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.