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 GijΞβ(ΟΛβΞ»iβΞΟ)(ΟΛβΞ»jβΞΟ), for the scalar and
pseudoscalar channels (Ξ=I,iΞ³5β) and i,j=0.1,...Nf2ββ1.
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 (Ξfβ, 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 Ξ·'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