equation of state admitting a quark-hadron phase transition. A quantitative explanation of the data requires a large initial temperature (at a small formation time of about 0.2 fm/$c$) and a moderate increase in the prompt yield which could perhaps be attributed to the Cronin effect in nuclei. The data can also be explained using a moderate initial temperature (at a formation time of about 1 fm/$c$) with a very large $K$-factor multiplying the prompt yield. We show that different initial times give rise to different values for the elliptic flow parameter ${v}_{2}$ for thermal photons. We also argue that a measurement of ${v}_{2}$ for thermal photons could also distinguish between the scenarios with or without a phase transition.

J/ψ azimuthal anisotropy relative to the reaction plane in Pb-Pb collisions at 158 GeV per nucleon

The J/$\psi$ azimuthal distribution relative to the reaction plane has been measured by the NA50 experiment in Pb-Pb collisions at 158 GeV/nucleon. Various physical mechanisms related to charmonium dissociation in the medium created in the heavy ion collision are expected to introduce an anisotropy in the azimuthal distribution of the observed J/$\psi$ mesons at SPS energies. Hence, the measurement of J/$\psi$ elliptic anisotropy, quantified by the Fourier coefficient v$_2$ of the J/$\psi$ azimuthal distribution relative to the reaction plane, is an important tool to constrain theoretical models aimed at explaining the anomalous J/$\psi$ suppression observed in Pb-Pb collisions. We present the measured J/$\psi$ yields in different bins of azimuthal angle relative to the reaction plane, as well as the resulting values of the Fourier coefficient v$_{2}$ as a function of the collision centrality and of the J/$\psi$ transverse momentum. The reaction plane has been estimated from the azimuthal distribution of the neutral transverse energy detected in an electromagnetic calorimeter. The analysis has been performed on a data sample of about 100 000 events, distributed in five centrality or p$_{\rm T}$ sub-samples. The extracted v$_{2}$ values are significantly larger than zero for non-central collisions and are seen to increase with p$_{\rm T}$.

Eccentricity Scaling of Elliptic Flow in Relativistic Au+Au Collisions

Elliptic flow for Au+Au non-central collisions at = 200 GeV is investigated within a (2+1)-dimensional hydrodynamic model. The results show that the eccentricity scaling for the collisions is almost perfect. The evolution including the phase transition conforms to the demand of scaling invariance of hydrodynamics of the collision system.

Azimuthal anisotropy: Ridges, recombination, and breaking of quark number scaling

Azimuthal anisotropy is studied by taking into account the ridges created by semihard scattering, which is sensitive to the initial spatial configuration in noncentral heavy-ion collisions. No rapid thermalization is required. Although hydrodynamics is not used in this study, the validity of hydrodynamical expansion is not excluded at later time after equilibration is achieved. Phenomenological properties of the bulk and ridge behaviors are used as inputs to determine the elliptic flow of pion and proton at low p{sub T}. At intermediate p{sub T} the recombination of shower partons with thermal partons becomes more important. The {phi} dependence arises from the variation of the in-medium path length of the hard parton that generates the shower. The p{sub T} dependence of v{sub 2} is therefore very different at intermediate p{sub T} compared to that at low p{sub T}. Quark number scaling of v{sub 2} is shown to be only approximately valid at low p{sub T}, but is broken at intermediate p{sub T}, even though recombination is the mechanism of hadronization in all p{sub T} regions considered.

High-pT direct photon spectra and azimuthal anisotropy measurements in 200 GeV Au+Au collisions at RHIC-PHENIX

Direct photons are a powerful probe to study the property of quark–gluon plasma (QGP) in high energy heavy-ion collisions. In non-central collisions, the anisotropy of the collision region produces the different pressure gradients and particle density that results in different anisotropy of particle emission, depending on the production processes of photons. Therefore, an azimuthal anisotropy parameter v2 is a powerful tool to explore the source of direct photons. We report on the latest direct photon analysis of the nuclear modification factor in and 62.4 GeV Au + Au collisions, and v2 at high pT in 200 GeV Au + Au collisions at RHIC-PHENIX (Run4). We also present the analysis status, using a larger statistics and better reaction plane information from a new detector available from RHIC Run7 data.

