Finite Temperature Lattice QCD Research Articles

Frontiers of finite temperature lattice QCD

I review a selection of recent finite temperature lattice results of the past years. First I discuss the extension of the equation of state towards high temperatures and fi- nite densities, then I show recent results on the QCD topological susceptibility at high temperatures and highlight its relevance for dark matter search.

In-medium heavy-quarkonium from lattice QCD spectral functions

We discuss recent progress in the study of in-medium heavy quarkonium using first-principles lattice QCD calculations and effective field theory. In particular our focus lies on real-time information carried by QCD spectral functions and we report on a novel strategy for their extraction from Euclidean-time simulations. Combining an effective description for heavy quarks with finite temperature lattice QCD we compute in-medium spectra providing insight in heavy quarkonium melting in a static thermal medium. On the other hand we use spectral information to extract the complex in-medium potential which provides the basis for a dynamical description of quarkonium real-time evolution via the Schrödinger equation.

Mixed phase effects on high-mass twin stars

Recently it has been found that a certain class of hybrid star equations of state with a large latent heat (strong first order phase transition obtained by a Maxwell construction) between stiff hadronic hadronic and stiff quark matter phases allows for the appearance of a third family of compact stars (including "twins") at high mass of $\sim 2 M_\odot$. We investigate how robust this high-mass twin phenomenon is against a smoothing of the transition which would occur, e.g., due to pasta structures in the mixed phase. To this end we propose a simple construction of a pasta-like equation of state with a parameter that quantifies the degree of smoothing of the transition and could eventually be related to the surface tension of the pasta structures. It is interesting to note that the range of energy densities for the transition as well as the pressure at the onset of the transition of this class of hybrid star matter at zero temperature corresponds well to values of the same quantities found in finite temperature lattice QCD simulations for the 1 $\sigma$ region at the pseudocritical temperature $T_c=154 \pm 9$ MeV. The pattern of the speed of sound as a function of energy density is very different.

Vector Meson Mass in Finite Density and Temperature Lattice QCD* *Supported by the National Science Foundation of China (NSFC) under Grant Nos. 11335001, 11105153, 11405178. It is also supported in part by the DFG and the NSFC (No. 11261130311) through funds provided to the Sino-Germen CRC 110 “Symmetries and the Emergence of Structure in QCD”. The numerical calculations were performed

Vector meson mass values are studied at finite chemical potential and temperature in lattice QCD with lattice size of 24 × 122 × 6 using two flavors of staggered quarks. The investigation focuses on the change of the vector meson mass in the critical region close to Tc with two different types of chemical potentials switched on: the isoscalar chemical potential μs and its isovector counterpart μv. It is found that the vector meson mass increases in the QGP phase with both chemical potentials and decreases with μs in the confinement phase.

Fixed-scale approach to finite-temperature lattice QCD with shifted boundaries

We study the thermodynamics of the SU(3) gauge theory using the fixed-scale approach with shifted boundary conditions. The fixed-scale approach can reduce the numerical cost of the zero-temperature part in the equation of state calculations, while the number of possible temperatures is limited by the integer $N_t$, which represents the temporal lattice extent. The shifted boundary conditions can overcome such a limitation while retaining the advantages of the fixed-scale approach. Therefore, our approach enables the investigation of not only the equation of state in detail, but also the calculation of the critical temperature with increased precision even with the fixed-scale approach. We also confirm numerically that the boundary conditions suppress the lattice artifact of the equation of state, which has been confirmed in the non-interacting limit.

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.

Investigation on the contribution of particle mass to the interaction measure

Collective phenomena from RHIC and LHC experiments indicate a strongly coupled quark gluon plasma. Finite temperature lattice QCD calculations show that the interaction measure, Δ ≡ (ϵ − 3p)/T4, is sizeable over a considerable range of temperatures above the deconfinement temperature, which may also indicate that the plasma is strongly interacting. For the ideal gas with massless particles, the interaction measure is zero. A nonzero value is probably due to either the interaction or the mass. In order to see the contribution of particle mass to the interaction measure, in this paper we study a system without any interactions, i.e. an ideal gas with massive particles. After assembling the standard formulas of the quantum statistics with relativistic energy, we calculate the energy density, the pressure and the interaction measure. We find that their dependences on temperature reproduce the qualitative features of the lattice result. The interaction measure is nonzero for an ideal gas, which demonstrates that the particle mass contributes to the interaction measure. By our estimate, in the interaction measure obtained by the lattice calculation, quark mass contributes less than (40–50)%. There are sizeable residue interactions in the deconfined phase.

