Thermodynamics and in-medium hadron properties from lattice QCD

TL;DR

This paper surveys non-perturbative lattice QCD studies of QCD thermodynamics, focusing on bulk properties, the phase diagram, and in-medium hadron behavior, including advances in nonzero density via imaginary chemical potential and reweighting techniques. It details lattice-formulated thermodynamics, the nature of the QCD transition, and the equation of state across temperatures and flavors, highlighting small μ-dependence of Tc at low μ and the approach to Stefan–Boltzmann behavior at high T. A major theme is how hadrons and heavy quark bound states are modified in the hot medium, with progress in extracting spectral functions via the maximum entropy method and connecting these to dilepton rates and quarkonia dissolution. The review emphasizes both the progress and remaining challenges, notably the need for lighter physical quark masses and continuum extrapolations to provide precise inputs for heavy-ion phenomenology and the QCD phase diagram.

Abstract

Non-perturbative studies of the thermodynamics of strongly interacting elementary particles within the context of lattice regularized QCD are being reviewed. After a short introduction into thermal QCD on the lattice we report on the present status of investigations of bulk properties. In particular, we discuss the present knowledge of the phase diagram including recent developments of QCD at non-zero baryon number density. We continue with the results obtained so far for the transition temperature as well as the temperature dependence of energy and pressure and comment on screening and the heavy quark free energies. A major section is devoted to the discussion of thermal modifications of hadron properties, taking special account of recent progress through the use of the maximum entropy method.

Figures (25)

• Figure 1: Discretization errors in the calculation of the pressure of a non-interacting gluon gas on lattices with temporal extent $N_\tau$. Shown are results for the standard one plaquette action introduced by K. G. Wilson Wilson and the renormalization group improved action constructed by Y. Iwasaki Iwasaki. Both actions lead to discretization errors of ${\cal O}(a^2) \equiv {\cal O}(1/N_\tau^2)$. Also shown are results obtained with an Symanzik-improved action SymanzikWeisz which has discretization errors of ${\cal O}(a^4)$ only.
• Figure 2: The QCD phase diagram of 3-flavor QCD with degenerate (u,d)-quark masses and a strange quark mass $m_s$.
• Figure 3: The chiral critical line in the light and strange quark mass plane. All the results shown have been obtained with a standard staggered fermion discretization schmidt.
• Figure 4: 3d sketch of the QCD phase diagram schmidt: Shown is the critical surface of second order phase transition which separates the regime of first order phase transitions at large values of the chemical potential and/or small values of the light ($m_{u,d}$) and strange ($m_s$) quark masses from the regime of continuous, non-singular transitions (crossover) to the QCD plasma phase.
• Figure 5: The QCD phase diagram in the $T-\mu$ as it might look like in the case of non-zero but light up and down quarks and a heavier strange quark.