Lambda-Sigma Mixing Induced by Condensed Pions in Dense Matter

Abstract

It has been expected that there appear various hadron phases in dense nuclear matter, such as pion condensation, K condensation, admixture of hyperons and so on. These phases provide us of more excitements in studying nuclear matter under low-temperature high-density extreme conditions. In many of preceding works, each of these phases has been considered separately. Towards an unified understanding of dense matter, we investigate the coexisting phase of hyperon admixture and pion condensation, which have different mechanisms in energy gain. In hyperonic matter, condensed pions would mix Λ with Σ baryons coherently through the ΛΣπ coupling. Recently, this coherent ΛΣ coupling has been applied to solve the long standing problem – consistent understanding of Λ separation energy of three-, four-, and five-body hypernuclei .1) If this coherent coupling is induced by OPEP, it would be equivalent to the pion condensation through the p-wave ΛΣπ coupling. We have included the S = 0,−1 octet and decouplet baryons into the traditional treatment of pion condensation.2) In addition to the p-wave BBπ couplings, we have included the short range repulsion in the form of the Landau-Migdal interaction with a universal parameter g′ = 0.6. The FD ratio parameter for hyperons is selected to be F/(F + D) = 0.35. The left panel of Fig. 1 shows the energy per baryon under charged pion condensation in dense neutral matter. First, we consider those cases without decouplet resonance contributions. At low densities, the energy is lower without hyperons because of the mass difference of nucleons and hyperons. However, at higher densities, hyperon mixed matter becomes more favorable due to the large nucleon Fermi energy and ΛΣπ coupling, and hyperon admixture in the pion condensed phase would emerge. Next, we include the effects of decouplet baryon resonances with S = 0,−1, ∆(1232) and Σ∗(1385). The coupling constants of BB∗π and B∗B∗π are estimated by using the SU(6) quark model. The octet-decouplet couplings in the S = 0 and −1 baryons are given as fN∆π/fNNπ = √ 72/5, fΛΣ∗π/fNNπ = √ 36/5, and fΣΣ∗π/fNNπ = √ 12/5, respectively. In spite of large mass differences of octet and decouplet baryons, the effects of resonance baryons are very large due to these large BB∗π couplings. Especially, since the coupling of N∆π is very large, it generates large energy gain. Although there is also a large energy gain in hyperon mixed matter from ΛΣ∗π coupling, it is smaller than that from N∆π coupling and hyperons cannot appear even at very high densities.