Dense Baryonic Matter in Hidden Local Symmetry Approach: Half-Skyrmions and Nucleon Mass

TL;DR

This paper models dense baryonic matter using a skyrmion approach with hidden local symmetry, revealing a phase transition to half-skyrmions that affects the nucleon mass and the equation of state, with implications for nuclear physics experiments.

Contribution

It introduces a unified skyrmion model with hidden local symmetry to study dense matter, identifying a phase transition to half-skyrmions and its effects on hadron properties and nucleon mass.

Findings

Identification of the half-skyrmion phase at density n_1/2.

The pion decay constant f_pi remains nearly constant in the half-skyrmion phase.

Baryon mass stays non-scaling in the half-skyrmion phase, suggesting a non-vanishing chirally invariant 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 rho and 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 - apart from f_pi and m_rho - are fixed by the master formula derived from the relation between 5-D hQCD and 4-D HLS. This 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 EoS of dense matter. We find that the U(1) field that figures in the CS term in the hQCD action or equivalently the omega field in the hWZ term in the dimensionally reduced HLS action plays a crucial role in the half-skyrmion phase. The importance of the omega degree of freedom may be connected to what happens in the instanton structure of elementary baryon noticed in hQCD. The most striking and intriguing in what is found in the model is that f_pi 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 non-scaling 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 EFT with the parameters of the Lagrangian scaling modified at the skyrmion-half-skyrmion phase transition. It also matches with one-loop RG analysis based on HLS. A link between a non-vanishing 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 RIB machines under construction.