Abstract
Pion propagator is studied in the chiral σ model at the zero temperature nuclear matter. Due to the tachyon pole of the π and σ tree approximation propagators, only the nucleon polarization insertion loop (explicitly density dependent part and vacuum fluctuation part) can be fully included into the pion propagator. The vacuum fluctuation as a function of nucleon effective mass or pion external momentum (after Wick rotation) is negative for most of the cases. So the variation of nucleon effective mass is restricted to a very limited region where is free of pion condensation (otherwise the nucleon energy density will be complex). The effect of NN short-range correlation is calculated and it is very small for low momentum.
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