A Dispersive Analysis on the $f_0(600)$ and $f_0(980)$ Resonances in $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ Processes

Abstract

We estimate the di-photon coupling of $f_0(600)$, $f_0(980)$ and $f_2(1270)$ resonances in a coupled channel dispersive approach. The $f_0(600)$ di-photon coupling is also reinvestigated using a single channel $T$ matrix for $\pi \pi$ scattering with better analyticity property, and it is found to be significantly smaller than that of a $\bar{q}q$ state. Especially we also estimate the di-photon coupling of the third sheet pole located near $\bar{K}K$ threshold, denoted as $f_0^{III}(980)$. It is argued that this third sheet pole may be originated from a coupled channel Breit-Wigner description of the $f_0(980)$ resonance.

Comments: 24 pages and 13 eps figures. A nuerical bug in previous version is fixed. Some results changed. References and new figures added. Version to appear in Phys. Rev. D