A Dispersive Analysis on the $f_0(600)$ and $f_0(980)$ Resonances in $γγ\toπ^+π^-, π^0π^0$ 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 $ππ$ scattering with better analyticity property, and it is found to be significantly smaller than that of a $\bar qq$ state. Especially we also estimate the di-photon coupling of the third sheet pole located near $\bar KK$ 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.

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