Determination of Radiative Widths of Scalar Mesons from Experimental Results on $γγ\toππ$

The scalar mesons in the 1 GeV region constitute the Higgs sector of the strong interactions. They are responsible for the masses of all light flavour hadrons. However, the composition of these scalar states is far from clear, despite decades of experimental effort. The two photon couplings of the $f_{0}$'s are a guide to their structure. Two photon results from Mark II, Crystal Ball and CELLO prompt a new Amplitude Analysis of $\gamma\gamma\to\pi^+\pi^-$, $\pi^0\pi^0$ cross-sections. Despite their currently limited angular coverage and lack of polarized photons, we use a methodology that provides the nearest one can presently achieve to a model-independent partial wave separation. We find two distinct classes of solutions. Both have very similar two photon couplings for the $f_0(980)$ and $f_0(400-1200)$. Hopefully these definitive results will be a spur to dynamical calculations that will bring us a better understanding of these important states.