Two variants of the Nambu--Jona-Lasinio model -- the model with 4-dimensional
cutoff and the model with dimensionally-analytical regularization -- are
systematically compared. It is shown that they are, in essence, two different
models of light-quark interaction. In the mean-field approximation the
distinction becomes apparent in a behavior of scalar amplitude near the
threshold. For 4-dimensional cutoff the pole term can be extracted, which
corresponds to sigma-meson. For dimensionally-analytical regularization the
singularity of the scalar amplitude is not pole, and this singularity is quite
disappeared at some value of the regularization parameter.
Still more essential distinction of these models exists in the
next-to-leading order of mean-field expansion. The calculations of meson
contributions in the quark chiral condensate and in the dynamical quark mass
demonstrate, that these contributions though their relatively smallness can
destabilize the Nambu--Jona-Lasinio model with 4-dimensional cutoff. On the
contrary, the Nambu--Jona-Lasinio model with dimensionally-analytical
regularization is stabilized with the next-to-leading order, i.e. the value of
the regularization parameter shifts to the stability region, where these
contributions decrease.Comment: 14 pages; Journal version; parameter fixing procedure is modifie