Partonic effect on anisotropic flows of Ω baryon for Au+Au at 62.4 and 200 GeV/c

The elliptic flow v₂ and the fourth order anisotropic flow v₄ of (Ω+Ω̄) have been studied in the framework a parton–hadronic transport model, namely a multi-phase transport (AMPT) model, for ¹⁹⁷Au+¹⁹⁷Au collisions at = 200 GeV and 62.4 GeV. The transverse momentum (p_T) and the transverse kinetic energy (m_T-m₀) dependence of v₂ and v₄ are presented. The calculation in the AMPT model seems consistent with the STAR data. The results show that the v₂ of (Ω+Ω̄) in 200 GeV obeys the constituent quark number scaling that has been observed for other mesons and baryons. Comparison of (Ω+Ω̄) elliptic flow v₂ in the default version of AMPT, the melting version of AMPT and the RQMD model calculation, shows that the parton cascade process is important to reproduce the sizeable v₂, and the string melting AMPT model preferably reproduces (Ω+Ω̄) elliptic flow v₂ in ¹⁹⁷Au+¹⁹⁷Au collisions at = 200 GeV. The v₂ of (Ω+Ω̄) in the 62.4 and 200 GeV collisions seem similar, and the p_T dependence of (Ω+Ω̄) baryons’ v₄ in 62.4 GeV and 200 GeV looks also similar in the string melting AMPT model, which indicates that a similar partonic matter phase has been reached in both energies.     

Spin physics in the high energy hadron productions. A systematic study of the spin asymmetries induced by <Emphasis Type="Italic">pp, γp,ep</Emphasis> and λ<Emphasis Type="Italic">p</Emphasis> collisions

The spin polarizations of hadrons inclusively produced by pp, γp and λp collisions are studied by the quark rearrangement model. The present model is a phenomenological one based on the relativistic spin equations of motion and using the quark distribution functions in hadrons and photon. A general success of the model is demonstrated. We find usefulness of the present formulation for studying the dynamics producing spin asymmetry distributions and the statics determining signs and magnitudes of the spin polarization by reflecting the characteristic quark structure in hadrons.     

The analysis of π− mesons produced in nucleus-nucleus collisions at a momentum of 4.5 GeV/c nucleon in light front variables

The light front analysis of π⁻ mesons in He(Li,C), C-Ne, C-Cu and O-Pb collisions is carried out. The phase space of secondary pions is divided into two parts in one of which the thermal equilibrium assumption seems to be in a good agreement with the data. Corresponding temperatures T are extracted and their dependence on (A _P·A _T)^1/2 is studied. The results are compared with the predictions of the Quark-Gluon String Model (QGSM). The QGSM satisfactorily reproduces the experimental data for light and intermediate-mass nuclei. Received: 29 September 1999     

The comparison of characteristics of π− mesons produced in central Mg-Mg interactions with the quark gluon string model predictions

A detailed study of pion production in central Mg-Mg collisions at a momentum of 4.3 GeV/c per incident nucleon was carried out with use of the setup GIBS. The average kinematical characteristics of pions (multiplicity n ₋, momentum P, transverse momentum P _T, emission angle Θ, rapidity Y) and corresponding distributions have been obtained. The experimental results have been compared with the predictions of the Quark Gluon String Model (QGSM) and satisfactory agreement between the experimental data and the model has been found. The QGSM reproduces also the dependence of average P _T on n ₋. The temperatures of π⁻ mesons have been estimated in the rapidity interval of 0.5 ≤ Y ≤ 2.1. A satisfactory fit for π⁻ mesons has been achieved by using a form involving two temperatures T ₁ and T ₂. It is found that the QGSM underestimates T ₂ by (10−15)%. The data have been analyzed using the transverse momentum technique. The observed dependence of the <P _x ^′(Y)> on Y shows the S-shape behaviour. The slope at midrapidity F has been determined. The QGSM reproduces the <P _x> distribution satisfactorily, but underestimates the parameter F. Received: 2 August 1997 / Revised version: 17 November 1997     

Understanding of radial and elliptic expansion with quark number scaling and blast wave model in 200 GeV Au+Au at RHIC-PHENIX

Measurement of azimuthal anisotropy is one of the most important study because of its relation to the initial stage. Especially, the elliptical anisotropy which is measured as the second coefficient of Fourier expansion of particle azimuthal distribution is believed to carry the information about the initial geometrical anisotropy. It seems the identified hadron v ₂ depends on the number of quark contents of the hadron. The experimental result of quark number scaling of v ₂ suggests quark level collectivity in the hot dense matter and quark coalescence mechanism to form hadron from quark matter via quark-gluon phase transition. The measured v ₂ and p _T spectra are analyzed with various assumptions based on the blast wave model in order to understand the freeze-out temperature and collective flow after the system expansion.     

