Lattice QCD Equation Of State Research Articles

Jet transport coefficients by elastic and radiative scatterings in the strongly interacting quark-gluon plasma

We extend the investigation of jet transport coefficients within the effective dynamical quasiparticle model (DQPM)—constructed to describe nonperturbative QCD phenomena of the strongly interacting quark-gluon plasma (sQGP) in line with the lattice QCD equation of state—by accounting for inelastic 2→3 reactions with gluon radiation in addition to the elastic scattering of partons. The elastic and inelastic reactions are calculated explicitly within leading-order Feynman diagrams with effective propagators and vertices from the DQPM by accounting for all channels and their interferences. We present the results for the jet transport coefficients such as the transverse momentum transfer squared q̂ per unit length as well as the energy loss dE/dx per unit length in the sQGP and investigate their dependence on the temperature T and momentum of the jet parton depending on the choice of the strong coupling constant αs in thermal, jet parton, and radiative vertices. For the latter, we consider different scenarios used in the literature and find a very strong dependence of q̂ and dE/dx on the choice of αs. Moreover, we explore the relation of q̂/T3 to the ratio of specific shear viscosity to entropy density η/s and show that the ratio T3/q̂ to η/s has a strong T dependence—especially when approaching Tc—on the choice of αs in scattering vertices. Published by the American Physical Society 2024

Machine learning holographic black hole from lattice QCD equation of state

Based on lattice QCD results of equation of state and baryon number susceptibility at zero baryon chemical potential, and supplemented by machine learning techniques, we construct the analytic form of the holographic black hole metric in the Einstein-Maxwell-Dilaton framework for pure gluon, 2-flavor, and (2+1)-flavor systems, respectively. The dilaton potentials solved from Einstein equations are in good agreement with the extended nonconformal DeWolfe-Gubser-Rosen type dilaton potentials fixed by lattice QCD equation of state, which indicates the robustness of the Einstein-Maxwell-Dilaton framework. The predicted critical end point in the (2+1)-flavor system is located at (Tc=0.094 GeV, μBc=0.74 GeV), which is close to the results from the realistic Polyakov-Nambu-Jona-Lasinio model, the functional renormalization group, and the holographic model with extended DeWolfe-Gubser-Rosen dilaton potential. Published by the American Physical Society 2024

Inelastic and elastic parton scattering in the strongly interacting quark-gluon plasma

We investigate the role of inelastic processes in the strongly interacting quark-gluon plasma (sQGP) based on the effective dynamical quasiparticle model (DQPM). In the DQPM the nonperturbative properties of the sQGP at finite temperature T and baryon chemical potential μB are described in terms of strongly interacting off-shell partons (quarks and gluons) with dynamically generated spectral functions whose properties are adjusted to reproduce the lattice QCD equation of state for the quark-gluon plasma in thermodynamic equilibrium. For the first time the massive gluon radiation processes from the off-shell quark-quark (q+q) and quark-gluon (q+g) scatterings are calculated explicitly within leading-order Feynman diagrams with effective propagators and vertices from the DQPM without any further approximations. We present the results for the energy and temperature dependencies of the total and differential radiative cross sections and compare them to the corresponding elastic cross sections. We show that our results reproduce the perturbative QCD calculations in the limit of zero masses and widths of quasiparticles. Also we study the μB dependence of the inelastic cross sections. Moreover, we present estimates for the transition rate and relaxation time of radiative versus elastic scatterings in the sQGP. Published by the American Physical Society 2024

Equation of State and Energy Loss of Hot and Dense Quark-Gluon matter from Holographic Black Holes

By using gravity/gauge correspondence, we construct a holographic model, constrained to mimic the lattice QCD equation of state at zero density, to investigate the temperature and baryon chemical potential dependence of the equation of state. We also obtained the energy loss of light and heavy partons within the hot and dense plasma represented by the heavy quark drag force, Langevin diffusion coefficients and jet quenching parameter at the critical point and across the first-order transition line predicted by the model.

QCD Equilibrium and Dynamical Properties from Holographic Black Holes

By using gravity/gauge correspondence, we employ an Einstein-Maxwell-Dilaton model to compute the equilibrium and out-of-equilibrium properties of a hot and baryon rich strongly coupled quark-gluon plasma. The family of 5-dimensional holographic black holes, which are constrained to mimic the lattice QCD equation of state at zero density, is used to investigate the temperature and baryon chemical potential dependence of the equation of state. We also obtained the baryon charge conductivity, and the bulk and shear viscosities with a particular focus on the behavior of these observables on top of the critical end point and the line of first order phase transition predicted by the model.

