Several relevant thermodynamic observables obtained within the (2+1) flavor and spin zero NJL and PNJL models with inclusion of the t Hooft determinant and $8q$ interactions are compared with lattice-QCD (lQCD) results. In the case that a small ratio
$R=frac{mu_B}{T_c}sim 3$ at the critical end point (CEP) associated with the hadron gas to quark-gluon plasma transition is considered, combined with fits to the lQCD data of the trace anomaly[1], subtracted light quark condensate[1] and continuum extrapolated data of the light quark chiral condensate[2], a reasonable description for the PNJL model is obtained with a strength $g_1sim 5...6 times 10^3$ GeV$^{-8}$ of the $8q$ interactions. The dependence on the further model parameters is discussed.
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.
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 a connection between the location of the endpoint in the phase diagram and the mechanism of chiral symmetry breaking at the quark level. Constraints on the coupling strengths based on groundstate stability and physical considerations are explained.
In this talk attention is drawn to thermal properties due to the addition of eight quark interactions in the standard $SU(3)times SU(3)$ chiral Nambu-Jona-Lasinio model (NJL) with t Hooft interaction (NJLH). The schematic SU(3) flavor limit with mass
less current quarks as well as the realistic case $m_u=m_d e m_s$ are discussed.
A NJL Lagrangian extended to six and eight quark interactions is applied to study temperature effects (SU(3) flavor limit, massless case), and (realistic massive case). The transition temperature can be considerably reduced as compared to the standar
d approach, in accordance with recent lattice calculations. The mesonic spectra 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, undergoes a rapid crossover to the unbroken phase, with a slope and at a temperature which is regulated by the strength of the OZI violating eight-quark interactions. This strength can be adjusted in consonance with the four-quark coupling and leaves the spectra unchanged, except for the sigma meson mass, which decreases. A first order transition behavior is also a possible solution within the present approach.
The thermodynamic potential and thermal dependence of low lying mass spectra of scalars and pseudoscalars are evaluated in a generalized Nambu -- Jona-Lasinio model, which incorporates eight-quark interactions. These are necessary to stabilize the sc
alar effective potential for the light and strange quark flavors, which would be otherwise unbounded from below. In addition it turns out that they are also crucial to i) lower the temperature of the chiral transition, in conformity with lattice calculations, ii) sharpen the temperature interval in which the crossover occurs, iii) or even allow for first order transitions to occur with realistic quark mass values, from certain critical values of the parameters. These are unprecedented results which cannot be obtained within the NJL approaches restricted to quartic and six-quark interactions.
This work is a follow-up of our recent observation that in the SU(3) flavor limit with vanishing current quark masses the temperature for the chiral transition is substantially reduced by adding eight-quark interactions to the Nambu - Jona-Lasinio La
grangian with U_A(1) breaking. Here we generalize the case to realistic light and strange quark masses and confirm our prior result. Additionally, we demonstrate that depending on the strength of OZI violating eight-quark interactions, the system undergoes either a rapid crossover or a first order phase transition. The meson mass spectra of the low lying pseudoscalars and scalars at T=0 are not sensitive to the difference in the parameter settings that correspond to these two alternatives, except for the singlet-octet mixing scalar channels, mainly the sigma meson.