Elliptic flow in a hadron-string cascade model at 130 GeV energy

We present the analysis of elliptic flow at =130 A GeV energy in a hadron-string cascade model. We find that the final hadronic yields are qualitatively described. The elliptic flow v ₂ is reasonably well-described at low transverse momentum (p t<1 GeV/c) in mid-central collisions. On the other hand, this model does not explain v ₂ at high p t or in peripheral collisions and thus generally, it underestimates the elliptic flow at RHIC energy.     

Momentum spectra,anisotropic flow,and ideal fluids

If the matter produced in ultrarelativistic heavy-ion collisions reaches thermal equilibrium, its subsequent evolution follows the laws of ideal fluid dynamics. We show that general predictions can be made on this basis alone, irrespective of the details of the hydrodynamical model. We derive several scaling rules for momentum spectra and anisotropic flow (in particular the elliptic flow, v₂$v_2$, and the hexadecupole flow, v₄$v_4$) of identified particles. Comparison with existing data is briefly discussed, and qualitative predictions are made for LHC.     

Sensitivity of the dynamics of Na + Na$\mathsf{_2}$ collisions on the three-body interaction at ultralow energies

We have studied the quantum dynamics of collisions between spin-stretched Na atoms and Na₂ molecules. Cross-sections and rate coefficients for vibrational relaxation of Na₂(v,j = 0) have been computed in the 1 nK-0.1 mK energy range using an accurate time-independent method based on hyperspherical coordinates. The complex scattering length and the extension of the Wigner region have been determined. A detailed study of the sensitivity of collisional quantities on the three-body interaction at short distance has been performed. They are very sensitive to three-body effects for the vibrational state v = 1 of Na₂. Rotational distributions have also been calculated and show a more pronounced sensitivity on the three-body interaction, even for v = 2 and 3.Received: 29 March 2004, Published online: 22 June 2004PACS: 34.50.-s Scattering of atoms and molecules     

Sub-leading flow modes in PbPb collisions at sNN = 2.76 TeV from the HYDJET++ model

Recent LHC results on the appearance of sub-leading flow modes in PbPb collisions at 2.76 TeV, related to initial-state fluctuations, are analyzed and interpreted within the HYDJET++ model. Using the newly introduced Principal Component Analysis (PCA) method applied to two-particle azimuthal correlations extracted from the model calculations, the leading and sub-leading flow modes are studied as a function of the transverse momentum (p_T) over a wide centrality range. The leading modes of the elliptic (v₂⁽¹⁾) and triangular (v₃⁽¹⁾) flow calculated with the HYDJET++ model reproduce rather well the v₂{2} and v₃{2} coefficients measured experimentally using the two-particle correlations. Within the p_T ≤ 3 GeV/c range, where hydrodynamics dominates, the sub-leading flow effects are greatest at the highest p_T of around 3 GeV/c. The sub-leading elliptic flow mode (v₂⁽²⁾), which corresponds to the n = 2 harmonic, has a small non-zero value and slowly increases from central to peripheral collisions, while the sub-leading triangular flow mode (v₃⁽²⁾), which corresponds to the n = 3 harmonic, is even smaller and does not depend on centrality. For n = 2, the relative magnitude of the effect measured with respect to the leading flow mode shows a shallow minimum for semi-central collisions and increases for very central and for peripheral collisions. For the n = 3 case, there is no centrality dependence. The sub-leading flow mode results obtained from the HYDJET++ model are in rather good agreement with the experimental measurements of the CMS Collaboration.     

