Vector-type four-quark interaction and its impact on QCD phase structure

Abstract

Effects of the vector-type four-quark interaction on QCD phase structure are investigated in the imaginary chemical potential ($\ensuremath{\mu}$) region, by using the Polyakov-loop extended Nambu--Jona-Lasinio model with the extended ${\mathbb{Z}}_{3}$ symmetry. We clarify analytically the Roberge-Weiss periodicity and symmetry properties of various quantities under the existence of a vector-type four-quark interaction. In the imaginary $\ensuremath{\mu}$ region, the chiral condensate and the quark-number density are sensitive to the strength of the interaction. Based on this result, we propose a possibility to determine the strength of the vector-type interaction, which largely affects QCD phase structure in the real $\ensuremath{\mu}$ region, by comparing the results of lattice simulations and effective model calculations in the imaginary $\ensuremath{\mu}$ region.