Abstract. We present recent results on a systematic method to calculate transport coefficients for a meson gas (in particular, we analyze a pion gas) at low temperatures in the context of Chiral Perturbation Theory (ChPT). Our method is based on the study of Feynman diagrams taking into account collisions in the plasma by means of the non-zero particle width. This implies a modification of the standard ChPT power counting scheme. We discuss the importance of unitarity, which allows for an accurate high energy description of scattering amplitudes, generating dynamically the ρ(770) and f0(600) mesons. Our results are compatible with analyses of kinetic theory, both in the non-relativistic very low-T regime and near the transition. We show the behavior with temperature of the electrical and thermal conductivities as well as of the shear and bulk viscosities. We obtain that bulk viscosity is negligible against shear viscosity, except near the chiral phase transition where the conformal anomaly might induce larger bulk effects. Different asymptotic limits for transport coefficients, large-Nc scaling and some applications to heavy-ion collisions are studied. PACS

The electrical conductivity of a pion gas at low temperatures is studied in the framework of linear response and chiral perturbation theory. The standard ChPT power counting has to be modified to include pion propagator lines with a nonzero thermal width in order to properly account for collision effects typical of kinetic theory. With this modification, we discuss the relevant chiral power counting to be used in the calculation of transport coefficients. The leading order contribution is found and we show that the dominant higher order ladder diagrams can be treated as perturbative corrections at low temperatures. We find that the DC conductivity T is a decreasing function of T, behaving for very low T as T e 2 m m =T p , consistently with nonrelativistic kinetic theory. When unitarization effects are included, T increases slowly as T approaches the chiral phase transition. We compare with related works and discuss some physical consequences, especially in the context of the low-energy hadronic photon spectrum in relativistic heavy ion collisions.

We calculate the bulk viscosity of the massive pion gas within unitarized chiral perturbation theory. We obtain a low-temperature peak arising from explicit conformal breaking due to the pion mass and another peak near the critical temperature, dominated by the conformal anomaly through gluon condensate terms. The correlation between bulk viscosity and conformal breaking supports a recent QCD proposal. We discuss the role of resonances, heavier states, and large-N_(c) counting.

We compute three particle correlations in the Glasma flux tube model of high energy heavy ion collisions. We obtain a simple geometrical picture of these correlations; when convoluted with final state radial flow, it results in distinct predictions for the near side three particle correlation in central heavy ion collisions.

We consider an interacting pion gas in a stage of the system evolution where thermal but not chemical equilibrium has been reached, i.e., for temperatures between thermal and chemical freezeout T ther < T < T chem reached in Relativistic Heavy ion Collisions. Approximate particle number conservation is implemented by a nonvanishing pion number chemical potential µπ within a diagrammatic thermal field theory approach, valid in principle for any bosonic field theory in this regime. The resulting Feynman rules are derived here and applied within the context of Chiral Perturbation Theory to discuss thermodynamical quantities of interest for the pion gas such as the free energy, the quark condensate and thermal self-energy. In particular, we derive the µπ = 0 generalization of Luscher and Gell-Mann-Oakes-Renner type relations. We pay special attention to the comparison with the conventional kinetic theory approach in the dilute regime, which allows for a check of consistency of our approach. Several phenomenological applications are discussed, concerning chiral symmetry restoration, freeze-out conditions and Bose-Einstein pion condensation.