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 theor y 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 b oth f(pi) and the pion mass into uncorrelated time- and space-like par ts. We emphasize the different in-medium renormalizations of the corre lation functions, show the inequivalence between the in-medium values of f(pi) deduced from Walecka-type models, on the one hand, and QCD su m rules, on the other hand, and elaborate on the importance for some n uclear physics observables. (C) 1997 Elsevier Science B.V.