  We analyse data on pi pi and gamma gamma scattering below 700 MeV within an
improved analytic K-matrix model. This model is based on an effective theory
with couplings between resonances, hadrons and photons. The two-photon decay of
a resonance can proceed through intermediate transition into charged hadrons
(here: pi^+ pi^-) and their subsequent annihilation or through a ``direct''
transition into photons. Our analysis confirms the rather large total radiative
width of the sigma/f_0(600) resonance which we find as (3.9 \pm 0.6) keV but
suggests its dominance by the pi pi rescattering process. This process is not
sensitive to the internal structure of the resonance contrary to the direct
component which we find small, (0.13 \pm 0.05) keV, and well consistent with
the expectations for an unmixed glueball according to the QCD sum rule
calculations.
