ππ-correlations in hot and dense matter

Properties of the ππ-interactions in hot and dense matter are studied within a nonperturbative and symmetry conserving approach. The pion and its chiral partner, the σ-meson, are described within the linear σ model and special attention is given to the conservation of the underlying chiral symmetry. The first part deals with the properties of pion and σ in the vacuum, the further being the ''Goldstone''-boson of the theory, while the latter is a broad resonance. The results in the vacuum are tested against experimental results like ππ-phase shifts as well as the mass and the width of the σ-meson. Besides the propagator of the σ-meson, the preservation of the chiral symmetry is explicitly examined and chiral Ward identities for the n-point functions of the theory are fulfilled. Furthermore the ππ-scattering matrix is calculated and shown to be consistent with predictions from chiral perturbation theory. In the second part of this work the model is extended to finite temperature with special emphasis on the chiral phase transition. The transition temperature and the critical exponent β are determined, and the influence of the temperature on the propagator of the s-meson as well as on the ππ-scattering matrix is examined. The third part deals with the properties of pion and σ in dense matter. Additional couplings like the ones to particle-hole excitations and short range repulsion have to be included to ensure stability at nuclear matter density. At zero three momentum one observes a strong downward shift of the σ-mass accompanied by an accumulation of strength near the two-pion threshhold in the spectral function. Taking into account a finite three momentum for the ππ-pair, respectively the σ-meson, one observes a weakening of the aforementioned effect. Having thus developed a model for the ππ-interaction at finite temperature and density, we try to describe and explain two experiments with our model in the last part of the work. Both experiments have measured cross sections for pion pairs in dense matter and observe an accumulation of strength near the two-pion threshhold with increasing density of the reaction. This effect could be explained by the modification of the σ-meson in dense matter, as shown in our calculations. A closer look at the kinematics of the experiment though shows, that most of the events take place at a finite three momentum of the pion pair, where the modification of the pair is already weakened in our calculation. Therefore the result of the experiment can only be partly attributed to the softening of the σ-meson in dense matter apparent in our calculations. (orig.)