No abstract

We calculate the three-loop thermodynamic potential of QCD at finite temperature and chemical potential(s) using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature and density QCD. The resulting analytic thermodynamic potential allows us to compute the pressure, energy density, and entropy density of the quark-gluon plasma. Using these we calculate the trace anomaly, speed of sound, and second-, fourth-, and sixth-order quark number susceptibilities. For all observables considered we find good agreement between our three-loop HTLpt calculations and available lattice data for temperatures above approximately 300 MeV.

We calculate and compare bremsstrahlung and collisional energy loss of hard partons traversing a quark-gluon plasma. Our treatment of both processes is complete at leading order in the coupling and accounts for the probabilistic nature of the jet energy loss. We find that the nuclear modification factor RAA for neutral π 0 production in heavy ion collisions is sensitive to the inclusion of collisional and radiative energy loss contributions while the averaged energy loss only slightly increases if collisional energy loss is included for parent parton energies E ≫ T . These results are important for the understanding of jet quenching in Au+Au collisions at 200 AGeV at RHIC. Comparison with data is performed applying the energy loss calculation to a relativistic ideal (3+1)-dimensional hydrodynamic description of the thermalized medium formed at RHIC.Introduction -Relativistic heavy ion collisions are designed to produce and study strongly interacting matter at high temperatures and densities. Experiments at the Relativistic Heavy Ion Collider (RHIC) have demonstrated that high p T hadrons in central A + A collisions are significantly suppressed in comparison with those in binary p + p collisions, scaled to nucleus-nucleus collisions [1,2,3]. This result has been referred to as jet quenching and has been attributed to the energy loss of hard p T partons due to induced gluon bremsstrahlung in a hot quark-gluon plasma. Bremsstrahlung energy loss has been calculated in several theoretical formalisms before [4,5,6,7,8,9]. Recently such bremsstrahlung calculations were implemented in models employing relativistic ideal (3+1)-dimensional hydrodynamics in order to calculate the nuclear modification factor R AA of neutral pions at RHIC [10,11,12]. Early estimates of the collisional energy loss which used asymptotic arguments indicated that the radiative energy loss is much larger than elastic energy loss [13]. Zakarhov compared radiative energy loss in the light-cone path integral approach and collisional energy loss employing the Bjorken method and concluded collisional energy loss is relatively small in comparison to the radiative one [7]. Renk derives phenomenological limits on radiative vs. collisional energy loss by considering quadratic vs. linear pathlength dependence and concludes that any elastic energy loss component has to be small [14]. In contrast, Mustafa and Thoma find that collisional energy loss has a significant influence on jet quenching [15,16]. Recent studies by Gyulassy and collaborators also point in this direction, see e.g. [17,18].The purpose of this study is to consistently incorporate collisional and radiative energy loss in the same formalism and to employ this formalism in a realistic description of energy loss of hard p T leading partons in the soft nuclear medium as described by (3+1)-dimensional hydrodynamics in 200 AGeV Au+Au collisions at RHIC.We will emphasize three points (the first two of which have been elucidated earlier [19] for bremsstrahlung energy loss). First, in many previous a...

No abstract

No abstract

We have extended the Polyakov-Nambu-Jona-Lasinio (PNJL) model for two degenerate flavours to include the isospin chemical potential (µI ). All the diagonal and mixed derivatives of pressure with respect to the quark number (proportional to baryon number) chemical potential (µ0) and isospin chemical potential upto sixth order have been extracted at µ0 = µI = 0. These derivatives give the generalized susceptibilities with respect to quark and isospin numbers. Similar estimates for the flavour diagonal and off-diagonal susceptibilities are also presented. Comparison to Lattice QCD (LQCD) data of some of these susceptibilities for which LQCD data are available, show similar temperature dependence, though there are some quantitative deviations above the crossover temperature. We have also looked at the effects of instanton induced flavour-mixing coming from the UA(1) chiral symmetry breaking 't Hooft determinant like term in the NJL part of the model. The diagonal quark number and isospin susceptibilities are completely unaffected. The off-diagonal susceptibilities show significant dependence near the crossover. Finally we present the chemical potential dependence of specific heat and speed of sound within the limits of chemical potentials where neither diquarks nor pions can condense.

