  Using a nonlocal version of the Polyakov-loop-extended Nambu--Jona-Lasinio
model, we investi- gate effects of a nonderivative vector-current interaction
(relating to the quark-number density) at both real and imaginary chemical
potentials. This repulsive vector interaction between quarks has the following
impact on the chiral first-order phase transition: at imaginary chemical
potential it sharpens the transition at the Roberge-Weiss (RW) end point and
moves this critical point toward lower temperatures; at real chemical
potential, the critical end point moves on a trajectory towards larger chemical
potentials and lower temperatures with increasing vector coupling strength. The
conditions are discussed at which the first-order phase transition disappears
and turns into a smooth crossover.
