A Novel State for Kaon Condensation

Abstract

An SU(2)-invariant hadronic sector of the Kaplan-Nelson model is analyzed to find an energetically improved variational ground state of neutral nucleonic matter which consists of nucleons and kaons. Our state yields a vanishing expectation value of the K- field and a finite three-body correlation (ntpK-). The variational problem of finding the ground state is solved almost analytically. It is shown that the solution consisting of equal numbers of neutrons, protons and K- together with KO(or KG) in excess suppresses the kinetic term of the kaon and results in a remarkable improvement of the variational energy. 953 1. Kaon condensation in the Kaplan-Nelson (KN) modeP) is due mainly to the sig­ nificance of the sigma term EKN in reducing the effective kaon mass in medium. The term EKN is dominated by a3 in the KN-model and provides a large attractive force between the kaon and nucleon in the s-wave state. Variational calculations which utilize the time-dependent classical K--field have been performed.l)~l1) They show that kaons start to condense at a few times the normal nuclear matter density for EKN = 2 ' 3m7r • For the ground state I~) of a given Hamiltonian H, however, we have i(O) = (~I[B, HJI~) = 0 where B is any field operator. In fact, in a simple model which consists of terms quadratic in mesonic and baryonic fields,12) the author explicitly constructed a state with (K-) = 0 that has a lower energy than the coherent state with (k-) =1: o. In this paper, we construct a variational state which is an eigenstate of the electric charge and gives a vanishing expectation value of K- and a nonvanishing three-body correlation (ntpK-). We then apply these to the KN-model and evaluate the energy of dense nuclear matter. 2. The effective lagrangian of the KN-model is expressed in terms of the usual meson and baryon fields U and B as