Charmonium spectral functions with the variational method in zero and finite temperature lattice QCD

We propose a method to evaluate spectral functions on the lattice based on a variational method. On a lattice with a finite spatial extent, spectral functions consist of discrete spectra only. Adopting a variational method, we calculate the locations and the heights of spectral functions at low-lying discrete spectra. We first test the method in the case of analytically solvable free Wilson quarks at zero and finite temperatures and confirm that the method well reproduces the analytic results for low-lying spectra. We find that we can systematically improve the results by increasing the number of trial states. We then apply the method to calculate the charmonium spectral functions for S and P-wave states at zero-temperature in quenched QCD and compare the results with those obtained using the conventional maximum entropy method (MEM). The results for the ground state are consistent with the location and the area of the first peak in spectral functions from the MEM, while the variational method leads to a mass which is closer to the experimental value for the first excited state. We also investigate the temperature dependence of the spectral functions for S-wave states below and above $T_c$. We obtain no clear evidences for dissociation of $J/\psi$ and $\eta_c$ up to 1.4$T_c$.

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.

Phases and properties of quark matter

I review recent developments in finite temperature lattice QCD which are useful for the study of heavy-ion collisions. I pay particular attention to studies of the equation of state and the light they throw on conformal symmetry and the large Nc limit, and to the structure of the phase diagram for Nf = 2 + 1.

Progress in finite temperature lattice QCD

I review recent progress in finite temperature lattice calculations, including the determination of the transition temperature, equation of state, screening of static quarks and meson spectral functions. The analysis of the meson correlators in the vector channel indicate a quite small value of the heavy quark thermal velocity.

Lattice QCD at finite temperature

I discuss recent developments in finite temperature lattice QCD, including the calculation of the transition temperature, equation of state, color screening and meson spectral functions.

Testing Algorithms for Finite Temperature Lattice QCD

We discuss recent algorithmic improvements in simulating finite temperature QCD on a lattice. In particular, the Rational Hybrid Monte Carlo(RHMC) algorithm is employed to generate lattice configurations for 2+1 flavor QCD. Unlike the Hybrid R Algorithm, RHMC is reversible, admitting a Metropolis accept/reject step that eliminates the O ( δ t 2 ) errors inherent in the R Algorithm. We also employ several algorithmic speed-ups, including multiple time scales, the use of a more efficient numerical integrator, and Hasenbusch pre-conditioning of the fermion force.

Quarkonium at Finite Temperature

Lattice QCD studies on charmonium at finite temperature are presented After a discussion about problems for the Maximum Entropy Method applied to finite temperature lattice QCD, I show several results on charmonium spectral functions. The “wave function” of charmonium is also discussed to study the spatial correlation between quark and anti-quark in deconfinement phase.

Results from Lattice QCD

I present our recent results on the critical end point in the μB-Tphase diagram of QCD with two flavours of light dynamical quarks and compare them with similar results from other groups. Implications for a possible energy scan at the RHIC are discussed. I also comment briefly on the new results of great relevance to heavy ion collisions from finite temperature lattice QCD simulations on speed of sound, specific heat and on the fate of J/ψ.

CRITICAL BEHAVIOUR IN STATISTICAL QCD

We survey the critical behaviour of strongly interacting matter, as determined in finite temperature lattice QCD.

Running coupling constant from lattice data and bulk viscosity of strange quark matter

We study the bulk viscosity of strange quark matter (SQM) in a quasiparticle model at finite chemical potential by extrapolating the previous quasiparticle model of finite temperature lattice QCD. The more proper bulk viscosity coefficient can be given in this model where chemical potential $\mu$ and coupling constant $\emph{g}$ are interdependent. We also apply our result to determine the critical rotation of strange stars by r-mode instability window. Our model is compatible to the millisecond pulsar data for a wide range of mass and radius of the stars.

Finite temperature phase transition in lattice QCD with Nf = 2 nonperturbatively improved Wilson fermions at Nt = 8

The finite temperature lattice QCD with N f = 2 nonperturbatively improved Wilson fermions is studied on 16 38 lattice. Using abelian projection after fixing to MA gauge we determine the transition temperature for m π / m ϱ ∼ 0.8 .

Infrared behavior of the gluon propagator in nonequilibrium situations

The infrared behaviour of the medium modified gluon propagator in non-equilibrium situations is studied in the covariant gauge using the Schwinger-Keldysh closed-time path formalism. It is shown that the magnetic screening mass is non-zero at the one loop level whenever the initial gluon distribution function is non isotropic with the assumption that the distribution function of the gluon is not divergent at zero transverse momentum. For isotropic gluon distribution functions, such as those describing local equilibrium, the magnetic mass at one loop level is zero which is consistent with finite temperature field theory results. Assuming that a reasonable initial gluon distribution function can be obtained from a perturbative QCD calculation of minijets, we determine these out of equilibrium values for the initial magnetic and Debye screening masses at energy densities appropriate to RHIC and LHC. We also compare the magnetic masses obtained here with those obtained using finite temperature lattice QCD methods at similar temperatures at RHIC and LHC.

Quarkonium suppression

I discuss quarkonium suppression in equilibriated strongly interacting matter. After a brief review of basic features of quarkonium production I discuss the application of recent lattice data on the heavy quark potential to the problem of quarkonium dissociation as well as the problem of direct lattice determination of quarkonium properties in finite temperature lattice QCD.