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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-photoncoupling is also reinvestigated using a single channel $T$ matrix for $\pi\pi$scattering with better analyticity property, and it is found to besignificantly smaller than that of a $\bar qq$ state. Especially we alsoestimate 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 coupledchannel Breit-Wigner description of the $f_0(980)$ resonance.

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