Chiral Symmetry and light resonances in hot and dense matter
We present a study of the $\pi\pi$ scattering amplitude in the $\sigma$ and $\rho$ channels at finite temperature and nuclear density within a chiral unitary framework. Meson resonances are dynamically generated in our approach, which allows us to analyze the behavior of their associated scattering poles when the system is driven towards chiral symmetry restoration. Medium effects are incorporated in three ways: (a) by thermal corrections of the unitarized scattering amplitudes, (b) by finite nuclear density effects associated to a renormalization of the pion decay constant, and complementarily (c) by extending our calculation of the scalar-isoscalar channel to account for finite nuclear density and temperature effects in a microscopic many-body implementation of pion dynamics. Our results are discussed in connection with several phenomenological aspects relevant for nuclear matter and Heavy-Ion Collision experiments, such as $\rho$ mass scaling vs broadening from dilepton spectra and chiral restoration signals in the $\sigma$ channel. We also elaborate on the molecular nature of $\pi\pi$ resonances.