Nature of Roberge-Weiss transition end points for heavy quarks in $N_f=2$ lattice QCD with Wilson fermions

The phase structure of QCD with imaginary chemical potential provides information on the phase diagram of QCD with real chemical potential. With imaginary chemical potential $i\mu_I=i\pi T$, previous studies show that the Roberge-Weiss (RW) transition end points are triple points at both large and small quark masses, and second order transition points at intermediate quark masses. The triple and second order end points are separated by two tricritical ones. We present simulations with $ N_f=2 $ Wilson fermions to investigate the nature of RW transition end points. The simulations are carried out at 8 values of the hopping parameter $\kappa$ ranging from 0.020 to 0.140 on different lattice volumes. The Binder cumulant, susceptibility and reweighted distribution of the imaginary part of Polyakov loop are employed to determine the nature of RW transition end points. The simulations show that the two tricritical points are within the range $0.070-0.080$ and $0.120-0.140$, respectively.