In-medium chiral perturbation theory and pion weak decay in the presence of background matter

Two-point functions related to the pion weak decay constant f(pi) are calculated from the generating functional of chiral perturbation theory in the mean field approximation and the heavy-baryon limit. The aim is to demonstrate that Lorentz invariance is violated in the presence of background matter. This fact manifests itself in the splitting of both f(pi) and the pion mass into uncorrelated time- and space-like parts. We emphasize the different in-medium renormalizations of the correlation functions, show the inequivalence between the in-medium values of f(pi) deduced from Walecka-type models, on the one hand, and QCD sum rules, on the other hand, and elaborate on the importance for some nuclear physics observables. (C) 1997 Elsevier Science B.V.