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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.'
author:
- 'B. Hiller, J. Moreira, A. A. Osipov[^1], A. H. Blin'
title: '**The phase diagram for the Nambu–Jona-Lasinio model with ’t Hooft and eight-quark interactions**'
---

Introduction
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The last two decades have witnessed great efforts towards the understanding of the QCD phase diagram, in terms of effective low energy theories paralleled by QCD lattice calculations, see e.g. the recent reviews [@Wilczek:2001]-[@Fukushima:2008], or the paper [@Weise:2006]. The domain of small to moderate baryonic chemical potential $0<\mu <400$ MeV and temperatures $0<T < 200$ MeV, 