In-medium Chiral Perturbation Theory beyond the Mean-Field Approximation

Abstract

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 √ 6π f π 0.7 GeV for standard and 6π 2 f 2 π /2m N 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 a mass shift for negatively charged pions in heavy nuclei, M π − = (18 ± 5) MeV, that agrees with recent determinations from deeply bound pionic 207 Pb. We have also established the absence of in-medium renormalization in the π 0 → γ γ decay amplitude up to the same order. The study of ππ 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)

Search for η′ Mesic Nuclei in GSI/FAIR

“…The deduced order parameter of the chiral symmetry, chiral condensate ⟨qq⟩, at the nuclear saturation density ρ 0 presented reduction of ∼ 30% compared to that in the vacuum. The result agrees fairly well with theoretical expectations based on QCD sum rule [21] or on chiral perturbation theory [22].…”

In-medium pion and partial restoration of chiral symmetry

“…Generalization of our approach to the pion-pion interaction inside a nuclear medium following the idea of [8] is one of the interesting future problems to be examined and may provide us with a further insight into the in-medium pions and possible partial restoration of chiral symmetry in nuclei. It is also an interesting and important task to estimate contributions beyond the linear density approximation [21,22,23]. …”

The chiral quark condensate and pion decay constant in nuclear matter at next-to-leading order

“…The fact that f t = f s in nuclear matter and some consequences thereof have already been discussed in [17][18][19][20][21][55][56][57][58][59]. The calculations in [21] indicate a linear decrease of f t with density, f t = f π (1 − (0.26 ± 0.04)ρ/ρ 0 ), where f π = 92.4 MeV is the weak pion decay constant in vacuum and ρ 0 is the nuclear matter saturation density. This result indicates that it makes sense to use chiral Lagrangians in the nuclear medium up to central nuclear densities.…”

“…As we show below, the linear reduction with density of f t as obtained in ref. [21] holds up to NLO.…”