Relations among effective hadron masses, effective interactions and equations of state are studied using a generalized mean-field theory that includes the implicit and explicit density dependence of the effective masses and couplings. We find that we can make the effective ω-meson mass smaller and the equation of state softer simultaneously if the ω-meson mean field is proportional to the baryon density. In this case, there is a simple and exact relation between the effective ω-meson mass and the effective ω-nucleon coupling. According to this relation, the effective ω-nucleon coupling automatically decreases if the effective ωmeson mass decreases. Consequently, the equation of state becomes softer. An attempt to incorporate the QCD sum-rule results into the hadron field theory is also made.

Using the generalized mean field theory, we have studied the relation among the effective meson masses, the effective meson-nucleon couplings and the equation of state (EOS) in asymmetric nuclear matter. If the effective ωmeson mass becomes smaller at high density, the EOS becomes stiffer. However, if we require that the ω-meson mean field is proportional to the baryon density, the effective ω-nucleon coupling automatically becomes smaller at the same time as the effective ω-meson mass becomes smaller. Consequently, the EOS becomes softer. A similar relation is found for the effective ρ-meson mass and the effective ρ-nucleon coupling. We have also studied the relation among the effective meson masses, the effective meson-nucleon couplings and a radius R of a neutron star. The R depends somewhat on the value of the effective ω-meson mass and the effective ω-nucleon coupling. The ambiguity of R is a few hundred meters if |m * ω0 2 − m 2 ω | ∼ 0.1m 2 ω at the normal density.