Finite Temperature QCD Research Articles

Dual simulation of a Polyakov loop model at finite baryon density: Correlations and screening masses

Computations of screening masses in finite-temperature QCD at finite density are plagued by the sign problem and have been performed so far with an imaginary chemical potential. Here, we use a dual formulation of a Polyakov-loop model which allows the determination of screening masses at real baryon chemical potential. This is a second paper in a series devoted to a detailed study of dual Polyakov-loop models at finite density. While the first paper was mainly devoted to establishing the phase diagram of the model, here we compute correlation functions of the Polyakov loops and the second-moment correlation length at non-zero chemical potential. This enables us to evaluate numerically the screening masses from correlations of the real and imaginary parts of the Polyakov loops. We also compute these masses in the mean-field approximation and compare with numerical results. In addition, we provide a quantitative improvement of the general phase diagram presented in the first paper.

Effective potential of the Polyakov loop in the Hamiltonian approach to QCD

We investigate the effective potential of the Polyakov loop, which is the order parameter for the deconfinement phase transition in finite temperature QCD. Our work is based on the Hamiltonian approach in Coulomb gauge where finite temperature $T$ is introduced by compactifying one space direction. We briefly review this approach and extend earlier work in the Yang-Mills sector by including dynamical quarks. In a first approximation, we follow the usual functional approach and include only 1-loop contributions to the energy, with the finite temperature propagators replaced by their $T=0$ counterparts. It is found that this gives a poor description of the phase transition, in particular for the case of full QCD with ${N}_{f}=3$ light flavors. The physical reasons for this unexpected result are discussed, and pinned down to a relative weakness of gluon confinement compared to the deconfining tendency of the quarks. We attempt to overcome this issue by including the relevant gluon contributions from the 2-loop terms to the energy. We find that the 2-loop corrections have indeed a tendency to strengthen the gluon confinement and weaken the unphysical effects in the confining phase, while slightly increasing the (pseudo)critical temperature ${T}^{*}$ at the same time. To fully suppress artifacts in the confining phase, we must tune the parameters to rather large values, increasing the critical temperature to ${T}^{*}\ensuremath{\approx}340\text{ }\text{ }\mathrm{MeV}$ for $G=SU(2)$.

Topological susceptibility in finite temperature QCD with physical (u/d,s,c) domain-wall quarks

We perform hybrid Monte-Carlo (HMC) simulation of lattice QCD with $N_f=2+1+1$ domain-wall quarks at the physical point, on the $64^3 \times (64,20,16,12,10,8,6)$ lattices, each with three lattice spacings. The lattice spacings and the bare quark masses are determined on the $64^4$ lattices. The resulting gauge ensembles provide a basis for studying finite temperature QCD with $N_f=2+1+1 $ domain-wall quarks at the physical point. In this paper, we determine the topological susceptibility of the QCD vacuum for $T > T_c \sim 150 $ MeV. The topological charge of each gauge configuration is measured by the clover charge in the Wilson flow at the same flow time in physical units, and the topological susceptibility $ \chi_t(a,T) $ is determined for each ensemble with lattice spacing $a$ and temperature $T$. Using the topological susceptibility $\chi_t(a,T) $ of 15 gauge ensembles with three lattice spacings and different temperatures in the range $T \sim 155-516 $ MeV, we extract the topological susceptibility $\chi_t(T)$ in the continuum limit. To compare our results with others, we survey the continuum extrapolated $\chi_t(T)$ in lattice QCD with $N_f=2+1(+1)$ dynamical quarks at/near the physical point, and discuss their discrepancies. Moreover, a detailed discussion on the reweighting method for domain-wall fermion is presented.

Finite temperature QCD phase transition and its scaling window from Wilson twisted mass fermions

We study the properties of finite temperature QCD using lattice simulations with Nf = 2 + 1 + 1 Wilson twisted mass fermions for pion masses from physical up to heavy quark regime. In particular, we investigate the scaling properties of the chiral phase transition close to the chiral limit. We found compatibility with O(4) universality class for pion masses up to physical and in the temperature range [120 : 300] MeV. We also discuss other alternatives, including mean field behaviour or Z2 scaling. We provide an estimation of the critical temperature in the chiral limit, T0 = 134−4+6 MeV, which is stable against various scaling scenarios.

