  The flavour and glue structure of the light scalar mesons in QCD are probed
by studying the couplings of the I=0 mesons $\sigma(600)$ and $f_0(980)$ to the
operators $\bar{q}q$, $\alpha_s G^2$ and to two photons. The Roy dispersive
representation for the $\pi\pi$ amplitude $t_0^0(s)$ is used to determine the
pole positions as well as the residues in the complex plane. On the real axis,
$t_0^0$ is constrained to solve the Roy equation together with elastic
unitarity up to the $K\Kbar$ threshold leading to an improved description of
the $f_0(980)$. The problem of using a two-particle threshold as a matching
point is discussed. A simple relation is established between the coupling of a
scalar meson to an operator $j_S$ and the value of the related pion form-factor
computed at the resonance pole. Pion scalar form-factors as well as two-photon
partial-wave amplitudes are expressed as coupled-channel Omn\`es dispersive
representations. Subtraction constants are constrained by chiral symmetry and
experimental data. Comparison of our results for the $\bar{q}q$ couplings with
earlier determinations of the analogous couplings of the lightest I=1 and
$I=1/2$ scalar mesons are compatible with an assignment of the $\sigma$,
$\kappa$, $a_0(980)$, $f_0(980)$ into a nonet. Concerning the gluonic operator
$\alpha_s G^2$ we find a significant coupling to both the $\sigma$ and the
$f_0(980)$.
