Chiral effective model of cold and dense two-color QCD: The linear sigma model approach

TL;DR

This paper reviews the application of a linear sigma model to describe the low-energy hadron spectrum and properties of cold, dense two-color QCD, successfully matching lattice simulation results and exploring various physical quantities.

Contribution

The paper introduces a linear sigma model based on Pauli-Gürsey symmetry that accurately reproduces lattice results for hadron masses and other properties in two-color QCD at finite density.

Findings

The LSM reproduces the low-lying hadron mass spectrum across a range of chemical potentials.

Topological susceptibility and sound velocity are consistent with lattice data.

The extended LSM includes spin-1 hadrons for broader physical descriptions.

Abstract

This review is devoted to summarizing recent developments of the linear sigma model (LSM) in cold and dense two-color QCD (QC$_2$D), in which lattice simulations are straightforwardly applicable thanks to the disappearance of the sign problem. In QC$_2$D, both theoretical and numerical studies derive the presence of the so-called baryon superfluid phase at sufficiently large chemical potential ($\mu_q$), where diquark condensates govern the ground state. The hadron mass spectrum simulated in this phase shows that the mass of an iso-singlet ($I=0$) and $0^-$ state is remarkably reduced, but such a mode cannot be described by the chiral perturbation theory. Motivated by this fact, I invent the LSM constructed upon the linear representation of chiral symmetry, or more precisely the Pauli-G\"ursey symmetry. Then, it is shown that my LSM successfully reproduces the low-lying hadron mass spectrum in a broad range of $\mu_q$ simulated on the lattice. As applications of the LSM, topological susceptibility and sound velocity in cold and dense QC$_2$D are evaluated to compare with lattice results. Besides, generalized Gell-Mann-Oakes-Renner relation and hardon mass spectrum in the presence of a diquark source are analyzed. I also introduce an extended version of the LSM incorporating spin-$1$ hadrons.