arXiv subjects
Publications and source records attributed to R. Rapp.
It is discussed how chiral symmetry restoration manifests itself through mixing of vector and axial-vector correlators. The vector correlator is directly accessible in relativistic heavy-ion collisions. Within models of the vector correlator its implications for low-mass dilepton spectra are reviewed.
We discuss the similarities and differences for the theories of Rapp, Wambach and collaborators (called R/W in short) and those based on Brown-Rho scaling (called B/R), as applied to reproduce the dileptons measured by the CERES collaboration in the CERN experiments. In both theories the large number of dileptons at invariant masses $\sim$~$m_ρ/2$ are shown to be chiefly produced by a density-dependent $ρ$-meson mass. In R/W the medium dependence is dynamically calculated using hadronic variables defined in the matter-free vacuum. In B/R scaling it follows from movement towards chiral symmetry restoration due to medium-induced vacuum change, and is described in terms of constituent (or quasiparticle) quarks. We argue that the R/W description should be reliable up to densities somewhat beyond nuclear density, where hadrons are the effective variables. At higher density there should be a crossover to constituent quarks as effective variables scaling according to B/R. In the crossover region, the two descriptions must be ``dual''.
The properties of the QCD partition function at finite chemical potential are studied within the instanton liquid model. It is shown that the density dependence of the quark-induced instanton-antiinstanton (I-A) interaction leads to the formation of topologically neutral I-A pairs ('molecules'), resulting in a first order chiral phase transition at a critical chemical potential $μ_q^c\simeq 310$ MeV. At somewhat higher densities ($μ_q\ge360$ MeV), the quark Fermi surface becomes instable with respect to diquark condensation (Cooper pairs) generating BCS-type energy gaps of order 50 MeV.
Medium Effects in low-mass dilepton production in ultra-relativistic heavy-ion collisions are investigated using hadronic models. The rescattering of pions and rho mesons within a hot and dense hadron gas leads to substantial modifications in the $π^+π^- \to e^+ e^-$ annihilation process, which are shown to be important for understanding the recently observed dilepton enhancement at the CERN-SpS. Possible implications for the nature of the chiral phase transition are outlined.
We present a dynamical study of $e^+e^-$ production in C + C and Ca + Ca collisions at BEVALAC/SIS energies on the basis of the covariant transport approach HSD employing momentum-dependent $ρ$-meson spectral functions that include the pion modifications in the nuclear medium as well as the polarization of the $ρ$-meson due to resonant $ρ- N$ scattering. We find that the experimental data from the DLS collaboration cannot be described within the $ρ$-meson spectral function approach. A dropping $η$-mass scenario leads to a good reproduction of the DLS dilepton data, however, violates the $m_T$-scaling of $π^0$ and $η$ spectra as observed by the TAPS collaboration as well as $η$ photoproduction on nuclei.
An overview is given of chiral symmetry restoration at finite temperature and baryochemical potential. Within hadronic models of the vector correlator its implications for low-mass dilepton spectra in ultrarelativistic heavy-ion collisions are discussed.
We discuss the role of strangeness in dense matter and especially in neutron stars. The early (in density) introduction of hyperons found in many calculations is probably delayed by the decrease in vector mean field acting on the neutron. The decrease results from both conventional many-body rescattering effects and from the movement towards asymptotic freedom at high densities. Subthreshold $K^-$-meson production by the KaoS collaboration at GSI shows that the $K^-$-mass must be substantially lowered, by $\gtrsim$ 200 MeV at $ρ\sim 2ρ_0$. It is shown that explicit chiral symmetry breaking through the kaon mass may be responsible for $Σ^-$-nucleon and $Ξ^-$-nucleon scalar attraction being weaker than obtained by simple quark scaling. The normal mode of the strangeness minus, charge $e^-$, excitation is constructed as a linear combination of $K^-$-meson and $Σ^-$, neutron-hole state. Except for zero momentum, where the terms are unmixed the "kaesobar" is a linear combination of these two components.
Instantons lead to strong correlations between up and down quarks with spin zero and anti-symmetric color wave functions. In cold and dense matter, $n_b>n_c\simeq 1 fm^{-3}$ and $T $ condensate and restoring chiral symmetry. At high density, the ground state is a color superconductor in which diquarks play the role of Cooper pairs. An interesting toy model is provided by QCD with two colors: it has a particle-anti-particle symmetry which relates $<\bar qq>$ and $< qq>$ condensates.
We present a dynamical study of $e^+e^-$ and $μ^+ μ^-$ production in proton-nucleus and nucleus-nucleus collisions at CERN-SPS energies on the basis of the covariant transport approach HSD employing a momentum-dependent $ρ$-meson spectral function that includes the pion modifications in the nuclear medium as well as the polarization of the $ρ$-meson due to resonant $ρ$$-N$ scattering. We find that the experimental data from the CERES and HELIOS-3 Collaborations can be described equally well as within the dropping $ρ$-mass scenario. Whereas corresponding dilepton $q_T$-spectra are found to be very similar, the inclusive dilepton yield in the invariant mass range $0.85 \leq M \leq 1.0$ GeV should allow to disentangle the two scenarios experimentally.
