The phase diagram for the Nambu--Jona-Lasinio model with 't Hooft and eight-quark interactions

Understand

It is shown that the endpoint 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 towards vanishing chemical potential and higher temperatures with increasing strength of the OZI-violating eight-quark interactions.

• We clarify the connection between the location of the endpoint 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.