Effects of eight-quark interactions on the hadronic vacuum and mass spectra of light mesons

Abstract

The combined effective low energy QCD Lagrangians of Nambu -- Jona-Lasinio (NJL) and 't Hooft are supplemented with eight-quark interactions. This work is a follow-up of recent findings, namely (i) the six quark flavour determinant 't Hooft term destabilizes the NJL vacuum, (ii) the addition of a chiral invariant eight-fermion contact term renders the ground state of the theory globally stable; (iii) stability constrains the values of coupling constants of the model, meaning that even in the presence of eight-quark forces the system can be unstable in a certain parameter region. In the present work we study a phenomenological output of eight-quark interactions considering the mass spectra of pseudoscalar and scalar mesons. Mixing angles are obtained and their equivalence to the two angle approach is derived. We show that the masses of pseudoscalars are almost neutral to the eight-quark forces. The only marked effect of the second order in the SU(3) breaking is found in the $η-η'$ system. The scalars are more sensitive to the eight-quark interactions. A strong repulsion between the singlet-octet members is the reason for the obtained low mass of the $σ$ state within the model considered.