Pion pion scattering is studied in a generalized linear sigma model which
contains two scalar nonets (one of quark-antiquark type and the other of
diquark-antidiquark type) and two corresponding pseudoscalar nonets. An
interesting feature concerns the mixing of the four isosinglet scalar mesons
which yield poles in the scattering amplitude. Some realism is introduced by
enforcing exact unitarity via the K-matrix method.
It is shown that a reasonable agreement with experimental data is obtained up
to about 1 GeV. The poles in the unitarized scattering amplitude are studied in
some detail. The lowest pole clearly represents the sigma meson (or f0(600))
with a mass and decay width around 500 MeV. The second pole invites comparison
with the f0(980) which has a mass around 1 GeV and decay width around 100 MeV.
The third and fourth poles, resemble some of the isosinglet state in the
complicated 1-2 GeV region. Some comparison is made to the situation in the
usual SU(3) linear sigma model with a single scalar nonet
