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

TL;DR

This paper investigates how eight-quark interactions influence the phase diagram of the Nambu--Jona-Lasinio model, especially the location of the critical endpoint and chiral symmetry breaking, using Pauli-Villars regularization.

Contribution

It demonstrates the impact of eight-quark interactions on the phase diagram and clarifies their role in chiral symmetry breaking within the NJL model.

Findings

The endpoint moves towards zero chemical potential with stronger eight-quark interactions.

Eight-quark interactions alter the effective quark degrees of freedom.

Correct asymptotic behavior at high temperatures is achieved using Pauli-Villars regularization.

Abstract

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.