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

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-Gürsey 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.

Invited contribution to a Special Issue of Symmetry (review): "Chiral Symmetry, and Restoration in Nuclear Dense Matter". 63 pages, 15 figures

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Cited by in corpus (5)

• Chiral symmetry restoration in QC_2D from effective model using the functional renormalization group
• Speed of sound peak in two-color dense QCD: confronting effective models with lattice data
• Enhancement of axial anomaly effects in hot two-color QCD: FRG approach in the linear sigma model
• Roles of $U(1)$ axial anomaly effects in cold and dense two-color QCD with $2+2$ flavors
• Thermal quarks and Polyakov loops in two-color dense QCD