Resummed lattice QCD equation of state at finite baryon density: Strangeness neutrality and beyond

We calculate a resummed equation of state with lattice QCD simulations at imaginary chemical potentials. This work presents a generalization of the scheme introduced in 2102.06660 to the case of non-zero $\mu_S$, focusing on the line of strangeness neutrality. We present results up to $\mu_B/T \leq 3.5$ on the strangeness neutral line $\left\langle S \right\rangle = 0$ in the temperature range $130 \rm{MeV} \leq T \leq 280 \rm{MeV}$. We also extrapolate the finite baryon density equation of state to small non-zero values of the strangeness-to-baryon ratio $R=\left\langle S \right\rangle / \left\langle B \right\rangle$. We perform a continuum extrapolation using lattice simulations of the 4stout-improved staggered action with 8, 10, 12 and 16 timeslices.

Analytical structure of the equation of state at finite density: Resummation versus expansion in a low energy model

For theories plagued with a sign problem at finite density, a Taylor expansion in the chemical potential is frequently used for lattice gauge theory-based computations of the equation of state. Recently, a new resummation scheme was proposed [S. Mondal, S. Mukherjee, and P. Hegde, Lattice QCD Equation of State for Nonvanishing Chemical Potential by Resumming Taylor Expansions, Phys. Rev. Lett. 128, 022001 (2022).] for such an expansion that resums contributions of correlation functions of conserved currents to all orders in the chemical potential. Here, we study the efficacy of this resummation scheme using a low energy model, namely the mean-field quark-meson model. After adapting the scheme for a mean-field analysis, we confront the results of this scheme with the direct solution of the model at finite density as well as compare with results from Taylor expansions. We study to what extent the two methods capture the analytical properties of the equation of state in the complex chemical potential plane. As expected, the Taylor expansion breaks down as soon as the baryon chemical potential reaches the radius of convergence defined by the Yang-Lee edge singularity. Encouragingly, the resummation not only captures the location of the Yang-Lee edge singularity accurately, but is also able to describe the equation of state for larger chemical potentials beyond the location of the edge singularity for a wide range of temperatures.

Lattice QCD Equation of State for Nonvanishing Chemical Potential by Resumming Taylor Expansions.

Taylor expansion in powers of baryon chemical potential (μ_{B}) is an oft-used method in lattice QCD to compute QCD thermodynamics for μ_{B}>0. Based only upon the few known lowest order Taylor coefficients, it is difficult to discern the range of μ_{B} where such an expansion around μ_{B}=0 can be trusted. We introduce a resummation scheme for the Taylor expansion of the QCD equation of state in μ_{B} that is based on the n-point correlation functions of the conserved current (D_{n}). The method resums the contributions of the first N correlation function D_{1},…,D_{N} to the Taylor expansion of the QCD partition function to all orders in μ_{B}. We show that the resummed partition function is an approximation to the reweighted partition function at μ_{B}≠0. We apply the proposed approach to high-statistics lattice QCD calculations using 2+1 flavors of Highly Improved Staggered Quarks with physical quark masses on 32^{3}×8 lattices and for temperatures T≈145-176 MeV. We demonstrate that, as opposed to the Taylor expansion, the resummed version not only leads to improved convergence but also reflects the zeros of the resummed partition function and severity of the sign problem, leading to its eventual breakdown. We also provide a generalization of scheme to include resummation of powers of temperature and quark masses in addition to μ_{B}, and show that the alternative expansion scheme of [S. Borsányi et al., Phys. Rev. Lett. 126, 232001 (2021).PRLTAO0031-900710.1103/PhysRevLett.126.232001] is a special case of this generalized resummation.

Heavy quark transport coefficients in a viscous QCD medium with collisional and radiative processes

The heavy quark drag and momentum diffusion coefficients in the presence of both the collisional and radiative processes have been studied in a hot viscous QCD medium. The thermal medium effects are incorporated by employing the effective fugacity quasiparticle model based on the lattice QCD equation of state. Viscous effects are embedded into the heavy quark transport through the near-equilibrium distribution functions of the constituent medium particles of the quark-gluon plasma. The viscous corrections to the momentum distributions have been estimated from the effective Boltzmann equation. The effect of shear viscous correction to drag and diffusion is investigated by considering the soft gluon radiation by heavy quarks along with the elastic collisional processes of the heavy quark with the light quarks and gluons within the QGP medium. The momentum and temperature dependence of the heavy quark transport coefficients are seen to be sensitive to the viscous coefficient of the QGP for the collisional and radiative processes. The collisional and radiative energy loss of the heavy quark in the viscous quark-gluon plasma has also been explored.

Lattice QCD Equation of State at Finite Chemical Potential from an Alternative Expansion Scheme.

