Valon-hadron crossover and phenomenology of quark-gluon plasma in the context of lattice calculations

The phase crossover in the energy range ΔT ? 50–60 MeV as explicitly suggested by the results of lattice calculations at μ = 0 is interpreted here in terms of an evolving superposition of hadron and subhadron states of nuclear matter, the former being gradually displaced by the latter with increasing temperature. It is shown that the expected imperfectness of the quark-gluon gas even at temperatures substantially higher the chiral-transition temperature may be a direct consequence of a slow decrease [in proportion to 1/ln(T/Λ)] in the Coulomb part of the color particle interaction at short distances.     

Strange-quark matter within the Nambu-Jona-Lasinio model

The equation of state of baryon-rich quark matter is studied within the SU(3) Nambu-Jona-Lasinio model with flavor-mixing interaction. Possible bound states (strangelets) and chiral phase transitions in this matter are investigated at various values of the strangeness fraction r _s. Model predictions are very sensitive to the ratio of the vector and scalar coupling constants, ξ=G _V/G _S. At ξ=0.5 and zero temperature, the binding energy takes a maximum value of about 15 MeV per baryon at r _s?0.4. Such strangelets are negatively charged and have typical lifetimes of about 10^?7s. Calculations are performed at finite temperatures as well. According to these calculations, bound states exist up to temperatures of about 15 MeV. The model predicts a first-order chiral phase transition at finite baryon densities. The parameters of this phase transition are calculated as functions of r _s.     

Thermostatic properties of symmetric nuclear matter

The thermostatic properties of symmetric nuclear matter are calculated by extension of a recent Thomas-Fermi approach to ground-state nuclei by Myers and Swiatecki [1]. We have computed the free energy per nucleon f(T, n) in Landau's quasiparticle approximation and have derived from it the relevant thermostatic properties. In view of its application to finite excited nuclei, the degenerate limit of nuclear matter is discussed in particular. As an interesting result we find at higher temperatures van-der-Waals-like isotherms in the p-n plane. Below the critical temperature T_c = 17.3 MeV two phases of nuclear matter, liquid and vapour, are defined by these. Comparing these results with the reduced phase transition data of ³He, ⁴He, and “inert gases,” we find that nuclear matter is similar to the He-isotopes, but differs considerably from the inert gases.     

Hadron-quark phase coexistence in a hybrid MIT-Bag model

The phase transition of hadronic to quark matter and the boundaries of the hadron-quark coexistence phase are studied within the two Equation of State (EoS) models. The relativistic effective mean-field approach with constant and density-dependent meson-nucleon couplings is used to describe hadronic matter, and the MIT-Bag model is adopted to describe quark matter. The boundaries of the mixed phase for different Bag constants are obtained solving the Gibbs equations. We notice that the dependence on the Bag parameter of the critical temperatures (at zero chemical potential) can be well reproduced by a fermion ultrarelativistic quark gas model, without contribution from the hadron part. At variance, the critical chemical potentials (at zero temperature) are very sensitive to the EoS of the hadron sector. Hence, the contribution of the hadronic interaction is much more relevant for the determination of the transition to the quark-gluon plasma at finite baryon density and low T . Moreover, in the low-temperature and finite chemical potential region no solutions of the Gibbs conditions are existing for small Bag-constant values, B < (135 MeV)⁴ . Isospin effects in asymmetric matter appear important in the high chemical-potential regions at lower temperatures, of interest for the inner-core properties of neutron stars and for heavy-ion collisions at intermediate energies.     

On the role of quantum tunnelling and statistical effects in the liquid gas phase transition of hot nuclei

The triggering of the liquid-gas phase transition in hot nuclear matter by quantum and statistical fluctuations is studied in a microscopic approach to nucleation which is a fluid-dynamical version of the imaginary-time dependent mean-field theory at finite temperature. It is found that quantum tunnelling processes are only important below T = 1 MeV.     

Self-consistent calculations of hypernuclear properties with the Skyrme interaction

An extension of the Skyrme-Hartree-Fock formalism is proposed for calculating Λ binding energies (B_Λ) in hypernuclei throughout the periodic table. The calculation includes the self-consistent nuclear polarization by the Λ hyperon. Realistic estimates for ground state B_Λ's are obtained with a simple effective ΛN force and are compared with a Λ-nucleus potential model. The Λ particle excitation spectra have also been calculated. They are discussed in the context of strangeness analog state formation and the emphasis is put on the symmetry between Λ and nuclear states.     

