Lightest scalar and tensor resonances in $\gamma \gamma \to \pi \pi$ after the Belle experiment

Abstract

New high statistics Belle data on the $\gamma \gamma \to {\pi }^{+}{\pi }^{-}$ reaction cross section measured in the range of pion-pair invariant masses $\sqrt{s}$ between 0.8 GeV and 1.5 GeV are analyzed to clarify the current situation around the $\sigma (600)$, $f_0(980)$, and $f_2(1270)$ resonances in $\gamma \gamma$ collisions. The present analysis shows that the direct coupling constants of the $\sigma (600)$ and $f_0(980)$ resonances to $\gamma \gamma$ are small, and the $\sigma (600)\to \gamma \gamma$ and $f_0(980)\to \gamma \gamma$ decays are four-quark transitions caused by the ${\pi }^{+}{\pi }^{-}$ and $K^{+}{K}^{-}$ loop mechanisms, respectively. The chiral shielding of the $\sigma (600)$ resonance takes place in the reactions $\gamma \gamma \to \pi \pi$ as well as in $\pi \pi$ scattering. Some results of a simultaneous description of the $\gamma \gamma \to {\pi }^{+}{\pi }^{-}$ and $\gamma \gamma \to {\pi }^0{\pi }^0$ Belle data are also presented. In particular, the following tentative estimate of the $f_2(1270)\to \gamma \gamma$ decay width is obtained: ${\Gamma }_{f_2\to \gamma \gamma }(m_{f_2}^2)\approx 3.68$ keV.

Comments: 14 pages, 5 figures. Fitted for the publication in Physical Review D