Role of current quark mass dependent multi-quark interactions in low lying meson mass spectra

We call attention to a class of current-quark mass dependent multi-quark interaction terms which break explicitly the chiral $SU(3)_L\times SU(3)_R$ and $U_A(1)$ symmetries. They complete the set of effective quark interactions that contribute at the same order in $N_c$ as the 't Hooft flavor determinant interaction and the eight quark interactions in the phase of spontaneously broken chiral symmetry. The $N_c$ classification scheme matches the counting rules based on arguments set by the scale of spontaneous chiral symmetry breaking. Together with the leading in $N_c$ four quark Nambu-Jona-Lasinio Lagrangian and current quark mass matrix, the model is apt to account for the correct empirical ordering and magnitude of the splitting of states in the low lying mass spectra of spin zero mesons. The new terms turn out to be essential for the ordering $m_K < m_\eta$ in the pseudoscalar sector and $m_{\kappa_0} < m_{a_0}\sim m_{f0}$ for the scalars.Comment: 6 pages, 1 figure, prepared for the proceedings of the workshop "Excited QCD 2013", 03-09 February 2013 in Bjelasnica Mountain, Sarajevo, Bosni

The phase diagram in the SU(3) Nambu-Jona-Lasinio model with 't Hooft and eight-quark interactions

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.Comment: 5 pages, 3 figures, prepared for the proceedings of Hadron 2009 - XIII International Conference on Hadron Spectroscopy, November 29 - December 4, Florida State University (USA