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The in-medium modifications of hadron properties such as masses and decay widths have been a major focus of the scientific work of Gerry Brown and the insights gained by him and his collaborators made them major drivers of this field for several decades. Their prediction of experimental signals in di-lepton pair production in relativistic heavy-ion collisions were instrumental in initiating large experimental campaigns which continue until today. In this chapter we review recent results which elucidate the relation of hadronic spectral properties at finite temperature and density to the restoration of spontaneously broken chiral symmetry.
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Properties of r{ho}-meson in symmetric nuclear matter are investigated within a light-front constituent quark model (LFCQM), using the in-medium input calculated by the quark-meson coupling (QMC) model. The LFCQM used here was previously applied in vacuum to calculate the r{ho}-meson electromagnetic properties, namely, charge G 0 , magnetic G 1 , and quadrupole G 2 form factors, as well as the electromagnetic radius and decay constant. We predict the in-medium modifications of the r{ho}-meson electromagnetic form factors in symmetric nuclear matter.
We present results for in-medium spectral functions obtained within the Functional Renormalization Group framework. The analytic continuation from imaginary to real time is performed in a well-defined way on the level of the flow equations. Based on this recently developed method, results for the sigma and the pion spectral function for the quark-meson model are shown at finite temperature, finite quark-chemical potential and finite spatial momentum. It is shown how these spectral function become degenreate at high temperatures due to the restoration of chiral symmetry. In addition, results for vector- and axial-vector meson spectral functions are shown using a gauged linear sigma model with quarks. The degeneration of the $rho$ and the $a_1$ spectral function as well as the behavior of their pole masses is discussed.
We employ the functional renormalization group approach formulated on the Schwinger-Keldysh contour to calculate real-time correlation functions in scalar field theories. We provide a detailed description of the formalism, discuss suitable truncation schemes for real-time calculations as well as the numerical procedure to self-consistently solve the flow equations for the spectral function. Subsequently, we discuss the relations to other perturbative and non-perturbative approaches to calculate spectral functions, and present a detailed comparison and benchmark in $d=0+1$ dimensions.
Second-order susceptibilities $chi^{11}_{ij}$ of baryon, electric, and strangeness, $B$, $Q$, and $S$, charges, are calculated in the Chiral Mean Field (CMF) model and compared to available lattice QCD data. The susceptibilities are sensitive to the short range repulsive interactions between different hadron species, especially to the hardcore repulsion of hyperons. Decreasing the hyperons size, as compared to the size of the non-strange baryons, does improve significantly the agreement of the CMF model results with the Lattice QCD data. The electric charge-dependent susceptibilities are sensitive to the short range repulsive volume of mesons. The comparison with lattice QCD data suggests that strange baryons, non-strange mesons and strange mesons have significantly smaller excluded volumes than non-strange baryons. The CMF model with these modified hadron volumes allows for a mainly hadronic description of the QCD susceptibilities significantly above the chiral pseudo-critical temperature. This improved CMF model which is based on the lattice QCD data, has been used to study the properties of both cold QCD matter and neutron star matter. The phase structure in both cases is essentially unchanged, i.e. a chiral first-order phase transition occurs at low temperatures ($T_{rm CP}approx 17$ MeV), and hyperons survive deconfinement to higher densities than non-strange hadrons. The neutron star maximal mass remains close to 2.1$M_odot$ and the mass-radius diagram is only modified slightly due to the appearance of hyperons and is in agreement with astrophysical observations.
We describe two independent frameworks which provide unambiguous determinations of the deconfinement and the decoupling conditions of a relativistic gas at finite temperature. First, we use the Polyakov-Nambu-Jona-Lasinio model to compute meson and baryon masses at finite temperature and determine their melting temperature as a function of their strangeness content. Second, we analyze a simple expanding gas within a Friedmann-Robertson-Walker metric, which admits a well-defined decoupling mechanism. We examine the decoupling time as a function of the particle mass and cross section. We find evidences of an inherent dependence of the hadronization and freeze-out conditions on flavor, and on mass and cross section, respectively.
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