Shape of the $f_0(980)$ in $\gamma \gamma \to {\pi }^{+}{\pi }^{-}$

Abstract

The Belle Collaboration results on the observation of the $f_0(980)$ resonance in the reaction $\gamma \gamma \to {\pi }^{+}{\pi }^{-}$ are analyzed. It is argued that they point to the presence of mechanisms which give rise to a strong distortion of the $f_0(980)$ resonance shape in comparison with the shape of a solitary Breit-Wigner resonance. It is shown that the main factors responsible for the formation of the specific, steplike, shape of the $f_0(980)$ resonance in the $\gamma \gamma \to {\pi }^{+}{\pi }^{-}$ reaction cross section are the $K^{+}{K}^{-}$ loop mechanism of the $f_0(980)$ coupling to the $\gamma \gamma$ system and the destructive interference between the background and $f_0(980)$ resonance contributions in the ${\pi }^{+}{\pi }^{-}$ invariant mass region below the $K^{+}{K}^{-}$ threshold.

Comments: 10 pages, 6 figures, published version