Scale-chiral symmetry, $\omega$ meson and dense baryonic matter

TL;DR

This paper explores the role of explicit scale symmetry breaking in dense baryonic matter using hidden local symmetry theory, highlighting the importance of the gluon field's anomalous dimension for consistency with fixed points.

Contribution

It demonstrates that explicit scale symmetry breaking is crucial for modeling dense skyrmion matter and establishes the necessary range for the gluon field's anomalous dimension for theoretical consistency.

Findings

Explicit scale symmetry breaking is essential in dense skyrmion matter.

The anomalous dimension of the gluon field must be between 0 and 3.

Consistency with fixed points constrains the quantum trace anomaly.

Abstract

It is shown that explicitly broken scale symmetry is essential for dense skyrmion matter in hidden local symmetry theory. Consistency with the vector manifestation fixed point for the hidden local symmetry of the lowest-lying vector mesons and the dilaton limit fixed point for scale symmetry in dense matter is found to require that the anomalous dimension ($\gamma_{G^2}$) of the gluon field strength tensor squared ($G^2$) that represents the quantum trace anomaly should be $0 <\gamma_{G^2} <3$.