Lattice study of thermodynamic properties of dense QC$_2$D

TL;DR

This lattice study investigates the thermodynamic behavior of dense two-color QCD, revealing the transition from chiral perturbation theory applicability to a BCS-like phase with diquark pairing at high densities.

Contribution

The paper provides the first detailed lattice simulation analysis of dense $SU(2)$ QCD, including baryon density, condensates, and gluon fields, across a wide range of chemical potentials.

Findings

ChPT describes the system well up to 540 MeV.

Formation of a Fermi sphere occurs above 900 MeV.

Chromoelectric field and topological susceptibility decrease with density.

Abstract

In this paper we study thermodynamic properties of dense cold $SU(2)$ QCD within lattice simulation with dynamical rooted staggered quarks which in the continuum limit correspond to $N_f=2$ quark flavours. We calculate baryon density, renormalized chiral and diquark condensates for various baryon chemical potentials in the region $\mu \in (0,\,2000)$ MeV. It is found, that in the region $\mu \in (0,\,540)$ MeV the system is well described by the ChPT predictions. In the region $\mu > 540$ MeV the system becomes sufficiently dense and ChPT is no longer applicable to describe lattice data. For chemical potentials $\mu > 900$ MeV we observe formation of the Fermi sphere, and the system is similar to the one described by the Bardeen-Cooper-Schrieffer theory where the the diquarks play a role of Cooper pairs. In order to study how nonzero baryon density influences the gluon background we calculate chromoelectric and chromomagnetic fields, as well as the topological susceptibility. We find that the chromoelectric field and the topological susceptibility decrease, whereas the chromomagnetic field increases with rising of baryon chemical potential. Finally we study the equation of state of dense two-color quark matter.