Finite Temperature QCD Research Articles

Free energy versus internal energy potential for heavy quark systems at finite temperature

Abstract The strength of the J / ψ wave function at origin | ψ ( 0 ) | is calculated by using the finite temperature QCD sum rule with the gluon condensates determined from the lattice QCD. The result is compared with that from a potential model based on the static free or internal energy obtained from lattice calculations. We find that the | ψ ( 0 ) | decreases with temperature around the deconfinement transition temperature both in the QCD sum rule and in the potential model with the free energy potential. Our result thus suggests that the free energy potential from lattice calculations is appropriate for describing the properties of charmonia at finite temperature.

Three-loop HTLpt thermodynamics at finite temperature and chemical potential

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.

QCD phase diagram: overview of recent lattice results

Two parameters that have a strong influence on the finite temperature QCD transition, and play an important role in various physical scenarios are the quark density and the external magnetic field. The effect of these parameters on the thermal properties of QCD is discussed, and an overview of the latest lattice results is given.

QCD chiral transition,U(1)Asymmetry and the dirac spectrum using domain wall fermions

We report on a study of the finite-temperature QCD transition region for temperatures between 139 and 196 MeV, with a pion mass of 200 MeV and two space-time volumes: $24^3\times8$ and $32^3\times8$, where the larger volume varies in linear size between 5.6 fm (at T=139 MeV) and 4.0 fm (at T=195 MeV). These results are compared with the results of an earlier calculation using the same action and quark masses but a smaller, $16^3\times8$ volume. The chiral domain wall fermion formulation with a combined Iwasaki and dislocation suppressing determinant ratio gauge action are used. This lattice action accurately reproduces the $\sua$ and $\ua$ symmetries of the continuum. Results are reported for the chiral condensates, connected and disconnected susceptibilities and the Dirac eigenvalue spectrum. We find a pseudo-critical temperature, $T_c$, of approximately 165 MeV consistent with previous results and strong finite volume dependence below $T_c$. Clear evidence is seen for $\ua$ symmetry breaking above $T_c$ which is quantitatively explained by the measured density of near-zero modes in accordance with the dilute instanton gas approximation.

An overview of (selected) recent results in finite-temperature lattice QCD

I discuss recent results on the lattice with the main emphasis on the thermodynamics of the crossover region, restoration of the chiral symmetry and fluctuations of conserved charges as an indicator of deconfinement, that may also be used to determine the chemical freeze-out conditions in heavy-ion collision experiments.

Deconfining Chiral Transition in QCD on the Lattice

The deconfining chiral transition in finite-temperature QCD is studied on the lattice using Wilson quarks. After discussing the nature of chiral limit with Wilson quarks, we first study the case of two degenerate quarks NF=2, and find that the transition is smooth in the chiral limit on both Nt=4 and 6 lattices. For NF=3, on the other hand, clear two state signals are observed for mq≲140 MeV on Nt=4 lattices. For a more realistic case of NF=2+1, i.e. two degenerate u and d-quarks and a heavier s-quark, we study the cases ms≃150 and 400 MeV with mu=md≃0: In contrast to a previous result with staggered quarks, clear two state signals are observed for both cases, suggesting a first order QCD phase transition in the real world.

The [formula omitted] meson and chiral symmetry restoration and deconfinment at finite temperature QCD

We consider the light-quark axial-vector current correlator in the framework of thermal QCD sum rules to: (a) find a relation between chiral-symmetry restoration and deconfinement, and (b) determine the temperature behaviour of the a1(1260) width and coupling. Our results show that deconfinement takes place at a slightly lower temperature than chiral-symmetry restoration.This difference is not significant given the accuracy of the method. The behaviour of the a1(1260) parameters is consistent with quark-gluon deconfinement, since the width grows and the coupling decreases with increasing temperature.

