Abstract
The nonanalyticity and the sign problem in the Z3-symmetric heavy quark model at low temperature are studied phenomenologically. For the free heavy quarks, the nonanalyticity is analyzed in the relation to the zeros of the grand canonical partition function. The Z3-symmetric effective Polyakov-line model (EPLM) in strong coupling limit is also considered as an phenomenological model of Z3-symmetric QCD with large quark mass at low temperature. We examine how the Z3-symmetric EPLM approaches to the original one in the zero-temperature limit. The effects of the Z3-symmetry affect the structure of zeros of the microscopic probability density function at the nonanalytic point. The average value of the Polyakov line can detect the structure, while the other thermodynamic quantities are not sensible to the structure in the zero-temperature limit. The effect of the imaginary quark chemical potential is also discussed. The imaginary part of the quark number density is very sensitive to the symmetry structure at the nonanalytical point. For a particular value of the imaginary quark number chemical potential, large quark number may be induced in the vicinity of the nonanalytical point.
Highlights
Study of the quantum chromodynamics (QCD) phase structure at finite temperature T and quark chemical potential μ is one of the most important subjects in particle and nuclear physics, astrophysics and cosmology
We have studied the nonanalyticity and the sign problem in the Z3-symmetric heavy quark model at low temperature and examined how the Z3-symmetrized models approach to the original ones in the zero temperature limit
For the free fermion quark model (FHQM), the nonanalyticity at μ 1⁄4 M is related to the existence of zeros of the grand canonical partition function Z at finite temperature and complex chemical potential
Summary
Study of the quantum chromodynamics (QCD) phase structure at finite temperature T and quark chemical potential μ is one of the most important subjects in particle and nuclear physics, astrophysics and cosmology. [22], it was shown that the phase diagram of the Z3-symmetric Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model coincides with the one in the original PNJL model [36,37,38,39,40] in the zero-temperature limit This limit may be nontrivial at finite μ since nonanalyticity occurs at zero temperature due to the fermion sphere formation, and this phenomena itself is related to the change of the boundary condition and the zeros of the grand canonical partition function. In Z3-symmetric theory, the expectation value of the Polyakov line (loop) vanishes due to the exact Z3 symmetry, while it can be finite in the original model It is nontrivial whether the Polyakov line coincides or not in two models in the zero-temperature limit.
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