Dense baryonic matter in the hidden local symmetry approach: Half-skyrmions and nucleon mass

Abstract

Hadron properties in dense medium are treated in a unified way in a skyrmion model constructed with an effective Lagrangian, in which the $\ensuremath{\rho}$ and $\ensuremath{\omega}$ vector mesons are introduced as hidden gauge bosons, valid up to $O({p}^{4})$ terms in chiral expansion including the homogeneous Wess-Zumino terms. All the low energy constants of the Lagrangian---apart from the pion decay constant and the vector meson mass---are fixed by the master formula derived from the relation between the five-dimensional holographic QCD and the four-dimensional hidden local symmetry Lagrangian. This Lagrangian allows one to pin down the density ${n}_{1/2}$ at which the skyrmions in medium fractionize into half-skyrmions, bringing in a drastic change in the equation of state of dense baryonic matter. We find that the $U(1)$ field that figures in the Chern-Simons term in the five-dimensional holographic QCD action or equivalently the $\ensuremath{\omega}$ field in the homogeneous Wess-Zumino term in the dimensionally reduced hidden local symmetry action plays a crucial role in the half-skyrmion phase. The importance of the $\ensuremath{\omega}$ degree of freedom may be connected to what happens in the instanton structure of elementary baryon noticed in holographic QCD. The most striking and intriguing in what is found in the model is that the pion decay constant that smoothly drops with increasing density in the skyrmion phase stops decreasing at ${n}_{1/2}$ and remains nearly constant in the half-skyrmion phase. In accordance with the large ${N}_{c}$ consideration, the baryon mass also stays nonscaling in the half-skyrmion phase. This feature which is reminiscent of the parity-doublet baryon model with a chirally invariant mass ${m}_{0}$ is supported by the nuclear effective field theory with the parameters of the Lagrangian scaling modified at the skyrmion--half-skyrmion phase transition. It also matches with one-loop renormalization group analysis based on hidden local symmetry. A link between a nonvanishing ${m}_{0}$ and the origin of nucleon mass distinctive from dynamically generated mass is suggested. We briefly discuss the possible consequences of the topology change found in this paper on the forthcoming experiments at the rare isotope beam machines under construction.