Chiral transition andU(1)Asymmetry restoration from lattice QCD using domain wall fermions

We present results on both the restoration of the spontaneously broken chiral symmetry and the effective restoration of the anomalously broken U(1)_A symmetry in finite temperature QCD at zero chemical potential using lattice QCD. We employ domain wall fermions on lattices with fixed temporal extent N_\tau = 8 and spatial extent N_\sigma = 16 in a temperature range of T = 139 - 195 MeV, corresponding to lattice spacings of a \approx 0.12 - 0.18 fm. In these calculations, we include two degenerate light quarks and a strange quark at fixed pion mass m_\pi = 200 MeV. The strange quark mass is set near its physical value. We also present results from a second set of finite temperature gauge configurations at the same volume and temporal extent with slightly heavier pion mass. To study chiral symmetry restoration, we calculate the chiral condensate, the disconnected chiral susceptibility, and susceptibilities in several meson channels of different quantum numbers. To study U(1)_A restoration, we calculate spatial correlators in the scalar and pseudo-scalar channels, as well as the corresponding susceptibilities. Furthermore, we also show results for the eigenvalue spectrum of the Dirac operator as a function of temperature, which can be connected to both U(1)_A and chiral symmetry restoration via Banks-Casher relations.

Erratum: Phase structure of finite temperature QCD in the heavy quark region [Phys. Rev. D84, 054502 (2011)

Erratum: Phase structure of finite temperature QCD in the heavy quark region [Phys. Rev. D<b>84</b>, 054502 (2011)

Dimensionally reduced QCD at high temperature

Finite-temperature QCD at high temperature T exhibits three different momentum scales T,gT and g2T. Naive perturbation theory in a small gauge coupling g does not work beyond leading order. In the framework of effective theories, a separation of contributions originating from the different momentum scales can be systematically performed, allowing for higher-order weak-coupling expansions. In this talk, we review finite-temperature QCD in the EQCD/MQCD framework, and outline a specific high-precision calculation of matching coefficients therein.

Investigation of heavy–heavy pseudoscalar mesons in thermal QCD sum rules

We investigate the mass and decay constant of the heavy–heavy pseudoscalar, Bc, ηc and ηb mesons in the framework of finite-temperature QCD sum rules. The annihilation and scattering parts of spectral density are calculated in the lowest order of perturbation theory. Taking into account the additional operators arising at finite temperature, the nonperturbative corrections are also evaluated. The masses and decay constants remain unchanged under T≅100 MeV, but after this point, they start to diminish with increasing temperature. At critical or deconfinement temperature, the decay constants reach approximately 35% of their values in vacuum, while the masses are decreased about 7%, 12% and 2% for Bc, ηc and ηb states, respectively. The results at zero temperature are in good consistency with the existing experimental values as well as predictions of the other nonperturbative approaches.

Phase structure of finite temperature QCD in the heavy quark region

We study the quark mass dependence of the finite temperature QCD phase transition in the heavy quark region using an effective potential defined through the probability distribution function of the average plaquette. Performing a simulation of SU(3) pure gauge theory, we first confirm that the distribution function has two peaks indicating that the phase transition is of first order in the heavy quark limit, while the first order transition turns into a crossover as the quark mass decreases from infinity, where the mass dependence of the distribution function is evaluated by the reweighting method combined with the hopping parameter expansion. We determine the endpoint of the first order transition region for N_f=1, 2, 3 and 2+1 cases. The quark mass dependence of the latent heat is also evaluated in the first order transition region.

Analysis of the chiral phase transition in finite temperature QCD by using non-perturbative renormalization group

Analysis of the chiral phase transition in finite temperature QCD by using non-perturbative renormalization group

BtoD(D*)eνetransitions at finite temperature in QCD

In this article, we work out the properties of the $B$, $D$, and ${D}^{*}$ mesons as well as the $B\ensuremath{\rightarrow}D({D}^{*})e{\ensuremath{\nu}}_{e}$ decay properties at finite temperature QCD. The behavior of the masses, decay constants and widths of the $B$, $D$, and ${D}^{*}$ mesons in terms of the temperature is studied. The temperature dependency of the form factors responsible for such decays are also obtained. These temperature-dependent form factors are used to investigate the variation of the branching ratios with respect to the temperature. It is shown that the branching ratios do not change up to $T/{T}_{c}=0.3$, however they start to diminish with increasing the temperature after this region and vanish at the critical or deconfinement temperature.