Spin physics in the high energy hadron productions —A systematic study of the spin asymmetries induced by pp, γp, ep and νp collisions

The spin polarizations of hadrons inclusively produced by pp, γp and νp collisions are studied by the quark rearrangement model. The present model is a phenomenological one based on the relativistic spin equations of motion and using the quark distribution functions in hadrons and photon. A general success of the model is demonstrated. We find usefulness of the present formulation for studying the dynamics producing spin asymmetry distributions and the statics determining signs and magnitudes of the spin polarization by reflecting the characteristic quark structure in hadrons.     

Current status of quark-gluon plasma signals

Compelling evidence for the creation of a new form of matter has been claimed to be found in Pb+Pb collisions at SPS. We discuss the uniqueness of often proposed experimental signatures for quark matter formation in relativistic heavy ion collisions. It is demonstrated that so far none of the proposed signals like J/? meson production/suppression, strangeness enhancement, dileptons, and directed flow unambiguously show that a phase of deconfined matter has been formed in SPS Pb+Pb collisions. We emphasize the need for systematic future measurements to search for simultaneous irregularities in the excitation functions of several observables in order to come close to pinning the properties of hot, dense QCD matter from data.     

Strange-quark collectivity of the φ-meson at RHIC

Based on A Multi-Phase Transport (AMPT) model, the elliptic flow v₂ of φ-mesons which is reconstructed from K ⁺ K ^- at the Relativistic Heavy-Ion Collider (RHIC) energy has been studied. The results show that the reconstructed v₂ of the φ-meson can keep the earlier information before φ decays and it seems to obey the number of constituent-quark scaling as other mesons and baryons. This result indicates that the φ v₂ mostly reflects the parton level collectivity developed during the early stage of the collisions and the strange and light up/down quarks have similar collectivity properties before the hadronization.     

Constraints for the nuclear sea quark distributions from the Drell–Yan process at the SPS

Nuclear modifications to the Drell–Yan dilepton production cross sections in and collisions in the leading twist approximation are caused by nuclear effects in the parton distributions of bound nucleons. For non-isoscalar nuclei, isospin corrections must also be considered. We calculate these effects for and Pb+Pb collisions at CERN SPS energies. Our goal is to place constraints on nuclear effects in sea quark distributions in the region . We show that the net nuclear corrections remain small for collisions at GeV. However, in collisions at GeV, effects of are predicted at large M. The data collected by the NA50 collaboration could thus be used to constrain the nuclear effects in the sea quark distributions in the region of the EMC effect, . Received: 6 October 2000 / Revised version: 2 July 2001 / Published online: 19 September 2001     

Predictions of HBT parameters in Pb + Pb collisions at √<Emphasis Type="Italic">s</Emphasis><Subscript><Emphasis Type="Italic">NN</Emphasis></Subscript> = 2.76 TeV from a hadronic rescattering model

A kinematic model based on the superposition of p + p collisions, relativistic geometry and final-state hadronic rescattering is used to predict two-boson HBT parameters in √s _NN = 2.76 TeV Pb + Pb collisions. A short proper time for hadronization is assumed. Previous calculations using this model which were performed for √s _NN = 200 GeV Au + Au collisions were shown to describe reasonably well the trends of two-pion HBT in experiments carried out at that energy, giving the present predictions for Pb + Pb at higher energy some degree of credibility.     

Spectroscopy and Regge trajectories of heavy quarkonia and <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> mesons

The mass spectra of charmonia, bottomonia and B _c mesons are calculated in the framework of the QCD-motivated relativistic quark model based on the quasipotential approach. The dynamics of heavy quarks and antiquarks is treated fully relativistically without application of the nonrelativistic v ²/c ² expansion. The known one-loop radiative corrections to the heavy quark potential are taken into account perturbatively. The heavy quarkonium masses are calculated up to rather high orbital and radial excitations (L=5, n _r =5). On this basis the Regge trajectories are constructed both in the total angular momentum J and radial quantum number n _r . It is found that the daughter trajectories are almost linear and parallel, while parent trajectories exhibit some nonlinearity in the low mass region. Such nonlinearity is most pronounced for bottomonia and is only marginal for charmonia. The obtained results are compared with the available experimental data, and a possible interpretation of the new charmonium-like states above open charm production threshold is discussed.     