A recently developed model for $ρ$-meson propagation in dense hadronic matter is applied to total photoabsorption cross sections in $γ$-proton and $γ$-nucleus reactions. Within the vector dominance model the photon coupling to the virtual pion cloud of the nucleon, two-body meson-exchange currents, as well as $γ$-nucleon resonances are included. Whereas the $γp$ reaction is determined by the low-density limit of the model, higher orders in the nuclear density are important to correctly account for the experimental spectra observed on both light and heavy nuclei over a wide range of photon energies, including the region below the pion threshold. In connection with soft dilepton spectra in high-energy heavy-ion collisions we emphasize the importance of photoabsorption to further constrain the parameters of the model.
We show that the assumption of dropping meson masses together with conventional many-body effects, implemented in the relativistic Dirac-Brueckner formalism, explains nuclear saturation. We use a microscopic model for correlated $2π$ exchange and include the standard many-body effects on the in-medium pion propagation, which initially increase the attractive nucleon-nucleon ($NN$) potential with density. For the vector meson exchanges in both the $ππ$ and $NN$ sector, we assume Brown-Rho scaling which---in concert with `chiral' $ππ$ contact interactions---reduces the attraction at higher densities.
A realistic model for the free rho meson with coupling to two-pion states is employed to calculate the rho propagator in a hot and dense hadron gas. The medium modifications are based on hadronic rescattering processes: intermediate two-pion states are renormalized through interactions with surrounding nucleons and deltas, and rho meson scattering is considered off nucleons, deltas, pions and kaons. Constraints from gauge invariance as well as the full off-shell dynamics of the interactions are accounted for. Within the vector dominance model we apply the resulting in-medium rho spectral function to compute $e^+e^-$ production rates from $π^+π^-$ annihilation. The calculation of corresponding $e^+e^-$ spectra as recently measured in central collisions of heavy-ions at CERN/SpS energies gives reasonable agreement with the experimental data.
Based on a realistic model for the rho meson in free space we investigate it's medium modifications in a hot hadron gas generated by hadronic rescattering processes, i.e. renormalization of intermediate two-pion states as well as direct rho meson scattering off hadrons. Within the vector dominance model the resulting in-medium rho spectral function is applied to calculate $e^+e^-$ spectra as recently measured in heavy-ion collisions at CERN-SpS energies in the CERES experiment.
A meson exchange model of the $ππ$ interaction which fits free $ππ$ scattering data is used to calculate the interactions of pions in nuclear matter as a function of nuclear density. Polarization of the nuclear medium by the pions results in a marked increase in the s-wave $ππ$ attraction at low energy. The influence of this effect on the nucleon-nucleon interaction is a corresponding increase with density of the $NN$ central potential due to the exchange of two correlated pions, resulting in an $NN$ interaction which fails to saturate. A possible mechanism for restoring the theoretical stability of nuclear matter is explored and found to be effective.
We study the influence of mass splitting between the charged and neutral pions and kaons in the Juelich meson exchange model for $ππ$ and $πη$ scattering. The calculations are performed in the particle basis, which permits the use of physical masses for the pseudoscalar mesons and a study of the distinct thresholds associated with the neutral and the charged kaons. Within this model we also investigate the isospin violation which arises from the mass splitting and an apparent violation of G-parity in $ππ$ scattering which stems from the coupling to the $K\overline{K}$ channel. Nonvanishing cross sections for $ππ\rightarrow π^{0}η$ indicate a mixing of the $f_{0}(980)$ and $a_{0}(980)$ states.
Within the finite-temperature Greens-function formalism we study the equation of state of a hot interacting pion gas at zero chemical potential. Employing realistic $ππ$ meson-exchange interactions we selfconsistently calculate the in-medium single-pion selfenergy and the $ππ$ scattering amplitude in the quasiparticle approximation. These quantities are then used to evaluate the thermodynamic potential, $Ω_π$(T), from which the state variables: pressure-, entropy- and energy-density can be derived. In contrast to earlier calculations based on the low-energy Weinberg Lagrangian we find an overall increase as compared to the free-gas results. We also consider the possibility of a dropping $ρ$-meson mass as suggested by the 'Brown-Rho Scaling' law.
Rho meson propagation in hot hadronic matter is studied in a model with coupling to $ππ$ states. Medium modifications are induced by a change of the pion dispersion relation through collisions with nucleons and $Δ's$ in the fireball. Maintaining gauge invariance dilepton production is calculated and compared to the recent data of the CERES collaboration in central S+Au collisions at 200 GeV/u. The observed enhancement of the rate below the rho meson mass can be largely accounted for.
A general prescription for the construction of $ππ$ interaction potentials which preserve scattering length constraints from chiral symmetry when iterated in scattering equations is derived. The prescription involves only minor modifications of typical meson-exchange models, so that coupling constants and cut-off masses in the models are not greatly affected. Calculations of $s$-wave $ππ$ scattering amplitudes in nuclear matter for two models are compared with those for similar models which violate the chiral constraint. While the prescription tends to suppress the accumulation of the near sub-threshold strength of the $ππ$ interaction, an earlier conjecture that amplitudes which satisfy chiral constraints will not exhibit an instability towards $ππ~s-$wave pair condensation appears to be incorrect. At the same time, however, conventional $ππ$ interaction models which fit scattering data well can readily be adjusted to avoid the instability in nuclear matter without recourse to exotic mechanisms.