Amplitude Analysis of High Statistics Results on $\gamma\gamma\to\pi^+\pi^-$ and the Two Photon Width of Isoscalar States

Abstract

We perform an Amplitude Analysis of the world published data on $\gamma\gamma\to\pi^+\pi^-$ and $\pi^0\pi^0$. These are dominated in statistics by the recently published results from Belle on the charged pion channel. Nevertheless, having only limited angular information, a range of solutions remain possible. We present two solutions with $\Gamma(f_0(980)\to\gamma\gamma) = 0.42$ and 0.10 keV, and $\Gamma(f_2(1270)\to\gamma\gamma) = 3.14 \pm 0.20$ 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 $\gamma\gamma \to\pi^0\pi^0$ can not only discriminate between, but also refine, these classes of partial wave solutions.