Unstable particles in matter at a finite temperature: the rho and omega mesons
Unstable particles (such as the vector mesons) have an important role to play in low mass dilepton production resulting from heavy ion collisions and this has been a subject of several investigations. Yet subtleties, such as the implications of the generalization of the Breit-Wigner formula for nonzero temperature and density, e.g. the question of collisional broadening, the role of Bose enhancement, etc., the possibility of the kinematic opening (or closing) of decay channels due to environmental effects, the problem of double counting through resonant and direct contributions, are often given insufficient emphasis. The present study attempts to point out these features using the rho and omega mesons as illustrative examples. The difference between the two versions of the Vector Meson Dominance Model in the present context is also presented. Effects of non-zero temperature and density, through vector meson masses and decay widths, on dilepton spectra are studied, for concreteness within the framework of a Walecka-type model, though most of the basic issues highlighted apply to other scenarios as well.