We extend our recent study of dilepton invariant-mass spectra from the decays of ρ mesons produced by photon reactions off nuclei. We specifically focus on experimental spectra as recently measured by the CLAS Collaboration at the Thomas Jefferson National Accelerator Facility using carbon and iron nuclei. Building on our earlier work, we broaden our description to a larger set of observables to identify sensitivities to the medium effects predicted by microscopic calculations of the ρ spectral function. We compute mass spectra for several target nuclei and study the spectral shape as a function of the three-momentum of the outgoing lepton pair. We also compute the so-called nuclear transparency ratio, which provides an alternative means (and thus consistency check) of estimating the ρ width in the cold nuclear medium.

A modified self-consistent Hartree-Fock approximation to the λφ 4 theory with spontaneously broken O(N ) symmetry is proposed. It preserves all the desirable features, like conservation laws and thermodynamic consistency, of the self-consistent Schwinger-Dyson scheme generated from a 2PI functional, also known as the Φ-derivable scheme, while simultaneously respecting the Nambu-Goldstone theorem in the chiral-symmetry broken phase. Various approximate resummation schemes are discussed.

A thermodynamic T -matrix approach for elastic two-body interactions is employed to calculate spectral functions of open and hidden heavy-quark systems in the quark-gluon plasma. This enables the evaluation of quarkonium bound-state properties and heavy-quark diffusion on a common basis and thus to obtain mutual constraints. The two-body interaction kernel is approximated within a potential picture for spacelike momentum transfers. An effective field-theoretical model combining color-Coulomb and confining terms is implemented with relativistic corrections and for different color channels. Four pertinent model parameters, characterizing the coupling strengths and screening, are adjusted to reproduce the color-average heavy-quark free energy as computed in thermal lattice QCD. The approach is tested against vacuum spectroscopy in the open (D, B) and hidden ( and ϒ) flavor sectors, as well as in the high-energy limit of elastic perturbative QCD scattering. Theoretical uncertainties in the static reduction scheme of the four-dimensional Bethe-Salpeter equation are elucidated. The quarkonium spectral functions are used to calculate Euclidean correlators which are discussed in light of lattice QCD results, while heavy-quark relaxation rates and diffusion coefficients are extracted utilizing a Fokker-Planck equation.

A selfconsistent calculation of heavy-quark (HQ) and quarkonium properties in the Quark-Gluon Plasma (QGP) is conducted to quantify flavor transport and color screening in the medium. The main tool is a thermodynamic T -matrix approach to compute HQ and quarkonium spectral functions in both scattering and bound-state regimes. The T -matrix, in turn, is employed to calculate HQ selfenergies which are implemented into spectral functions beyond the quasiparticle approximation. Charmonium spectral functions are used to evaluate eulcidean-time correlation functions which are compared to results from thermal lattice QCD. The comparisons are performed in various hadronic channels including zero-mode contributions consistently accounting for finite charm-quark width effects. The zero modes are closely related to the charm-quark number susceptibility which is also compared to existing lattice "data". Both the susceptibility and the heavy-light quark T -matrix are applied to calculate the thermal charm-quark relaxation rate, or, equivalently, the charm diffusion constant in the QGP. Implications of our findings in the HQ sector for the viscosity-to-entropydensity ratio of the QGP are briefly discussed.

Technical concepts are presented that improve the selfconsistent treatment of vector-mesons in a hot and dense medium. First applications concern an interacting gas of pions and ρ mesons. As an extension of earlier studies we thereby include RPA-type vertex corrections and further use dispersion relations in order to calculate the real part of the vector-meson selfenergy. An improved projection method preserves the four transversality of the vector-meson polarisation tensor throughout the selfconsistent calculations, thereby keeping the scheme void of kinematical singularities.

We compute dilepton invariant mass spectra from the decays of ρ mesons produced by photon reactions off nuclei. Our calculations employ a realistic model for the ρ photoproduction amplitude on the nucleon which provides fair agreement with measured cross sections. Medium effects are implemented via an earlier constructed ρ propagator based on hadronic many-body theory. At incoming photon energies of 1.5-3 GeV as used by the CLAS experiment at JLAB, the average density probed for iron targets is estimated at about half saturation density. At the pertinent 3-momenta the predicted medium effects on the ρ propagator are rather moderate. The resulting dilepton spectra approximately agree with recent CLAS data.

The renormalization of a gapless Φ-derivable Hartree-Fock approximation to the O(N )-symmetric λφ 4 theory is considered in the spontaneously broken phase. This kind of approach was proposed by three of us in a previous paper [1] in order to preserve all the desirable features of Φ-derivable DysonSchwinger resummation schemes (i.e., validity of conservation laws and thermodynamic consistency) while simultaneously restoring the Nambu-Goldstone theorem in the broken phase. It is shown that unlike for the conventional Hartree-Fock approximation this approach allows for a scale-independent renormalization in the vacuum. However, the scale dependence still persists at finite temperatures. Various branches of the solution are studied. The occurrence of a limiting temperature inherent in the renormalized Hartree-Fock approximation at fixed renormalization scale µ is discussed.

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