We study the phase diagram of dense, locally neutral three-flavor quark matter within the framework of the Nambu–Jona-Lasinio model. In the analysis, dynamically generated quark masses are taken into account self-consistently. The phase diagram in the plane of temperature and quark chemical potential is presented. The results for two qualitatively different regimes, intermediate and strong diquark coupling strength, are presented. It is shown that the role of gapless phases diminishes with increasing diquark coupling strength.

We study scalar, pseudoscalar, vector, and axial-vector mesons with nonstrange and strange quantum numbers in the framework of a linear sigma model with global chiral $U(N_f{)}_L\times U(N_f{)}_R$ symmetry. We perform a global fit of meson masses, decay widths, as well as decay amplitudes. The quality of the fit is, for a hadronic model that does not consider isospin-breaking effects, surprisingly good. We also investigate the question whether the scalar $\overline{q}q$ states lie below or above 1 GeV and find the scalar states above 1 GeV to be preferred as $\overline{q}q$ states. Additionally, we also describe the axial-vector resonances as $\overline{q}q$ states.

We derive relativistic second-order dissipative fluid-dynamical equations of motion for massive spin-$1/2$ particles from kinetic theory using the method of moments. Besides the usual conservation laws for charge, energy, and momentum, such a theory of relativistic dissipative spin hydrodynamics features an equation of motion for the rank-3 spin tensor, which follows from the conservation of total angular momentum. Extending the conventional method of moments for spin-0 particles, we expand the spin-dependent distribution function near local equilibrium in terms of moments of the momentum and spin variables. We work to next-to-leading order in the Planck constant $\hslash$. As shown in previous work, at this order in $\hslash$ the Boltzmann equation for spin-$1/2$ particles features a nonlocal collision term. From the Boltzmann equation, we then obtain an infinite set of equations of motion for the irreducible moments of the deviation of the single-particle distribution function from local equilibrium. In order to close this system of moment equations, a truncation procedure is needed. We employ the “$14+24$-moment approximation”, where “14” corresponds to the components of the charge current and the energy-momentum tensor and “24” to the components of the spin tensor, which completes the derivation of the equations of motion of second-order dissipative spin hydrodynamics. For applications to heavy-ion phenomenology, we also determine dissipative corrections to the Pauli-Lubanski vector.

Chiral symmetry restoration at nonzero temperature is studied in the framework of the $O\left(4\right)\mathrm{}$ linear sigma model and the ${U(N}_f{)}_r\times {U(N}_f{)}_{\mathcal{l}}$ linear sigma model with $N_f=2,3$ and 4 quark flavors. We investigate the temperature dependence of the masses of the scalar and pseudoscalar mesons, and the nonstrange, strange, and charm condensates within the Hartree approximation as derived from the Cornwall-Jackiw-Tomboulis formalism. We find that the masses of the nonstrange and strange mesons at nonzero temperature depend sensitively on the particular symmetry of the model and the number of light quark flavors $N_f.$ On the other hand, because of the large charm quark mass, neither do charmed mesons significantly affect the properties of the other mesons, nor do their masses change appreciably in the temperature range around the chiral symmetry restoration temperature. In the chiral limit, the transition temperatures for chiral symmetry restoration are surprisingly close to those found in lattice QCD.

We derive relativistic dissipative spin hydrodynamics from kinetic theory featuring a nonlocal collision term using the method of moments. In this framework, the components of the spin tensor are dynamical variables which obey relaxation-type equations. We find that the corresponding relaxation times are determined by the local part of the collision term, while the nonlocal part contributes to the Navier-Stokes terms in these equations of motion. The spin relaxation timescales are comparable to those of the usual dissipative currents. Finally, the Navier-Stokes limit of the Pauli-Lubanski vector receives contributions proportional to the shear tensor of the fluid, which implies that the polarization of hadrons observed in heavy-ion collisions is influenced by dissipative effects.

Relativistic dissipative fluid dynamics finds widespread applications in high-energy nuclear physics and astrophysics. However, formulating a causal and stable theory of relativistic dissipative fluid dynamics is far from trivial; efforts to accomplish this reach back more than 50 years. In this review, we give an overview of the field and attempt a comparative assessment of (at least most of) the theories for relativistic dissipative fluid dynamics proposed until today and used in applications.