QCD equation of state for heavy ion collisions

In this work, we calculate the equation of state(EoS) of quark gluon-plasma(QGP) using the CornwallJackiw-Tomboulis(CJT) effective action. We get the quark propagator by using the rank-1 separable model within the framework of the Dyson-Schwinger equations(DSEs). The results from CJT effective action are compared with lattice QCD data. We find that, when μ is small, our results generally fit the lattice QCD data when TT_c,but show deviations at and below T_c. It can be concluded that the EoS of CJT is reliable when TT_c. Then,by adopting the hydrodynamic code UVH2+1, we compare the CJT results of the multiplicity and elliptic flow v2 with the PHENIX data and the results from the original EoS in UVH2+1. While the CJT results of multiplicities generally match the original UVH2+1 results and fit the experimental data, the CJT results of v2 are slightly larger than the original UVH2+1 results for centralities smaller than 40% and smaller than the original UVH2+1 results for higher centralities.     

Hot QCD equations of state and RHIC

We show how hot QCD equations of states can be adapted to make definite predictions for quarkgluon plasma at RHIC.We consider equations of state up to O(g⁵) and O[g⁶(ln(1/g)+δ)]. Our method involves the extraction of equilibrium distribution functions for gluons and quarks from these equations of state by capturing the interaction effects entirely in the effective chemical potentials. We further utilize these distribution functions to study the screening length in hot QCD and dissociation phenomenon of heavy quarkonia states by combining this understanding with the semi-classical transport theory.     

Equations of state of MgO,Au, Pt,NaCl-B1, and NaCl-B2: Internally consistent high-temperature pressure scales

Semiempirical equations of state (EoS) of Au, Pt, MgO, NaCl-B1, and NaCl-B2 based on expanded Mie–Grüneisen–Debye approach, which are consistent both with the Mie–Grüneisen–Bose–Einstein approach and the thermochemical, X-ray, ultrasonic and shock-wave data in a wide pressure-temperature range, have been constructed. It is shown that to determine the volume dependence of the Grüneisen parameter, not only shock-wave and static compression data, but also experimental information on heat capacity, bulk moduli, volume, and thermal expansion coefficient at zero pressure need to be taken into account. Intrinsic anharmonicity is of great importance at construction of EoS at high temperatures and x=V/V ₀>1. Cross-comparison of the current equations of state with independent measurements shows that these EoS may be used as the internally consistent and independent pressure scales in a wide range of temperatures and pressures.     

Non-perturbative effects for the Quark-Gluon Plasma equation of state

The non-perturbative effects for the Quark-Gluon Plasma (QGP) equation of state (EoS) are considered. The modifications of the bag model EoS are constructed to satisfy the main qualitative features observed for the QGP EoS in the lattice QCD calculations. A quantitative comparison with the lattice results is done for the SU(3) gluon plasma and for the QGP with dynamical quarks. Our analysis advocates a negative value of the bag constant B.     

On the chromo-electric permittivity and Debye screening in hot QCD

We study the response functions (chromo-electric susceptibilities) for an interacting quark-gluon plasma. The interaction effects have been encoded in the effective fugacities for quasi-partons which are extracted self-consistently from the two equations of state for hot QCD. The first one is the fully perturbative O(g ⁵) EOS and the second one, which is O(g ⁶ln(1/g)) , incorporates some non-perturbative effects. We find that the response function shows large deviations from the ideal behavior. We further determine the temperature dependence of the Debye mass by fixing the effective coupling constant Q² which appears in the transport equation. We show that our formalism naturally yields the leading-order HTL expression for the Debye mass if we employ the ideal EOS. Employing the Debye mass, we estimate the dissociation temperatures for various charmonium and bottomonium bound states. These results are consistent with the current theoretical studies.     

Nonperturbative phenomena in QCD at finite temperature

The main objective of the present study is to analyze various nonperturbative phenomena in QCD both at low, T < T _c , and at high, T > T _c , temperatures. New methods are developed that make it possible, on one hand, to describe data obtained by numerically simulating QCD on a lattice and, on the other hand, to study new physical phenomena in QCD at finite temperature.     

Barrier-disorder induced exciton relaxation via LO-phonons in GaAs/Al x Ga1−x As multiple quantum wells

Hot exciton relaxation is observed in GaAs/Al _x Ga_1–x As multiple quantum wells. The photolumnescence excitation spectra of the localized exciton emission at low temperatures and excitation densities are composed of narrow equidistant peaks exactly separated by the GaAs LO-phonon energy (36 meV). The relaxation mechanism via LO-phonons is found to be important for localized excitons in multiple quantum wells with GaAs layer thicknesses of about 50 Å, where pronounced alloy fluctuations in the barriers provide a strong additional lateral potential which suppresses the dissociation of hot excitons.     

