Theta vacuum and entanglement interaction in the three-flavor   Polyakov-loop extended Nambu-Jona-Lasinio model
  We investigate theta-vacuum effects on the QCD phase diagram for the realistic 2+1 flavor system, using the three-flavor Polyakov-extended Nambu-Jona-Lasinio (PNJL) model and the entanglement PNJL model as an extension of the PNJL model. The theta-vacuum effects make the chiral transition sharper. For large theta-vacuum angle the chiral transition becomes first order even if the quark number chemical potential is zero, when the entanglement coupling between the chiral condensate and the Polyakov loop is taken into account. We finally propose a way of circumventing the sign problem on lattice QCD with finite theta. 
Takahiro Sasaki, Junichi Takahashi, Yuji Sakai, Hiroaki Kouno,   Masanobu Yahiro
hep-ph hep-lat nucl-th