Phase diagram for the Nambu–Jona-Lasinio model with ’t Hooft and eight-quark interactions

Abstract

It is shown that the end point of the first-order transition line, which merges into a crossover regime in the phase diagram of the Nambu--Jona-Lasinio model, extended to include the six-quark 't Hooft and eight-quark interaction Lagrangians, is pushed toward vanishing chemical potential and higher temperatures with increasing strength of the Okubo-Zweig-Iizuka--violating eight-quark interactions. We clarify the connection between the location of the end point in the phase diagram and the mechanism of chiral symmetry breaking at the quark level. We show how the $8q$ interactions affect the number of effective quark degrees of freedom. We are able to obtain the correct asymptotics for this number at large temperatures by using the Pauli-Villars regularization.