The spatial string tension and dimensional reduction in QCD

The spatial string tension is calculated in 2+1 flavor QCD with a physical strange quark mass and almost physical light quark masses on lattices with N_t=4,6 and 8. The results are compared with predictions of dimensionally reduced QCD. They suggest that dimensional reduction works also in the presence of light dynamical quarks down to temperatures of about 1.5T_c.     

Fragmentation function in non-equilibrium QCD using closed-time path integral formalism

In this paper we implement the Schwinger–Keldysh closed-time path integral formalism in non-equilibrium QCD in accordance to the definition of the Collins–Soper fragmentation function. We consider a high-p _T parton in QCD medium at initial time τ ₀ with an arbitrary non-equilibrium (non-isotropic) distribution function fragmenting to a hadron. We formulate the parton-to-hadron fragmentation function in non-equilibrium QCD in the light-cone quantization formalism. It may be possible to include final-state interactions with the medium via a modification of the Wilson lines in this definition of the non-equilibrium fragmentation function. This may be relevant to the study of hadron production from a quark–gluon plasma at RHIC and LHC.     

Thermodynamic properties of the mixtures of some ionic liquids with alcohols using a simple equation of state

In the present work, we have used a simple equation of state called the GMA EoS to calculate the density of three ionic liquid mixtures including 1-butyl-3-methylimidazolum hexafluorophosphate, [BMIM] [PF₆] + methanol, 1-butyl-3-methylimidazolum tetrafluoroborate, [BMIM] [BF₄] + methanol, and [BMIM] [BF₄] + ethanol at different temperatures, pressures, and compositions. The isothermal compressibility, excess molar volumes, and excess Gibbs molar energy of these mixtures have been computed using this equation of state. The values of statistical parameters show that the GMA EoS can predict these thermodynamic properties very well within the experimental errors. The results show that isothermal compressibility of ionic liquids is lower than alcohols and the effect of temperature and pressure on the isothermal compressibility of ionic liquids is lower than alcohols. The excess molar volumes and excess molar Gibbs energy for these ionic liquid mixtures with alcohols are all negative at various temperatures and pressures over the whole composition range. The results have been interpreted in terms of intermolecular interactions and structural factors of the ionic liquids and alcohols.     

The quark-nucleon phase diagram and quantum chromodynamics

The temperature dependence of a conjectured first-order phase transition between nuclear matter and quark-gluon matter is calculated for temperatures below T = 200 MeV. On the nuclear side a rather successful meson-nucleon mean field theory is applied while quark-gluon matter at large densities and finite temperatures is described perturbatively by quantum chromodynamics. Outside the finite volume of hot and dense quark-gluon matter the physical vacuum is characterized, by the newly determined bag parameter Λ_B = 235 MeV. We observe a dramatic drop in the density of nuclear matter at the phase transition point as the temperature increases, if the scale parameter Λ of QCD is chosen as Λ = 100 MeV. For larger values of Λ the effect is less pronounced. Further work is required to settle this problem.     

Comparison of radiative energy loss models in a hot QCD medium

The suppression of high pT$p_T$ hadron production in heavy ion collisions is thought to be due to energy loss by gluon radiation off hard partons in a QCD medium. Existing models of QCD radiative energy loss in a color-charged medium give estimates of the coupling strength of the parton to the medium which differ by a factor of 5. We will present a side-by-side comparison of two different formalisms to calculate the energy loss of light quarks and gluons: the multiple soft scattering approximation (ASW-MS) and the opacity expansion formalism (ASW-SH and WHDG-rad). A common time-temperature profile is used to characterize the medium. The results are compared to the single hadron suppression R_AA$R_{AA}$ at RHIC energies.     

Hard-thermal-loop QCD trace anomaly

In this proceedings I summarize results of QCD trace anomaly from recent three-loop hard-thermal-loop perturbation theory (HTLpt) calculations. I focus on the trace anomaly scaled by T ² for pure-glue and N _f = 3 QCD. The comparison to available lattice data suggests that for pure-glue QCD agreement between HTLpt results and lattice data for the trace anomaly begins at temperatures above 8 T _c while when including quarks (N _f = 3) agreement begins already at temperatures above 2 T _c . The results in both cases indicate that at very high temperatures the T ²-scaled trace anomaly increases with temperature in accordance with the predictions of HTLpt.     