Dyson-Schwinger approach to color superconductivity at finite temperature and density

We investigate the phases of dense QCD matter at finite temperature with Dyson-Schwinger equations for the quark propagator for N _f = 2 + 1 flavors. For the gluon propagator we take a fit to quenched lattice data and add quark-loop effects perturbatively in a hard-thermal-loop-hard-dense-loop approximation. We consider 2SC and CFL-like pairing with chiral up and down quarks and massive strange quarks and present results for the condensates and the phase diagram. We find a dominant CFL phase at chemical potentials larger than 500-600MeV. At lower values of the chemical potential we find a 2SC phase, which also exists in a small band at higher temperatures for larger chemical potentials. With values of 20–30 MeV, the critical temperatures to the normal phase turn out to be quite small.     

Production of strange particles in antineutrino interactions at the CERN PS

We have studied neutral strange particle production in the bubble chamber Gargamelle filled with propane and exposed to antineutrinos from the CERN PS. Cross sections are presented for Λ, Σ⁰ and K⁰ production. Associated production reactions (ΔS = 0) have been observed in the charged and the neutral current channels. From 45 candidates for the quasi-elastic reaction $\text{ν}\text{p}\text{→ μ}{}^{\mathrm{+}}\text{Λ}$, on bound and free protons, estimates of the axial transition form factor M_A have been made using the total cross section and the t distribution. The weighted average from the two methods is M_A = 862 ± 190 MeV. From a subsample of 15 candidates for $\text{ν}$ interactions on free protons in propane, with (28±6)% background from $\text{ν}$ interactions on bound protons, we obtain M_A = 883 ± 243 MeV. The polarization of the Λ hyperons has been studied for the quasi-elastic reaction. We observe a significant Λ polarization in the production plane, normal to the Λ line of flight. The observed polarizations agree well with the predicted theoretical polarizations without any contribution from second-class axial coupling.     

Properties of hot nuclei originating from collisions of light relativistic ions with heavy targets

Nuclear multifragmentation is the main channel of decay of hot nuclei at temperatures of 5 to 6 MeV. Investigation of this process permits experimentally determining the critical temperature for the liquid-gas nuclear phase transition. It was found that T _c = 17±2 MeV. Characteristic times of the process are measured by analyzing correlation functions for fragment pairs. The mean fragment-emission time was found to be 1 to 2 × 10^?22 s.     

Relativistic nuclear and neutron matter at finite temperatures

Nuclear matter as well as neutron matter is studied in the framework of a relativistic nuclear field theory at finite temperature. A spectral representation for the two-point Green's function at finite temperature and finite density is constructed. The bulk properties of the interacting system are calculated in the Hartree and Hartree-Fock approach. In additionσ ³- andσ ⁴-self-interactions have been taken into account. We present and discuss the results of hot and dense matter for temperaturesT≦ 50 MeV and densitiesθ≦6θ ₀ (ρ ₀≈0.17 fm^?3) using six different model parameter sets.     

Thermodynamic properties of superconducting nuclear matter

Phase diagrams of superconducting nuclear matter are calculated by solving a set of finite temperature gap equations, using several Skyrme effective interactions. Our results indicate that nuclear matter may have a superconducting phase in a small region with density near one half of the normal nuclear matter density and temperature k_BT ≲ 1.4 MeV. Our calculation is based on a finite temperature Green's function method with an abnormal pair cutoff approximation. The same approximation is employed in deriving the internal energy, entropy and chemical potential of superconducting nuclear matter. In this way, its equation of state is obtained, and compared with that of normal nuclear matter. The energy gap of superconducting nuclear matter is found to depend rather sensitively on both density and temperature. This dependence is analysed in terms of the Skyrme interaction parameters. The correlation effect on chemical potential is found to be important at high density, and its inclusion is essential in determining the equation of state of superconducting nuclear matter.     

High-energy photons as a thermometer for ultra-relativistic nuclear collisions

I calculate the transverse momentum distribution for high-energy (p _T =1–3 GeV) photons produced in ultra-relativistic nuclear collisions. I assume a strong first-order deconfinement phase transition, and consider transition temperatures in the range 150–200 MeV. For simplicity, I also assume thermal and chemical equilibrium throughout the collision. I then fit the transverse momentum distribution in the range 1–2 GeV to a thermal distribution. The fitting temperature depends only on the transition temperature, so this provides an accurate (although theory-dependent) measure of the QCD transition temperature.     

