ar X iv : h ep - p h / 01 07 14 6 v 1 1 3 Ju l 2 00 1 1 Hadronic and Quark - Gluon Excitations of Dense and Hot Matter ∗

We summarize recent developments in our understanding of low-mass quark-antiquark excitations in hadronic matter under various different conditions. This includes the ther-modynamics of the chiral condensate, pions as Goldstone bosons in normal nuclear matter, and excursions into extreme territory of the QCD phase diagram: lepton pair production from a fireball expanding through the transition boundary between the quark-gluon and hadron phases of QCD. Exploring the QCD phase diagram is undoubtedly one of the great challenges in the physics of strong interactions. At temperatures exceeding T C ≃ Λ QCD ∼ 0.2 GeV, one expects a plasma of quarks and gluons released from their confining forces. At T < T C and at moderate baryon densities, the relevant QCD degrees of freedom are color-singlet hadrons. Chiral symmetry is spontaneously broken. The vacuum is a condensate of scalar quark-antiquark pairs. Pions act as Goldstone bosons. Their decay constant, f π = 92.4 MeV, determines the chiral scale 4πf π ∼ 1 GeV which governs the low mass hadron spectrum. The lightest vector mesons (ρ, ω) can be seen as the lowest q ¯ q " dipole " excitations of the QCD vacuum. Current algebra combined with QCD sum rules [1] connects their masses directly with the chiral scale, √ 2m V = 4πf π , to leading order (and in the large N c limit). Evidently, investigating the changes of the spectral distributions of pseudoscalar and vector (as well as axial vector) excitations of the QCD vacuum with changing temperatures and baryon densities, from moderate to extreme, is a key to understanding QCD thermodynamics, its phases and symmetry breaking patterns. 2. Chiral thermodynamics: selected topics A central point in the discussion of the QCD phase diagram is the transition from the Nambu-Goldstone realization of chiral symmetry (with non-zero condensate ¯ qq) to the " restored " Wigner-Weyl realization in which the chiral condensate vanishes. Lattice QCD indicates that chiral restoration is probably linked to the transition between composite hadrons and deconfined quarks and gluons.