Directed flow of baryons from high-energy heavy-ion collisions

The collective motion of nucleons from high-energy heavy-ion collisions is analyzed within a relativistic two-fluid model for different equations of state (EoS). As function of beam energy the theoretical slope parameter F _y of the differential directed flow is in good agreement with experimental data, when calculated for the QCD-consistent EoS described by the statistical mixed-phase model. Within this model, which takes the deconfinement phase transition into account, the excitation function of the directed flow (P _x ) turns out to be a smooth function in the whole range from SIS till SPS energies. This function is close to that for pure hadronic EoS and exhibits no minimum predicted earlier for a two-phase bag-model EoS. Attention is also called to a possible formation of nucleon antiflow (F _y < 0) at energies ? 100 A·GeV.     

Lattice quantum chromodynamics equation of state: A better differential method

We propose a better differential method for the computation of the equation of state of QCD from lattice simulations. In contrast to the earlier differential method, our technique yields positive pressure for all temperatures including the temperatures in the transition region. Employing it on temporal lattices of 8, 10 and 12 sites and by extrapolating to zero lattice spacing we obtained the pressure, energy density, entropy density, specific heat and speed of sound in quenched QCD for 0.9 ≤ T/T _c ≤ 3. At high temperatures comparisons of our results are made with those from the dimensional reduction approach and also with those from a conformal symmetric theory.      

Thermal equation of state of goethite (α-FeOOH)

ABSTRACT

The pressure–volume–temperature (P–V–T) equation of state (EoS) of natural goethite (α-FeOOH) has been determined by an X-ray diffraction study using synchrotron radiation. Fitting the volume data to the third-order Birch–Murnaghan EoS yielded an isothermal bulk modulus, B₀ of 85.9(15)?GPa, and a pressure derivative of the bulk modulus, B′, of 12.6(8). The temperature derivative of the bulk modulus, (?B/?T)_P, was –0.022(9)?GPa?K^?1. The thermal expansion coefficient α₀ was determined to be 4.0(5)?×?10^?5?K^?1.     

Nuclear stopping and collective flow in CSR/LanZhou energy region

Nuclear stopping and collective flow for two pairs of symmetric colliding nuclei: ²³⁸U+²³⁸U and ¹²⁹Xe+¹²⁹Xe, which are proposed to be accelerated on Cooling Storage Ring (CSR), External Target Facility (ETF), LanZhou, China, are studied by a hadronic transport model ART1.0. The incident beam energy of Uranium and Xenon can be delivered up to 520 MeV/nucleon and 900MeV/nucleon, respectively. At this CSR energy region, the hot, dense nuclear matter are thought to be obtained in the lab, which is an idea circumstance to study the nuclear equation of state (EoS). As deformation of the Uranium nuclei, it is predicted that significant large baryon density in the tip-tip U+U collision patterns and the large elliptic flow in body-body collision pattern are both avail to study the nuclear EoS.     

Radiative energy loss of high-energy quarks in finite-size nuclear matter and quark-gluon plasma

The induced gluon radiation of a high-energy quark in a finite-size QCD medium is studied. For a sufficiently energetic quark produced inside a medium we find the radiative energy loss ΔE _q∝L ², where L is the distance traveled by quark in the medium. It has a weak dependence on the initial quark energy E _q. The L ² dependence turns to L ¹ as the quark energy decreases. Numerical calculations are performed for a cold nuclear matter and a hot quark-gluon plasma. For a quark incident on a nucleus we predict ΔE _q ≈0.1E _q (L/10fm) ^β , with β close to unity. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 585–589 (25 April 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Quarkonia at Finite T: An Approach Based On QCD Sum Rules and the Maximum Entropy Method

Quarkonium spectral functions at finite temperature are studied, making use of a recently developed method of analyzing QCD sum rules by the maximum entropy method. This approach enables us to directly obtain the spectral function from the sum rules, without having to introduce any specific assumption about its functional form. QCD sum rules for heavy quarkonia incorporate finite temperature effects in form of changing values of the various gluonic condensates that appear in the operator product expansion. These changes depend on the energy density and pressure at finite temperature, which we extract from quenched lattice QCD calculations. As a result, it is found that the charmonium ground states of both S-wave and P-wave channels dissolve into the continuum already at temperatures around or slightly above the critical temperature T _c , while the bottomonium states are less influenced by temperature effects, surviving up to about 2.5 T _c or higher for S-wave and about 2.0 T _c for P-wave states.