Kaon condensation in “nuclear star” matter

Abstract

The critical density for kaon condensation in "nuclear star" matter is computed up to two-loop order in medium (corresponding to next-to-next-to-leading order in chiral perturbation theory in free space) with a heavy-baryon effective chiral Lagrangian whose parameters are determined from KN scattering and kaonic atom data. To the order considered, the kaon self-energy has highly non-linear density dependence in dense matter. We find that the four-Fermi interaction terms in the chiral Lagrangian play an important role in triggering condensation, predicting for "natural" values of the four-Fermi interactions a rather low critical density, ρ c < 4ρ 0 .

A renormalization group flow analysis of meson condensations in dense matter

“…It turns out to play a minor role (as an irrelevant term) in the RG-flow argument, lending a support to the similar finding in chiral perturbation theory of [3,4]. #5 [O] stands for the scaling dimension of the object O.…”

“…Specifically in chiral perturbation theory [3,4] K † KNN and a higher derivative term, ∼ ω 2 K † KN N . (Here K is the doublet kaon field, N the doublet nucleon field and ω is the kaon frequency that equals µ K at condensation.)…”

“…Recently Lee et al [3,4] have shown by chiral perturbation theory (χP T ) treated to in-medium two-loop order (corresponding to next-to-next-to leading order) that kaons can condense in dense nuclear-star matter at a matter density ρ < ∼ 4 ρ 0 where ρ 0 is the normal nuclear matter density. However to the order considered, many terms are involved and it is not transparent which mechanism is in action for triggering the condensation process.…”

Kaon Condensation in Neutron Stars

“…The theoretical investigations that go beyond pure phenomenology [23] have mainly followed two different strategies. One line of approach is that of the mean field models, built within the framework of chiral Lagrangians [21,24,25,26] or based on the relativistic Walecka model which are extended to incorporate strangeness in the form of hyperons or kaons [27] or by using explicitly the quark degrees of freedom~28].The other type of approach aims at obtaining the in-medium 17N interaction microscopically by incorporating the medium modifications in a~lV amplitude using (chiral) effective interactions that reproduces the low energy scattering data and generates the A(1405) resonance dynamically [29,30,31,32,33,34,35]. In this section, we focus on this latter perspective, since it allows one to systematically study the importance of all the different mechanisms that might modify the _f?iV interaction in the medium from that in free space.…”

Chiral perturbation theory

“…The static electromagnetic moments of the decuplet have also been computed in CHPT (Butler et al, 1994). The kaon-nucleon scattering lengths have recently been calculated by various groups (Lee et al, 1994a(Lee et al, , 1994b. The off-shell KN scattering amplitude is of interest for kaonic atoms and kaon condensation in dense nuclear matter (e.g., Brown et al, 1994;Lee et al, 1994c).…”