Investigation of the Thermal QCD Matter from Canonical Sectors

Abstract

We discuss the thermal phase structure of quantum chromodynamics (QCD) at zero real chemical potential (μR=0) from the viewpoint of canonical sectors. The canonical sectors take the system to pieces of each elementary excitation mode and thus seem to be useful in the investigation of the confinement–deconfinement nature of QCD. Since the canonical sectors themselves are difficult to compute, we propose a convenient quantity which may determine the structural changes of the canonical sectors. We discuss the quantity qualitatively by adopting lattice QCD prediction for the phase structure with finite imaginary chemical potential. In addition, we numerically estimate this quantity by using the simple QCD effective model. It is shown that there should be a sharp change of the canonical sectors near the Roberge–Weiss endpoint temperature at μR=0. Then, the behavior of the quark number density at finite imaginary chemical potential plays a crucial role in clarifying the thermal QCD properties.

Roberge-Weiss periodicity, canonical sector, and modified Polyakov loop

“…In this paper, we consider the sufficiently large but finite spatial volume. This formulation is already applied to the lattice QCD [10][11][12][13][14][15] and QCD effective models [18,[23][24][25][26]. The canonical partition function, of course, obeys a canonical ensemble.…”

Persistent Homology Analysis for Dense QCD Effective Model with Heavy Quarks

“…There are some approaches to weaken the sign problem in QCD and in some other theories/models at moderate µ R with low T. Famous examples are the complexification of dynamical variables such as the comlpex Langevin dynamics [8,9], the Lefshcetz thimble method [10,11], and the path optimization method [12,13] . In addition, we can discuss the region using the canonical approach [14][15][16][17][18][19][20][21], partially. However, those methods are not perfect yet, and therefore, it is difficult to apply those methods in the whole µ R region.…”