Interplay between ω-nucleon interaction and nucleon mass in dense baryonic matter

The dilaton-limit fixed point and the scaling properties of hadrons in the close vicinity of the fixed point in dense baryonic matter uncovered in hidden local symmetry implemented with spontaneously broken scale symmetry are shown to reveal a surprisingly intricate interplay, hitherto unsuspected, between the origin of the bulk of proton mass and the renormalization-group flow of the omega-nuclear interactions. This rends theoretical support to the previous (phenomenologically) observed correlation between the dropping nucleon mass and the behavior of the omega-nuclear interactions in dense matter described in terms of half Skyrmions that appear at a density denoted n(1/2) in Skyrmion crystals. The role of the omega-meson degree of freedom in the source for nucleon mass observed in this paper is highly reminiscent of its important role in the Skyrmion description of nucleon mass in hidden local symmetric theory. One of the most notable novel results found in this paper is that the nucleon mass in a dense baryonic medium undergoes a drop roughly linear in density up to a density (denoted (n) over tilde) slightly above the nuclear matter density (n(0)) and then stays more or less constant up to the dilaton-limit fixed point. The possibility that we entertain is that (n) over tilde coincides with or is at least close to n(1/2). We note that this feature can be economically captured by the parity-doublet model for nucleons with the chiral-invariant mass m(0) similar to (0.7-0.8)m(N). It is found in one-loop renormalization-group analysis with the Lagrangian adopted that, while the rho-NN coupling runs'' in density, the omega-NN coupling does not scale: It will scale at two-loop or higher-loop order, but at a slower pace, so it is more appropriate to say it walks'' rather than runs. The former implies a drastic change in the nuclear tensor forces, affecting, among others, the nuclear symmetry energy and the latter generating the stiffness of the equation of state at density higher than that of normal nuclear matter.