Dense baryonic matter in conformally-compensated hidden local symmetry: Vector manifestation and chiral symmetry restoration

TL;DR

This paper explores how the behavior of the omega meson influences chiral symmetry restoration in dense baryonic matter within a conformally-compensated hidden local symmetry framework, revealing the omega's crucial role in baryon structure and mass.

Contribution

It demonstrates that breaking the flavor U(2) symmetry via omega meson behavior can restore chiral symmetry restoration predictions in dense matter, highlighting the omega's essential role.

Findings

Chiral symmetry restoration is suppressed unless omega meson behavior deviates from rho meson.

In half-skyrmion phase, nucleon mass remains largely unchanged, indicating a significant chiral-invariant component.

The omega meson plays a crucial role in the structure of baryons and multibaryon systems.

Abstract

We find that, when the dilaton is implemented as a (pseudo-)Nambu-Goldstone boson using a conformal compensator or "conformon" in a hidden gauge symmetric Lagrangian written to $O(p^4)$ from which baryons arise as solitons, namely, skyrmions, the vector manifestation and chiral symmetry restoration at high density predicted in hidden local symmetry theory --- which is consistent with Brown-Rho scaling --- are lost or sent to infinite density. It is shown that they can be restored if in medium the behavior of the $\omega$ field is taken to deviate from that of the $\rho$ meson in such a way that the flavor $U(2)$ symmetry is strongly broken at increasing density. The hitherto unexposed crucial role of the $\omega$ meson in the structure of elementary baryon and multibaryon systems is uncovered in this work. In the state of half-skyrmions to which the skyrmions transform at a density $n_{1/2}^{} \gtrsim n_0^{}$ (where $n_0^{}$ is the normal nuclear matter density), characterized by the vanishing (space averaged) quark condensate but nonzero pion decay constant, the nucleon mass remains more or less constant at a value $\gtrsim$ 60 \% of the vacuum value indicating a large component of the nucleon mass that is not associated with the spontaneous breaking of chiral symmetry. We discuss its connection to the chiral-invariant mass $m_0^{}$ that figures in the parity-doublet baryon model.