Dimensionally regularized Polyakov loop correlators in hot QCD

A popular observable in finite-temperature lattice QCD is the so-called singlet quark-antiquark free energy, conventionally defined in Coulomb gauge. In an effort to interpret the existing numerical data on this observable, we compute it at order \( \mathcal{O}\left( {\alpha_s^2} \right) \) in continuum, and analyze the result at various distance scales. At short distances (r ≪ 1/πT) the behaviour matches that of the gauge-independent zero-temperature potential; on the other hand at large distances (r ≫ 1/πT) the singlet free energy appears to have a gauge-fixing related power-law tail. At infinite distance the result again becomes physical in the sense that it goes over to a gauge-independent disconnected contribution, the square of the expectation value of the trace of the Polyakov loop; we recompute this quantity at \( \mathcal{O}\left( {\alpha_s^2} \right) \), finding for pure SU(N c ) a different non-logarithmic term than in previous literature, and adding for full QCD the quark contribution. We also discuss the value of the singlet free energy in a general covariant gauge, as well as the behaviour of the cyclic Wilson loop that is obtained if the singlet free energy is made gauge-independent by inserting straight spacelike Wilson lines into the observable. Comparisons with lattice data are carried out where possible.

Holographic approach to finite temperature QCD: The case of scalar glueballs and scalar mesons

We study scalar glueballs and scalar mesons at $T \neq 0$ in the soft wall holographic QCD model. We find that, using the Anti-de Sitter-Black Hole metric for all values of the temperature, the masses of the hadronic states decrease and the widths become broader when T increases, and there are temperatures for which the states disappear from the scalar glueball and scalar meson spectral functions. However, the values of the temperatures in correspondence of which such phenomena occur are low, of the order of 40-60 MeV. A consistent holographic description of in-medium effects on hadron properties should include the Hawking-Page transition, which separates the phase with the Anti-de Sitter metric at small temperatures from the phase with Anti-de Sitter-Black Hole metric at high temperatures.

Spatial string tension of finite temperature QCD matter in gauge/gravity duality

The computation of the spatial string tension of finite temperature QCD is discussed in QCD and in a gravity+scalar model of gauge/gravity duality.Received 19 May 2009DOI:https://doi.org/10.1103/PhysRevD.80.075017©2009 American Physical Society

Fixed scale approach to equation of state in lattice QCD

A new approach to study the equation of state in finite-temperature QCD is proposed on the lattice. Unlike the conventional method in which the temporal lattice size ${N}_{t}$ is fixed, the temperature $T$ is varied by changing ${N}_{t}$ at the fixed lattice scale. The pressure of the hot QCD plasma is calculated by the integration of the trace anomaly with respect to $T$ at the fixed lattice scale. This ``$T$-integral method'' is tested in quenched QCD on isotropic and anisotropic lattices and is shown to give reliable results, especially at intermediate and low temperatures.

DECONFINEMENT AND THERMODYNAMICS IN 5D HOLOGRAPHIC MODELS OF QCD

We review 5D holographic approaches to finite temperature QCD. Thermodynamic properties of the "hard-wall" and the "soft-wall" models are derived. Various non-realistic features in these models are rectified by the setup of improved holographic QCD, that we review here.

Nonperturbative phenomena in QCD at finite temperature in a magnetic field

The norperturbative QCD vacuum at finite temperature in a external magnetic field is studied. Equations that relate nonperturbative QCD condensates at finite temperature to the thermodynamic pressure at T ≠ 0 and H ≠ 0 are obtained, and low-energy theorems are derived. The free energy of the QCD vacuum in the hadronic phase at H ≠ 0 is calculated, and expressions for the quark and gluon condensates are obtained. Various limiting cases for the behavior of the condensates at low and high temperatures and in weak and strong magnetic fields are investigated. A new interesting phenomenon that consists in the freezing of the quark condensate by a magnetic field is found. The character of spontaneous chiral-symmetry breaking in finite-temperature QCD in a magnetic field is studied. For this purpose, the Gell-Mann-Oakes-Renner formula relating the pion mass Mπ and the axial-vector coupling constant Fπ to the quark condensate is derived at T ≠ 0 and H ≠ 0. It is shown that this formula preserves its form at finite temperature after taking into account a magnetic field—that is, no additional terms independent of T and H appear. Thus, the scheme of soft chiral-symmetry breaking remains unchanged. The quark-hadron phase transition in QCD in a magnetic field is studied. It is shown that the phase-transition temperature becomes lower than that in the case of zero magnetic field.