Moat regimes within a $2+1$ flavor Polyakov-quark-meson model

To better understand recent predictions on the moat regime of quantum chromodynamics (QCD) matter, this paper extends the previous work within the two-flavor quark-meson (QM) model to the more realistic $2+1$ flavor Polyakov-quark-meson (PQM) model. Mainly, two effects are further taken into account: strange quark and confinement coded through Polyakov loop. Model parameters are chosen to consistently reproduce the pseudocritical temperature from lattice QCD, $T_{\rm C}\sim 156~ {\rm MeV}$, and the baryon chemical potential at the critical end point (CEP) from FRG-QCD, $\mu_{\rm B(CEP)}\sim 635~ {\rm MeV}$. It is found that the basic features of moat regimes for $\sigma$ and $\pi$ mesons remain similar to those from QM model: Moat regimes cover the region where temperature or baryon chemical potential is large; reentrances occur around the critical baryon chemical potential of chiral transition at zero temperature. Thus, the FRG-QCD results can still not be well understood, especially why the CEP should locate at the entrances of moat regimes for $\sigma$ and $\pi$ mesons. Nevertheless, some basic features can be understood qualitatively, and it is consistent that the pole energies are increasing functions of momenta in the whole $T-\mu_{\rm B}$ plane. The moat regime and pole energy of $K$ mesons are also studied with the features similar.