Chiral phase transition in an extended NJL model with higher-order   multi-quark interactions
  The chiral phase transition is studied in an extended Nambu--Jona-Lasinio model with eight-quark interactions. Equations for scalar and vector quark densities, derived in the mean field approximation, are nonlinear and mutually coupled. The scalar-type nonlinear term hastens the restoration of chiral symmetry, while the scalar-vector mixing term makes the transition sharper. The scalar-type nonlinear term shifts the critical endpoint toward the values predicted by lattice QCD simulations and the QCD-like theory. 
Kouji Kashiwa, Hiroaki Kouno, Tomohiko Sakaguchi, Masayuki Matsuzaki   and Masanobu Yahiro