Elliptic flow arising from ridges due to semi-hard scattering

Azimuthal anisotropy in heavy-ion collisions is studied by taking into account the ridges generated by semi-hard scattering of intermediate-momentum partons, which can be sensitive to the initial spatial configuration of the medium in non-central collisions. In a simple treatment of the problem where the recombination of only thermal partons is considered, analytical formulas can be derived that yield results in accord with the data on v2 for pT<1–2 GeV/c. Centrality dependence is described by a geometrical factor. Ridge phenomenology is used to determine the initial slopes of v2 at low pT for both pion and proton. For higher pT, shower partons from high-pT jets must be included, but they are not considered here.

Chiral transition in a strong magnetic background

The presence of a strong magnetic background can modify the nature and the dynamics of the chiral phase transition at finite temperature. We compute the modified effective potential in the linear sigma model with quarks to one loop in the MS scheme for N{sub f}=2. For fields eB{approx}5m{sub {pi}}{sup 2} and larger a crossover is turned into a weak first-order transition. We discuss possible implications for noncentral heavy ion collisions at the Relativistic Heavy Ion Collider and the Large Hadron Collider and for the primordial QCD transition.

Superhorizon fluctuations and acoustic oscillations in relativistic heavy-ion collisions

We focus on the initial-state spatial anisotropies, originating at the thermalization stage, for central collisions in relativistic heavy-ion collisions. We propose that a plot of the root-mean-square values of the flow coefficients $\sqrt{\overline{{v}_{n}^{2}}}\ensuremath{\equiv}{v}_{n}^{\mathrm{rms}}$, calculated in a laboratory fixed coordinate system, for a large range of $n$ from 1 to about 30, can give nontrivial information about the initial stages of the system and its evolution. We also argue that for all wavelengths \ensuremath{\lambda} of the anisotropy (at the surface of the plasma region) much larger than the acoustic horizon size ${H}_{s}^{\mathrm{fr}}$ at the freeze-out stage, the resulting values of ${v}_{n}^{\mathrm{rms}}$ should be suppressed by a factor of order $2{H}_{s}^{\mathrm{fr}}/\ensuremath{\lambda}$. For noncentral collisions, these arguments naturally imply a certain amount of suppression of the elliptic flow. Further, by assuming that initial flow velocities are negligible at thermalization stage, we discuss the possibility that the resulting flow could show imprints of coherent oscillations in the plot of ${v}_{n}^{\mathrm{rms}}$ for subhorizon modes. For gold-gold collision at 200 GeV/nucleon center-of-mass energy, these features are expected to occur for $n\ensuremath{\geqslant}5$, with $n&lt;4$ modes showing suppression due to being superhorizon. This has strong similarities with the physics of the anisotropies of the cosmic microwave background radiation (CMBR) resulting from inflationary density fluctuations in the universe (despite important differences such as the absence of gravity effects for the heavy-ion case). It seems possible that the statistical fluctuations due to finite multiplicity may not be able to mask such features in the flow data or at least a nontrivial overall shape of the plot of ${v}_{n}^{\mathrm{rms}}$ may be inferred. In that case, the successes of analysis of CMBR anisotropy power spectrum to get cosmological parameters can be applied for relativistic heavy-ion collisions to learn about various relevant parameters at the early stages of the evolving system.

