Sigma and omega meson propagation in a dense nuclear medium

The propagation of the scalar ($σ$) and vector ($ω$) 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 $σ$ width through the inclusion of a two-pion loop. We calculate the dispersion relation and spectral functions of the $σ$ and (transverse and longitudinal) $ω$ mesons, including the effect of $σ$-$ω$ mixing in matter. It is shown that the mixing effect is quite important in the propagation of the (longitudinal) $ω$ and $σ$ mesons above normal nuclear matter density. We find that there is a two-peak structure in the spectral function of the $σ$ channel, caused by $σ$-$ω$ mixing.

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