Finite Temperature QCD Research Articles

Four-loop vacuum energy density of the SU(Nc) + adjoint Higgs theory

We compute the dimensionally regularised four-loop vacuum energy density of the SU(N_c) gauge + adjoint Higgs theory, in the disordered phase. ``Scalarisation'', or reduction to a small set of master integrals of the type appearing in scalar field theories, is carried out in d dimensions, employing general partial integration identities through an algorithm developed by Laporta, while the remaining scalar integrals are evaluated in d = 3 - 2\epsilon dimensions, by expanding in \epsilon << 1 and evaluating a number of coefficients. The results have implications for the thermodynamics of finite temperature QCD, allowing to determine perturbative contributions of orders O(g^6 ln(1/g)), O(g^6) to the pressure, while the general methods are applicable also to studies of critical phenomena in QED-like statistical physics systems.

Quark-Gluon Plasma in Equilibrium State

The thermodynamic potential of quark-gluon plasma (QGP) in equilibrium state is calculated by finite temperature QCD. The pressure correction of QGP and the critical temperature correction of deconfinement phase transition of hadron are discussed.

Real-time pion propagation in finite-temperature QCD

We argue that in QCD near the chiral limit, at all temperatures below the chiral phase transition, the dispersion relation of soft pions can be expressed entirely in terms of three temperature-dependent quantities: the pion screening mass, a pion decay constant, and the axial isospin susceptibility. The definitions of these quantities are given in terms of equal-time (static) correlation functions. Thus, all three quantities can be determined directly by lattice methods. The precise meaning of the Gell-Mann--Oakes--Renner relation at finite temperature is given.

Bulk QCD thermodynamics and sterile neutrino dark matter

We point out that the relic densities of singlet (sterile) neutrinos of interest in viable warm and cold dark matter scenarios depend on the characteristics of the QCD transition in the early universe. In the most promising of these dark matter scenarios, the production of the singlets occurs at or near the QCD transition. Since production of the singlets, their dilution, and the disappearance of weak scatterers occur simultaneously, we calculate these processes contemporaneously to obtain accurate predictions of relic sterile neutrino mass density. Therefore, a determination of the mass and superweak mixing of the singlet neutrino through, for example, its radiative decay, along with a determination of its contribution to the critical density, can provide insight into the finite-temperature QCD transition.

Thermodynamics with 2+1 and 3 flavors of improved staggered quarks

We present preliminary results from exploring the phase diagram of finite temperature QCD with three degenerate flavors and with two light flavors and the mass of the third held approximately at the strange quark mass. We use an order $\alpha_s^2 a^2, a^4$ Symanzik improved gauge action and an order $\alpha_s a^2, a^4$ improved staggered quark action. The improved staggered action leads to a dispersion relation with diminished lattice artifacts, and hence better thermodynamic properties. It decreases the flavor symmetry breaking of staggered quarks substantially, and we estimate that at the transition temperature for an $N_t=8$ to $N_t=10$ lattice {\em all} pions will be lighter than the lightest kaon. Preliminary results on lattices with $N_t=4$, 6 and 8 are presented.

Thermodynamic properties of QCD with two flavors of Wilson-type lattice quarks

I report on a study of finite temperature QCD by the CP-PACS Collaboration toward a precise determination of the equation of state with dynamical u,d quarks. Based on a systematic simulation using improved Wilson-type quarks on lattices with temporal size $N_t=4$ and 6, the energy density and pressure are calculated as functions of temperature and renormalized light quark mass in the range $T/T_c \approx 0.7$--2.5 and $m_{\rm PS}/m_{\rm V} = 0.65$--0.95. Results for $N_t=4$ are found to contain significant scaling violations, while results for $N_t=6$ are suggested to be not far from the continuum limit. On the other hand, the quark mass dependence in the EOS turned out to be small for $m_{\rm PS}/m_{\rm V} \simlt 0.8$.

Thermodynamics with 3 and 2+1 flavors of improved staggered quarks

We present preliminary results [1] from exploring the phase diagram of finite temperature QCD with three degenerate flavors and with two light flavors and the mass of the third held approximately at the strange quark mass. We use an order α 2 s a 2, a 4 Symanzik improved gauge action and an order α s a 2, a 4 improved staggered quark action. The improved staggered action leads to a dispersion relation with diminished lattice artifacts, and hence better thermodynamic properties. It decreases the flavor symmetry breaking of staggered quarks substantially, and we estimate that at the transition temperature for an N t = 8 to N t = 10 lattice all pions will be lighter than the lightest kaon. Preliminary results on lattices with N t = 4, 6 and 8 are presented.

The QCD phase transition with domain wall fermions

Earlier QCD thermodynamics studies on 8 3 × 4 and 16 3 × 4 volumes are enhanced with increased statistics and extended to a smaller lattice spacing using a 16 3 × 6 volume. A comparison between the N t = 4 and 6 results and additional data regarding anomalous symmetry breaking suggests that the domain wall method provides a consistent description of finite temperature QCD. We also present direct evidence for topological effects and provide a critique of the imperfect chiral properties of the domain wall method at these strong couplings.

Finite baryon number simulations in the static limit

We study finite temperature QCD with non-zero baryon number in the heavy quark limit, first investigated by Blum, Hetrick and Toussaint. In the simulations reported here we extend the work of those authors to larger volumes and lower baryon densities, examining both the character of the finite temperature phase transition and the increase in measurement errors with lattice volume.