Quark-gluon plasma in 4 GeV/c antiproton annihilations on nuclei

Recent data on strange particle production in 4 GeV/c antiproton annihilations on Ta can be successfully interpreted if quark-gluon plasma formation is assumed along with a simple reaction model in which antiprotons deposit energy in the forward cone of nuclear matter within the target nucleus. The observed spectra and total abundances of lambdas and kaons are consistent with the hypothesis that (super cooled) quark matter phase has been formed at a rather modest temperature T≲60 MeV. The spectra can then be successfully interpreted both with reference to their form and relative abundance.     

Thermal dileptons from quark and hadron phases of an expanding fireball

A fireball model with time evolution based on transport calculations is used to examine the dilepton emission rate of an ultra-relativistic heavy-ion collision. A transition from hadronic matter to a quark-gluon plasma at a critical temperature T _C between 130-170 MeV is assumed. We also consider a possible mixed phase scenario. We include thermal corrections to the hadronic spectra below T _C and use perturbation theory above T _C. The sensitivity of the spectra with respect to the freeze-out temperature, the initial fireball temperature and the critical temperature is investigated. Received: 4 August 2000 / Accepted: 14 November 2000     

Pion condensation in heavy ion collisions

We calculate the pion spectrum in dense nuclear matter for finite temperatures. The critical temperatureT _c(ρ) that marks the beginning of a second order phase transition due to pion condensation is given in a phase diagram. We show that in heavy ion collisions, pion condensation should occur, leading to an enhancement in the formation of nuclear shock waves.     

The large-N deconfinement phase transition in a partially reduced Eguchi-Kawal model

We construct generalized twisted Eguchi-Kawai models which for large-N reduce space-time to a lattice of arbitrary size. Large-N lattice gauge theory at finite temperature is investigated in a model on a lattice with L₀ time slices and two lattice points in very time slice. We observe the large-N deconfinement phase transition in the weak coupling region. Assuming asymptotic scaling we find a transition temperature T_c = (101±4)Λ_L.     

A mechanical definition of the thermodynamic pressure

A dynamical definition of pressure for grand-canonical Gibbs measures in bounded regions Λ is rigorously discussed: It measures the momentum transferred to the walls of the container by the elastically colliding particles. The local pressureP(r, δΛ) so obtained is proportional to the temperature and the local density at the boundaries of Λ. This allows us to obtain a rigorous proof of the virial theorem of Clausius. In this picture the thermodynamic pressureP ^d (Λ) is obtained as the average ofP(r, δΛ) onδΛ. Its relationship with the usual equilibrium pressureP _eq(Λ) = (βsΛ¦)^?1lnZ _Λ (Z _Λ is the grand-canonical partition function) is then discussed. In the particular case in which the regions A are spheres, it is shown that P_d(Λ) converges in average so that, if the limit of P_d(Λ) exists, it equals P_eq, the thermodynamic limit of the equilibrium pressure P_eq(Λ). Finally, convergence ofP _d(Λ) is proven to hold in the particular case of one-dimensional hard cores in the absence of phase transitions.     

Magnetized Quark-Gluon Plasma at the LHC

In QCD, the strengths of the large scale temperature dependent chromomagnetic, B₃, B₈, and usual magnetic, H fields spontaneously generated in quark-gluon plasma after the deconfinement phase transition (DPT), are estimated. The consistent at high temperature effective potential accounting for the oneloop plus daisy diagrams is used. The heavy ion collisions at the LHC and temperatures T not much higher than the phase transition temperature T_d are considered. The critical temperature for the magnetized plasma is found to be T_d (H) ～ 110–120 MeV. This is essentially lower compared to the zero field value T_d (H=0) ～ 160–180 MeV usually discussed in the literature. Due to contribution of quarks, the color magnetic fields act as the sources generating H. The strengths of the fields are B₃(T), B₈(T) ～ 10¹⁸–10¹⁹ G, H(T) ～ 10¹⁶–10¹⁷ G for temperatures T ～ 160–220 MeV. At temperatures T < 110–120 MeV the effective potential minimum value being negative approaches to zero. This is signaling the absence of the background fields and color confinement.