Effective Hadron Masses and Effective Interactions in Nuclear Matter

Abstract

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.

Chiral phase transition in an extended NJL model with higher-order multi-quark interactions

“…In the relativistic meson-nucleon theory, it is known that nonlinear meson-nucleon interactions suppress the effective coupling between mesons and nucleons in the higher density region [28,29,30,31]. It is then strongly expected that a similar situation takes place in the NJL model as soon as higher-order multi-quark interactions are introduced.…”

Effective Meson Masses, Effective Meson–nucleon Couplings and Neutron Star Radii

“…Therefore, we get the relation among the effective masses, the effective couplings and the incompressibility. [10,13]…”

“…For the wellknown parameter sets, [20,22,8,24] this quantity almost vanishes at ρ B = ρ B0 and ρ 3 = 0. [10,13] Similarly, the symmetry energy a 4 is given by…”

“…If the effective ω-meson mass becomes smaller (larger) at high density, the EOS becomes stiffer (softer). However, as is in the case of the symmetric nuclear matter, [13] if we require that the ω-meson mean field is proportional to the baryon density, the effective ω-nucleon coupling automatically becomes smaller (larger) at the same time as the effective ω-meson mass becomes smaller (larger). The effect of the reduction (enhancement) of the effective ω-nucleon coupling overcomes the effect of the reduction (enhancement) of the effective ω-meson mass.…”

“…[11,12] Recently, Kouno et al showed that the effective ω-nucleon coupling automatically decreases as the effective ω-meson mass decreases, if we require that the ω-meson mean field is proportional to the baryon density. [13] In that case, the EOS becomes softer in spite of the reduction of the effective ω-meson mass.…”