An effective field theory for neutron stars with many‐body forces, strong ∑– repulsion, and K– and $\bar K^0$ condensation. Issue 8 (November 2015) - Mesquita, A.; Razeira, M.; Ruffini, R.; Rueda, J. A.; Hadjimichef, D.; Gomes, R. O.; Zen Vasconcellos, C. A.
Abstract: The role of many‐body correlations (many‐body forces) and K – ‐ $\bar K^0$ condensation in β‐equilibrated hyperonic matter is investigated in order to shed some light in the hyperonization puzzle, ie that neutron star mass of 2 M ® cannot be obtained in the presence of exotic degree of freedoms. In this investigation, we use an effective relativistic QHD‐model with parameterized couplings which represents an extended compilation of other effective models found in the literature. Our theoretical approach exhausts the whole fundamental baryon octet ( n, p, ∑ –, ∑ 0, ∑ +, Λ, Ξ –, Ξ 0 ) and simulates n‐order corrections to the minimal Yukawa couplings by considering many‐body nonlinear self‐couplings and meson‐meson interaction terms involving scalar‐isoscalar (σ, σ * ), vector‐isoscalar ( ω, φ ), vector‐isovector (ϱ ), and scalar‐isovector (δ ) sectors. Following recent experimental results, we consider in our calculations the extreme case where the ∑ – experiences such a strong repulsion that its influence in the nuclear structure of a neutron star is excluded at all. We study the effects of this exclusion on the phase transition of conventional exotic hadronic matter to hadronic matter containing a condensate of kaons and anti‐kaons. As a novelty in the treatment of kaon and anti‐kaon condensation in high density nuclear matter, we consider a Lagrangian formulation which describes, in addition to the interaction involving baryons and mesons and the contribution of kaons and anti‐kaons in free propagation, the presence of many‐body forces involving kaon, anti‐kaon and meson fields. To implement the corresponding phase transition we considered the Gibbs conditions combined with the mean‐field approximation, giving rise to a mixed phase of coexistence between baryon matter and the condensed of kaons and anti‐kaons. Our investigation show that even with kaon condensation, the nuclear equation of state satisfies both the maximum mass and the allowed ranges of mass and radius of neutron stars. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)