Temperature effects in the Nambu--Jona-Lasinio model with six and eight quark interaction

Abstract

The extension of the Nambu–Jona-Lasinio Model (NJL) [1] with ’t Hoof determinant [2, 3, 4] to include eight quark interactions [5] has been proposed as a solution for the vacuum stability problems which have been shown to afflict this model [6]. While the mesonic spectra, which can now be built on the spontaneously broken vacuum induced by the ‘t Hooft interaction strength, as opposed to the commonly considered case driven by the four-quark coupling, remains relatively unchanged (except for the sigma meson mass, which decreases), the study of temperature effects [7, 8] (SU f (3) massless case and realistic massive cases) has shown interesting new features: chiral symmetry restoration can occur through a rapid crossover to the unbroken phase with a slope and critical temperature (Tc) which are regulated by the OZI violating part of the added eight quark interactions. As a consequence, Tc can be considerably reduced as compared to the standard approach, in accordance with recent lattice calculations [9]. A first order transition behavior is also a possible solution within this approach.