QCD transition at the physical point, and its scaling window from twisted mass Wilson fermions

We study the scaling properties of the finite temperature QCD phase transition, for light quark masses ranging from the heavy quark regime to their physical values. The lattice results are obtained in the fixed scale approach from simulations of Nf=2+1+1 flavours of Wilson fermions at maximal twist. We identify an order parameter free from the linear contributions in mass due to additive renormalization and regular terms in the Equation of State, which proves useful for the assessment of the hypothesized universal behaviour. We find compatibility with the 3D O(4) universality class for the physical pion mass and temperatures 120 MeV ≲T≲300 MeV. We discuss violation of scaling at larger masses and a possible cross-over to mean field behaviour. The chiral extrapolation T0=134−4+6 MeV of the pseudocritical temperature is robust against predictions of different universality classes and consistent with its estimate from the O(4) Equation of State for the physical pion mass.

Conserved Charge Fluctuations in the Chiral Limit

We study the signs of criticality in conserved charge fluctuations and related observables of finite temperature QCD at vanishing chemical potential, as we approach the chiral limit of two light quarks. Our calculations have been performed on gauge ensembles generated using Highly Improved Staggered Quark (HISQ) fermion action, with pion masses ranging from 140 MeV to 55 MeV.

Finite temperature QCD with $$N_f=2+1+1$$ Wilson twisted mass fermions at physical pion, strange and charm masses

We discuss recent progress in studying Quantum Chromodynamics at finite temperature using $N_f=2+1+1$ Wilson twisted mass fermions. Particular interest is in QCD symmetries and their breaking and restoration. First, we discuss the behaviour of the $\eta'$ meson at finite temperature, which is tightly connected to the axial and chiral symmetries. The results suggest a small decrease of the $\eta'$ mass in the pseudo-critical region coming close to the non-anomalous contribution and subsequent growth at large temperatures. Second, we present the first results of lattice simulations of Quantum Chromodynamics with $N_f=2+1+1$ twisted mass Wilson fermions at physical pion, strange and charm masses. We estimate the chiral pseudo-critical temperatures for different observables. Our preliminary results are consistent with a second order transition in the chiral limit, however other scenarios are not excluded.

Charting the scaling region of the Ising universality class in two and three dimensions

We study the behaviour of a universal combination of susceptibility and correlation length in the Ising model in two and three dimensions, in presence of both magnetic and thermal perturbations, in the neighbourhood of the critical point. In three dimensions we address the problem using a parametric representation of the equation of state. In two dimensions we make use of the exact integrability of the model along the thermal and the magnetic axes. Our results can be used as a sort of "reference frame" to chart the critical region of the model. While our results can be applied in principle to any possible realization of the Ising universality class, we address in particular, as specific examples, three instances of Ising behaviour in finite temperature QCD related in various ways to the deconfinement transition. In particular, in the last of these examples, we study the critical ending point in the finite density, finite temperature phase diagram of QCD. In this finite density framework, due to well know sign problem, Montecarlo simulations are not possible and thus a direct comparison of experimental results with QFT/Statmech predictions like the one we discuss in this paper may be important. Moreover in this example it is particularly difficult to disentangle "magnetic-like" from "thermal-like" observables and thus universal quantities which do not need a precise identification of the magnetic and thermal axes, like the one we address in this paper, can be particularly useful.

