The propagation of 𝜎-meson in nuclear matter is studied in the Walecka model, by assuming that the sigma couples to a pair of nucleon–antinucleon states and to particle–hole states. The in-medium effect of $\sigma -\omega$ mixing is also studied. For completeness, the coupling of sigma to two virtual pions was also considered. It is found that the 𝜎-meson mass decreases with respect to its value in vacuum and that the contribution of the $\sigma -\omega$ mixing effect on the mass shift is relatively small.
