UNDERSTANDING THE SCALAR MESON Q(Q)OVER-BAR NONET

It is shown that one can fit the available data on the alpha(o)(980), f(o)(980), f(o)(1300) and K-o*(1430) mesons as a distorted O++ q $($) over bar$$ q nonet using very few (5-6) parameters and an improved version of the unitarized quark model. This includes all light two-pseudoscalar thresholds, constraints from Adler zeroes, flavour symmetric couplings, unitarity and physically acceptable analyticity. The parameters include a bare u $($) over bar$$ u or d $($) over bar$$ d mass, an over-all coupling constant, a cutoff and a strange quark mass of 100 MeV, which is in accord with expectations from the quark model. It is found that in particular for the alpha(o)(980) and f(o)(980) the K $($) over bar$$ K component in the wave function is large, i.e., for a large fraction of the time the q $($) over bar$$ q state is transformed into a virtual K $($) over bar$$ K pair. This K $($) over bar$$ K component, together with a similar component of eta'pi for the alpha(o)(980), and eta eta, eta eta' and eta'eta' components for the f(o)(980), causes the substantial shift to a lower mass than what is naively expected from the q $($) over bar$$ q component alone. Mass, width and mixing parameters, including sheet and pole positions, of the four resonances are given, with a detailed pedagogical discussion of their meaning.