Quark number susceptibility in hard thermal loop approximation

Abstract

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...

Structure functions and pair correlations of the quark-gluon plasma

“…This result also agrees with the free quark number susceptibility χ q (T ) = N f T 2 [21]. Let us note here that using the 1-loop polarization tensor beyond the HTL limit [26][27][28] in (16) also leads to an unphysical result, namely a monotonically decreasing S(p).…”

“…The longitudinal part of the polarization tensor also determines the quark number susceptibility χ q (T ), which is proportional to the p = 0 limit of the static structure function (16), χ q (T ) = (n/2T ) S(0) [21]. In the case of an isotropic and homogeneous plasma the polarization tensor depends only on ω and p = |p|.…”

“…Using (28) the radial distribution function becomes unphysical, i.e., negative, for small r indicating the failure of the Vlasov approach at small inter-particle distances [18]. In a next step one could use HTL-resummed quark propagators and quark-gluon vertices in the polarization tensor as done for the quark number susceptibility [21]. However, to look for a strongly-coupled liquid phase within the structure functions and pair correlation functions, one has to adopt non-perturbative methods.…”

Three-loop HTLpt thermodynamics at finite temperature and chemical potential

“…HTLpt has been used to calculate thermodynamic functions at one loop HTLpt [40][41][42][43][44], at two loops [45][46][47][48], and at three loops at zero chemical potential [49][50][51][52][53][54] as well as at finite chemical potential [55]. Application of some hard-thermal-loop motivated approaches can be found in [56][57][58][59][60][61][62][63][64][65][66][67]. In addition to lattice QCD and HTLpt, there are also various model calculations on the market.…”

Vector meson spectral function and dilepton production rate in a hot and dense medium within an effective QCD approach

“…tion [45][46][47][48][49][50][51][52][53][54][55][56][57][58], and in dimensional reduction [59,60] appropriate for weakly interacting QGP. Nevertheless, at RHIC and LHC energies the maximum temperature reached is not very far from the phase transition temperature T c and a hot and dense matter created in these collisions is nonperturbative in nature (semi-QGP).…”