In this Letter, we introduce a novel scheme for extrapolating the equation of state of QCD to finite chemical potential that features considerably improved convergence properties and allows us to extend its reach to unprecedentedly high baryonic chemical potentials. We present continuum extrapolated lattice results for the new expansion coefficients and show the thermodynamic observables up to μ_{B}/T≤3.5. This novel expansion does not suffer from the shortcomings that characterize the traditional Taylor expansion method, such as difficulties inherent in performing such an expansion with a limited number of coefficients and the poor signal-to-noise ratio that affects Taylor coefficients determined from lattice calculations.

Thermodynamics of strongly interacting matter in a hybrid model

The equation of state and fluctuations of conserved charges in a strongly interacting medium under equilibrium conditions form the baseline upon which various possible scenarios in relativistic heavy-ion collision experiments are built. Many of these quantities have been obtained in the lattice QCD framework with reliable continuum extrapolations. Recently the Polyakov$-$Nambu$-$Jona-Lasinio model has been reparametrized to some extent to reproduce quantitatively the lattice QCD equation of state at vanishing chemical potentials. The agreement was precise except at low temperatures, possibly due to inadequate representation of the hadronic degrees of freedom in the model. This disagreement was also observed for some of the fluctuation and correlations considered. Here we address this issue by introducing the effects of hadrons through the Hadron Resonance Gas model. The total thermodynamic potential is now a weighted sum of the thermodynamic potential of the Polyakov$-$Nambu$-$Jona-Lasinio model and that of the Hadron Resonance Gas model. We find that the equation of state and the fluctuations and correlations obtained in this hybrid model agrees satisfactorily with the lattice QCD data in the low temperature regime.

( 3+1 )-dimensional anisotropic fluid dynamics with a lattice QCD equation of state

Anisotropic hydrodynamics improves upon standard dissipative fluid dynamics by treating certain large dissipative corrections nonperturbatively. Relativistic heavy-ion collisions feature two such large dissipative effects: (i) Strongly anisotropic expansion generates a large shear stress component which manifests itself in very different longitudinal and transverse pressures, especially at early times. (ii) Critical fluctuations near the quark-hadron phase transition lead to a large bulk viscous pressure on the conversion surface between hydrodynamics and a microscopic hadronic cascade description of the final collision stage. We present a new dissipative hydrodynamic formulation for nonconformal fluids where both of these effects are treated nonperturbatively. The evolution equations are derived from the Boltzmann equation in the 14-moment approximation, using an expansion around an anisotropic leading-order distribution function with two momentum-space deformation parameters, accounting for the longitudinal and transverse pressures. To obtain their evolution we impose generalized Landau matching conditions for the longitudinal and transverse pressures. We describe an approximate anisotropic equation of state that relates the anisotropy parameters with the macroscopic pressures. Residual shear stresses are smaller and are treated perturbatively, as in standard second-order dissipative fluid dynamics. The resulting optimized viscous anisotropic hydrodynamic evolution equations are derived in $3+1$ dimensions and tested in a ($0+1$)-dimensional Bjorken expansion, using a state-of-the-art lattice equation of state. Comparisons with other viscous hydrodynamical frameworks are presented.

Thermal noise in a boost-invariant matter expansion in relativistic heavy-ion collisions

We formulate a general theory of thermal fluctuations within causal second-order viscous hydrodynamic evolution of matter formed in relativistic heavy-ion collisions. The fluctuation is treated perturbatively on top of a boost-invariant longitudinal expansion. Numerical simulation of thermal noise is performed for a lattice QCD equation of state and for various second-order dissipative evolution equations. Phenomenological effects of thermal fluctuations on the two-particle rapidity correlations are studied.

Scaling Properties of Spectra in New Exact Solutions of Rotating, Multi-Component Fireball Hydrodynamics

We describe fireballs that rehadronize from a perfect fluid of quark matter, characterized by the lattice QCD equation of state, to a chemically frozen, multi-component mixture, that contains various kinds of observable hadrons. For simplicity and clarity, we apply a non-relativistic approximation to describe the kinematics of this expansion. Unexpectedly, we identify a secondary explosion that may characterize fireball hydrodynamics at the QCD critical point. After rehadronization, the multi-component mixture of hadrons keeps on rotating and expanding together, similarly to a single component fluid. After kinetic freeze-out, the effective temperature T i of the single-particle spectra of hadron type h i is found to be a sum of the kinetic freeze-out temperature T f (that is independent of the hadron type h i ) and a term proportional to the mass m i of hadron type h i . The coefficient of proportionality to m i is found to be independent of the hadron type h i but to be dependent on the radial flow and vorticity of collective dynamics.