Impact parameter dependence of the scaling of anisotropic flowsin intermediate energy heavy-ion collisions

The scaling behaviors of anisotropic flows of light charged particles are studied for 25 MeV/u ⁴⁰Ca+⁴⁰Ca collisions at different impact parameters by the isospin-dependent quantum molecular dynamics model. The nucleon-number scaling of elliptic flow exists and the scaling of the ratios of v₄/v₂² and v₃/(v₁v₂) is applicable to collisions at almost all impact parameters except for peripheral collisions.     

Ionization of hydrogen and helium atoms by highly charged fast ions in collisions with small momentum transfer

Ionization of hydrogen and helium atoms is studied for the case of “soft” collisions with highly charged fast ions with v≲Z≪v² and v≫v ₀, where Z is the ion charge, v is the collision velocity, and v ₀∼1 is the characteristic velocity of the electron in the ground state of the atom. Analytical expressions are derived for the singly and doubly differential cross section for ionization of a hydrogen atom accompanied by the ejection of a slow electron v _e≲v ₀, where v _e is the velocity of the ejected electron with respect to the recoil ion). The results are generalized to the case of single ionization of helium. It is shown that soft collisions provide the main contribution to the hydrogen ionization cross section and for all practical purposes determine the cross section for single ionization of helium. The asymmetry in the angular distribution of the ejected slow electrons and the properties of momentum exchange in such collisions are discussed. Finally, a formula for the cross section for single ionization of helium is proposed. Zh. éksp. Teor. Fiz. 112, 1966–1977 (December 1997)     

Studying the energy dependence of elliptic and directed flow within a relativistic transport approach

The energy excitation functions of directed flow (v₁) and elliptic flow (v₂) from E_beam=90 A MeV to E_cm=200 A GeV are explored within the UrQMD framework and discussed in the context of the available data. The radial and the elliptic flow of the particles produced in a relativistic heavy-ion collision are intimately connected to the pressure and its gradients in the early stage of the reaction. Therefore, these observables should also be sensitive to changes in the equation of state. To prove this connection, the temporal evolution of the pressure, pressure gradients and elliptic flow are shown. For the flow excitation functions it is found that, in the energy regime below E_beam≤10 A GeV, the inclusion of nuclear potentials is necessary to describe the data. Above 40 A GeV beam energy, the UrQMD model starts to underestimate the elliptic flow. Around the same energy the slope of the rapidity spectra of the proton directed flow develops negative values. This effect is known as the third flow component (“antiflow”) and cannot be reproduced by the transport model. The difference between the data and the UrQMD model can possibly be explained by assuming a phase transition from hadron gas to quark–gluon plasma around E_lab=40 A GeV. This would be consistent with the model calculations, indicating a transition from hadronic matter to “string matter” in this energy range. Thus, we speculate that the missing pressure might be generated by strong interactions in the early pre-hadronic/partonic phase of central Au + Au (Pb + Pb) collisions already at lower SPS energies. PACS 25.75.-q; 25.75.Ld; 25.75.Dw; 25.75.Gz; 24.10.Lx     

Azimuthal anisotropy of electrons from heavy flavor decays in \sqrt{s_{NN}} =200 GeV Au-Au collisions at PHENIX

The PHENIX experiment has measured the azimuthal anisotropy parameter v₂, the second harmonic of the azimuthal distribution, for electrons at mid-rapidity (|η|<0.35) as a function of transverse momentum (0.5<p_T (GeV/c)<5.0) in Au+Au collisions at  =200 GeV. From the result we have calculated the non-photonic electron v₂, which is expected to reflect charm quark azimuthal anisotropy, by subtracting the v₂ of electrons from other sources such as photon conversions and Dalitz decays.     

Heavy-flavour spectra in high-energy nucleus–nucleus collisions

The propagation of the heavy quarks produced in relativistic nucleus–nucleus collisions at RHIC and LHC is studied within the framework of Langevin dynamics in the background of an expanding deconfined medium described by ideal and viscous hydrodynamics. The transport coefficients entering into the relativistic Langevin equation are evaluated by matching the hard-thermal-loop result for soft collisions with a perturbative QCD calculation for hard scatterings. The heavy-quark spectra thus obtained are employed to compute the differential cross sections, the nuclear modification factors R _AA and the elliptic-flow coefficients v ₂ of electrons from heavy-flavor decay.