In-medium chiral perturbation theory beyond the mean-field approximation

An explicit expression for the generating functional of two-flavor low-energy QCD with external sources in the presence of nonvanishing nucleon densities was derived recently (J. A. Oller, Phys. Rev. C 65 (2002) 025204). Within this approach we derive power counting rules for the calculation of in-medium pion properties. We develop the so-called standard rules for residual nucleon energies of the order of the pion mass and a modified scheme (nonstandard counting) for vanishing residual nucleon energies. We also establish the different scales for the range of applicability of this perturbative expansion, which are root6pif(pi) similar or equal to 0.7 GeV for standard and 6pi(2)f(pi)(2)/2m(N) similar or equal to 0.27 GeV for nonstandard counting, respectively. We have performed a systematic analysis of n-point in-medium Green functions up to and including next-to-leading order when the standard rules apply. These include the in-medium contributions to quark condensates, pion propagators, pion masses, and couplings of the axial-vector, vector, and pseudoscalar currents to pions. In particular, we find amass shift for negatively charged pions in heavy nuclei, DeltaM(pi)- =(18 +/- 5) MeV, that agrees with recent determinations from deeply bound pionic Pb-207. We have also established the absence of in-medium renormalization in the pi(0) --> gammagamma decay amplitude up to the same order, The study of pipi scattering requires the use of the nonstandard counting and the calculation is done at leading order. Even at that order we establish new contributions not considered so far. We also point toward further possible improvements of this scheme and touch upon its relation to more conventional many-body approaches. (C) 2002 Elsevier Science (USA).