Thermalization in a small hadron gas system and high-multiplicity pp events

We study the system-size dependence of Knudsen number, a measure of degree of thermalization, for hadron resonance gas that follows the Lattice-QCD equation of state at zero chemical potential. A comparison between Knudsen numbers for the AuAu collisions at RHIC and the hadron gas of size similar to the size of high-multiplicity pp events at LHC, reassures the applicability of hydrodynamics in interpreting the features of particle production in high-multiplicity pp events.

Thermodynamically Consistent Formulation of Quasiparticle Viscous Hydrodynamics

A novel formulation of second-order relativistic viscous fluid dynamics based on the effective Boltzmann equation for quasi-particles with medium-dependent masses is briefly reviewed.~The evolution equations for the shear and bulk dissipative corrections, and the corresponding transport coefficients, are presented. Resulting approach allows for thermodynamically-consistent incorporation of lattice QCD equation of state in the fluid dynamical framework.

Toward a consistent evolution of the quark-gluon plasma and heavy quarks

Heavy-quark observables in ultrarelativistic heavy-ion collisions, like the nuclear modification factor and the elliptic flow, give insight into the mechanisms of high-momentum suppression and low-momentum thermalization of heavy quarks. Here, we present a global study of these two observables within a coupled approach of the heavy-quark propagation in a realistic fluid dynamical medium, MC@sHQ+EPOS2, and compare to experimental data from RHIC and LHC experiments. The heavy quarks scatter elastically and inelastically with the quasiparticles of the quark-gluon plasma (QGP), which are represented consistently with the underlying equation of state. We examine two scenarios: first, we interpret the lattice QCD equation of state as a sum of partonic and hadronic contributions, and second, as a gas of massive partonic quasiparticles. It is observed that independent of their momentum the energy loss of heavy quarks depends strongly on how the lattice QCD equation of state is translated into degrees of freedom of the QGP.

Baryon number fluctuations from a crossover equation of state compared to heavy-ion collision measurements in the beam energy rangesNN=7.7to 200 GeV

Fluctuations of the proton number distribution in central Au-Au collisions have been measured by the STAR collaboration in a beam energy scan at the Relativistic Heavy Ion Collider (RHIC). The motivation is a search for evidence of a critical point in the equation of state. It was found that the skewness and kurtosis display an interesting energy dependence. We compare these measurements to an equation of state which smoothly interpolates between an excluded volume hadron resonance gas at low energy density to a perturbative plasma of quarks and gluons at high energy density. This crossover equation of state agrees very well with the lattice QCD equation of state. The crossover equation of state can reproduce the data if the fluctuations are frozen at a temperature significantly lower than the average chemical freeze-out.

Effective distributions of quasiparticles for thermal photons

It has been found in recent heavy-ion experiments that the second and the third flow harmonics of direct photons are larger than most theoretical predictions. In this study, I construct effective parton phase-space distributions with in-medium interaction using quasi-particle models so that they are consistent with a lattice QCD equation of state. Then I investigate their effects on thermal photons using a hydrodynamic model. Numerical results indicate that elliptic flow and transverse momentum spectra are modified by the corrections to Fermi-Dirac and Bose-Einstein distributions.

Color path-integral Monte-Carlo simulations of quark-gluon plasma: Thermodynamic and transport properties

Based on the quasiparticle model of the quark-gluon plasma (QGP), a color quantum path-integral Monte-Carlo (PIMC) method for calculation of thermodynamic properties and -- closely related to the latter -- a Wigner dynamics method for calculation of transport properties of the QGP are formulated. The QGP partition function is presented in the form of a color path integral with a new relativistic measure instead of the Gaussian one traditionally used in the Feynman-Wiener path integral. It is shown that the PIMC method is able to reproduce the lattice QCD equation of state at zero baryon chemical potential at realistic model parameters (i.e. quasiparticle masses and coupling constant) and also yields valuable insight into the internal structure of the QGP. Our results indicate that the QGP reveals quantum liquid-like (rather than gas-like) properties up to the highest considered temperature of 525 MeV. The pair distribution functions clearly reflect the existence of gluon-gluon bound states, i.e. glueballs, at temperatures just above the phase transition, while meson-like $q\bar{q}$ bound states are not found. The calculated self-diffusion coefficient agrees well with some estimates of the heavy-quark diffusion constant available from recent lattice data and also with an analysis of heavy-quark quenching in experiments on ultrarelativistic heavy ion collisions, however, appreciably exceeds other estimates. The lattice and heavy-quark-quenching results on the heavy-quark diffusion are still rather diverse. The obtained results for the shear viscosity are in the range of those deduced from an analysis of the experimental elliptic flow in ultrarelativistic heavy ions collisions, i.e. in terms the viscosity-to-entropy ratio, $1/4\pi < \eta/S < 2.5/4\pi$, in the temperature range from 170 to 440 MeV.