Finite-density QCD transition in a magnetic background field

Using numerical simulations of lattice QCD with physical quark masses, we reveal the influence of magnetic-field background on chiral and deconfinement crossovers in finite-temperature QCD at low baryonic density. In the absence of thermodynamic singularity, we identify these transitions with inflection points of the approximate order parameters: normalized light-quark condensate and renormalized Polyakov loop, respectively. We show that the quadratic curvature of the chiral transition temperature in the ``temperature--chemical potential'' plane depends rather weakly on the strength of the background magnetic field. At weak magnetic fields, the thermal width of the chiral crossover gets narrower as the density of the baryon matter increases, possibly indicating a proximity to a real thermodynamic phase transition. Remarkably, the curvature of the chiral thermal width flips its sign at $eB_{\mathrm{fl}} \simeq 0.6\,\mathrm{GeV}^2$, so that above the flipping point $B > B_{\mathrm{fl}}$, the chiral width gets wider as the baryon density increases. Approximately at the same strength of magnetic field, the chiral and deconfining crossovers merge together at $T \approx 140\,\mathrm{MeV}$. The phase diagram in the parameter space ``temperature-chemical potential-magnetic field'' is outlined, and single-quark entropy and single-quark magnetization are explored. The curvature of the chiral thermal width allows us to estimate an approximate position of the chiral critical endpoint at zero magnetic field: $(T_c^{\text{CEP}}, \mu_B^{\text{CEP}})= (100(25)\, \text{MeV},\ 800(140)\,\text{MeV})$.

Chiral symmetry restoration at finite temperature within the Hamiltonian approach to QCD in Coulomb gauge

The chiral phase transition of the quark sector of QCD is investigated within the Hamiltonian approach in Coulomb gauge. Finite temperature $T$ is introduced by compactifying one spatial dimension, which makes all thermodynamical quantities accessible from the ground state on the spatial manifold ${\mathbb{R}}^{2}\ifmmode\times\else\texttimes\fi{}{S}^{1}(1/T)$. Neglecting the coupling between quarks and transversal gluons, the equations of motion of the quark sector are solved numerically and the chiral quark condensate is evaluated and compared to the results of the usual canonical approach to finite-temperature Hamiltonian QCD based on the density operator of the grand canonical ensemble. For zero bare quark masses, we find a second-order chiral phase transition with a critical temperature of about 92 MeV. If the Coulomb string tension is adjusted to reproduce the phenomenological value of the quark condensate, the critical temperature increases to 118 MeV.

Hadron thermodynamics from imaginary chemical potentials

We use 4stout improved staggered lattice data at imaginary chemical potentials to calculate fugacity expansion coefficients in finite temperature QCD. We discuss the phenomenological interpretation of our results within the hadron resonance gas (HRG) model, and the hints they give us about the hadron spectrum. We also discuss features of the higher order coefficients that are not captured by the HRG. This conference contribution is based on our recent papers [1, 2].,

Finite temperature QCD four-point function in the presence of a weak magnetic field within the hard thermal loop approximation

We compute the weak magnetic field correction to the four-point quark-gluon vertex at finite temperature and chemical potential within the hard thermal loop approximation. The resulting four-point quark-gluon vertex satisfies the Ward identity with the three-point quark-gluon vertex.

Localization and chiral properties near the ordering transition of an Anderson-like toy model for QCD

The Dirac operator in finite temperature QCD is equivalent to the Hamiltonian of an unconventional Anderson model, with on-site noise provided by the fluctuations of the Polyakov lines. The main features of its spectrum and eigenvectors, concerning the density of low modes and their localization properties, are qualitatively reproduced by a toy-model random Hamiltonian, based on an Ising-type spin model mimicking the dynamics of the Polyakov lines. Here we study the low modes of this toy model in the vicinity of the ordering transition of the spin model, and show that at the critical point the spectral density at the origin has a singularity, and the localization properties of the lowest modes change. This provides further evidence of the close relation between deconfinement, chiral transition and localization of the low modes.

Finite Temperature QCD Sum Rules: A Review

The method of QCD sum rules at finite temperature is reviewed, with emphasis on recent results. These include predictions for the survival of charmonium and bottonium states, at and beyond the critical temperature for deconfinement, as later confirmed by lattice QCD simulations. Also included are determinations in the light-quark vector and axial-vector channels, allowing analysing the Weinberg sum rules and predicting the dimuon spectrum in heavy-ion collisions in the region of the rho-meson. Also, in this sector, the determination of the temperature behaviour of the up-down quark mass, together with the pion decay constant, will be described. Finally, an extension of the QCD sum rule method to incorporate finite baryon chemical potential is reviewed.