Global quark polarization in noncentralA+Acollisions

Partons produced in the early stage of noncentral heavy-ion collisions can develop a longitudinal fluid shear because of the unequal local number densities of participant target and projectile nucleons. Under such fluid shear, local parton pairs with nonvanishing impact parameters have finite local relative orbital angular momentum along the direction opposite to the reaction plane. Such a finite relative orbital angular momentum among locally interacting quark pairs can lead to global quark polarization along the same direction because of spin-orbital coupling. Local longitudinal fluid shear is estimated within both the Landau fireball and the Bjorken scaling model of initial parton production. Quark polarization through quark-quark scatterings with the exchange of a thermal gluon is calculated beyond the small-angle scattering approximation in a quark-gluon plasma. The polarization is shown to have a nonmonotonic dependence on the local relative orbital angular momentum dictated by the interplay between electric and magnetic interactions. It peaks at a value of relative orbital angular momentum which scales with the magnetic mass of the exchanged gluons. With the estimated small longitudinal fluid shear in semiperipheral Au+Au collisions at energies currently available at the BNL Relativistic Heavy Ion Collider (RHIC), the final quark polarization is found to be small $|{P}_{q}|&lt;0.04$ in the weak coupling limit. Possible behavior of the quark polarization in the strong coupling limit and implications on the experimental detection of such global quark polarization at RHIC and CERN Large Hadron Collider (LHC) are also discussed.

Simulating elliptic flow with viscous hydrodynamics

In this work we simulate a viscous hydrodynamical model of non-central Au-Au collisions in 2+1 dimensions, assuming longitudinal boost invariance. The model fluid equations were proposed by \"{O}ttinger and Grmela \cite{OG}. Freezeout is signaled when the viscous corrections become large relative to the ideal terms. Then viscous corrections to the transverse momentum and differential elliptic flow spectra are calculated. When viscous corrections to the thermal distribution function are not included, the effects of viscosity on elliptic flow are modest. However, when these corrections are included, the elliptic flow is strongly modified at large $p_T$. We also investigate the stability of the viscous results by comparing the non-ideal components of the stress tensor ($\pi^{ij}$) and their influence on the $v_2$ spectrum to the expectation of the Navier-Stokes equations ($\pi^{ij} = -\eta \llangle \partial_i u_j \rrangle$). We argue that when the stress tensor deviates from the Navier-Stokes form the dissipative corrections to spectra are too large for a hydrodynamic description to be reliable. For typical RHIC initial conditions this happens for $\eta/s \gsim 0.3$.

Centrality dependence of isospin effect signatures inSn124+64Ni andSn112+Ni58reactions

Signatures of isospin effects were investigated for neutron-rich (Sn124+Ni64) and neutron-poor (Sn112+Ni58) systems at 35 MeV/nucleon for noncentral collisions. The centrality dependence of these signatures was tested for several impact parameter estimators. Our main observations are (i) the yields of H1 and He3 particles in the neutron-poor system are strongly enhanced with respect to the neutron-rich system, and the yields of H3, He6, and Li7,8 are suppressed at all impact parameters, (ii) the yields of H2, He4, and Li6 particles are almost the same for both systems, (iii) the N/Z ratio of intermediate mass fragments is correlated with the neutron richness of the system and is weakly dependent on the centrality of the collision, and (iv) the neutron richness of the detected fragments increases strongly with decreasing rapidity in the range from that of the projectile-like fragment to the c.m. region. The gross features of experimental data are reproduced by quantum molecular dynamics model calculations. A comparison between model calculations and the data indicates that the fragments produced in the c.m. regions are weakly excited.6 MoreReceived 8 October 2007DOI:https://doi.org/10.1103/PhysRevC.77.014610©2008 American Physical Society

Fast hadron freeze-out generator. II. Noncentral collisions

The fast Monte Carlo procedure of hadron generation developed in our previous work is extended to describe noncentral collisions of nuclei. We consider different possibilities to introduce appropriate asymmetry of the freeze-out hypersurface and flow velocity profile. For comparison with other models and experimental data, we demonstrate the results based on the standard parametrizations of the hadron freeze-out hypersurface and flow velocity profile assuming either a common chemical and thermal freeze-out or the chemically frozen evolution from chemical to thermal freeze-out. The ++ generator code is written under the framework and is available for public use at http://uhkm.jinr.ru/.

