Sigma and omega meson propagation in a dense nuclear medium

The propagation of the scalar ($\sigma$) and vector ($\omega$) mesons in nuclear matter is studied in detail using the Walecka model over a wide range of densities and including the effects of a finite $\sigma$ width through the inclusion of a two-pion loop. We calculate the dispersion relation and spectral functions of the $\sigma$ and (transverse and longitudinal) $\omega$ mesons, including the effect of $\sigma$-$\omega$ mixing in matter. It is shown that the mixing effect is quite important in the propagation of the (longitudinal) $\omega$ and $\sigma$ mesons above normal nuclear matter density. We find that there is a two-peak structure in the spectral function of the $\sigma$ channel, caused by $\sigma$-$\omega$ mixing.