In-Medium Chiral Perturbation Theory and Pion Weak Decay in the Presence of Background Matter
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Two-point functions related to the pion weak decay constant f_πare 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_πand the pion mass into uncorrelated time- and spacelike parts. We emphasize the different in-medium renormalizations of the correlation functions, show the inequivalence between the in-medium values of f_πdeduced 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.
14 pages, RevTex, no figures, to appear in Nucl.Phys. A
14 pages, RevTex, no figures, to appear in Nucl.Phys. A