Radiative jet energy loss in a three-dimensional hydrodynamical medium and highpTazimuthal asymmetry ofπ0suppression at mid and forward rapidity in Au+Au collisions atsNN=200GeV

The nuclear modification factor ${R}_{\mathit{AA}}$ for ${\ensuremath{\pi}}_{0}$ production in Au+Au collisions at $\sqrt{s}=200A$ GeV is calculated and studied at high transverse momenta ${p}_{T}$. The soft thermalized nuclear medium is described within the framework of relativistic ideal three-dimensional hydrodynamics. The energy loss of partonic jets is evaluated in the context of gluon bremsstrahlung in the thermalized partonic matter. We provide a systematic analysis of the azimuthal asymmetry of ${\ensuremath{\pi}}_{0}$ suppression at high ${p}_{T}$ in central and noncentral collisions at mid and forward rapidity. The determination of ${R}_{\mathit{AA}}$ as a function of ${p}_{T}$ at different azimuthal angles and different rapidities makes for a stringent test of our theoretical understanding of jet energy loss over a variety of in-medium path lengths, temperatures, and initial partonic jet energies. This lays the groundwork for a tomography of the nuclear medium.

Suppression of elliptic flow in a minimally viscous quark–gluon plasma

We compute the time evolution of elliptic flow in non-central relativistic heavy-ion collisions, using a (2+1)-dimensional code with longitudinal boost-invariance to simulate viscous fluid dynamics in the causal Israel–Stewart formulation. We show that even “minimal” shear viscosity η/s=ℏ/(4π) leads to a large reduction of elliptic flow compared to ideal fluid dynamics, raising questions about the interpretation of recent experimental data from the Relativistic Heavy Ion Collider.

SINGLE-EVENT HANBURY-BROWN–TWISS INTERFEROMETRY

Large spatial density fluctuations in high energy heavy-ion collisions can come from many sources: initial transverse density fluctuations, non-central collisions, phase transitions, surface tension, and fragmentations. The common presence of some of these sources in high energy heavy-ion collisions suggests that large scale density fluctuations may often occur. The detection of large density fluctuations by single-event Hanbury-Brown–Twiss interferometry in heavy-ion collisions will provide useful information on density fluctuations and the dynamics of heavy-ion collisions.

Selected results on strong and coulomb-induced correlations from the STAR experiment

Using recent high-statistics STAR data from Au+Au and Cu+Cu collisions at full RHIC energy I discuss strong and Coulomb-induced final state interaction effects on identical ($\pi-\pi$) and non-identical ($\pi-\Xi$) particle correlations. Analysis of $\pi-\Xi$ correlations reveals the strong and Coulomb-induced FSI effects allowing for the first time to estimate space extension of $\pi$ and $\Xi$ sources and average shift between them. Source imaging technique providing clean separation of these effects from effects due to the source function itself is applied to one-dimensional relative momentum correlation function of identical pions. For low momentum pions and/or non-central collisions large departure from a single-Gaussian shape is observed.

Global polarization measurement in Au+Au collisions

The system created in noncentral relativistic nucleus-nucleus collisions possesses large orbital angular momentum. Because of spin-orbit coupling, particles produced in such a system could become globally polarized along the direction of the system angular momentum. We present the results of Lambda and (Lambda) over bar hyperon global polarization measurements in Au+Au collisions at root s(NN)=62.4 and 200 GeV performed with the STAR detector at the BNL Relativistic Heavy Ion Collider (RHIC). The observed global polarization of Lambda and (Lambda) over bar hyperons in the STAR acceptance is consistent with zero within the precision of the measurements. The obtained upper limit, |P-Lambda,P-(Lambda) over bar|<= 0.02, is compared with the theoretical values discussed recently in the literature.