  In this work, we perform the one-loop calculation of the scalar and
pseudoscalar form factors in the framework of U(3) chiral perturbation theory
with explicit tree level exchanges of resonances. The meson-meson scattering
calculation from Ref.[1] is extended as well. The spectral functions of the
nonet scalar-scalar (SS) and pseudoscalar-pseudoscalar (PP) correlators are
constructed by using the corresponding form factors. After fitting the unknown
parameters to the scattering data, we discuss the resonance content of the
resulting scattering amplitudes. We also study spectral-function sum rules in
the SS-SS, PP-PP and SS-PP sectors as well as semi-local duality from
scattering. The former relate the scalar and pseudoscalar spectra between
themselves while the latter mainly connects the scalar spectrum with the vector
one. Finally we investigate these items as a function of Nc for Nc > 3. All
these results pose strong constraints on the scalar dynamics and spectroscopy
that are discussed. They are successfully fulfilled by our meson-meson
scattering amplitudes and spectral functions.
