  A guide to the composition of the enigmatic f_0(980) and a_0(980) states is
their formation in phi-radiative decays. Precision data are becoming available
from the KLOE experiment at the DAPHNE machine at Frascati, as well as results
from SND and CMD-2 at VEPP-2M at Novosibirsk. We show how the coupling of the
f_0(980) to this channel can be extracted from these, independently of the
background provided by sigma production. To do this we use the fact that the
behaviour of both the f_0(980) and sigma cannot be determined by these data
alone, but is strongly constrained by experimental results from other hadronic
processes as required by unitarity. We find that the resulting coupling for the
phi -> gamma f_0(980) is about 10^{-4} GeV with a background that is quite
unlike that assumed if unitarity is neglected. This provides an object lesson
in how unitarity teaches us to add resonances. Not surprisingly the result is
crucially dependent on the pole position of the f_0(980), for which there are
still sizeable uncertainties. At present this leads to an uncertainty in the
phi -> f_0 gamma branching ratio which can only be fixed by further precision
data on the f_0(980).

High Energy Physics - Phenomenology