Researching Roberge-Weiss Phase Transition Using Effective Model

Recently,the QCD-like theory with center symmetry,namely Z(NC)—QCD,was proposed.In this theory,the flavor number of quark is same with the color one and the flavor-dependent chemical potentials form an arithmetic progression with a tolerance of i2πC/NC.The Roberge-Weiss(RW)transition may happen in this theory once the center symmetry is explicitly broken.Studying the RWtransitions in this QCD-like theory,especially its dependence on the center symmetry breaking patterns,is helpful to understand the mechanism of quark deconfinement.The Polyakov-loop extended QCD models(PNJL and PQM)with different numbers of flavor and colorare used as the low energy effective theories of Z(2)-QCD,QCD and Z(3)-QCD,respectively,to study the RW and deconfinement transitions under different center symmetry patterns.In two-flavor and color cases,itisfoundthatmore seriousthe center symmetry breaking due to the chemical potentialdifference or mass nondegeneracy,more strong the RW phase transition.The RW transition pointdepends obviously on the center symmetry breaking pattern.For the PQM model with 2+1 flavors,the RW transitions appear atθ=π/3(mod 2π/3).In this case,it is found that the improved Polyakov-loop potential with quark backreaction makes the RW endpoint changes from the critical endpoint to the triple point where three first-order transition lines meet,and the temperature of both chiral and deconfinement transition decrease.When the center symmetry of Z(3)-QCDis explicitly spoken due to the mass difference with two mass-degenerate light flavors,the RW transition happens at θ＝2π/3(mod 2π/3),but θ=π/3(mod 2π/3)when two heavy flavors are mass-degenerate.The RW endpoints are found to be triple points in both cases.The RW transition causedsolely by the chemical potential difference is significantly stronger than that causedby the mass mismatch.The study suggests that how the RW and deconfinement transitions depend on the center symmetry breaking pattern in three-flavor PQM is qualitatively consistent with that obtained in PNJL,whichmaybe are model-independent.However,the nature of the RW endpointdepends on the model details,which should be further checked in lattice QCD simulations.