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 $\overline{qq}qq$. 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.

arXiv comment34 pages, 23 figures. Version with minor changes to be published in European Journal of Physics C

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