Roberge-Weiss transitions at different center symmetry breaking patterns in a $\mathbb{Z}_{3}$-QCD model

Abstract

We study how the Roberge-Weiss (RW) transition depends on the pattern of center symmetry breaking using a $\mathbb{Z}_{3}$-QCD model. We adopt flavor-dependent quark imaginary chemical potentials, namely $(μ_{u},μ_{d},μ_{s})/iT=(θ-2π{C}/3,\,θ,\,θ+2π{C}/3)$ with $C\in[0,1]$. The RW periodicity is guaranteed and the center symmetry of $\mathbb{Z}_{3}$-QCD is explicitly broken when $C\neq{1}$ or/and quark masses are non-degenerate. For $N_{f}=3$ and $C\neq{1}$, the RW transition occurs at $θ=θ_{RW}=(2k+1)π/3\,(k\in\mathbb{Z})$, which becomes stronger with decrease of $C$. When $C={1}$, the $θ_{RW}$ turns into $2kπ/3$ for $N_{f}=2+1$, but keeps $(2k+1)π/3$ for $N_{f}=1+2$; in both cases, the RW transitions get stronger with the mass mismatch. For other $C\neq{0}$ cases, the $θ_{RW}$'s are not integral multiples of $π/3$. We find that the RW transition is more sensitive to the deviation of $C$ from one compared to the mass non-degeneracy and thus the strength of the traditional RW transition with $C=0$ is the strongest. The nature of RW endpoints and its implications to deconfinement transition are investigated.