Pion properties at finite nuclear density based on in-medium chiral perturbation theory

The in-medium pion properties, i.e. the temporal pion decay constant ft, the pion mass m∗π, and the wave function renormalization in symmetric nuclear matter are calculated in an in-medium chiral perturbation theory up to the next-to-leading order of the density expansion O(k4F). The chiral Lagrangian for the pion–nucleon interaction is determined in vacuum, and the low-energy constants are fixed by experimental observables. We carefully define the in-medium state of the pion and find that the pionwave function renormalization plays an essential role in the in-medium pion properties. We show that the linear density correction is dominant and the next-to-leading corrections are not so large at the saturation density, while their contributions can be significant at higher densities. The main contribution of the next-to-leading order comes from the double scat-tering term. We also discuss whether the low-energy theorems, the Gell-Mann–Oakes–Renner relation and the Glashow–Weinberg relation, are satisfied in the nuclear medium beyond the lin-ear density approximation. We also find that the wave function renormalization is enhanced as much as 50 % at the saturation density including the next-to-leading contribution, and that the wave function renormalization can be measured in the in-medium π0 → γ γ decay. Subject Index D3