The effects of explicit chiral symmetry breaking multiquark interactions on the spin 0 and 1 meson nonets: the ruling of the vector mesons

We have recently extended the scalar-pseudoscalar sector of a generalized NJL Lagrangian that includes all NLO non derivative interactions in Nc counting (including explicit symmetry breaking ones) in order to incorporate the spin 1 mesons in the low-lying ground state of QCD [1]. Upon bosonization, the well known mixing of the scalar-vector and of the pseudoscalar- axial-vector fields occurs in the quadratic part of the Lagrangian. We show that a linearized diagonalization of these terms can be effected in a completely general way without compromising the underlying symmetries of the Lagrangian [2]. The resulting spin 1 mass spectra evidence a relation involving only the vector and axial-vector meson masses and the constituent quark masses. We discuss the dominant role of this relation in the fits and we show that the model may be fitted to accommodate to a very good accuracy the 4 low-lying meson spectra.Comment: 5 pages, 3 tables; based on a talk given at Hadron 2017, Salamanc

A general framework to diagonalize vector--scalar and axial-vector--pseudoscalar transitions in the effective meson Lagrangian

A new mathematical framework for the diagonalization of the nondiagonal vector--scalar and axial-vector--pseudoscalar mixing in the effective meson Lagrangian is described. This procedure has unexpected connections with the Hadamard product of $n\times n$ matrices describing the couplings, masses, and fields involved. The approach is shown to be much more efficient as compared with the standard methods employed previously. The difference is especially noticeable if the chiral symmetry is broken explicitly. The paper ends with an illustrative application to the chiral model with broken $SU(3)_L\times SU(3)_R$ symmetry.Comment: 16 page

Multi-quark interactions with a globally stable vacuum

It is shown that $U(3)_L\times U(3)_R$ 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) f\mbox{}lavour symmetry is explicitly broken by the general current quark mass term with $\hat{m}_u\neq\hat{m}_d\neq\hat{m}_s$.Comment: LaTeX, 17 pages, 2 figures, version to appear in Phys. Lett.