We have evaluated the electromagnetic spectral function and its spectral properties by computing the one-loop photon polarization tensor involving quarks in the loop, particularly in a strong field approximation compared to the thermal scale. When the magnetic scale is higher than the thermal scale the lowest Landau level (LLL) becomes effectively (1+1) dimensional strongly correlated system that provides a kinematical threshold based on the quark mass scale. Beyond this threshold the photon strikes the LLL and the spectral strength starts with a high value due to the dimensional reduction and then falls off with increase of the photon energy due to LLL dynamics in a strong field approximation. We have obtained analytically the dilepton production rates from LLL considering the lepton pair remains unaffected by the magnetic field when produced at the edge of a hot magnetized medium or affected by the magnetic field if produced inside a hot magnetized medium. For the later case the production rate is of O[|eB| 2 ] along with an additional kinematical threshold due to lepton mass than the former one. We have also investigated the electromagnetic screening by computing the Debye screening mass and it depends distinctively on three different scales (mass of the quasiquark, temperature and the magnetic field strength) of a hot magnetized system. The mass dependence of the Debye screening supports the occurrence of a magnetic catalysis effect in the strong field approximation.

We calculate the quark number susceptibility in the deconfined phase of QCD using the hard thermal loop (HTL) approximation for the quark propagator. This improved perturbation theory takes into account important medium effects such as thermal quark masses and Landau damping in the quark-gluon plasma. We explicitly show that the Landau damping part in the quark propagator for spacelike quark momenta does not contribute to the quark number susceptibility due to the quark number conservation. We find that the quark number susceptibility only due to the collective quark modes deviates from the free one around the critical temperature but approaches free results at infinite temperature limit. The results are in conformity with recent lattice calculations.In recent years substantial experimental and theoretical efforts have been undertaken to investigate the versatile physics issues involved in ultra-relativistic heavy-ion collisions, i.e., collisions of atomic nuclei in which centre-of-mass energy per nucleon is much larger than the nucleon rest mass. The principal goal of this initiative is to explore the phase structure of the underlying theory of strong interactions -Quantum Chromodynamics (QCD) -by creating in the laboratory a new state of matter, the so-called Quark-Gluon Plasma (QGP). This new state of matter is predicted to exist under extreme conditions like at high temperatures and/or densities, when a phase transition takes place from a hadronic to a deconfined state of quarks and gluons [1]. Such information has essentially been confirmed by numerical lattice QCD calculations [2] at finite temperature, which show a rapid increase in energy density and entropy density as a function of temperature. Numerical solutions of QCD also suggest that the critical temperature is about 160 MeV [3] and provide information on the equation of state [4].The various measurements taken at CERN SPS within the Lead Beam Programme do lead to strong 'circumstantial evidence' for the formation of the QGP [5,6]. Evidence is circumstantial as any direct formation of the QGP cannot be identified. Only by some noble indirect diagnostic probes like the suppression of the J/Ψ particle, the enhanced production of strange particles, specially strange antibaryons, excess production of photons and dileptons, the formation of disoriented chiral condensates, etc. the discovery can be achieved. An extensive amount of theoretical study has also been devoted over the last two decades in favour of these well accepted probes of a deconfinement (QGP) phase.Recently screening and fluctuation of conserved quantities have been considered as an important and relevant probes of the QGP formation in heavy-ion collisions [7][8][9][10]. In the confined/chirally broken phase charges are associated with the hadrons in integer units whereas in the deconfined/chirally restored phase they are associated with the quarks in fractional units which could lead to charge fluctuations which are different in the two phases [7,10]. The fluctuations can generally be r...