F. Riek

Quarkonia and Heavy-Quark Relaxation Times in the Quark-Gluon Plasma

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 ({Psi} and {Upsilon}) 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.

Selfconsistent description of vector-mesons in matter

Abstract We study the influence of the virtual pion cloud in nuclear matter at finite densities and temperatures on the structure of the ρ - and ω -mesons. The in-matter spectral function of the pion is obtained within a selfconsistent scheme of coupled Dyson equations where the coupling to the nucleon and the Δ(1232)-isobar resonance is taken into account. The selfenergies are determined using a two-particle irreducible (2PI) truncation scheme ( Φ -derivable approximation) supplemented by Migdals short range correlations for the particle–hole excitations. The so obtained spectral function of the pion is then used to calculate the in-medium changes of the vector-meson spectral functions. With increasing density and temperature a strong interplay of both vector-meson modes is observed. The four-transversality of the polarisation tensors of the vector-mesons is achieved by a projector technique. The resulting spectral functions of both vector-mesons and, through vector dominance, the implications of our results on the dilepton spectra are studied in their dependence on density and temperature.

Renormalization of a gapless Hartree-Fock approximation to a theory with spontaneously broken O ( N ) symmetry

The renormalization of a gapless {phi}-derivable Hartree-Fock approximation to the O(N)-symmetric {lambda}{phi}{sup 4} theory is considered in the spontaneously broken phase. This kind of approach was proposed by three of us in a previous paper [Yu. B. Ivanov, F. Riek, and J. Knoll, Phys. Rev. D 71, 105016 (2005).] in order to preserve all the desirable features of {phi}-derivable Dyson-Schwinger 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 {mu} is discussed.

Medium modifications of the {rho} meson in nuclear photoproduction.

We extend our recent study of dilepton invariant-mass spectra from the decays of {rho} 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 {rho} 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 {rho} width in the cold nuclear medium.

In-Medium Excitations

1 Introduction 2 Electromagnetic probes and light vector mesons 3 Hadronic resonance spectroscopy 4 Strangeness 5 Open charm probes 6 Charmonium 7 Excitations of color-superconducting matter 8 Summary and relations to observables

Medium effects in ρ-meson photoproduction

Abstract 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.

Dynamics of resonances in strongly interacting systems

The effects of the propagation of particles which have a finite life-time and an according broad distribution in their mass spectrum are discussed in the context of a transport descriptions. In the first part some example cases of mesonic modes in nuclear matter at finite densities and temperatures are presented. These equilibrium calculations illustrate the dynamical range of spectral distributions to be adequately covered by non-equilibrium description of the dynamics of two nuclei colliding at high energies. The second part addresses the problem of transport descriptions which properly account for the damping width of the particles. A systematic and general gradient approximation is presented in the form of diagrammatic rules which permit to derive a self-consistent transport scheme from the Kadanoff-Baym equation. The scheme is conserving and thermodynamically consistent provided the self-energies are obtained within the phi-derivable two-particle irreducible (2PI) method of Baym. The merits, the limitations and partial cures of the limitations of this transport scheme are discussed in detail.

Covariant and self-consistent vertex corrections for pions and isobars in nuclear matter

We evaluate the pion and isobar propagators in cold nuclear matter self-consistently applying a covariant form of the isobar-hole model. Migdals vertex correction effects are considered systematically in the absence of phenomenological soft form factors. Saturated nuclear matter is modeled by scalar and vector mean fields for the nucleon. It is shown that the short-range dressing of the {pi}N{delta} vertex has a significant effect on the pion and isobar properties. Using realistic parameters sets we predict a downward shift of about 50 MeV for the {delta} resonance at nuclear saturation density. The pionic soft modes are much less pronounced than in previous studies.

Photoabsorption off nuclei with self-consistent vertex corrections

We study photoproduction off nuclei based on a self-consistent and covariant many-body approach for the pion and isobar propagation in infinite nuclear matter. For the first time the t-channel exchange of an in-medium pion is evaluated in the presence of vertex correction effects consistently. In particular the interference pattern with the s-channel in-medium nucleon and isobar exchange contribution is considered. Electromagnetic gauge invariance is kept as a consequence of various Ward identities obeyed by the computation. Adjusting the set of Migdal parameters to the data set we predict an attractive mass shift for the isobar of about 50 MeV at nuclear saturation density.

Nonperturbative Heavy-Quark Interactions in the QGP

We adopt a T -matrix approach to study quarkonium properties and heavy-quark transport in a Quark-Gluon Plasma. The T -matrix approach is well suited to implement potential scattering and thus provides a common framework for low-momentum transfer interactions in heavy-heavy and heavy-light quark systems. We assume that the underlying potentials can be estimated from the heavy-quark free energy computed in lattice QCD. We discuss constraints from vacuum spectroscopy, uncertainties arising from different choices of the potential, and the role of elastic and inelastic widths which are naturally accounted for in the T -matrix formalism.