  It is well known that the instanton approach to QCD generates an effective
term which looks like a three flavor determinant of quark bilinears. This has
the right behavior to explain the unusual mass and mixing of the $\eta(958)$
meson, as is often simply illustrated with the aid of a linear SU(3) sigma
model. It is less well known that the instanton analysis generates another term
which has the same transformation property but does not have a simple
interpretation in terms of this usual linear sigma model. Here we point out
that this term has an interpretation in a generalized linear sigma model
containing two chiral nonets. The second chiral nonet is taken to correspond to
mesons having two quarks and two antiquarks in their makeup. The generalized
model seems to be useful for learning about the spectrum of low lying scalar
mesons which have been emerging in the last few years. The physics of the new
term is shown to be related to the properties of an "excited" $\eta'$ state
present in the generalized model and for which there are some experimental
candidates.
