We investigate the "family" relationship of a possible scalar nonet composed
of the a_0(980), the f_0(980) and the \sigma and \kappa type states found in
recent treatments of \pi\pi and \pi K scattering. We work in the effective
Lagrangian framework, starting from terms which yield "ideal mixing" according
to Okubo's original formulation. It is noted that there is another solution
corresponding to dual ideal mixing which agrees with Jaffe's picture of scalars
as qq\bar q \bar q states rather than as q\bar q states. At the Lagrangian
level there is no difference in the formulation of the two cases (other than
the numerical values of the coefficients). In order to agree with experiment,
additional mass and coupling terms which break ideal mixing are included. The
resulting model turns out to be closer to dual ideal mixing than to
conventional ideal mixing; the scalar mixing angle is roughly -17 degrees in a
convention where dual ideal mixing is 0 degrees.Comment: 24 pages, 3 figure