The topological susceptibility in finite temperature QCD and axion cosmology

We study the topological susceptibility in 2+1 flavor QCD above the chiral crossover transition temperature using Highly Improved Staggered Quark action and several lattice spacings, corresponding to temporal extent of the lattice, $N_\tau=6,8,10$ and $12$. We observe very distinct temperature dependences of the topological susceptibility in the ranges above and below $250$ MeV. While for temperatures above $250$ MeV, the dependence is found to be consistent with dilute instanton gas approximation, at lower temperatures the fall-off of topological susceptibility is milder. We discuss the consequence of our results for cosmology wherein we estimate the bounds on the axion decay constant and the oscillation temperature if indeed the QCD axion is a possible dark matter candidate.

An Anderson-like model of the QCD chiral transition

We study the problems of chiral symmetry breaking and eigenmode localisation in finite-temperature QCD by looking at the lattice Dirac operator as a random Hamiltonian. We recast the staggered Dirac operator into an unconventional three-dimensional Anderson Hamiltonian ("Dirac-Anderson Hamiltonian") carrying internal degrees of freedom, with disorder provided by the fluctuations of the gauge links. In this framework, we identify the features relevant to chiral symmetry restoration and localisation of the low-lying Dirac eigenmodes in the ordering of the local Polyakov lines, and in the related correlation between spatial links across time slices, thus tying the two phenomena to the deconfinement transition. We then build a toy model based on QCD and on the Dirac-Anderson approach, replacing the Polyakov lines with spin variables and simplifying the dynamics of the spatial gauge links, but preserving the above-mentioned relevant dynamical features. Our toy model successfully reproduces the main features of the QCD spectrum and of the Dirac eigenmodes concerning chiral symmetry breaking and localisation, both in the ordered (deconfined) and disordered (confined) phases. Moreover, it allows us to study separately the roles played in the two phenomena by the diagonal and the off-diagonal terms of the Dirac-Anderson Hamiltonian. Our results support our expectation that chiral symmetry restoration and localisation of the low modes are closely related, and that both are triggered by the deconfinement transition.

Three-loop hard-thermal-loop perturbation theory thermodynamics at finite temperature and finite baryonic and isospin chemical potential

In a previous paper (JHEP {\bf 05} (2014) 27), we calculated the three-loop thermodynamic potential of QCD at finite temperature $T$ and quark chemical potentials $\mu_q$ using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature and density QCD. The result allows us to study the thermodynamics of QCD at finite temperature and isospin chemical potential $\mu_I$. We calculate the pressure, energy density, and entropy density, the trace anomaly, and the speed of sound at zero and nonzero $\mu_I$. The second, fourth, and sixth-order isospin susceptibilities are calculated at zero $\mu_I$. Our results can be directly compared to lattice QCD without Taylor expansions around $\mu_q=0$ since QCD has no sign problem at finite isospin chemical potential.

Thermodynamics of QCD from Sakai-Sugimoto model

Till date, the only consistent description of the deconfinement phase of the Sakai-Sugimoto model appears to be provided by the analysis of [1] (arXiv:1107.4048). The current version of the analysis, however, has a subtlety regarding the monodromy of quarks around the Euclidean time circle. In this note, we revisit and resolve this issue by considering the effect of an imaginary baryon chemical potential on quark monodromies. With this ingredient, the proposal of [1] for investigating finite temperature QCD using holography is firmly established. Additionally, our technique allows a holographic computation of the free energy as a function of the imaginary chemical potential in the deconfinement phase; we show that our result agrees with the corresponding formula obtained from perturbative QCD, namely the Roberge-Weiss potential.

Instanton dynamics in finite temperature QCD via holography

We investigate instantons in finite temperature QCD via Witten's holographic QCD. To study the deconfinement phase, we use the setup proposed in [1]. We find that the sizes of the instantons are stabilized at certain values both in the confinement and deconfinement phases. This agrees with the numerical result in the lattice gauge theory. Besides we find that the gravity duals of the large and small instantons in the deconfinement phase have different topologies. We also argue that the fluctuation of the topological charges is large in confinement phase while it is exponentially suppressed in deconfinement phase, and a continuous transition occurs at the Gross–Witten–Wadia (GWW) point. It would be difficult to observe the counterpart of this transition in lattice QCD, since the GWW point in QCD may stay at an unstable branch.

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.