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 with degenerate up and down quarks. They break flavor and chiral symmetries and they can be written as $G_{ij}^\Gamma (\bar{\psi} \lambda_i \Gamma \psi) ( \bar{\psi} \lambda_j \Gamma \psi)$, for the scalar and pseudoscalar channels ($\Gamma=I , i \gamma_5$) and $i,j = 0.1,... N_f^2-1$. Their contributions to different observables are computed: quark-antiquark scalar condensates, masses of quark-antiquark meson states (pseudoscalar and scalar) and pseudoscalar meson weak decay constants. The non-covariant three dimensional regularization scheme is employed according to which a three-dimensional momentum cutoff has an unique interpretation for light and heavy quarks. Besides that, flavor dependence of cutoffs is implemented in an unambiguous way.Their values ($\Lambda_f$, f=u,s,c,b) , however, are found to be very close to each other, i.e. the best results are obtained for nearly flavor-independent cutoffs. The NJL-gap equations are found to overestimate the heavy quark condensates at the usual mean field level usually adopted for model. The polarization tensor is calculated entirely in the adjoint representation what may lead to mixing terms. A quite surprisingly good description of all the pseudoscalar -- including the pseudoscalar $\eta$'s -- and most of the scalar meson masses -- is obtained within 5$\%$ to 10$\%$. However, the usual problems to describe the correct mass hierarchy of some light scalar mesons still remains. In spite of the good description of the meson masses, the pseudoscalar meson weak decay constant cannot be described by the NJL model (with relativistic heavy quark propagators) without further interactions or effects.Comment: 20 pages. Abstract above was reduced to cope with filling-form, improved tex