Interplay between \omega-Nucleon Interaction and Nucleon Mass in Dense Baryonic Matter

TL;DR

This paper explores the complex relationship between the -nucleon interaction and nucleon mass in dense baryonic matter, revealing how the -meson influences nucleon mass behavior near the dilaton limit fixed point.

Contribution

It uncovers the interplay between -nuclear interactions and nucleon mass scaling in dense matter using hidden local symmetry and renormalization-group analysis, highlighting the -meson's role.

Findings

Nucleon mass drops roughly linearly with density up to .8 m_N.

-NN coupling remains nearly constant at one-loop level.

-NN coupling may scale at higher-loop orders.

Abstract

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 a 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 dense baryonic medium undergoes a drop roughly linear in density up to a density (denoted $\tilde{n}$) slightly above 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 $\tilde{n}$ coincides with or 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 $m_0\sim (0.7-0.8) m_N$. 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.