U(5) Nambu-Jona-Lasinio model with flavor dependent coupling constants: pseudoscalar and scalar mesons masses

Abstract

By considering the background field method we calculate one-loop polarization corrections to the coupling constant of the flavor-U(5) Nambu-Jona-Lasinio (NJL) model. They break flavor and chiral symmetries and they can be written as G Γ ij ( ψλiΓψ)( ψλjΓψ), for the scalar and pseudoscalar channels (Γ = I, iγ5) and i, j = 0.1, ...N 2 f − 1. Their contribution to different observables are computed: masses of quark-antiquark meson states (pseudoscalar and scalar), pseudoscalar meson weak decay constants, quark-antiquark scalar condensates. The quantum mixing effect is responsible for a lowering of quark effective masses and a slight improvement of predictions of observables, although a certain flavor dependence of the ultraviolet cutoff (Λ f ) is still needed. By considering a non-covariant three dimensional regularization scheme this cutoff flavor dependence is implemented in an unambiguous way for the computation of the one loop integrals, and their values (Λ f ) are in fact found to be very close to each other, i.e. nearly flavor-independent. The NJL-gap equations are found to overestimate the heavy quark condensates. The pseudoscalar and scalar mesons are defined in terms of the generators of the adjoint representation and the complete polarization tensors lead to surprisingly good descriptions of all the pseudoscalar and scalar meson masses -within 5% or 7% -including controversial states such as the light scalars f0(500) − f0(980) (as quarkantiquark states) and the pseudoscalar η's. However, the usual problem to describe the correct mass hierarchy of some light scalar mesons still remains. In spite of the surprisingly good description of the meson masses the pseudoscalar meson weak decay constant cannot be described by the NJL model without further interactions or effects.