Amplitude Analysis of two photon production of $pipi$ and ${overline K}K$, using S-matrix constraints and fitting all available data, including the latest precision results from Belle, yields a single partial wave solution up to 1.4 GeV. The two phot
on couplings of the $sigma/f_0(500)$, $f_0(980)$ and $f_2(1270)$ are determined from the residues of the resonance poles.
We adapt the Veneziano model to the analysis of vector charmonium decays. Starting from a set of covariant Veneziano terms we show how to construct partial waves amplitudes that receive contributions from selected Regge trajectories. The amplitudes,
nevertheless retain the proper asymptotic limit. This arises from duality between directly produced resonances and cross-channel Reggeon and in practical applications helps remove uncertainties in the parametrization of backgrounds.
We perform an Amplitude Analysis of the world published data on $gammagammatopi^+pi^-$ and $pi^0pi^0$. These are dominated in statistics by the recently published results from Belle on the charged pion channel. Nevertheless, having only limited angul
ar information, a range of solutions remain possible. We present two solutions with $Gamma(f_0(980)togammagamma) = 0.42$ and 0.10 keV, and $Gamma(f_2(1270)togammagamma) = 3.14 pm 0.20$ and $3.82 pm 0.30$ keV, respectively: the former being the solution favoured by $chi^2$, the latter at the edge of acceptability. Models of the structure of the $f_0(980)$ predict two photon widths to be between 0.2 and 0.6 keV, depending on its composition as mainly ${bar K}K$, ${bar s}s$ or ${bar{qq}}qq$. Presently available data cannot yet distinguish unambiguously between these predictions. However, we show how forthcoming results on $gammagamma topi^0pi^0$ can not only discriminate between, but also refine, these classes of partial wave solutions.
