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.
Highlights
Exploring the phase structure of quantum chromodynamics (QCD) at a finite temperature (T) and real chemical potential is an important subject in elementary particle, hadron and nuclear physics and in astrophysics
Those quantities are not preferable to see the information of pure canonical sectors; the pressure is, a good quantity, but the pressure is difficult to calculate precisely compared with the quark number density in the lattice QCD simulation
We have investigated the QCD phase structure at a finite temperature (T) and zero real chemical potential by using the canonical ensemble
Summary
Exploring the phase structure of quantum chromodynamics (QCD) at a finite temperature (T) and real chemical potential (μR) is an important subject in elementary particle, hadron and nuclear physics and in astrophysics. The ground-state degeneracy cannot be directly implemented to the thermal system, but it enhances our expectation that the QCD confinement–deconfinement nature is related to the topological phase transition even with a realistic quark mass. In [12], the authors showed that the investigation of canonical sectors represented by the Fourier decomposition is a useful and powerful tool to understand the QCD phase structure at a finite μR with a sufficiently small T. This result enhances our expectation that the canonical ensemble can provide us with important information about the confinement– deconfinement nature of QCD even with a finite T.
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