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 $(\mu_{ u},\mu_{ d},\mu_{ s})/iT=(\theta-2\pi{ C}/3,\,\theta,\,\theta+2\pi{ C}/3)$ 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 $\theta=\theta_{ RW}=(2k+1)\pi/3\,(k\in\mathbb{ Z})$, which becomes stronger with decrease of $C$. When $C={ 1}$, the $\theta_{ RW}$ turns into $2k\pi/3$ for $N_{ f}=2+1$, but keeps $(2k+1)\pi/3$ for $N_{ f}=1+2$; in both cases, the RW transitions get stronger with the mass mismatch. For other $C\neq{ 0}$ cases, the $\theta_{ RW}$'s are not integral multiples of $\pi/3$. 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.
Categories: hep-ph