Equation of state in finite-temperature QCD with two flavors of improved Wilson quarks

We present results of a first study of equation of state in finite-temperature QCD with two flavors of Wilson-type quarks. Simulations are made on lattices with temporal size $N_t=4$ and 6, using an RG-improved action for the gluon sector and a meanfield-improved clover action for the quark sector. The lines of constant physics corresponding to fixed values of the ratio $m_{\rm PS}/m_{\rm V}$ of the pseudo-scalar to vector meson masses at zero temperature are determined, and the beta functions which describe the renormalization-group flow along these lines are calculated. Using these results, the energy density and the pressure are calculated as functions of temperature along the lines of constant physics in the range $m_{\rm PS}/m_{\rm V} = 0.65$--0.95. The quark mass dependence in the equation of state is found to be small for $m_{\rm PS}/m_{\rm V} \simlt 0.8$. Comparison of results for $N_t=4$ and $N_t=6$ lattices show significant scaling violation present in the $N_t=4$ results. At high temperatures the results for $N_t=6$ are quite close to the continuum Stefan-Boltzmann limit, suggesting the possibility of a precise continuum extrapolation of thermodynamic quantities from simulations at $N_t\simgt 6$.

Finite temperature QCD phase transition with domain wall fermions

The domain wall formulation of lattice fermions is expected to support accurate chiral symmetry, even at finite lattice spacing. Here we attempt to use this new fermion formulation to simulate two-flavor, finite temperature QCD near the chiral phase transition. In this initial study, a variety of quark masses, domain wall heights and domain wall separations are explored using an 8^3 x 4 lattice. Both the expectation value of the Wilson line and the chiral condensate show the temperature dependence expected for the QCD phase transition. Further, the desired chiral properties are seen for the chiral condensate, suggesting that the domain wall fermion formulation may be an effective approach for the numerical study of QCD at finite temperature.

Testing imaginary vs. real chemical potential in finite-temperature QCD

One suggestion for determining the properties of QCD at finite temperatures and densities is to carry out lattice simulations with an imaginary chemical potential whereby no sign problem arises, and to convert the results to real physical observables only afterwards. We test the practical feasibility of such an approach for a particular class of physical observables, spatial correlation lengths in the quark–gluon plasma phase. Simulations with imaginary chemical potential followed by analytic continuation are compared with simulations with real chemical potential, which are possible by using a dimensionally reduced effective action for hot QCD (in practice we consider QCD with two massless quark flavours). We find that for imaginary chemical potential the system undergoes a phase transition at | μ/ T|≈ π/3, and thus observables are analytic only in a limited range. However, utilising this range, relevant information can be obtained for the real chemical potential case.

Domain wall fermions and applications

Domain wall fermions provide a complimentary alternative to traditional lattice fermion approaches. By introducing an extra dimension, the amount of chiral symmetry present in the lattice theory can be controlled in a linear way. This results in improved chiral properties as well as robust topological zero modes. A brief introduction on the subject and a discussion of chiral properties and applications, such as zero and finite temperature QCD, N = 1 Super Yang-Mills, and four-fermion theories, is presented.

Thermodynamics of free domain wall and overlap fermions

Studies of non-interacting lattice fermions give an estimate of the size of discretization errors and finite size effects for more interesting problems like finite temperature QCD. We present a calculation of the thermodynamic equation of state for free domain wall and overlap fermions.

Lattice QCD at finite temperature

Recent developments in finite-temperature QCD with dynamical quarks are reviewed focusing on the topics of critical temperature, the equation of state, and critical behaviors around the chiral phase transition.

Finite temperature QCD on anisotropic lattices

Finite temperature QCD on anisotropic lattices

Microscopic universality and the chiral phase transition in two flavor QCD

We re-analyze data from available finite-temperature QCD simulations near the chiral transition, with the help of Chiral Random Matrix Theory (chRMT). Statistical properties of the lowest-lying eigenvalues of the staggered Dirac operator for SU(3) lattice gauge theory with dynamical fermions are examined. We consider temperatures below, near, and above the critical temperature $T_c$ for the chiral phase transition. Below and above $T_c$ the statistics are in agreement with the exact analytical predictions in the microscopic scaling regime. Above $T_c$ we observe a gap in the spectral density and a distribution compatible with the Airy distribution. Near $T_c$ the eigenvalue correlations appear inconsistent with chRMT.

Topology and chiral symmetry in finite temperature QCD

We investigate the realization of chiral symmetry in the vicinity of the deconfinement transition in quenched QCD using overlap fermions. Via the index theorem obeyed by the overlap fermions, we gain insight into the behavior of topology at finite temperature. We find small eigenvalues, clearly separated from the bulk of the eigenvalues, and study the properties of their distribution. We compare the distribution with a model of a dilute gas of instantons and anti-instantons and find good agreement.

Equation of state in finite-temperature QCD with improved Wilson quarks

We study finite-temperature phase transition and equation of state for two-flavor QCD at N t = 4 using an RG-improved gauge action and a meanfield-improved clover quark action. The pressure is computed using the integral method. The O(4) scaling of chiral order parameter is also examined.

The finite temperature QCD phase transition with domain wall fermions

Results from the Columbia lattice group study of the QCD finite temperature phase transition with dynamical domain wall fermions on 16 3 × 4 lattices are presented. These results include an investigation of the U(1) axial symmetry breaking above but close to the transition, the use of zero temperature calculations that set the scale at the transition and preliminary measurements close to the transition.