Kaon condensation in dense stellar matter

Abstract

Kaon-nucleon scattering, kaonic atom and kaon condensation are treated on the same footing by means of the chiral perturbation theory to the next-to-next-to-leading order (“N 2LO”). Constraining the low-energy constants in the chiral Lagrangian by on-shell KN scattering lengths and kaonic atom data, the off-shell s-wave scattering amplitude up to one-loop order corresponding to N 2LO and the critical density of kaon condensation up to in-medium two-loop order are computed. The effects on kaon-proton scattering of the quasi-bound Λ(1405) and on kaonic atoms and kaon condensation of Λ(1405)-proton-hole excitations through four-Fermi interactions are studied to all orders in density within the in-medium two-loop approximation. It is found that the four-Fermi interaction terms in the chiral Lagrangian play an essential role in providing attraction for kaonic atoms thereby inducing condensation, but the critical density is insensitive to the strength of the four-Fermi interaction. The prediction for the critical density is robust against changes of the parameters in the chiral Lagrangian, and gives — for “natural” values of the four-Fermi interactions — a rather low critical density, ϱ c ≲ 4 ϱ 0, required to explain the maximum neutron star mass and the recent data of SN1987A. Once the BR (Brown-Rho) scaling sets in, the critical density, ϱ c < 3 ϱ 0, is completely insensitive to the parameters in which possible uncertainties of the theory lie.