It is shown that U(3) L × U(3) R eight-quark interactions stabilize the asymmetric ground state of the well-known model with four-quark Nambu-Jona-Lasinio and six-quark 't Hooft interactions. The result remains when the reduced SU(3) flavour symmetry is explicitly broken by the general current quark mass term withm u =m d =m s .

The necessity of adding higher order multiquark interactions to the three flavor NJL model with U A (1) breaking, in order to stabilize its vacuum, 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.

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Abstract. We suggest and discuss in detail a multi-quark three-flavor Lagrangian of the Nambu-JonaLasinio type, which includes a set of effective interactions proportional to the current quark masses. It is shown that within the dynamical chiral symmetry-breaking regime, the masses of the pseudo-Goldstone bosons and their chiral partners, members of the low-lying scalar nonet, are in perfect agreement with current phenomenological expectations. The role of the new interactions is analyzed.

It is shown that eight-quark interactions, which are needed to stabilize the ground state of the combined three flavor Nambu -- Jona-Lasinio and 't Hooft Lagrangians, play also an important role in determining the critical temperature at which transitions occur from the dynamically broken chiral phase to the symmetric phase.Comment: 4 pages, 2 figure

The momentum-space bosonization method of a Nambu and Jona-Lasinio type model with vector and axial-vector mesons is applied to ππ scattering. Unlike the case in earlier published papers, we obtain the ππ scattering amplitude using the linear and nonlinear realizations of chiral symmetry and fully taking into account the momentum dependence of meson vertices. We show the full physical equivalence between these two approaches. The chiral expansion procedure in this model is discussed in detail. Chiral expansions of the quark mass, pion mass and constant f π are obtained. The low-energy ππ phase shifts are compared to the available data. We also study the scalar form factor of the pion.

In a long distance Lagrangian approach to the low lying meson phenomenology, we present and discuss the most general spin zero multiquark interaction vertices of nonderivative type which include a set of effective interactions proportional to the current quark masses, breaking explicitly the chiral SUð3Þ L Â SUð3Þ R and U A ð1Þ symmetries. These vertices are of the same order in N c , counting as the 't Hooft flavor determinant interaction and the eight quark interactions which extend the original four quark interaction Lagrangian, leading in N c , of Nambu and Jona-Lasinio. The N c assignments match the counting rules based on arguments set by the scale of spontaneous chiral symmetry breaking. With path-integral bosonization techniques which appropriately take into account the quark mass differences, we derive the mesonic Lagrangian up to three-point mesonic vertices. We demonstrate that explicit symmetry breaking effects in interactions are essential to obtain the correct empirical ordering and magnitude of the splitting of certain states such as m K < m for the pseudoscalars and m 0 < m a 0 $ m f 0 in the scalar sector, and to achieve total agreement with the empirical low lying meson mass spectra. With all parameters of the model fixed by the spectra, we analyze further a bulk of two-body decays at the tree level of the bosonic Lagrangian: the strong decays of the scalars ! , f 0 ð980Þ ! , ð800Þ ! K, and a 0 ð980Þ ! , as well as the two photon decays of a 0 ð980Þ, f 0 ð980Þ, and mesons, and the anomalous decays of the pseudoscalars ! , ! , and 0 ! . Our results for the strong decays are within the current expectations and the pseudoscalar radiative decays are in very good agreement with data. The radiative decays of the scalars are smaller than the observed values for the f 0 ð980Þ and the , but reasonable for the a 0 . A detailed discussion accompanies all the results.